1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
5 \save_transient_properties true
6 \origin /systemlyxdir/doc/
9 % DO NOT ALTER THIS PREAMBLE!!!
11 % This preamble is designed to ensure that the file prints
12 % out as advertised. If you mess with this preamble,
13 % parts of this document may not print out as expected. If you
14 % have problems LaTeXing this file, please contact
15 % the documentation team
16 % email: lyx-docs@lists.lyx.org
18 % solves the following problem:
19 % If the dection number consits of too many numerals the section heading
20 % will be printed in the TOC without a space between it and the section number.
21 % As solution more space between the number and the heading is inserted:
22 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
23 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
25 % increase link area for cross-references and autoname them,
26 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
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28 \@ifpackageloaded{babel}{
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32 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
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37 % don't load packages twice
38 % see first footnote in sec. 9.3
39 \@ifundefined{textcolor}{\usepackage{color}}{}
41 % the pages of the TOC are numbered roman
42 % and a PDF-bookmark for the TOC is added
44 \let\myTOC\tableofcontents
45 \renewcommand{\tableofcontents}{%
47 \pdfbookmark[1]{\contentsname}{}
50 \pagenumbering{arabic}}
52 % add 0.5 mm vertical space for table rows
53 \@ifundefined{extrarowheight} {\usepackage{array}}{}
54 \setlength{\extrarowheight}{0.5mm}
56 % insert additional vertical space of 1.5 mm between footnotes,
58 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
60 % makes caption labels bold
61 \setkomafont{captionlabel}{\bfseries}
63 % enables calculation of values
66 % for multiple columns used in sec. 24.7
72 % for the Fourier transformation symbol
75 % define a color, used in sec.9.3
76 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
78 % declare operators (see sec. 10.4 and sec. 15.2)
79 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
80 \DeclareMathOperator{\sgn}{sgn}
82 % example definitions for sec. 20.1
83 \newcommand{\gr}{\Longrightarrow}
84 \newcommand{\us}[1]{\underline{#1}}
85 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
86 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
87 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
89 % example macro from sec. 19.4
90 %\def\tagform@#1{\maketag@@@{|#1|}}
93 % ------------------------------------
94 % used to check for needed LaTeX packages
97 % check for package undertilde
98 % used for the command \utilde
99 \newboolean{undertilde}
100 \IfFileExists{undertilde.sty}
101 {\usepackage{undertilde}
102 \setboolean{undertilde}{true}}
103 {\setboolean{undertilde}{false}}
105 % check for package eurosym
106 % used for the Euro symbol
108 \IfFileExists{eurosym.sty}
109 {\usepackage[gennarrow]{eurosym}
110 \setboolean{eurosym}{true}}
111 {\setboolean{eurosym}{false}}
113 % check for package braket
114 % used for physical vectors
116 \IfFileExists{braket.sty}
118 \setboolean{braket}{true}}
119 {\setboolean{braket}{false}}
121 % check for package cancel
123 \IfFileExists{cancel.sty}
125 \setboolean{cancel}{true}}
126 {\setboolean{cancel}{false}}
128 % check for package upgreek
130 \IfFileExists{upgreek.sty}
131 {\usepackage{upgreek}
132 \setboolean{upgreek}{true}}
133 {\setboolean{upgreek}{false}}
135 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
136 \use_default_options false
137 \maintain_unincluded_children false
139 \language_package default
142 \font_roman "lmodern" "default"
143 \font_sans "lmss" "default"
144 \font_typewriter "lmtt" "default"
145 \font_math "auto" "auto"
146 \font_default_family default
147 \use_non_tex_fonts false
150 \font_sf_scale 100 100
151 \font_tt_scale 100 100
153 \use_dash_ligatures false
155 \default_output_format pdf2
157 \bibtex_command default
158 \index_command default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
178 \use_package amsmath 2
179 \use_package amssymb 2
180 \use_package cancel 0
182 \use_package mathdots 1
183 \use_package mathtools 2
184 \use_package mhchem 1
185 \use_package stackrel 0
186 \use_package stmaryrd 0
187 \use_package undertilde 0
189 \cite_engine_type default
193 \paperorientation portrait
198 \notefontcolor #0000ff
205 \paragraph_separation skip
208 \math_numbering_side default
209 \quotes_style english
213 \paperpagestyle plain
217 \tracking_changes false
218 \output_changes false
221 \html_be_strict false
228 's detailed Math manual
232 by the \SpecialChar LyX
237 \begin_layout Plain Layout
239 If you have comments or error corrections, please send them to the \SpecialChar LyX
244 \begin_inset CommandInset href
246 name "lyx-docs@lists.lyx.org"
247 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
259 \begin_inset Note Note
262 \begin_layout Plain Layout
269 \begin_inset Newline newline
273 \begin_inset Newline newline
281 \begin_layout Standard
282 \begin_inset CommandInset toc
283 LatexCommand tableofcontents
290 \begin_layout Standard
291 \begin_inset Note Note
294 \begin_layout Plain Layout
295 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
298 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
305 If they are not installed the document can be exported anyway but the sections
306 where the packages are required will not appear in the output.
311 ; if it is not installed, this file cannot be exported.
314 \begin_layout Plain Layout
315 The latest PDF-version of this document can be found here:
316 \begin_inset Newline newline
321 http://wiki.lyx.org/LyX/Manuals#Math
329 \begin_layout Standard
330 \begin_inset Newpage newpage
336 \begin_layout Section
340 \begin_layout Standard
341 This document explains \SpecialChar LyX
342 's math features and is furthermore a collection
343 of \SpecialChar LaTeX
344 -commands used for mathematical characters and constructs.
345 The explanations are designed for the usage of commands.
346 It is therefore required that you have read the section
357 \begin_layout Standard
358 Most of the characters and many constructs explained in this manual are
359 also accessible via the menu
363 \SpecialChar menuseparator
379 But everybody who has to write lots of formulas will notice that it is
380 much faster to use commands instead of the math toolbar.
381 Therefore this manual is focused on commands but also mentions the correspondin
382 g toolbar buttons when available.
385 \begin_layout Standard
386 If not specially mentioned the commands are only available within formulas.
387 To be able to use all commands explained in this document, the option
391 must be checked in the document settings (menu
393 Document\SpecialChar menuseparator
394 Settings\SpecialChar menuseparator
405 \begin_layout Plain Layout
408 Use AMS math package automatically
414 \begin_layout Plain Layout
423 -math when math constructs are found that are supported by \SpecialChar LyX
432 \begin_layout Standard
433 This document doesn't list all
437 \begin_layout Plain Layout
450 \begin_layout Plain Layout
455 \begin_layout Plain Layout
464 -math commands is in the file
467 \begin_inset CommandInset href
470 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.pdf"
477 , which is part of every \SpecialChar LaTeX
478 standard installation.
483 for lucidity reasons.
486 \begin_layout Section
490 \begin_layout Standard
491 To create an inline formula
492 \begin_inset Index idx
495 \begin_layout Plain Layout
501 that is embedded into a text line, use one of the shortcuts
507 or the toolbar button
514 \begin_inset Newline newline
517 To create a display style formula
518 \begin_inset Index idx
521 \begin_layout Plain Layout
522 Formula ! display style
527 which will appear bigger, has a different format, and will be in a separate
528 paragraph, use one of these shortcuts:
537 \begin_layout Standard
538 To change a display style formula to an inline formula, set the cursor into
539 the formula and use one of the shortcuts
547 Edit\SpecialChar menuseparator
548 Math\SpecialChar menuseparator
552 The same way is used to change an inline formula to a display style formula.
555 \begin_layout Standard
556 To display parts of an inline formula in the size of a display style formula,
564 \begin_inset Index idx
567 \begin_layout Plain Layout
576 Then a new blue box appears in which the desired formula part is inserted.
579 \begin_layout Standard
580 Only inline formulas are allowed inside tables.
583 \begin_layout Standard
588 can be turned on in the menu
590 View\SpecialChar menuseparator
594 When you click there on
595 \begin_inset Quotes eld
599 \begin_inset Quotes erd
602 the toolbar will be shown permanently at the bottom; this state is visualized
607 menu with a checkmark.
608 When you click in this state again on
609 \begin_inset Quotes eld
613 \begin_inset Quotes erd
624 is only shown when the cursor is within a formula; this state is visualized
625 by the renaming of the menu entry from
626 \begin_inset Quotes eld
630 \begin_inset Quotes erd
634 \begin_inset Quotes eld
642 \begin_inset Quotes erd
648 \begin_layout Standard
651 \begin_inset Index idx
654 \begin_layout Plain Layout
661 is invoked by pressing the toolbar button
669 Insert\SpecialChar menuseparator
681 \begin_layout Standard
682 To change the \SpecialChar LaTeX
684 \begin_inset Index idx
687 \begin_layout Plain Layout
696 Document\SpecialChar menuseparator
697 Settings\SpecialChar menuseparator
707 \begin_layout Standard
708 To edit matrices, case differentiations and multiline formulas subsequently,
711 Edit\SpecialChar menuseparator
716 Edit\SpecialChar menuseparator
718 \begin_inset space \thinspace{}
722 \begin_inset space \thinspace{}
732 When lines and columns are swapped via the menu, the column or line where
733 the cursor is in is exchanged with the column to the right or the line
735 Is the cursor in the last column or row, the exchange is done with the
736 column to the left or the line above.
739 \begin_layout Standard
740 To write text in formulas
744 \begin_layout Plain Layout
745 For multiline formulas the command
752 \begin_inset CommandInset ref
754 reference "subsec:Text-in-multiline"
768 \begin_inset Index idx
771 \begin_layout Plain Layout
778 \begin_inset Index idx
781 \begin_layout Plain Layout
788 This mode is invoked with the shortcut
794 or by the insertion of the command
801 \begin_inset Index idx
804 \begin_layout Plain Layout
813 The text appears black in \SpecialChar LyX
814 and can therefore be distinguished from the
815 other formula parts which appear blue.
816 In the output mathematical text is set upright, in contrary to other formula
820 \begin_layout Subsection*
824 \begin_layout Standard
825 Most of the \SpecialChar LaTeX
826 -commands for math constructs have the following scheme:
829 \begin_layout Standard
845 \begin_layout Standard
846 A command always starts with a backslash
847 \begin_inset Quotes gld
857 \begin_inset Quotes grd
861 To omit optional arguments, also omit the associated brackets.
862 The braces around the required arguments are named in this document as
865 \begin_inset Index idx
868 \begin_layout Plain Layout
876 If you add in a formula a left brace to a command name, \SpecialChar LyX
878 creates a \SpecialChar TeX
880 In all other cases \SpecialChar TeX
881 braces are created in formulas with the command
889 braces appear red in \SpecialChar LyX
890 , in contrary to normal braces which appear blue.
892 mode no command is needed to get \SpecialChar TeX
895 braces don't appear in the output.
898 \begin_layout Standard
899 When commands without arguments, like commands for symbols are entered in
901 mode, a space character must
905 be behind the command to end it.
906 This space doesn't appear in the output.
907 When the space should appear in the output, the space must be followed
908 by a protected space in normal text.
911 \begin_layout Standard
912 A protected space is inserted with
915 arg "command-alternatives space-insert protected ; math-space"
921 \begin_layout Subsection*
922 \begin_inset Newpage newpage
928 \begin_layout Itemize
930 \begin_inset space \textvisiblespace{}
933 denotes a space character to be input.
936 \begin_layout Itemize
938 \begin_inset Formula $\to$
941 denotes the usage of the corresponding arrow key on the keyboard.
946 key can often be used instead of
947 \begin_inset Formula $\to$
951 \begin_inset Formula $\downarrow$
959 \begin_inset Formula $\leftarrow$
963 \begin_inset Formula $\uparrow$
969 \begin_layout Subsection*
973 \begin_layout Standard
975 \begin_inset Float table
981 \begin_layout Plain Layout
983 \begin_inset Caption Standard
985 \begin_layout Plain Layout
986 \begin_inset CommandInset label
988 name "tab:Available-units"
1000 \begin_layout Plain Layout
1002 \begin_inset Tabular
1003 <lyxtabular version="3" rows="13" columns="2">
1004 <features booktabs="true" tabularvalignment="middle">
1005 <column alignment="center" valignment="top">
1006 <column alignment="center" valignment="top" width="0pt">
1008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1011 \begin_layout Plain Layout
1017 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1020 \begin_layout Plain Layout
1028 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1031 \begin_layout Plain Layout
1037 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1040 \begin_layout Plain Layout
1048 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1051 \begin_layout Plain Layout
1057 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1060 \begin_layout Plain Layout
1068 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1071 \begin_layout Plain Layout
1077 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1080 \begin_layout Plain Layout
1082 \begin_inset space \thinspace{}
1086 \begin_inset space \thinspace{}
1096 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1099 \begin_layout Plain Layout
1105 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1108 \begin_layout Plain Layout
1110 \begin_inset space \thinspace{}
1114 \begin_inset space \thinspace{}
1124 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1127 \begin_layout Plain Layout
1133 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1136 \begin_layout Plain Layout
1138 \begin_inset space \thinspace{}
1142 \begin_inset space \thinspace{}
1152 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1155 \begin_layout Plain Layout
1161 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1164 \begin_layout Plain Layout
1166 \begin_inset space \thinspace{}
1170 \begin_inset space \thinspace{}
1180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1183 \begin_layout Plain Layout
1189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1192 \begin_layout Plain Layout
1194 \begin_inset space \thinspace{}
1198 \begin_inset space \thinspace{}
1208 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1211 \begin_layout Plain Layout
1217 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1220 \begin_layout Plain Layout
1222 \begin_inset space \thinspace{}
1226 \begin_inset Formula $\approx$
1230 \begin_inset space \thinspace{}
1240 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1243 \begin_layout Plain Layout
1249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1252 \begin_layout Plain Layout
1254 \begin_inset space \thinspace{}
1258 \begin_inset space \thinspace{}
1268 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1271 \begin_layout Plain Layout
1277 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1280 \begin_layout Plain Layout
1284 \begin_inset Quotes eld
1290 \begin_inset Quotes erd
1300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1303 \begin_layout Plain Layout
1309 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1312 \begin_layout Plain Layout
1314 \begin_inset Quotes eld
1322 \begin_inset Quotes erd
1332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1335 \begin_layout Plain Layout
1341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1344 \begin_layout Plain Layout
1346 \begin_inset space \thinspace{}
1350 \begin_inset Formula $\nicefrac{1}{18}$
1354 \begin_inset space \thinspace{}
1375 \begin_layout Standard
1376 \begin_inset Newpage newpage
1382 \begin_layout Section
1386 \begin_layout Subsection
1388 \begin_inset Index idx
1391 \begin_layout Plain Layout
1398 \begin_inset Index idx
1401 \begin_layout Plain Layout
1408 \begin_inset Index idx
1411 \begin_layout Plain Layout
1416 \begin_layout Plain Layout
1427 \begin_layout Plain Layout
1440 \begin_inset Index idx
1443 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1459 \begin_layout Plain Layout
1474 \begin_layout Standard
1475 Indices are created with an underscore
1476 \begin_inset Quotes eld
1480 \begin_inset Quotes erd
1483 or via the math toolbar button
1486 arg "math-subscript"
1489 , exponents with a caret
1490 \begin_inset Quotes eld
1494 \begin_inset Quotes erd
1497 or via the math toolbar button
1500 arg "math-superscript"
1506 \begin_layout Standard
1508 \begin_inset Tabular
1509 <lyxtabular version="3" rows="4" columns="2">
1510 <features booktabs="true" tabularvalignment="middle">
1511 <column alignment="center" valignment="top" width="0pt">
1512 <column alignment="center" valignment="top" width="0pt">
1514 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1517 \begin_layout Plain Layout
1523 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1526 \begin_layout Plain Layout
1534 <cell alignment="center" valignment="top" usebox="none">
1537 \begin_layout Plain Layout
1543 <cell alignment="center" valignment="top" usebox="none">
1546 \begin_layout Plain Layout
1547 \begin_inset Formula $B_{V}$
1556 <row topspace="1.5mm">
1557 <cell alignment="center" valignment="top" usebox="none">
1560 \begin_layout Plain Layout
1566 <cell alignment="center" valignment="top" usebox="none">
1569 \begin_layout Plain Layout
1570 \begin_inset Formula $B^{V}$
1579 <row topspace="1.5mm">
1580 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1583 \begin_layout Plain Layout
1585 \begin_inset space \textvisiblespace{}
1593 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1596 \begin_layout Plain Layout
1597 \begin_inset Formula $B^{A}$
1613 \begin_layout Standard
1614 As the caret is in some languages an accent, vowels will be accentuated
1615 in this case and not set as exponents
1619 \begin_layout Plain Layout
1620 Depending on the used keyboard settings this can also happen for characters
1627 To get exponents in this case, press
1631 after the caret as in the last example.
1634 \begin_layout Subsection
1636 \begin_inset CommandInset label
1638 name "subsec:Fractions"
1643 \begin_inset Index idx
1646 \begin_layout Plain Layout
1655 \begin_layout Standard
1656 Fractions are generated with the command
1663 \begin_inset Index idx
1666 \begin_layout Plain Layout
1674 or via the math toolbar button
1677 arg "math-insert \\frac"
1681 The font size is adjusted automatically, depending on whether the fraction
1682 is in an inline or display style formula.
1683 With the math toolbar button
1686 arg "math-insert \\frac-square"
1689 you can select different fraction types.
1692 \begin_layout Standard
1700 \begin_inset Index idx
1703 \begin_layout Plain Layout
1711 a fraction can be created that always has the size of a display style formula.
1719 \begin_inset Index idx
1722 \begin_layout Plain Layout
1730 the fraction appears always with the size of an inline formula.
1734 \begin_layout Standard
1735 A line with the fraction
1736 \begin_inset Formula $\frac{1}{2}$
1739 that was created with the command
1748 \begin_layout Standard
1749 A line with the fraction
1750 \begin_inset Formula $\dfrac{1}{2}$
1753 that was created with the command
1762 \begin_layout Standard
1764 \begin_inset Tabular
1765 <lyxtabular version="3" rows="4" columns="2">
1766 <features booktabs="true" tabularvalignment="middle">
1767 <column alignment="center" valignment="top" width="0pt">
1768 <column alignment="center" valignment="top" width="0pt">
1770 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1773 \begin_layout Plain Layout
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1789 <row topspace="1.5mm">
1790 <cell alignment="center" valignment="top" usebox="none">
1793 \begin_layout Plain Layout
1797 \begin_inset space \textvisiblespace{}
1801 \begin_inset Formula $\downarrow$
1809 <cell alignment="center" valignment="top" usebox="none">
1812 \begin_layout Plain Layout
1813 \begin_inset Formula $\frac{A}{B}$
1822 <row topspace="2mm">
1823 <cell alignment="center" valignment="top" usebox="none">
1826 \begin_layout Plain Layout
1830 \begin_inset space \textvisiblespace{}
1834 \begin_inset Formula $\downarrow$
1842 <cell alignment="center" valignment="top" usebox="none">
1845 \begin_layout Plain Layout
1846 \begin_inset Formula $\dfrac{A}{B}$
1855 <row topspace="2mm" bottomspace="1mm">
1856 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1859 \begin_layout Plain Layout
1863 \begin_inset space \textvisiblespace{}
1869 \begin_inset space \textvisiblespace{}
1873 \begin_inset Formula $\downarrow$
1877 \begin_inset Formula $\downarrow\downarrow$
1885 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1888 \begin_layout Plain Layout
1889 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1905 \begin_layout Standard
1906 \begin_inset VSpace bigskip
1910 \begin_inset Newpage newpage
1913 For nested fractions the command
1920 \begin_inset Index idx
1923 \begin_layout Plain Layout
1933 \begin_inset VSpace -3mm
1939 \begin_layout Standard
1940 \begin_inset Formula
1942 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1943 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1951 \begin_layout Standard
1952 The command for the example above is:
1955 \begin_layout Standard
1961 \begin_inset space \textvisiblespace{}
1965 \begin_inset Formula $\downarrow$
1971 \begin_inset space \textvisiblespace{}
1977 \begin_inset space \textvisiblespace{}
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow$
1991 \begin_layout Standard
1992 \begin_inset VSpace medskip
1998 \begin_layout Standard
2005 sets the fraction always in the size of a displayed formula, also when
2006 it is part of another fraction.
2009 \begin_layout Standard
2010 It is possible to specify the alignment of the numerator.
2017 is used to left align it, the command
2030 centers the numerator.
2031 These fractions demonstrate the different alignments:
2034 \begin_layout Standard
2037 \begin_inset Formula
2039 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2047 \begin_layout Standard
2048 \begin_inset Note Greyedout
2051 \begin_layout Plain Layout
2068 are no real \SpecialChar LaTeX
2069 commands but represent the command
2073 cfrac[alignment]{numerator}{denominator}
2076 Therefore you cannot use them in \SpecialChar TeX
2085 \begin_layout Standard
2086 \begin_inset VSpace medskip
2089 It is often advantageous to combine
2102 \begin_inset Formula
2104 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2112 \begin_layout Standard
2113 For inline fractions with a sloped fraction stroke you can use the command
2121 \begin_inset Index idx
2124 \begin_layout Plain Layout
2133 \begin_inset Formula $\nicefrac{5}{31}$
2143 \begin_inset Index idx
2146 \begin_layout Plain Layout
2155 \begin_inset Formula $\unitfrac{5}{31}$
2158 There is furthermore the command
2164 that offers to write a fraction in combination with a number:
2165 \begin_inset Formula $\unitfrac[2]{1}{3}$
2171 \begin_layout Standard
2172 \begin_inset Note Greyedout
2175 \begin_layout Plain Layout
2186 is not a real \SpecialChar LaTeX
2187 command but the command
2188 \begin_inset Newline newline
2195 unitfrac[number]{numerator}{denominator}
2198 Therefore you cannot use it in \SpecialChar TeX
2207 \begin_layout Standard
2208 How to define own fractions where the fraction stroke can be changed, is
2210 \begin_inset CommandInset ref
2212 reference "subsec:Self-defined-Fractions"
2219 \begin_layout Standard
2220 Multiline fractions are explained in
2221 \begin_inset CommandInset ref
2223 reference "subsec:Multiline-Fractions"
2230 \begin_layout Subsection
2232 \begin_inset Index idx
2235 \begin_layout Plain Layout
2244 \begin_layout Standard
2245 Square roots are created with
2252 \begin_inset Index idx
2255 \begin_layout Plain Layout
2263 or the math toolbar button
2266 arg "math-insert \\sqrt"
2269 , all other roots with the command
2276 \begin_inset Index idx
2279 \begin_layout Plain Layout
2287 or with the math toolbar button
2290 arg "math-insert \\root"
2296 \begin_layout Standard
2298 \begin_inset Tabular
2299 <lyxtabular version="3" rows="3" columns="2">
2300 <features booktabs="true" tabularvalignment="middle">
2301 <column alignment="center" valignment="top" width="0pt">
2302 <column alignment="center" valignment="top" width="0pt">
2304 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2307 \begin_layout Plain Layout
2313 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2316 \begin_layout Plain Layout
2323 <row topspace="1mm">
2324 <cell alignment="center" valignment="top" usebox="none">
2327 \begin_layout Plain Layout
2331 \begin_inset space \textvisiblespace{}
2339 <cell alignment="center" valignment="top" usebox="none">
2342 \begin_layout Plain Layout
2343 \begin_inset Formula $\sqrt{A-B}$
2352 <row topspace="1mm">
2353 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2356 \begin_layout Plain Layout
2360 \begin_inset space \textvisiblespace{}
2364 \begin_inset Formula $\downarrow$
2372 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2375 \begin_layout Plain Layout
2376 \begin_inset Formula $\sqrt[3]{A-B}$
2392 \begin_layout Standard
2393 A square root can also be created with
2399 when the root index field is left empty.
2402 \begin_layout Standard
2403 With certain indices the distance to the root is too small, like in this
2405 \begin_inset Formula $\sqrt[\beta]{B}$
2409 \begin_inset Newline newline
2413 \begin_inset Formula $\beta$
2417 To avoid this, the commands
2424 \begin_inset Index idx
2427 \begin_layout Plain Layout
2442 \begin_inset Index idx
2445 \begin_layout Plain Layout
2453 are used with the following scheme:
2456 \begin_layout Standard
2470 \begin_layout Standard
2471 Distance is the number of Big Points (unit bp;
2472 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2475 ), that the index should be moved to the left or top, resp..
2476 The commands are written to the index.
2477 This way the command
2478 \begin_inset Newline newline
2488 \begin_inset Formula $\to$
2494 \begin_inset Formula $\to$
2500 \begin_inset space \textvisiblespace{}
2504 \begin_inset Formula $\to$
2508 \begin_inset Newline newline
2513 produces a correct typeset formula:
2514 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2520 \begin_layout Subsection
2521 Binomial Coefficients
2522 \begin_inset Index idx
2525 \begin_layout Plain Layout
2526 Binomial coefficients
2534 \begin_layout Standard
2535 Binomial coefficients are inserted with the command
2542 \begin_inset Index idx
2545 \begin_layout Plain Layout
2553 or with the submenu of the math toolbar button
2556 arg "math-insert \\frac-square"
2572 there are the commands
2579 \begin_inset Index idx
2582 \begin_layout Plain Layout
2597 \begin_inset Index idx
2600 \begin_layout Plain Layout
2609 For other brackets around binomial coeficients there are the commands
2616 \begin_inset Index idx
2619 \begin_layout Plain Layout
2634 \begin_inset Index idx
2637 \begin_layout Plain Layout
2648 \begin_layout Standard
2650 \begin_inset Tabular
2651 <lyxtabular version="3" rows="6" columns="2">
2652 <features booktabs="true" tabularvalignment="middle">
2653 <column alignment="center" valignment="top" width="0pt">
2654 <column alignment="center" valignment="top" width="0pt">
2656 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2659 \begin_layout Plain Layout
2665 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2668 \begin_layout Plain Layout
2675 <row topspace="1mm">
2676 <cell alignment="center" valignment="top" usebox="none">
2679 \begin_layout Plain Layout
2683 \begin_inset space \textvisiblespace{}
2687 \begin_inset Formula $\downarrow$
2695 <cell alignment="center" valignment="top" usebox="none">
2698 \begin_layout Plain Layout
2699 \begin_inset Formula $\binom{A}{B}$
2708 <row topspace="2mm">
2709 <cell alignment="center" valignment="top" usebox="none">
2712 \begin_layout Plain Layout
2716 \begin_inset space \textvisiblespace{}
2720 \begin_inset Formula $\downarrow$
2728 <cell alignment="center" valignment="top" usebox="none">
2731 \begin_layout Plain Layout
2732 \begin_inset Formula $\dbinom{A}{B}$
2741 <row topspace="2mm" bottomspace="0.5mm">
2742 <cell alignment="center" valignment="top" usebox="none">
2745 \begin_layout Plain Layout
2749 \begin_inset space \textvisiblespace{}
2753 \begin_inset Formula $\downarrow$
2761 <cell alignment="center" valignment="top" usebox="none">
2764 \begin_layout Plain Layout
2765 \begin_inset Formula $\tbinom{A}{B}$
2774 <row topspace="1mm">
2775 <cell alignment="center" valignment="top" topline="true" usebox="none">
2778 \begin_layout Plain Layout
2782 \begin_inset space \textvisiblespace{}
2786 \begin_inset Formula $\downarrow$
2794 <cell alignment="center" valignment="top" topline="true" usebox="none">
2797 \begin_layout Plain Layout
2798 \begin_inset Formula ${A \brack B}$
2807 <row topspace="2mm" bottomspace="0.5mm">
2808 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2811 \begin_layout Plain Layout
2815 \begin_inset space \textvisiblespace{}
2819 \begin_inset Formula $\downarrow$
2827 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2830 \begin_layout Plain Layout
2831 \begin_inset Formula ${A \brace B}$
2847 \begin_layout Subsection
2848 Case Differentiations
2849 \begin_inset Index idx
2852 \begin_layout Plain Layout
2853 Case differentiations
2861 \begin_layout Standard
2863 \begin_inset Tabular
2864 <lyxtabular version="3" rows="3" columns="2">
2865 <features booktabs="true" tabularvalignment="middle">
2866 <column alignment="center" valignment="top" width="0pt">
2867 <column alignment="center" valignment="top" width="0pt">
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2872 \begin_layout Plain Layout
2878 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2881 \begin_layout Plain Layout
2889 <cell alignment="center" valignment="top" usebox="none">
2892 \begin_layout Plain Layout
2896 \begin_inset space \textvisiblespace{}
2900 \begin_inset Formula $\to$
2904 \begin_inset Index idx
2907 \begin_layout Plain Layout
2920 <cell alignment="center" valignment="top" usebox="none">
2923 \begin_layout Plain Layout
2924 \begin_inset Formula $\begin{cases}
2934 <row topspace="1.5mm">
2935 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2938 \begin_layout Plain Layout
2942 \begin_inset space \textvisiblespace{}
2948 arg "newline-insert newline"
2956 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2959 \begin_layout Plain Layout
2960 \begin_inset Formula $\begin{cases}
2961 A & \textrm{for }x>0\\
2962 B & \textrm{for }x=0
2979 \begin_layout Standard
2986 or pressing the math toolbar button
2989 arg "math-insert \\cases"
2992 you can create new lines with the shortcut
2995 arg "newline-insert newline"
2998 or the table toolbar button
3001 arg "tabular-feature append-row"
3007 \begin_layout Standard
3014 is also available via the menu
3016 Insert\SpecialChar menuseparator
3017 Math\SpecialChar menuseparator
3023 \begin_layout Subsection
3025 \begin_inset Index idx
3028 \begin_layout Plain Layout
3037 \begin_layout Standard
3045 \begin_inset Index idx
3048 \begin_layout Plain Layout
3056 every character can be displayed canceled.
3057 The characters are quasi accentuated by a slash.
3060 \begin_layout Standard
3062 \begin_inset Tabular
3063 <lyxtabular version="3" rows="4" columns="2">
3064 <features booktabs="true" tabularvalignment="middle">
3065 <column alignment="center" valignment="top" width="0pt">
3066 <column alignment="center" valignment="top" width="0pt">
3068 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3071 \begin_layout Plain Layout
3077 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3080 \begin_layout Plain Layout
3088 <cell alignment="center" valignment="top" usebox="none">
3091 \begin_layout Plain Layout
3099 <cell alignment="center" valignment="top" usebox="none">
3102 \begin_layout Plain Layout
3103 \begin_inset Formula $\not=$
3113 <cell alignment="center" valignment="top" usebox="none">
3116 \begin_layout Plain Layout
3126 <cell alignment="center" valignment="top" usebox="none">
3129 \begin_layout Plain Layout
3130 \begin_inset Formula $\not\le$
3140 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3143 \begin_layout Plain Layout
3153 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3156 \begin_layout Plain Layout
3157 \begin_inset Formula $\not\parallel$
3173 \begin_layout Standard
3174 The last example shows that not all negations look good.
3175 Therefore there are special commands for some negations (see
3176 \begin_inset CommandInset ref
3178 reference "subsec:Mathematical-Symbols"
3183 \begin_inset CommandInset ref
3185 reference "sec:Relations"
3192 \begin_layout Subsection
3194 \begin_inset CommandInset label
3196 name "subsec:Placeholders"
3201 \begin_inset Index idx
3204 \begin_layout Plain Layout
3211 \begin_inset Index idx
3214 \begin_layout Plain Layout
3215 Chemical characters ! Isotopes
3221 \begin_inset Index idx
3224 \begin_layout Plain Layout
3229 \begin_layout Plain Layout
3240 \begin_layout Plain Layout
3255 \begin_layout Standard
3257 \begin_inset space \thinspace{}
3261 \begin_inset space \space{}
3268 \begin_layout Plain Layout
3269 Typesetting isotopes and chemical symbols is described in
3270 \begin_inset CommandInset ref
3272 reference "subsec:Chemical-Symbols-and"
3281 the following problem occurs:
3284 \begin_layout Standard
3286 \begin_inset Tabular
3287 <lyxtabular version="3" rows="2" columns="2">
3288 <features booktabs="true" tabularvalignment="middle">
3289 <column alignment="center" valignment="top" width="0pt">
3290 <column alignment="center" valignment="top" width="0pt">
3292 <cell alignment="center" valignment="top" usebox="none">
3295 \begin_layout Plain Layout
3296 Indices created with sub- and superscripts:
3301 <cell alignment="center" valignment="top" usebox="none">
3304 \begin_layout Plain Layout
3305 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3314 <row topspace="1.5mm">
3315 <cell alignment="center" valignment="top" usebox="none">
3318 \begin_layout Plain Layout
3324 <cell alignment="center" valignment="top" usebox="none">
3327 \begin_layout Plain Layout
3328 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3344 \begin_layout Standard
3345 The shorter index is by default placed below or above the first character
3346 of the longer index.
3347 To avoid this there is the command
3354 \begin_inset Index idx
3357 \begin_layout Plain Layout
3365 or the math toolbar button
3366 \begin_inset space \thinspace{}
3373 \begin_layout Plain Layout
3374 can be found in the submenu of the toolbar button
3377 arg "math-insert \\space"
3391 that creates one or more phantom characters.
3398 a small blue box appears that is superposed with two red arrows.
3399 The arrows indicate that the complete width and height of the box content
3400 will be created as placeholder.
3401 Phantom characters are accordingly placeholders with the size of the characters.
3404 \begin_layout Standard
3406 \begin_inset Tabular
3407 <lyxtabular version="3" rows="4" columns="2">
3408 <features booktabs="true" tabularvalignment="middle">
3409 <column alignment="center" valignment="top" width="0pt">
3410 <column alignment="center" valignment="top" width="0pt">
3412 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3415 \begin_layout Plain Layout
3421 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3424 \begin_layout Plain Layout
3431 <row topspace="1.5mm">
3432 <cell alignment="center" valignment="top" usebox="none">
3435 \begin_layout Plain Layout
3437 \begin_inset space \textvisiblespace{}
3443 \begin_inset space \textvisiblespace{}
3447 \begin_inset Formula $\to$
3451 \begin_inset space \textvisiblespace{}
3459 <cell alignment="center" valignment="top" usebox="none">
3462 \begin_layout Plain Layout
3463 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3472 <row topspace="1.5mm" bottomspace="0.5mm">
3473 <cell alignment="center" valignment="top" usebox="none">
3476 \begin_layout Plain Layout
3478 \begin_inset space \textvisiblespace{}
3484 \begin_inset space \textvisiblespace{}
3488 \begin_inset Formula $\to$
3492 \begin_inset space \textvisiblespace{}
3500 <cell alignment="center" valignment="top" usebox="none">
3503 \begin_layout Plain Layout
3504 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3513 <row topspace="1.5mm" bottomspace="0.5mm">
3514 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3517 \begin_layout Plain Layout
3521 \begin_inset space \textvisiblespace{}
3527 \begin_inset space \textvisiblespace{}
3531 \begin_inset Formula $\to$
3535 \begin_inset space \textvisiblespace{}
3543 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3546 \begin_layout Plain Layout
3547 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3563 \begin_layout Standard
3564 Furthermore there are the commands
3571 \begin_inset Index idx
3574 \begin_layout Plain Layout
3595 \begin_inset Index idx
3598 \begin_layout Plain Layout
3619 creates only space for the maximal height of the characters in the box
3620 but not for its width.
3627 creates only space for the width of the box content.
3628 Therefore the boxes of both commands have only one red arrow.
3631 \begin_layout Standard
3632 For example the command
3637 \begin_inset space \textvisiblespace{}
3644 creates space for the height of the integral sign,
3648 \begin_layout Plain Layout
3655 creates an integral sign, see
3656 \begin_inset CommandInset ref
3658 reference "subsec:Big-Operators"
3667 because this is the larger character.
3668 An example application is in
3669 \begin_inset CommandInset ref
3671 reference "subsec:Multiline-Brackets"
3678 \begin_layout Standard
3679 Placeholders can also be used for text when they are inserted via the menu
3682 Insert\SpecialChar menuseparator
3683 Formatting\SpecialChar menuseparator
3689 \begin_layout Standard
3691 \begin_inset Newline newline
3695 \begin_inset Phantom Phantom
3698 \begin_layout Plain Layout
3707 \begin_layout Subsection
3709 \begin_inset Index idx
3712 \begin_layout Plain Layout
3719 \begin_inset Index idx
3722 \begin_layout Plain Layout
3723 Formula ! underlined
3731 \begin_layout Standard
3733 \begin_inset Tabular
3734 <lyxtabular version="3" rows="4" columns="2">
3735 <features booktabs="true" tabularvalignment="middle">
3736 <column alignment="center" valignment="top" width="0pt">
3737 <column alignment="center" valignment="top" width="0pt">
3739 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3742 \begin_layout Plain Layout
3748 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3751 \begin_layout Plain Layout
3758 <row topspace="2mm">
3759 <cell alignment="center" valignment="top" usebox="none">
3762 \begin_layout Plain Layout
3766 \begin_inset space \textvisiblespace{}
3770 \begin_inset Index idx
3773 \begin_layout Plain Layout
3786 <cell alignment="center" valignment="top" usebox="none">
3789 \begin_layout Plain Layout
3790 \begin_inset Formula $\overline{A+B}$
3799 <row bottomspace="1mm">
3800 <cell alignment="center" valignment="top" usebox="none">
3803 \begin_layout Plain Layout
3807 \begin_inset space \textvisiblespace{}
3811 \begin_inset Index idx
3814 \begin_layout Plain Layout
3827 <cell alignment="center" valignment="top" usebox="none">
3830 \begin_layout Plain Layout
3831 \begin_inset Formula $\underline{A+B}$
3840 <row topspace="2mm" bottomspace="1mm">
3841 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3844 \begin_layout Plain Layout
3848 \begin_inset space \textvisiblespace{}
3854 \begin_inset space \textvisiblespace{}
3862 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3865 \begin_layout Plain Layout
3866 \begin_inset Formula $\overline{\underline{A+B}}$
3882 \begin_layout Standard
3883 In the last example it doesn't matter if first
3898 \begin_layout Standard
3899 To double underline use
3908 \begin_layout Standard
3909 It is possible to place up to 6 lines above or below characters.
3912 \begin_layout Standard
3913 \begin_inset VSpace bigskip
3916 Custom lines can be created using the command
3923 \begin_inset Index idx
3926 \begin_layout Plain Layout
3934 which has the following scheme:
3937 \begin_layout Standard
3942 rule[vertical offset]{length}{thickness}
3945 \begin_layout Standard
3946 The optional vertical offset shifts the line upwards (or downwards, when
3947 the value is negative).
3949 \begin_inset CommandInset ref
3951 reference "tab:Available-units"
3955 can be used for the values.
3956 Here are two example lines created with the commands
3957 \begin_inset Newline newline
3964 rule[-2ex]{3cm}{2pt}
3975 \begin_layout Standard
3977 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
3983 \begin_layout Standard
3990 can also be used for text when a line is inserted via the menu
3992 Insert\SpecialChar menuseparator
3993 Formatting\SpecialChar menuseparator
3995 \begin_inset space ~
4003 \begin_layout Standard
4005 \begin_inset CommandInset line
4016 \begin_layout Subsection
4018 \begin_inset CommandInset label
4020 name "subsec:Ellipses"
4025 \begin_inset Index idx
4028 \begin_layout Plain Layout
4037 \begin_layout Standard
4038 There are different types of ellipses available.
4042 \begin_layout Plain Layout
4043 In the math toolbar in the submenu of the button
4046 arg "math-insert \\ldots"
4054 For listings dots at the baseline are used (
4061 \begin_inset Index idx
4064 \begin_layout Plain Layout
4072 ), while for operations dots are needed that are on the same height as the
4080 \begin_inset Index idx
4083 \begin_layout Plain Layout
4092 When using the command
4099 \begin_inset Index idx
4102 \begin_layout Plain Layout
4110 , \SpecialChar LaTeX
4111 decides on the basis of the next character what type is used.
4114 \begin_layout Standard
4116 \begin_inset Tabular
4117 <lyxtabular version="3" rows="9" columns="2">
4118 <features booktabs="true" tabularvalignment="middle">
4119 <column alignment="center" valignment="top" width="0pt">
4120 <column alignment="center" valignment="top" width="0pt">
4122 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4125 \begin_layout Plain Layout
4131 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4134 \begin_layout Plain Layout
4142 <cell alignment="center" valignment="top" usebox="none">
4145 \begin_layout Plain Layout
4147 \begin_inset space \textvisiblespace{}
4153 \begin_inset space \textvisiblespace{}
4161 <cell alignment="center" valignment="top" usebox="none">
4164 \begin_layout Plain Layout
4165 \begin_inset Formula $A_{1},\dots,A_{n}$
4175 <cell alignment="center" valignment="top" usebox="none">
4178 \begin_layout Plain Layout
4180 \begin_inset space \textvisiblespace{}
4186 \begin_inset space \textvisiblespace{}
4194 <cell alignment="center" valignment="top" usebox="none">
4197 \begin_layout Plain Layout
4198 \begin_inset Formula $A_{1}+\dots+A_{n}$
4208 <cell alignment="center" valignment="top" usebox="none">
4211 \begin_layout Plain Layout
4213 \begin_inset space \textvisiblespace{}
4219 \begin_inset space \textvisiblespace{}
4227 <cell alignment="center" valignment="top" usebox="none">
4230 \begin_layout Plain Layout
4231 \begin_inset Formula $A_{1},\ldots,A_{n}$
4241 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4244 \begin_layout Plain Layout
4246 \begin_inset space \textvisiblespace{}
4252 \begin_inset space \textvisiblespace{}
4260 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4263 \begin_layout Plain Layout
4264 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4274 <cell alignment="center" valignment="top" usebox="none">
4277 \begin_layout Plain Layout
4285 <cell alignment="center" valignment="top" usebox="none">
4288 \begin_layout Plain Layout
4289 \begin_inset Formula $\vdots$
4299 <cell alignment="center" valignment="top" usebox="none">
4302 \begin_layout Plain Layout
4310 <cell alignment="center" valignment="top" usebox="none">
4313 \begin_layout Plain Layout
4314 \begin_inset Formula $\ddots$
4324 <cell alignment="center" valignment="top" usebox="none">
4327 \begin_layout Plain Layout
4335 <cell alignment="center" valignment="top" usebox="none">
4338 \begin_layout Plain Layout
4339 \begin_inset Formula $\iddots$
4349 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4352 \begin_layout Plain Layout
4354 \begin_inset space \thinspace{}
4357 matrix with the different dots
4362 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4365 \begin_layout Plain Layout
4366 \begin_inset Formula $\begin{array}{ccc}
4367 A_{11} & \cdots & A_{1m}\\
4368 \vdots & \ddots & \vdots\\
4369 A_{n1} & \cdots & A_{nm}
4386 \begin_layout Standard
4387 The ellipses available in menu
4389 Insert\SpecialChar menuseparator
4391 \begin_inset space ~
4405 \begin_layout Standard
4406 \begin_inset VSpace medskip
4415 , one of the options
4417 Use mathdots package (automatically)
4419 must be set in the document settings under
4422 \begin_inset space ~
4428 \begin_inset Newline newline
4433 Use mathdots package
4435 will improve the appearance of all dots in the documents if their font
4436 style or size is not the default.
4439 \begin_layout Standard
4440 \begin_inset VSpace medskip
4443 Specially for matrices there are ellipses that span over several columns.
4444 They are created with the command
4451 \begin_inset Index idx
4454 \begin_layout Plain Layout
4462 , that has the following scheme:
4465 \begin_layout Standard
4470 hdotsfor[distance]{number of columns}
4473 \begin_layout Standard
4474 The number of columns specifies how many columns should be spanned.
4475 Distance is a factor for the distance between the dots.
4478 \begin_layout Standard
4479 In the following matrix the command
4485 was inserted in the first box of the second line, to get an ellipsis with
4486 a dot distance twice as long as with the command
4493 \begin_inset Formula
4495 \left(\begin{array}{cccc}
4504 Note that the matrix fields that should be spanned must be empty, otherwise
4505 you get \SpecialChar LaTeX
4509 \begin_layout Standard
4510 \begin_inset VSpace bigskip
4513 Furthermore you can fill with the command
4520 \begin_inset Index idx
4523 \begin_layout Plain Layout
4531 the rest of a line with dots.
4532 The effect of these commands is the same as with
4539 \begin_inset CommandInset ref
4541 reference "subsec:Variable-Space"
4548 \begin_layout Standard
4549 For example the command
4554 \begin_inset space \textvisiblespace{}
4562 \begin_layout Standard
4563 \begin_inset Formula $A\dotfill B$
4569 \begin_layout Standard
4576 there is for a line the command
4583 \begin_inset Index idx
4586 \begin_layout Plain Layout
4597 \begin_layout Standard
4598 \begin_inset Formula $A\hrulefill B$
4604 \begin_layout Standard
4605 To use the commands for text, they have to be inserted in \SpecialChar TeX
4609 \begin_layout Section
4611 \begin_inset CommandInset label
4618 \begin_inset Index idx
4621 \begin_layout Plain Layout
4630 \begin_layout Standard
4631 Matrices can be inserted via the math toolbar button
4634 arg "dialog-show mathmatrix"
4639 Insert\SpecialChar menuseparator
4640 Math\SpecialChar menuseparator
4644 In the matrix dialog you can specify the number of columns and rows, the
4645 alignment and the decoration.
4646 The vertical alignment is only of importance for matrices in inline formulas:
4649 \begin_layout Standard
4650 The first matrix is top
4651 \begin_inset Formula $\begin{array}[t]{cccc}
4659 \begin_inset Formula $\begin{array}{cccc}
4666 and the third bottom
4667 \begin_inset Formula $\begin{array}[b]{cccc}
4677 \begin_layout Standard
4678 The horizontal alignment specifies how the column entries should be aligned.
4679 It is set by entering a letter for every column.
4684 denotes left aligned,
4693 To create for example a 4
4698 \begin_inset space ~
4701 matrix where the first column is left aligned, the second and third are
4702 centered and the last one is right aligned, one enters for the horizontal
4708 Normally in a matrix all columns are centered, therefore the default for
4716 \begin_layout Standard
4717 Horizontal alignment:
4720 \begin_layout Standard
4726 \begin_inset Formula $\begin{array}{lll}
4738 \begin_inset Formula $\begin{array}{ccc}
4750 \begin_inset Formula $\begin{array}{rrr}
4760 \begin_layout Standard
4761 To add or delete rows and columns subsequently, the math toolbar buttons
4765 arg "tabular-feature append-row"
4771 arg "tabular-feature delete-row"
4775 \begin_inset space \thinspace{}
4780 Edit\SpecialChar menuseparator
4784 New rows can also be created with
4787 arg "newline-insert newline"
4793 \begin_layout Standard
4794 \begin_inset VSpace bigskip
4801 adds parentheses in the selected style around the matrix.
4802 Alternatively, parentheses can can either be created with the commands
4810 \begin_inset Index idx
4813 \begin_layout Plain Layout
4828 \begin_inset Index idx
4831 \begin_layout Plain Layout
4842 \begin_inset space ~
4848 \begin_inset CommandInset ref
4850 reference "subsec:Automatic-Bracket-Size"
4854 , or by using the following commands:
4855 \begin_inset VSpace medskip
4861 \begin_layout Standard
4862 \begin_inset space \hfill{}
4866 \begin_inset Tabular
4867 <lyxtabular version="3" rows="4" columns="2">
4868 <features booktabs="true" tabularvalignment="middle">
4869 <column alignment="center" valignment="top" width="0pt">
4870 <column alignment="center" valignment="top">
4872 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4875 \begin_layout Plain Layout
4881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4884 \begin_layout Plain Layout
4891 <row topspace="1.5mm">
4892 <cell alignment="center" valignment="top" usebox="none">
4895 \begin_layout Plain Layout
4899 \begin_inset space \textvisiblespace{}
4907 \begin_inset space \thinspace{}
4915 <cell alignment="center" valignment="top" usebox="none">
4918 \begin_layout Plain Layout
4919 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4920 0 & \textrm{-}\mathrm{i}\\
4922 \end{array}\end{bmatrix}$
4931 <row topspace="1.5mm" bottomspace="0.5mm">
4932 <cell alignment="center" valignment="top" usebox="none">
4935 \begin_layout Plain Layout
4939 \begin_inset space \textvisiblespace{}
4947 \begin_inset space \thinspace{}
4955 <cell alignment="center" valignment="top" usebox="none">
4958 \begin_layout Plain Layout
4959 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
4960 0 & \textrm{-}\mathrm{i}\\
4962 \end{array}\end{Bmatrix}$
4972 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4975 \begin_layout Plain Layout
4979 \begin_inset space \textvisiblespace{}
4987 \begin_inset space \thinspace{}
4995 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4998 \begin_layout Plain Layout
4999 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5000 0 & \textrm{-}\mathrm{i}\\
5002 \end{array}\end{pmatrix}$
5016 \begin_inset space \hfill{}
5020 \begin_inset Tabular
5021 <lyxtabular version="3" rows="4" columns="2">
5022 <features booktabs="true" tabularvalignment="middle">
5023 <column alignment="center" valignment="top" width="0pt">
5024 <column alignment="center" valignment="top">
5026 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5029 \begin_layout Plain Layout
5035 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5038 \begin_layout Plain Layout
5045 <row topspace="1.5mm">
5046 <cell alignment="center" valignment="top" usebox="none">
5049 \begin_layout Plain Layout
5053 \begin_inset space \textvisiblespace{}
5061 \begin_inset space \thinspace{}
5069 <cell alignment="center" valignment="top" usebox="none">
5072 \begin_layout Plain Layout
5073 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5074 0 & \textrm{-}\mathrm{i}\\
5076 \end{array}\end{vmatrix}$
5085 <row topspace="1.5mm" bottomspace="0.5mm">
5086 <cell alignment="center" valignment="top" usebox="none">
5089 \begin_layout Plain Layout
5093 \begin_inset space \textvisiblespace{}
5101 \begin_inset space \thinspace{}
5109 <cell alignment="center" valignment="top" usebox="none">
5112 \begin_layout Plain Layout
5113 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5114 0 & \textrm{-}\mathrm{i}\\
5116 \end{array}\end{Vmatrix}$
5126 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5129 \begin_layout Plain Layout
5133 \begin_inset space \textvisiblespace{}
5141 \begin_inset space \thinspace{}
5149 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5152 \begin_layout Plain Layout
5153 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5154 0 & \textrm{-}\mathrm{i}\\
5156 \end{array}\end{matrix}$
5170 \begin_inset space \hfill{}
5176 \begin_layout Standard
5177 \begin_inset VSpace medskip
5181 \begin_inset space \thinspace{}
5185 \begin_inset space \space{}
5194 is inserted, a blue box appears between two vertical lines where the matrix
5196 \begin_inset Newline newline
5199 Note that decorated matrices ignore the vertical alignment.
5202 \begin_layout Standard
5203 \begin_inset VSpace bigskip
5206 As all multiline formulas are matrices, the length
5213 \begin_inset Index idx
5216 \begin_layout Plain Layout
5224 that is described in
5225 \begin_inset CommandInset ref
5227 reference "subsec:Column-Separation"
5231 can also be used to change the column separation of matrices.
5234 \begin_layout Standard
5235 To change the row separation, the command
5242 \begin_inset Index idx
5245 \begin_layout Plain Layout
5254 It is used as follows:
5257 \begin_layout Standard
5264 arraystretch}{stretch factor}
5265 \begin_inset Index idx
5268 \begin_layout Plain Layout
5279 \begin_layout Standard
5286 assigns the stretch factor to the predefined command
5294 \begin_inset space \thinspace{}
5298 \begin_inset space \space{}
5301 the row separation, use the factor 2.
5302 This is then used for all following matrices.
5303 To go back to the original separation, assign the factor 1 to
5312 \begin_layout Standard
5313 To set matrices into a text line, the command
5320 \begin_inset Index idx
5323 \begin_layout Plain Layout
5332 When it is inserted a blue box with two dashed lines appears.
5333 In this box the matrix is inserted.
5336 \begin_layout Standard
5338 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5340 \end{smallmatrix}\right)$
5346 \begin_layout Section
5347 Brackets and Delimiters
5348 \begin_inset Index idx
5351 \begin_layout Plain Layout
5358 \begin_inset Index idx
5361 \begin_layout Plain Layout
5370 \begin_layout Subsection
5371 Vertical Brackets and Delimiters
5372 \begin_inset Index idx
5375 \begin_layout Plain Layout
5384 \begin_layout Standard
5385 \begin_inset space \hfill{}
5389 \begin_inset Tabular
5390 <lyxtabular version="3" rows="9" columns="2">
5391 <features booktabs="true" tabularvalignment="middle">
5392 <column alignment="center" valignment="top" width="0pt">
5393 <column alignment="center" valignment="top" width="0pt">
5395 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5398 \begin_layout Plain Layout
5404 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5407 \begin_layout Plain Layout
5415 <cell alignment="center" valignment="top" usebox="none">
5418 \begin_layout Plain Layout
5424 <cell alignment="center" valignment="top" usebox="none">
5427 \begin_layout Plain Layout
5428 \begin_inset Formula $($
5438 <cell alignment="center" valignment="top" usebox="none">
5441 \begin_layout Plain Layout
5447 <cell alignment="center" valignment="top" usebox="none">
5450 \begin_layout Plain Layout
5451 \begin_inset Formula $\{$
5461 <cell alignment="center" valignment="top" usebox="none">
5464 \begin_layout Plain Layout
5470 <cell alignment="center" valignment="top" usebox="none">
5473 \begin_layout Plain Layout
5474 \begin_inset Formula $[$
5484 <cell alignment="center" valignment="top" usebox="none">
5487 \begin_layout Plain Layout
5495 <cell alignment="center" valignment="top" usebox="none">
5498 \begin_layout Plain Layout
5499 \begin_inset Formula $\langle$
5509 <cell alignment="center" valignment="top" usebox="none">
5512 \begin_layout Plain Layout
5520 <cell alignment="center" valignment="top" usebox="none">
5523 \begin_layout Plain Layout
5524 \begin_inset Formula $\lceil$
5534 <cell alignment="center" valignment="top" usebox="none">
5537 \begin_layout Plain Layout
5545 <cell alignment="center" valignment="top" usebox="none">
5548 \begin_layout Plain Layout
5549 \begin_inset Formula $\lfloor$
5559 <cell alignment="center" valignment="top" usebox="none">
5562 \begin_layout Plain Layout
5568 <cell alignment="center" valignment="top" usebox="none">
5571 \begin_layout Plain Layout
5572 \begin_inset Formula $/$
5582 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5585 \begin_layout Plain Layout
5591 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5594 \begin_layout Plain Layout
5595 \begin_inset Formula $|$
5609 \begin_inset space \hfill{}
5613 \begin_inset Tabular
5614 <lyxtabular version="3" rows="9" columns="2">
5615 <features booktabs="true" tabularvalignment="middle">
5616 <column alignment="center" valignment="top" width="0pt">
5617 <column alignment="center" valignment="top" width="0pt">
5619 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5622 \begin_layout Plain Layout
5628 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5631 \begin_layout Plain Layout
5639 <cell alignment="center" valignment="top" usebox="none">
5642 \begin_layout Plain Layout
5648 <cell alignment="center" valignment="top" usebox="none">
5651 \begin_layout Plain Layout
5652 \begin_inset Formula $)$
5662 <cell alignment="center" valignment="top" usebox="none">
5665 \begin_layout Plain Layout
5671 <cell alignment="center" valignment="top" usebox="none">
5674 \begin_layout Plain Layout
5675 \begin_inset Formula $\}$
5685 <cell alignment="center" valignment="top" usebox="none">
5688 \begin_layout Plain Layout
5694 <cell alignment="center" valignment="top" usebox="none">
5697 \begin_layout Plain Layout
5698 \begin_inset Formula $]$
5708 <cell alignment="center" valignment="top" usebox="none">
5711 \begin_layout Plain Layout
5719 <cell alignment="center" valignment="top" usebox="none">
5722 \begin_layout Plain Layout
5723 \begin_inset Formula $\rangle$
5733 <cell alignment="center" valignment="top" usebox="none">
5736 \begin_layout Plain Layout
5744 <cell alignment="center" valignment="top" usebox="none">
5747 \begin_layout Plain Layout
5748 \begin_inset Formula $\rceil$
5758 <cell alignment="center" valignment="top" usebox="none">
5761 \begin_layout Plain Layout
5769 <cell alignment="center" valignment="top" usebox="none">
5772 \begin_layout Plain Layout
5773 \begin_inset Formula $\rfloor$
5783 <cell alignment="center" valignment="top" usebox="none">
5786 \begin_layout Plain Layout
5796 <cell alignment="center" valignment="top" usebox="none">
5799 \begin_layout Plain Layout
5800 \begin_inset Formula $\backslash$
5810 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5813 \begin_layout Plain Layout
5821 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5824 \begin_layout Plain Layout
5825 \begin_inset Formula $\|$
5839 \begin_inset space \hfill{}
5845 \begin_layout Standard
5848 \begin_inset Note Greyedout
5851 \begin_layout Plain Layout
5864 \begin_inset Index idx
5867 \begin_layout Plain Layout
5875 must be used for the backslash, because the command
5883 produces a line break there.
5891 \begin_layout Standard
5892 For all characters listed above the size can be adjusted with the commands
5893 described in the following two subsections.
5894 When using these commands, the characters < and > can directly be used
5895 instead of the commands
5910 \begin_layout Subsubsection
5912 \begin_inset CommandInset label
5914 name "subsec:Manual-Bracket-Size"
5919 \begin_inset Index idx
5922 \begin_layout Plain Layout
5923 Bracket size ! manual
5931 \begin_layout Standard
5932 The bracket size can be specified manually by the \SpecialChar LaTeX
5940 \begin_inset Index idx
5943 \begin_layout Plain Layout
5976 denotes the smallest and
5982 the largest bracket size.
5985 \begin_layout Standard
5986 These commands are used to emphasize levels of brackets:
5989 \begin_layout Standard
5991 \begin_inset Tabular
5992 <lyxtabular version="3" rows="2" columns="2">
5993 <features booktabs="true" tabularvalignment="middle">
5994 <column alignment="center" valignment="top" width="0pt">
5995 <column alignment="center" valignment="top" width="0pt">
5997 <cell alignment="center" valignment="top" usebox="none">
6000 \begin_layout Plain Layout
6001 all brackets in the same size:
6006 <cell alignment="center" valignment="top" usebox="none">
6009 \begin_layout Plain Layout
6010 \begin_inset Formula $((A+B)(A-B))^{C}$
6019 <row topspace="2mm">
6020 <cell alignment="center" valignment="top" usebox="none">
6023 \begin_layout Plain Layout
6029 <cell alignment="center" valignment="top" usebox="none">
6032 \begin_layout Plain Layout
6033 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6049 \begin_layout Standard
6050 For the second formula the command
6057 \begin_inset space \textvisiblespace{}
6065 \begin_layout Standard
6066 Here is an overview about all bracket sizes:
6069 \begin_layout Standard
6086 \begin_inset space \textvisiblespace{}
6094 \begin_inset space \textvisiblespace{}
6098 \begin_inset space \textvisiblespace{}
6108 \begin_layout Standard
6110 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6116 \begin_layout Standard
6123 -commands there is the variant
6130 \begin_inset Index idx
6133 \begin_layout Plain Layout
6141 that adds a bit more space between the bracket and its content, and the
6155 \begin_inset Index idx
6158 \begin_layout Plain Layout
6168 , that don't add additional space.
6173 at the end of the command
6179 is for a left bracket; for a right bracket this will be replaced by an
6185 A left or right bracket can each be an opening or closing bracket.
6188 \begin_layout Standard
6189 In the following table is a comparison of the variants:
6192 \begin_layout Standard
6194 \begin_inset Tabular
6195 <lyxtabular version="3" rows="5" columns="2">
6196 <features booktabs="true" tabularvalignment="middle">
6197 <column alignment="center" valignment="top" width="0pt">
6198 <column alignment="center" valignment="middle">
6200 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6203 \begin_layout Plain Layout
6209 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6212 \begin_layout Plain Layout
6219 <row topspace="2mm">
6220 <cell alignment="center" valignment="top" usebox="none">
6223 \begin_layout Plain Layout
6233 \begin_inset space \textvisiblespace{}
6243 <cell alignment="center" valignment="top" usebox="none">
6246 \begin_layout Plain Layout
6247 \begin_inset Formula $\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)$
6256 <row topspace="2mm">
6257 <cell alignment="center" valignment="top" usebox="none">
6260 \begin_layout Plain Layout
6270 \begin_inset space \textvisiblespace{}
6280 <cell alignment="center" valignment="top" usebox="none">
6283 \begin_layout Plain Layout
6284 \begin_inset Formula $\Big(\big(\ln(3x)\big)^{2}\Big)$
6293 <row topspace="2mm" bottomspace="0.5mm">
6294 <cell alignment="center" valignment="top" usebox="none">
6297 \begin_layout Plain Layout
6307 \begin_inset space \textvisiblespace{}
6317 <cell alignment="center" valignment="top" usebox="none">
6320 \begin_layout Plain Layout
6321 \begin_inset Formula $\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)$
6330 <row topspace="1.5mm" bottomspace="0.5mm">
6331 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6334 \begin_layout Plain Layout
6346 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6349 \begin_layout Plain Layout
6350 \begin_inset Formula $\bigl)\ln(3x)\bigr($
6366 \begin_layout Subsubsection
6367 Automatic Bracket Size
6368 \begin_inset CommandInset label
6370 name "subsec:Automatic-Bracket-Size"
6375 \begin_inset Index idx
6378 \begin_layout Plain Layout
6379 Bracket size ! automatic
6387 \begin_layout Standard
6388 Brackets with variable size can be inserted with the commands
6395 \begin_inset Index idx
6398 \begin_layout Plain Layout
6413 \begin_inset Index idx
6416 \begin_layout Plain Layout
6424 or via the math toolbar button
6427 arg "dialog-show mathdelimiter"
6443 the wanted bracket must be inserted.
6444 The bracket size will then automatically be calculated for the output.
6447 \begin_layout Standard
6449 normal bracket: The command
6456 \begin_inset space \textvisiblespace{}
6460 \begin_inset Formula $\downarrow$
6464 \begin_inset space \textvisiblespace{}
6470 \begin_inset Formula
6480 \begin_layout Standard
6482 multiline bracket: The command
6491 \begin_inset space \textvisiblespace{}
6495 \begin_inset Formula $\downarrow$
6499 \begin_inset space \textvisiblespace{}
6507 \begin_inset Formula
6509 \ln\left(\frac{A}{C}\right)
6517 \begin_layout Standard
6533 \begin_inset space ~
6539 This has the advantage that you can see in \SpecialChar LyX
6540 immediately the real bracket
6541 size and that the matching right bracket will be created too.
6542 \begin_inset Newline newline
6545 The command for the last example would then be:
6556 \begin_inset space \textvisiblespace{}
6560 \begin_inset Formula $\downarrow$
6566 \begin_layout Standard
6567 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6568 For example the command
6575 \begin_inset space \textvisiblespace{}
6579 \begin_inset Formula $\downarrow$
6583 \begin_inset space \textvisiblespace{}
6593 \begin_inset Formula
6595 \left.\frac{A}{B}\right\}
6614 will be converted by \SpecialChar LyX
6615 to brackets in the right size when the document is
6616 reloaded and an omitted bracket will appear as dashed line.
6619 \begin_layout Standard
6620 \begin_inset VSpace bigskip
6623 Because all popular \SpecialChar LaTeX
6624 distributions use e\SpecialChar TeX
6625 , an extension to \SpecialChar LaTeX
6634 \begin_inset Index idx
6637 \begin_layout Plain Layout
6645 is additionally available for all brackets and limits.
6646 With this command the height of the following character is adapted to the
6647 one of the surrounding brackets, what is e.
6648 \begin_inset space \thinspace{}
6652 \begin_inset space \space{}
6655 needed for physical vectors:
6656 \begin_inset Formula
6658 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6663 For physical vectors there is a special \SpecialChar LaTeX
6664 -package, described in
6665 \begin_inset CommandInset ref
6667 reference "subsec:Physical-Vectors"
6674 \begin_layout Subsection
6676 \begin_inset Index idx
6679 \begin_layout Plain Layout
6680 Brackets ! horizontal
6688 \begin_layout Standard
6690 \begin_inset Tabular
6691 <lyxtabular version="3" rows="4" columns="2">
6692 <features booktabs="true" tabularvalignment="middle">
6693 <column alignment="center" valignment="top" width="0pt">
6694 <column alignment="center" valignment="top" width="0pt">
6696 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6699 \begin_layout Plain Layout
6705 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6708 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" usebox="none">
6719 \begin_layout Plain Layout
6723 \begin_inset space \textvisiblespace{}
6727 \begin_inset space \textvisiblespace{}
6731 \begin_inset Index idx
6734 \begin_layout Plain Layout
6747 <cell alignment="center" valignment="top" usebox="none">
6750 \begin_layout Plain Layout
6751 \begin_inset Formula $\overbrace{A+B}^{3}$
6760 <row topspace="2mm">
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 $\underbrace{A+B}_{5}$
6806 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6809 \begin_layout Plain Layout
6813 \begin_inset space \textvisiblespace{}
6819 \begin_inset space \textvisiblespace{}
6823 \begin_inset space \textvisiblespace{}
6827 \begin_inset space \textvisiblespace{}
6831 \begin_inset space \textvisiblespace{}
6835 \begin_inset space \textvisiblespace{}
6839 \begin_inset space \textvisiblespace{}
6847 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6850 \begin_layout Plain Layout
6851 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
6867 \begin_layout Standard
6868 In the last example it doesn't matter if
6880 is inserted at first.
6883 \begin_layout Standard
6884 \begin_inset VSpace medskip
6890 \begin_layout Standard
6891 If you set in the document settings under
6894 \begin_inset space ~
6904 \begin_inset Index idx
6907 \begin_layout Plain Layout
6908 Packages ! mathtools
6916 \begin_inset space ~
6921 , you have access to square backets:
6924 \begin_layout Standard
6926 \begin_inset Tabular
6927 <lyxtabular version="3" rows="4" columns="2">
6928 <features booktabs="true" tabularvalignment="middle">
6929 <column alignment="center" valignment="top" width="0pt">
6930 <column alignment="center" valignment="top" width="0pt">
6932 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6935 \begin_layout Plain Layout
6941 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
6944 \begin_layout Plain Layout
6952 <cell alignment="center" valignment="top" usebox="none">
6955 \begin_layout Plain Layout
6983 \begin_inset space \textvisiblespace{}
6987 \begin_inset Index idx
6990 \begin_layout Plain Layout
7003 <cell alignment="center" valignment="top" usebox="none">
7006 \begin_layout Plain Layout
7007 \begin_inset Formula $\overbracket{A+B}^{3}$
7016 <row topspace="2mm">
7017 <cell alignment="center" valignment="top" usebox="none">
7020 \begin_layout Plain Layout
7048 \begin_inset space \textvisiblespace{}
7052 \begin_inset Index idx
7055 \begin_layout Plain Layout
7080 <cell alignment="center" valignment="top" usebox="none">
7083 \begin_layout Plain Layout
7084 \begin_inset Formula $\underbracket{A+B}_{5}$
7094 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7097 \begin_layout Plain Layout
7103 \begin_inset space \textvisiblespace{}
7107 \begin_inset space \textvisiblespace{}
7111 \begin_inset space \textvisiblespace{}
7115 \begin_inset space \textvisiblespace{}
7119 \begin_inset space \textvisiblespace{}
7127 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7130 \begin_layout Plain Layout
7131 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7147 \begin_layout Standard
7160 you can change the thickness of the bracket's stroke by specifying the
7161 desired thickness in square brackets behind the command:
7164 \begin_layout Standard
7166 \begin_inset Tabular
7167 <lyxtabular version="3" rows="3" columns="2">
7168 <features booktabs="true" tabularvalignment="middle">
7169 <column alignment="center" valignment="top" width="0pt">
7170 <column alignment="center" valignment="top" width="0pt">
7172 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7175 \begin_layout Plain Layout
7181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7184 \begin_layout Plain Layout
7192 <cell alignment="center" valignment="top" usebox="none">
7195 \begin_layout Plain Layout
7225 \begin_inset space \textvisiblespace{}
7233 <cell alignment="center" valignment="top" usebox="none">
7236 \begin_layout Plain Layout
7237 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7246 <row topspace="2mm">
7247 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7250 \begin_layout Plain Layout
7280 \begin_inset space \textvisiblespace{}
7288 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7291 \begin_layout Plain Layout
7292 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7308 \begin_layout Standard
7309 \begin_inset VSpace bigskip
7312 When brackets should overlap each other, multiline formulas, as described
7314 \begin_inset CommandInset ref
7316 reference "sec:Multiline-Formulas"
7321 \begin_inset Formula
7323 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7324 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7329 In the first row the formula is inserted together with the first brace.
7330 It is hereby important that the space command
7334 \begin_layout Plain Layout
7335 Space commands are explained in
7336 \begin_inset CommandInset ref
7338 reference "subsec:Predefined-Space"
7353 is inserted before the first
7354 \begin_inset Formula $d$
7357 , because the brace that ends behind the
7358 \begin_inset Formula $q$
7361 prevents that the following
7362 \begin_inset Quotes eld
7366 \begin_inset Quotes erd
7369 is surrounded by space.
7373 \begin_layout Plain Layout
7374 because a bracket is not handled as a character, see
7375 \begin_inset CommandInset ref
7377 reference "subsec:Binary-Operators"
7386 In the second row the second brace is inserted.
7387 As it should begin before the
7388 \begin_inset Formula $b$
7403 \begin_layout Plain Layout
7411 \begin_inset CommandInset ref
7413 reference "subsec:Placeholders"
7422 This space is needed because the
7423 \begin_inset Quotes eld
7427 \begin_inset Quotes erd
7430 is also surrounded by space in the formula.
7431 The brace is placed under the command
7440 \begin_layout Standard
7441 It gets more complicated when brackets overlap each other above and under
7442 the formula, like in the following example:
7446 \begin_layout Plain Layout
7458 \begin_inset Formula
7460 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7461 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7470 \begin_layout Plain Layout
7481 The first formula row is the same as the second row of the previous example,
7482 with the difference that the brace is above.
7483 The second row contains the formula together with the second brace.
7484 To avoid that there is space between the upper brace in the first row and
7485 the formula, the row spacing needs to be reduced.
7486 This is not easily possible due to a bug in \SpecialChar LyX
7491 \begin_layout Plain Layout
7492 \begin_inset CommandInset href
7494 name "LyX-bug #1505"
7495 target "http://www.lyx.org/trac/ticket/1505"
7505 As a solution for the problem, the global formula row separation
7512 \begin_inset Index idx
7515 \begin_layout Plain Layout
7523 must be changed to -6
7524 \begin_inset space \thinspace{}
7527 pt before the formula with the command
7543 is set back after the formula to the standard value of 3
7544 \begin_inset space \thinspace{}
7547 pt using the same command.
7548 More about the row separation in formulas is explained in
7549 \begin_inset CommandInset ref
7551 reference "subsec:Line-Separation"
7558 \begin_layout Section
7560 \begin_inset Index idx
7563 \begin_layout Plain Layout
7572 \begin_layout Standard
7573 Arrows can be inserted via the math toolbar button
7576 arg "math-insert \\leftarrow"
7579 or the commands listed in the following subsections.
7582 \begin_layout Subsection
7584 \begin_inset Index idx
7587 \begin_layout Plain Layout
7596 \begin_layout Standard
7597 \begin_inset space \hfill{}
7601 \begin_inset Tabular
7602 <lyxtabular version="3" rows="8" columns="2">
7603 <features booktabs="true" tabularvalignment="middle">
7604 <column alignment="center" valignment="top" width="0pt">
7605 <column alignment="center" valignment="top" width="0pt">
7607 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7610 \begin_layout Plain Layout
7616 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7619 \begin_layout Plain Layout
7627 <cell alignment="center" valignment="top" usebox="none">
7630 \begin_layout Plain Layout
7638 <cell alignment="center" valignment="top" usebox="none">
7641 \begin_layout Plain Layout
7642 \begin_inset Formula $\gets$
7652 <cell alignment="center" valignment="top" usebox="none">
7655 \begin_layout Plain Layout
7663 <cell alignment="center" valignment="top" usebox="none">
7666 \begin_layout Plain Layout
7667 \begin_inset Formula $\Leftarrow$
7677 <cell alignment="center" valignment="top" usebox="none">
7680 \begin_layout Plain Layout
7688 <cell alignment="center" valignment="top" usebox="none">
7691 \begin_layout Plain Layout
7692 \begin_inset Formula $\longleftarrow$
7702 <cell alignment="center" valignment="top" usebox="none">
7705 \begin_layout Plain Layout
7713 <cell alignment="center" valignment="top" usebox="none">
7716 \begin_layout Plain Layout
7717 \begin_inset Formula $\Longleftarrow$
7727 <cell alignment="center" valignment="top" usebox="none">
7730 \begin_layout Plain Layout
7738 <cell alignment="center" valignment="top" usebox="none">
7741 \begin_layout Plain Layout
7742 \begin_inset Formula $\leftharpoonup$
7752 <cell alignment="center" valignment="top" usebox="none">
7755 \begin_layout Plain Layout
7763 <cell alignment="center" valignment="top" usebox="none">
7766 \begin_layout Plain Layout
7767 \begin_inset Formula $\leftharpoondown$
7777 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7780 \begin_layout Plain Layout
7788 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7791 \begin_layout Plain Layout
7792 \begin_inset Formula $\hookleftarrow$
7806 \begin_inset space \hfill{}
7810 \begin_inset Tabular
7811 <lyxtabular version="3" rows="8" columns="2">
7812 <features booktabs="true" tabularvalignment="middle">
7813 <column alignment="center" valignment="top" width="0pt">
7814 <column alignment="center" valignment="top" width="0pt">
7816 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7819 \begin_layout Plain Layout
7825 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
7828 \begin_layout Plain Layout
7836 <cell alignment="center" valignment="top" usebox="none">
7839 \begin_layout Plain Layout
7847 <cell alignment="center" valignment="top" usebox="none">
7850 \begin_layout Plain Layout
7851 \begin_inset Formula $\to$
7861 <cell alignment="center" valignment="top" usebox="none">
7864 \begin_layout Plain Layout
7872 <cell alignment="center" valignment="top" usebox="none">
7875 \begin_layout Plain Layout
7876 \begin_inset Formula $\Rightarrow$
7886 <cell alignment="center" valignment="top" usebox="none">
7889 \begin_layout Plain Layout
7897 <cell alignment="center" valignment="top" usebox="none">
7900 \begin_layout Plain Layout
7901 \begin_inset Formula $\longrightarrow$
7911 <cell alignment="center" valignment="top" usebox="none">
7914 \begin_layout Plain Layout
7922 <cell alignment="center" valignment="top" usebox="none">
7925 \begin_layout Plain Layout
7926 \begin_inset Formula $\Longrightarrow$
7936 <cell alignment="center" valignment="top" usebox="none">
7939 \begin_layout Plain Layout
7947 <cell alignment="center" valignment="top" usebox="none">
7950 \begin_layout Plain Layout
7951 \begin_inset Formula $\rightharpoonup$
7961 <cell alignment="center" valignment="top" usebox="none">
7964 \begin_layout Plain Layout
7972 <cell alignment="center" valignment="top" usebox="none">
7975 \begin_layout Plain Layout
7976 \begin_inset Formula $\rightharpoondown$
7986 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
7989 \begin_layout Plain Layout
7997 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8000 \begin_layout Plain Layout
8001 \begin_inset Formula $\hookrightarrow$
8015 \begin_inset space \hfill{}
8021 \begin_layout Standard
8022 \begin_inset space \hfill{}
8026 \begin_inset Tabular
8027 <lyxtabular version="3" rows="6" columns="2">
8028 <features booktabs="true" tabularvalignment="middle">
8029 <column alignment="center" valignment="top" width="0pt">
8030 <column alignment="center" valignment="top" width="0pt">
8032 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8035 \begin_layout Plain Layout
8041 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8044 \begin_layout Plain Layout
8052 <cell alignment="center" valignment="top" usebox="none">
8055 \begin_layout Plain Layout
8063 <cell alignment="center" valignment="top" usebox="none">
8066 \begin_layout Plain Layout
8067 \begin_inset Formula $\leftrightarrow$
8077 <cell alignment="center" valignment="top" usebox="none">
8080 \begin_layout Plain Layout
8088 <cell alignment="center" valignment="top" usebox="none">
8091 \begin_layout Plain Layout
8092 \begin_inset Formula $\Leftrightarrow$
8102 <cell alignment="center" valignment="top" usebox="none">
8105 \begin_layout Plain Layout
8113 <cell alignment="center" valignment="top" usebox="none">
8116 \begin_layout Plain Layout
8117 \begin_inset Formula $\longleftrightarrow$
8127 <cell alignment="center" valignment="top" usebox="none">
8130 \begin_layout Plain Layout
8138 <cell alignment="center" valignment="top" usebox="none">
8141 \begin_layout Plain Layout
8142 \begin_inset Formula $\Longleftrightarrow$
8152 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8155 \begin_layout Plain Layout
8163 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8166 \begin_layout Plain Layout
8167 \begin_inset Formula $\rightleftharpoons$
8181 \begin_inset space \hspace{}
8186 \begin_inset space \hfill{}
8190 \begin_inset Tabular
8191 <lyxtabular version="3" rows="5" columns="2">
8192 <features booktabs="true" tabularvalignment="middle">
8193 <column alignment="center" valignment="top" width="0pt">
8194 <column alignment="center" valignment="top" width="0pt">
8196 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8199 \begin_layout Plain Layout
8205 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8208 \begin_layout Plain Layout
8216 <cell alignment="center" valignment="top" usebox="none">
8219 \begin_layout Plain Layout
8227 <cell alignment="center" valignment="top" usebox="none">
8230 \begin_layout Plain Layout
8231 \begin_inset Formula $\mapsto$
8241 <cell alignment="center" valignment="top" usebox="none">
8244 \begin_layout Plain Layout
8252 <cell alignment="center" valignment="top" usebox="none">
8255 \begin_layout Plain Layout
8256 \begin_inset Formula $\longmapsto$
8266 <cell alignment="center" valignment="top" usebox="none">
8269 \begin_layout Plain Layout
8277 <cell alignment="center" valignment="top" usebox="none">
8280 \begin_layout Plain Layout
8281 \begin_inset Formula $\leadsto$
8291 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8294 \begin_layout Plain Layout
8302 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8305 \begin_layout Plain Layout
8306 \begin_inset Formula $\dasharrow$
8320 \begin_inset space \hfill{}
8326 \begin_layout Standard
8327 \begin_inset VSpace medskip
8330 Arrows used as accents like e.
8331 \begin_inset space \thinspace{}
8335 \begin_inset space \space{}
8338 vector arrows are listed in
8339 \begin_inset CommandInset ref
8341 reference "sec:Accents"
8348 \begin_layout Standard
8349 \begin_inset VSpace bigskip
8352 Furthermore there are the labeled arrows
8353 \begin_inset Index idx
8356 \begin_layout Plain Layout
8369 \begin_inset Index idx
8372 \begin_layout Plain Layout
8387 \begin_inset Index idx
8390 \begin_layout Plain Layout
8397 \begin_layout Plain Layout
8412 When inserting one of these commands in a formula, an arrow with two blue
8413 boxes appear where the label can be inserted.
8414 The length of the arrow adapts to the label width.
8417 \begin_layout Standard
8419 \begin_inset Tabular
8420 <lyxtabular version="3" rows="3" columns="2">
8421 <features booktabs="true" tabularvalignment="middle">
8422 <column alignment="center" valignment="top" width="0pt">
8423 <column alignment="center" valignment="top" width="0pt">
8425 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8428 \begin_layout Plain Layout
8434 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8437 \begin_layout Plain Layout
8445 <cell alignment="center" valignment="top" usebox="none">
8448 \begin_layout Plain Layout
8452 \begin_inset space \textvisiblespace{}
8456 \begin_inset Formula $\downarrow$
8460 \begin_inset Formula $\to$
8468 <cell alignment="center" valignment="top" usebox="none">
8471 \begin_layout Plain Layout
8472 \begin_inset Formula $F(a)\xleftarrow[x>0]{x=a}F(x)$
8481 <row topspace="2mm">
8482 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8485 \begin_layout Plain Layout
8489 \begin_inset space \textvisiblespace{}
8493 \begin_inset Formula $\downarrow$
8497 \begin_inset Formula $\to$
8505 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8508 \begin_layout Plain Layout
8509 \begin_inset Formula $F(x)\xrightarrow[x>0]{x=a}F(a)$
8525 \begin_layout Standard
8526 \begin_inset VSpace medskip
8532 \begin_layout Standard
8533 If you set in the document settings under
8536 \begin_inset space ~
8546 \begin_inset Index idx
8549 \begin_layout Plain Layout
8550 Packages ! mathtools
8558 \begin_inset space ~
8563 , you have access to the following labeled arrows:
8566 \begin_layout Standard
8567 \begin_inset Newpage newpage
8573 \begin_layout Standard
8575 \begin_inset space \hspace*{\fill}
8579 \begin_inset Tabular
8580 <lyxtabular version="3" rows="7" columns="2">
8581 <features booktabs="true" tabularvalignment="middle">
8582 <column alignment="center" valignment="top" width="0pt">
8583 <column alignment="center" valignment="top" width="0pt">
8585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8588 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8597 \begin_layout Plain Layout
8605 <cell alignment="center" valignment="top" usebox="none">
8608 \begin_layout Plain Layout
8628 <cell alignment="center" valignment="top" usebox="none">
8631 \begin_layout Plain Layout
8632 \begin_inset Formula $\xleftrightarrow[x=a]{x>0}$
8641 <row topspace="2mm">
8642 <cell alignment="center" valignment="top" usebox="none">
8645 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\xLeftarrow[x=a]{x>0}$
8678 <row topspace="2mm">
8679 <cell alignment="center" valignment="top" usebox="none">
8682 \begin_layout Plain Layout
8702 <cell alignment="center" valignment="top" usebox="none">
8705 \begin_layout Plain Layout
8706 \begin_inset Formula $\xRightarrow[x=a]{x>0}$
8715 <row topspace="2mm">
8716 <cell alignment="center" valignment="top" usebox="none">
8719 \begin_layout Plain Layout
8739 <cell alignment="center" valignment="top" usebox="none">
8742 \begin_layout Plain Layout
8743 \begin_inset Formula $\xLeftrightarrow[x=a]{x>0}$
8752 <row topspace="2mm">
8753 <cell alignment="center" valignment="top" usebox="none">
8756 \begin_layout Plain Layout
8776 <cell alignment="center" valignment="top" usebox="none">
8779 \begin_layout Plain Layout
8780 \begin_inset Formula $\xhookleftarrow[x=a]{x>0}$
8789 <row topspace="2mm">
8790 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8793 \begin_layout Plain Layout
8813 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
8816 \begin_layout Plain Layout
8817 \begin_inset Formula $\xhookrightarrow[x=a]{x>0}$
8831 \begin_inset space \hspace*{\fill}
8835 \begin_inset Tabular
8836 <lyxtabular version="3" rows="7" columns="2">
8837 <features booktabs="true" tabularvalignment="middle">
8838 <column alignment="center" valignment="top" width="0pt">
8839 <column alignment="center" valignment="top" width="0pt">
8841 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8844 \begin_layout Plain Layout
8850 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
8853 \begin_layout Plain Layout
8861 <cell alignment="center" valignment="top" usebox="none">
8864 \begin_layout Plain Layout
8884 <cell alignment="center" valignment="top" usebox="none">
8887 \begin_layout Plain Layout
8888 \begin_inset Formula $\xleftharpoondown[x=a]{x>0}$
8897 <row topspace="2mm">
8898 <cell alignment="center" valignment="top" usebox="none">
8901 \begin_layout Plain Layout
8921 <cell alignment="center" valignment="top" usebox="none">
8924 \begin_layout Plain Layout
8925 \begin_inset Formula $\xleftharpoonup[x=a]{x>0}$
8934 <row topspace="2mm">
8935 <cell alignment="center" valignment="top" usebox="none">
8938 \begin_layout Plain Layout
8958 <cell alignment="center" valignment="top" usebox="none">
8961 \begin_layout Plain Layout
8962 \begin_inset Formula $\xrightharpoondown[x=a]{x>0}$
8971 <row topspace="2mm">
8972 <cell alignment="center" valignment="top" usebox="none">
8975 \begin_layout Plain Layout
8995 <cell alignment="center" valignment="top" usebox="none">
8998 \begin_layout Plain Layout
8999 \begin_inset Formula $\xrightharpoonup[x=a]{x>0}$
9008 <row topspace="2mm">
9009 <cell alignment="center" valignment="top" usebox="none">
9012 \begin_layout Plain Layout
9032 <cell alignment="center" valignment="top" usebox="none">
9035 \begin_layout Plain Layout
9036 \begin_inset Formula $\xleftrightharpoons[x=a]{x>0}$
9045 <row topspace="2mm">
9046 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9049 \begin_layout Plain Layout
9069 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9072 \begin_layout Plain Layout
9073 \begin_inset Formula $\xrightleftharpoons[x=a]{x>0}$
9087 \begin_inset space \hspace*{\fill}
9093 \begin_layout Standard
9094 The command scheme is for all these arrows:
9097 \begin_layout Standard
9099 \begin_inset Tabular
9100 <lyxtabular version="3" rows="2" columns="2">
9101 <features booktabs="true" tabularvalignment="middle">
9102 <column alignment="center" valignment="top" width="0pt">
9103 <column alignment="center" valignment="top" width="0pt">
9105 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9108 \begin_layout Plain Layout
9114 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9117 \begin_layout Plain Layout
9124 <row bottomspace="0.5mm">
9125 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9128 \begin_layout Plain Layout
9131 xleftrightarrow[x=a]
9134 \begin_inset Formula $\to$
9142 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9145 \begin_layout Plain Layout
9146 \begin_inset Formula $F(a)\xleftrightarrow[x=a]{x>0}F(x)$
9162 \begin_layout Subsection
9163 Vertical and diagonal Arrows
9164 \begin_inset Index idx
9167 \begin_layout Plain Layout
9174 \begin_inset Index idx
9177 \begin_layout Plain Layout
9186 \begin_layout Standard
9187 \begin_inset space \hfill{}
9191 \begin_inset Tabular
9192 <lyxtabular version="3" rows="7" columns="2">
9193 <features booktabs="true" tabularvalignment="middle">
9194 <column alignment="center" valignment="top" width="0pt">
9195 <column alignment="center" valignment="top" width="0pt">
9197 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9200 \begin_layout Plain Layout
9206 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9209 \begin_layout Plain Layout
9217 <cell alignment="center" valignment="top" usebox="none">
9220 \begin_layout Plain Layout
9228 <cell alignment="center" valignment="top" usebox="none">
9231 \begin_layout Plain Layout
9232 \begin_inset Formula $\uparrow$
9242 <cell alignment="center" valignment="top" usebox="none">
9245 \begin_layout Plain Layout
9253 <cell alignment="center" valignment="top" usebox="none">
9256 \begin_layout Plain Layout
9257 \begin_inset Formula $\Uparrow$
9267 <cell alignment="center" valignment="top" usebox="none">
9270 \begin_layout Plain Layout
9278 <cell alignment="center" valignment="top" usebox="none">
9281 \begin_layout Plain Layout
9282 \begin_inset Formula $\updownarrow$
9292 <cell alignment="center" valignment="top" usebox="none">
9295 \begin_layout Plain Layout
9303 <cell alignment="center" valignment="top" usebox="none">
9306 \begin_layout Plain Layout
9307 \begin_inset Formula $\Updownarrow$
9317 <cell alignment="center" valignment="top" usebox="none">
9320 \begin_layout Plain Layout
9328 <cell alignment="center" valignment="top" usebox="none">
9331 \begin_layout Plain Layout
9332 \begin_inset Formula $\Downarrow$
9342 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9345 \begin_layout Plain Layout
9353 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9356 \begin_layout Plain Layout
9357 \begin_inset Formula $\downarrow$
9371 \begin_inset space \hfill{}
9375 \begin_inset Tabular
9376 <lyxtabular version="3" rows="5" columns="2">
9377 <features booktabs="true" tabularvalignment="middle">
9378 <column alignment="center" valignment="top" width="0pt">
9379 <column alignment="center" valignment="top" width="0pt">
9381 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9384 \begin_layout Plain Layout
9390 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9393 \begin_layout Plain Layout
9401 <cell alignment="center" valignment="top" usebox="none">
9404 \begin_layout Plain Layout
9412 <cell alignment="center" valignment="top" usebox="none">
9415 \begin_layout Plain Layout
9416 \begin_inset Formula $\nearrow$
9426 <cell alignment="center" valignment="top" usebox="none">
9429 \begin_layout Plain Layout
9437 <cell alignment="center" valignment="top" usebox="none">
9440 \begin_layout Plain Layout
9441 \begin_inset Formula $\searrow$
9451 <cell alignment="center" valignment="top" usebox="none">
9454 \begin_layout Plain Layout
9462 <cell alignment="center" valignment="top" usebox="none">
9465 \begin_layout Plain Layout
9466 \begin_inset Formula $\swarrow$
9476 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9479 \begin_layout Plain Layout
9487 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9490 \begin_layout Plain Layout
9491 \begin_inset Formula $\nwarrow$
9505 \begin_inset space \hfill{}
9511 \begin_layout Standard
9512 \begin_inset VSpace medskip
9515 Vertical arrows can be used also as delimiters together with the commands
9517 \begin_inset CommandInset ref
9519 reference "subsec:Manual-Bracket-Size"
9524 \begin_inset CommandInset ref
9526 reference "subsec:Automatic-Bracket-Size"
9533 \begin_layout Section
9535 \begin_inset CommandInset label
9542 \begin_inset Index idx
9545 \begin_layout Plain Layout
9554 \begin_layout Standard
9555 Accents can be inserted via the math toolbar button
9558 arg "math-insert \\hat"
9561 or the commands listed in the following subsections.
9564 \begin_layout Subsection
9565 Accents for one Character
9569 \begin_layout Plain Layout
9582 \begin_layout Plain Layout
9584 \begin_inset CommandInset ref
9586 reference "subsec:Accents-in-Text"
9599 \begin_layout Plain Layout
9607 \begin_inset Note Note
9610 \begin_layout Plain Layout
9617 is used to avoid that the footnote appears in the PDF-bookmark.
9620 \begin_layout Plain Layout
9628 \begin_inset CommandInset ref
9630 reference "subsec:Formulas-in-Section"
9640 \begin_inset CommandInset label
9642 name "subsec:Accents-for-one"
9647 \begin_inset Index idx
9650 \begin_layout Plain Layout
9651 Accents ! for one character
9659 \begin_layout Standard
9660 \begin_inset space \hfill{}
9664 \begin_inset Tabular
9665 <lyxtabular version="3" rows="8" columns="2">
9666 <features booktabs="true" tabularvalignment="middle">
9667 <column alignment="center" valignment="top" width="0pt">
9668 <column alignment="center" valignment="top" width="0pt">
9670 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9673 \begin_layout Plain Layout
9679 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9682 \begin_layout Plain Layout
9689 <row topspace="1.5mm">
9690 <cell alignment="center" valignment="top" usebox="none">
9693 \begin_layout Plain Layout
9697 \begin_inset space \textvisiblespace{}
9705 <cell alignment="center" valignment="top" usebox="none">
9708 \begin_layout Plain Layout
9709 \begin_inset Formula $\dot{A}$
9718 <row topspace="1.5mm">
9719 <cell alignment="center" valignment="top" usebox="none">
9722 \begin_layout Plain Layout
9726 \begin_inset space \textvisiblespace{}
9734 <cell alignment="center" valignment="top" usebox="none">
9737 \begin_layout Plain Layout
9738 \begin_inset Formula $\ddot{A}$
9747 <row topspace="1.5mm">
9748 <cell alignment="center" valignment="top" usebox="none">
9751 \begin_layout Plain Layout
9755 \begin_inset space \textvisiblespace{}
9763 <cell alignment="center" valignment="top" usebox="none">
9766 \begin_layout Plain Layout
9767 \begin_inset Formula $\dddot{A}$
9776 <row topspace="1.5mm">
9777 <cell alignment="center" valignment="top" usebox="none">
9780 \begin_layout Plain Layout
9784 \begin_inset space \textvisiblespace{}
9792 <cell alignment="center" valignment="top" usebox="none">
9795 \begin_layout Plain Layout
9796 \begin_inset Formula $\ddddot{A}$
9805 <row topspace="1.5mm">
9806 <cell alignment="center" valignment="top" usebox="none">
9809 \begin_layout Plain Layout
9813 \begin_inset space \textvisiblespace{}
9817 \begin_inset Index idx
9820 \begin_layout Plain Layout
9831 <cell alignment="center" valignment="top" usebox="none">
9834 \begin_layout Plain Layout
9835 \begin_inset Formula $\vec{A}$
9844 <row topspace="1.5mm">
9845 <cell alignment="center" valignment="top" usebox="none">
9848 \begin_layout Plain Layout
9852 \begin_inset space \textvisiblespace{}
9860 <cell alignment="center" valignment="top" usebox="none">
9863 \begin_layout Plain Layout
9864 \begin_inset Formula $\bar{A}$
9873 <row topspace="1.5mm">
9874 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9877 \begin_layout Plain Layout
9881 \begin_inset space \textvisiblespace{}
9889 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
9892 \begin_layout Plain Layout
9893 \begin_inset Formula $\mathring{A}$
9907 \begin_inset space \hfill{}
9911 \begin_inset Tabular
9912 <lyxtabular version="3" rows="7" columns="2">
9913 <features booktabs="true" tabularvalignment="middle">
9914 <column alignment="center" valignment="top" width="0pt">
9915 <column alignment="center" valignment="top" width="0pt">
9917 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9920 \begin_layout Plain Layout
9926 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
9929 \begin_layout Plain Layout
9936 <row topspace="1.5mm">
9937 <cell alignment="center" valignment="top" usebox="none">
9940 \begin_layout Plain Layout
9944 \begin_inset space \textvisiblespace{}
9952 <cell alignment="center" valignment="top" usebox="none">
9955 \begin_layout Plain Layout
9956 \begin_inset Formula $\tilde{A}$
9965 <row topspace="1.5mm">
9966 <cell alignment="center" valignment="top" usebox="none">
9969 \begin_layout Plain Layout
9973 \begin_inset space \textvisiblespace{}
9981 <cell alignment="center" valignment="top" usebox="none">
9984 \begin_layout Plain Layout
9985 \begin_inset Formula $\hat{A}$
9994 <row topspace="1.5mm">
9995 <cell alignment="center" valignment="top" usebox="none">
9998 \begin_layout Plain Layout
10002 \begin_inset space \textvisiblespace{}
10010 <cell alignment="center" valignment="top" usebox="none">
10013 \begin_layout Plain Layout
10014 \begin_inset Formula $\check{A}$
10023 <row topspace="1.5mm">
10024 <cell alignment="center" valignment="top" usebox="none">
10027 \begin_layout Plain Layout
10031 \begin_inset space \textvisiblespace{}
10039 <cell alignment="center" valignment="top" usebox="none">
10042 \begin_layout Plain Layout
10043 \begin_inset Formula $\acute{A}$
10052 <row topspace="1.5mm">
10053 <cell alignment="center" valignment="top" usebox="none">
10056 \begin_layout Plain Layout
10060 \begin_inset space \textvisiblespace{}
10068 <cell alignment="center" valignment="top" usebox="none">
10071 \begin_layout Plain Layout
10072 \begin_inset Formula $\grave{A}$
10081 <row topspace="1.5mm">
10082 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10085 \begin_layout Plain Layout
10089 \begin_inset space \textvisiblespace{}
10097 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10100 \begin_layout Plain Layout
10101 \begin_inset Formula $\breve{A}$
10115 \begin_inset space \hfill{}
10121 \begin_layout Standard
10122 \begin_inset VSpace bigskip
10128 \begin_layout Standard
10129 You can directly insert accents like é to formulas.
10131 will transform them to the corresponding accent command.
10133 \begin_inset Index idx
10136 \begin_layout Plain Layout
10142 it is better to insert a quotation mark before the vowel.
10143 These two characters are then treated by \SpecialChar LaTeX
10148 character when the formula part with the umlaut is marked as German.
10156 \begin_inset Quotes eld
10160 \begin_inset Quotes erd
10163 umlauts are created as demonstrated in the following example:
10166 \begin_layout Standard
10167 \begin_inset VSpace -2mm
10173 \begin_layout Standard
10175 \begin_inset Tabular
10176 <lyxtabular version="3" rows="3" columns="2">
10177 <features booktabs="true" tabularvalignment="middle">
10178 <column alignment="center" valignment="top" width="0pt">
10179 <column alignment="center" valignment="top">
10181 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10184 \begin_layout Plain Layout
10190 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
10193 \begin_layout Plain Layout
10201 <cell alignment="center" valignment="top" usebox="none">
10204 \begin_layout Plain Layout
10205 \begin_inset Quotes grd
10213 <cell alignment="center" valignment="top" usebox="none">
10216 \begin_layout Plain Layout
10217 \begin_inset space \hspace{}
10224 \begin_inset Formula $"i$
10233 <row topspace="1.5mm">
10234 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10237 \begin_layout Plain Layout
10241 \begin_inset space \textvisiblespace{}
10249 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10252 \begin_layout Plain Layout
10253 \begin_inset Formula $\ddot{i}$
10269 \begin_layout Standard
10270 Another advantage to
10276 is that umlauts can directly be converted to mathematical text because
10277 the accent commands above are
10283 in mathematical text
10286 To convert an accented character to mathematical text, only the character
10287 under the accent may be converted.
10288 This applies also for all other conversions, e.
10289 \begin_inset space \thinspace{}
10293 \begin_inset space \space{}
10299 \begin_layout Standard
10300 In mathematical text, umlauts and other accented characters can directly
10304 \begin_layout Standard
10305 \begin_inset VSpace bigskip
10311 \begin_layout Standard
10313 also supports a tilde under the character if the \SpecialChar LaTeX
10319 \begin_inset Index idx
10322 \begin_layout Plain Layout
10323 Packages ! undertilde
10328 is installed on your system:
10331 \begin_layout Standard
10335 \begin_layout Plain Layout
10345 \begin_inset Note Note
10348 \begin_layout Plain Layout
10349 The following table will only be displayed when the \SpecialChar LaTeX
10362 \begin_layout Standard
10365 \begin_inset Tabular
10366 <lyxtabular version="3" rows="2" columns="2">
10367 <features booktabs="true" tabularvalignment="middle">
10368 <column alignment="center" valignment="top" width="0pt">
10369 <column alignment="center" valignment="top" width="0pt">
10371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10374 \begin_layout Plain Layout
10380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10383 \begin_layout Plain Layout
10391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10394 \begin_layout Plain Layout
10398 \begin_inset space \textvisiblespace{}
10406 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10409 \begin_layout Plain Layout
10410 \begin_inset Formula $\utilde{A}$
10426 \begin_layout Standard
10430 \begin_layout Plain Layout
10440 \begin_inset Note Note
10443 \begin_layout Plain Layout
10444 The following will be displayed when the \SpecialChar LaTeX
10457 \begin_layout Standard
10458 You need to install the \SpecialChar LaTeX
10463 to see the rest of this subsection in the output.
10466 \begin_layout Standard
10470 \begin_layout Plain Layout
10482 \begin_layout Standard
10483 \begin_inset Newpage newpage
10489 \begin_layout Subsection
10490 Accents for several Characters
10491 \begin_inset Index idx
10494 \begin_layout Plain Layout
10495 Accents ! for several characters
10503 \begin_layout Standard
10504 \begin_inset space \hfill{}
10508 \begin_inset Tabular
10509 <lyxtabular version="3" rows="5" columns="2">
10510 <features booktabs="true" tabularvalignment="middle">
10511 <column alignment="center" valignment="top" width="0pt">
10512 <column alignment="center" valignment="top" width="0pt">
10514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10517 \begin_layout Plain Layout
10523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10526 \begin_layout Plain Layout
10533 <row topspace="1.5mm">
10534 <cell alignment="center" valignment="top" usebox="none">
10537 \begin_layout Plain Layout
10541 \begin_inset space \textvisiblespace{}
10549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10552 \begin_layout Plain Layout
10553 \begin_inset Formula $\overleftarrow{A=B}$
10562 <row topspace="1.5mm">
10563 <cell alignment="center" valignment="top" usebox="none">
10566 \begin_layout Plain Layout
10570 \begin_inset space \textvisiblespace{}
10578 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10581 \begin_layout Plain Layout
10582 \begin_inset Formula $\underleftarrow{A=B}$
10591 <row topspace="1.5mm">
10592 <cell alignment="center" valignment="top" usebox="none">
10595 \begin_layout Plain Layout
10599 \begin_inset space \textvisiblespace{}
10607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10610 \begin_layout Plain Layout
10611 \begin_inset Formula $\overleftrightarrow{A=B}$
10620 <row topspace="1.5mm" bottomspace="1mm">
10621 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10624 \begin_layout Plain Layout
10627 underleftrightarrow
10628 \begin_inset space \textvisiblespace{}
10636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10639 \begin_layout Plain Layout
10640 \begin_inset Formula $\underleftrightarrow{A=B}$
10654 \begin_inset space \hfill{}
10658 \begin_inset Tabular
10659 <lyxtabular version="3" rows="5" columns="2">
10660 <features booktabs="true" tabularvalignment="middle">
10661 <column alignment="center" valignment="top" width="0pt">
10662 <column alignment="center" valignment="top" width="0pt">
10664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10667 \begin_layout Plain Layout
10673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10676 \begin_layout Plain Layout
10683 <row topspace="1.5mm">
10684 <cell alignment="center" valignment="top" usebox="none">
10687 \begin_layout Plain Layout
10691 \begin_inset space \textvisiblespace{}
10699 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10702 \begin_layout Plain Layout
10703 \begin_inset Formula $\overrightarrow{A=B}$
10712 <row topspace="1.5mm">
10713 <cell alignment="center" valignment="top" usebox="none">
10716 \begin_layout Plain Layout
10720 \begin_inset space \textvisiblespace{}
10728 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10731 \begin_layout Plain Layout
10732 \begin_inset Formula $\underrightarrow{A=B}$
10741 <row topspace="1.5mm">
10742 <cell alignment="center" valignment="top" usebox="none">
10745 \begin_layout Plain Layout
10749 \begin_inset space \textvisiblespace{}
10757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
10760 \begin_layout Plain Layout
10761 \begin_inset Formula $\widetilde{A=B}$
10770 <row topspace="1.5mm" bottomspace="1mm">
10771 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
10774 \begin_layout Plain Layout
10778 \begin_inset space \textvisiblespace{}
10786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10789 \begin_layout Plain Layout
10790 \begin_inset Formula $\widehat{A=B}$
10804 \begin_inset space \hfill{}
10810 \begin_layout Standard
10811 \begin_inset VSpace medskip
10814 With these commands as many characters as you like can be accented.
10827 will only be set in the output with a length of three characters, as shown
10828 in the following example:
10829 \begin_inset Formula
10831 \widetilde{A+B=C-D}
10839 \begin_layout Standard
10847 \begin_inset Index idx
10850 \begin_layout Plain Layout
10865 \begin_inset Index idx
10868 \begin_layout Plain Layout
10876 described in the previous subsection it is also possible to accent several
10883 \begin_inset space \textvisiblespace{}
10887 \begin_inset Formula $\downarrow$
10893 \begin_inset Formula
10895 \underset{***}{A=B}
10903 \begin_layout Section
10905 \begin_inset CommandInset label
10907 name "subsec:Space"
10912 \begin_inset Index idx
10915 \begin_layout Plain Layout
10924 \begin_layout Subsection
10926 \begin_inset CommandInset label
10928 name "subsec:Predefined-Space"
10933 \begin_inset Index idx
10936 \begin_layout Plain Layout
10937 Space ! horizontal ! predefined
10945 \begin_layout Standard
10946 Sometimes it is necessary to insert horizontal space into a formula.
10947 This is done by inserting a protected space (shortcut
10950 arg "command-alternatives space-insert protected ; math-space"
10955 \begin_inset Quotes eld
10961 \begin_inset space \textvisiblespace{}
10967 \begin_inset Quotes erd
10970 appears and by pressing
10974 several times one can select one of eight different space sizes.
10975 The spaces can also be inserted using the math toolbar button
10978 arg "math-insert \\space"
10981 or special commands.
10982 Independent from the inserted command, one can select the size again by
10990 \begin_layout Standard
10993 \begin_inset Tabular
10994 <lyxtabular version="3" rows="6" columns="3">
10995 <features booktabs="true" tabularvalignment="middle">
10996 <column alignment="center" valignment="top">
10997 <column alignment="center" valignment="top" width="15col%">
10998 <column alignment="center" valignment="top">
11000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11003 \begin_layout Plain Layout
11009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11012 \begin_layout Plain Layout
11022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11025 \begin_layout Plain Layout
11033 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11036 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11047 \begin_layout Plain Layout
11053 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11056 \begin_layout Plain Layout
11057 \begin_inset Formula $A\,B$
11067 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11070 \begin_layout Plain Layout
11078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11081 \begin_layout Plain Layout
11087 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11090 \begin_layout Plain Layout
11091 \begin_inset Formula $A\:B$
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 $A\quad B$
11169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11183 \begin_layout Plain Layout
11189 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\qquad B$
11207 \begin_inset space \hfill{}
11211 \begin_inset Tabular
11212 <lyxtabular version="3" rows="6" columns="3">
11213 <features booktabs="true" tabularvalignment="middle">
11214 <column alignment="center" valignment="top">
11215 <column alignment="center" valignment="top" width="15col%">
11216 <column alignment="center" valignment="top">
11218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11221 \begin_layout Plain Layout
11227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11230 \begin_layout Plain Layout
11240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11243 \begin_layout Plain Layout
11251 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11254 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11271 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11274 \begin_layout Plain Layout
11275 \begin_inset Formula $A\hfill B$
11285 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11288 \begin_layout Plain Layout
11296 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11308 \begin_layout Plain Layout
11309 \begin_inset Formula $A\hspace*{1em}B$
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 $A\hspace{1em}B$
11353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11360 \begin_inset space \textvisiblespace{}
11368 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11371 \begin_layout Plain Layout
11377 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11380 \begin_layout Plain Layout
11381 \begin_inset Formula $A\ B$
11391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11405 \begin_layout Plain Layout
11411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11414 \begin_layout Plain Layout
11415 \begin_inset Formula $A\!B$
11431 \begin_layout Standard
11433 \begin_inset space ~
11437 \begin_inset space \thinspace{}
11441 \begin_inset space \thinspace{}
11444 7 are variable spaces which are explained in
11445 \begin_inset CommandInset ref
11447 reference "subsec:Variable-Space"
11453 \begin_inset space ~
11456 9 seems to produce no space.
11457 It is displayed red in \SpecialChar LyX
11458 contrary to the other sizes, because it is a negative
11460 There are two more negative spaces:
11463 \begin_layout Standard
11465 \begin_inset Tabular
11466 <lyxtabular version="3" rows="3" columns="3">
11467 <features booktabs="true" tabularvalignment="middle">
11468 <column alignment="center" valignment="middle" width="6.8cm">
11469 <column alignment="center" valignment="top" width="0pt">
11470 <column alignment="center" valignment="top" width="0pt">
11472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11475 \begin_layout Plain Layout
11481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11484 \begin_layout Plain Layout
11492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11495 \begin_layout Plain Layout
11505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11508 \begin_layout Plain Layout
11513 keystrokes after inserting the protected space
11518 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11521 \begin_layout Plain Layout
11527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11530 \begin_layout Plain Layout
11538 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11541 \begin_layout Plain Layout
11547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11550 \begin_layout Plain Layout
11551 \begin_inset Formula $A\negmedspace B$
11559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11562 \begin_layout Plain Layout
11563 \begin_inset Formula $A\negthickspace B$
11579 \begin_layout Standard
11580 Negative spaces can lead to characters overlapping each other.
11581 Thus they can be used to enforce ligatures, which are e.
11582 \begin_inset space \thinspace{}
11586 \begin_inset space \space{}
11589 useful for summation operators:
11592 \begin_layout Standard
11594 \begin_inset Tabular
11595 <lyxtabular version="3" rows="3" columns="2">
11596 <features booktabs="true" tabularvalignment="middle">
11597 <column alignment="center" valignment="top" width="0pt">
11598 <column alignment="center" valignment="top">
11600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11603 \begin_layout Plain Layout
11609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11612 \begin_layout Plain Layout
11620 <cell alignment="center" valignment="top" leftline="true" usebox="none">
11623 \begin_layout Plain Layout
11629 \begin_inset space \textvisiblespace{}
11637 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
11640 \begin_layout Plain Layout
11641 \begin_inset Formula $\sum\sum f_{kl}$
11651 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11654 \begin_layout Plain Layout
11662 \begin_inset space \textvisiblespace{}
11670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11673 \begin_layout Plain Layout
11674 \begin_inset Formula $\sum\negmedspace\sum f_{kl}$
11690 \begin_layout Standard
11692 \begin_inset VSpace medskip
11698 \begin_layout Standard
11700 Relations like for example equal signs, are always surrounded by space.
11701 To suppress this, the equal sign is placed into a \SpecialChar TeX
11703 The following example demonstrates this:
11706 \begin_layout Standard
11708 \begin_inset Tabular
11709 <lyxtabular version="3" rows="2" columns="2">
11710 <features tabularvalignment="middle">
11711 <column alignment="center" valignment="top" width="0pt">
11712 <column alignment="center" valignment="top" width="0pt">
11714 <cell alignment="center" valignment="top" usebox="none">
11717 \begin_layout Plain Layout
11723 <cell alignment="center" valignment="top" usebox="none">
11726 \begin_layout Plain Layout
11727 \begin_inset Formula $A=B$
11737 <cell alignment="center" valignment="top" usebox="none">
11740 \begin_layout Plain Layout
11741 equation without space
11746 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11749 \begin_layout Plain Layout
11750 \begin_inset Formula $A{=}B$
11766 \begin_layout Standard
11768 The command for the last formula is:
11773 \begin_inset Formula $\to$
11779 \begin_layout Standard
11780 \begin_inset VSpace bigskip
11786 \begin_layout Standard
11787 Spaces are needed for physical units, because the space between the value
11788 and the unit is the smallest one and not a normal space.
11789 For units in text, the smallest space is inserted via the menu
11791 Insert\SpecialChar menuseparator
11792 Formatting\SpecialChar menuseparator
11794 \begin_inset space ~
11802 arg "space-insert thin"
11808 \begin_layout Standard
11809 An example to visualize the difference:
11812 \begin_layout Standard
11813 \begin_inset Tabular
11814 <lyxtabular version="3" rows="2" columns="2">
11815 <features tabularvalignment="middle">
11816 <column alignment="left" valignment="top">
11817 <column alignment="left" valignment="top">
11819 <cell alignment="center" valignment="top" usebox="none">
11822 \begin_layout Plain Layout
11824 \begin_inset Formula $\cdot$
11832 <cell alignment="center" valignment="top" usebox="none">
11835 \begin_layout Plain Layout
11836 space between value and unit
11843 <cell alignment="center" valignment="top" usebox="none">
11846 \begin_layout Plain Layout
11848 \begin_inset space \thinspace{}
11852 \begin_inset Formula $\cdot$
11860 <cell alignment="center" valignment="top" usebox="none">
11863 \begin_layout Plain Layout
11864 smallest space between value and unit
11877 \begin_layout Subsection
11882 \begin_layout Plain Layout
11895 \begin_layout Plain Layout
11896 for vertical space in formulas see
11897 \begin_inset CommandInset ref
11899 reference "subsec:Line-Separation"
11912 \begin_layout Plain Layout
11920 \begin_inset Note Note
11923 \begin_layout Plain Layout
11926 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11929 \begin_layout Plain Layout
11932 texorpdfstring is in section
11933 \begin_inset CommandInset ref
11935 reference "subsec:Formulas-in-Section"
11945 \begin_inset CommandInset label
11947 name "subsec:Variable-Space"
11952 \begin_inset Index idx
11955 \begin_layout Plain Layout
11956 Space ! horizontal ! variable
11964 \begin_layout Standard
11965 Space with a defined length can be inserted with the command
11972 \begin_inset Index idx
11975 \begin_layout Plain Layout
11985 \begin_inset Quotes eld
11991 \begin_inset space \textvisiblespace{}
11997 \begin_inset Quotes erd
12001 The length can be specified by left-clicking on the
12002 \begin_inset Quotes eld
12008 \begin_inset space \textvisiblespace{}
12014 \begin_inset Quotes erd
12018 The length may also be negative.
12019 When a space would be the first character in a line it would be omitted.
12020 To force its output use the command
12032 or left-click on the
12033 \begin_inset Quotes eld
12039 \begin_inset space \textvisiblespace{}
12045 \begin_inset Quotes erd
12048 and check the option
12053 \begin_inset Newline newline
12056 To insert as much space as is available, the command
12063 \begin_inset Index idx
12066 \begin_layout Plain Layout
12077 \begin_layout Standard
12079 \begin_inset Tabular
12080 <lyxtabular version="3" rows="4" columns="2">
12081 <features booktabs="true" tabularvalignment="middle">
12082 <column alignment="center" valignment="top" width="0pt">
12083 <column alignment="center" valignment="top">
12085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12088 \begin_layout Plain Layout
12096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12099 \begin_layout Plain Layout
12107 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12110 \begin_layout Plain Layout
12114 \begin_inset space \textvisiblespace{}
12120 \begin_inset space \thinspace{}
12128 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12131 \begin_layout Plain Layout
12132 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12142 <cell alignment="center" valignment="top" leftline="true" usebox="none">
12145 \begin_layout Plain Layout
12149 \begin_inset space \textvisiblespace{}
12155 \begin_inset space \thinspace{}
12163 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12166 \begin_layout Plain Layout
12167 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12180 \begin_layout Plain Layout
12184 \begin_inset space \textvisiblespace{}
12192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12195 \begin_layout Plain Layout
12196 \begin_inset Formula $A=A\hfill B=B$
12212 \begin_layout Standard
12213 In the last example the available space is given by the longest column entry
12215 In an inline formula the space depends on the length of the line in which
12223 Thus, when the line uses the full width, no space will be created.
12230 only has an effect on displayed formulas when the formula style
12235 (Formula styles are explained in
12236 \begin_inset CommandInset ref
12238 reference "sec:Formula-Styles"
12245 \begin_layout Standard
12252 , there are the commands
12264 that fill the space with a pattern, see
12265 \begin_inset CommandInset ref
12267 reference "subsec:Ellipses"
12274 \begin_layout Standard
12275 For text, variable space can be inserted via the menu
12277 Insert\SpecialChar menuseparator
12278 Formatting\SpecialChar menuseparator
12280 \begin_inset space ~
12288 \begin_layout Standard
12289 This is a line with
12290 \begin_inset space \hspace{}
12295 \begin_inset space \thinspace{}
12301 \begin_layout Standard
12302 This is a line with
12303 \begin_inset space \hfill{}
12309 \begin_layout Subsection
12310 Space besides inline Formulas
12311 \begin_inset Index idx
12314 \begin_layout Plain Layout
12315 Space ! besides inline formulas
12323 \begin_layout Standard
12324 The space that surrounds inline formulas can be adjusted with the length
12332 \begin_inset Index idx
12335 \begin_layout Plain Layout
12344 The value of a length is set with the command
12351 \begin_inset Index idx
12354 \begin_layout Plain Layout
12362 which has the following scheme:
12365 \begin_layout Standard
12370 setlength{length name}{value}
12373 \begin_layout Standard
12381 \begin_inset space \thinspace{}
12387 \begin_layout Standard
12397 \begin_layout Standard
12398 is inserted in \SpecialChar TeX
12401 \begin_inset space \thinspace{}
12404 mm space will now be set around all inline formulas:
12408 \begin_layout Plain Layout
12422 \begin_layout Standard
12423 This is a line with an inline formula
12424 \begin_inset Formula $A=B$
12428 \begin_inset space \thinspace{}
12431 mm surrounding space.
12435 \begin_layout Plain Layout
12449 \begin_layout Standard
12450 To return to the predefined value,
12456 is set to the value 0
12457 \begin_inset space \thinspace{}
12463 \begin_layout Standard
12464 \begin_inset Newpage newpage
12470 \begin_layout Section
12472 \begin_inset Index idx
12475 \begin_layout Plain Layout
12482 \begin_inset Index idx
12485 \begin_layout Plain Layout
12490 \begin_layout Plain Layout
12501 \begin_layout Plain Layout
12516 \begin_layout Standard
12517 Boxes for text are described in chapter
12524 \begin_inset space ~
12532 \begin_layout Subsection
12534 \begin_inset CommandInset label
12536 name "subsec:Boxes-with-Frame"
12541 \begin_inset Index idx
12544 \begin_layout Plain Layout
12553 \begin_layout Standard
12554 It is possible to frame a formula or part of one with the commands
12561 \begin_inset Index idx
12564 \begin_layout Plain Layout
12579 \begin_inset Index idx
12582 \begin_layout Plain Layout
12593 \begin_layout Standard
12594 When one of these commands is inserted in a formula, a blue box appears
12595 within a frame to enter formula parts.
12602 an additional formula has to be created by
12606 within this box, because the box content will otherwise be treated as mathemati
12614 is used, a new formula is automatically created inside the frame.
12617 \begin_layout Standard
12624 is not suitable to frame displayed formulas because the formula will always
12625 be set in the size of the text.
12632 is in contrary not suitable to frame inline formulas, because the formula
12633 will always be set in the size of a displayed formula.
12636 \begin_layout Standard
12650 \begin_inset Index idx
12653 \begin_layout Plain Layout
12661 where additionally the frame width and the alignment can be specified.
12668 is used in the following scheme:
12671 \begin_layout Standard
12676 framebox[frame width][position]{box content}
12679 \begin_layout Standard
12680 The position can either be
12697 right aligns the formula in the box.
12698 When no position is given, the formula will be centered.
12699 \begin_inset Newline newline
12702 If no width is given, also no position can be given.
12703 In this case the frame width is adjusted to the box content like for
12712 \begin_layout Standard
12719 is inserted, a box appears containing three blue boxes.
12720 The first two boxes are surrounded by brackets and denote the two optional
12722 The third box is for formula parts like for
12731 \begin_layout Standard
12733 \begin_inset Tabular
12734 <lyxtabular version="3" rows="5" columns="2">
12735 <features booktabs="true" tabularvalignment="middle">
12736 <column alignment="center" valignment="top" width="0pt">
12737 <column alignment="center" valignment="top">
12739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12742 \begin_layout Plain Layout
12748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12751 \begin_layout Plain Layout
12758 <row topspace="1.5mm">
12759 <cell alignment="center" valignment="top" usebox="none">
12762 \begin_layout Plain Layout
12766 \begin_inset space \textvisiblespace{}
12776 \begin_inset space \textvisiblespace{}
12784 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12787 \begin_layout Plain Layout
12788 \begin_inset Formula $\fbox{\ensuremath{\int A=B}}$
12797 <row topspace="1.5mm">
12798 <cell alignment="center" valignment="top" usebox="none">
12801 \begin_layout Plain Layout
12805 \begin_inset space \textvisiblespace{}
12811 \begin_inset space \textvisiblespace{}
12819 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12822 \begin_layout Plain Layout
12823 \begin_inset Formula $\boxed{\int A=B}$
12832 <row topspace="1.5mm">
12833 <cell alignment="center" valignment="top" usebox="none">
12836 \begin_layout Plain Layout
12840 \begin_inset space \textvisiblespace{}
12848 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
12851 \begin_layout Plain Layout
12852 \begin_inset Formula $A+\fbox{B}$
12861 <row topspace="1.5mm" bottomspace="1mm">
12862 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
12865 \begin_layout Plain Layout
12869 \begin_inset space \textvisiblespace{}
12873 \begin_inset Formula $\to$
12877 \begin_inset Formula $\to$
12887 \begin_inset space \textvisiblespace{}
12891 \begin_inset Formula $\downarrow$
12899 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
12902 \begin_layout Plain Layout
12903 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12919 \begin_layout Standard
12920 The frame thickness can also be adjusted.
12921 To do this the following commands have to be inserted in \SpecialChar TeX
12926 \begin_layout Standard
12936 \begin_inset Quotes eld
12940 \begin_inset Quotes erd
12954 \begin_inset Quotes eld
12958 \begin_inset Quotes erd
12964 \begin_layout Standard
12965 \begin_inset Quotes eld
12969 \begin_inset Quotes erd
12972 specifies the minimal distance between the frame and the first character
12974 An example for this is the following framed formula:
12978 \begin_layout Plain Layout
12990 \begin_inset Formula
12997 Before this formula the commands
13000 \begin_layout Standard
13022 \begin_layout Standard
13023 were inserted in \SpecialChar TeX
13025 The given values are used for all following boxes.
13028 \begin_layout Standard
13029 To return to the standard frame size, the command
13032 \begin_layout Standard
13057 \begin_layout Plain Layout
13071 \begin_layout Standard
13072 is inserted in \SpecialChar TeX
13073 mode before the next formula.
13076 \begin_layout Subsection
13077 Boxes without Frame
13078 \begin_inset CommandInset label
13080 name "subsec:Boxes-without-Frame"
13085 \begin_inset Index idx
13088 \begin_layout Plain Layout
13089 Boxes ! without frame
13097 \begin_layout Standard
13098 For boxes without a frame there are the following box commands:
13105 \begin_inset Index idx
13108 \begin_layout Plain Layout
13123 \begin_inset Index idx
13126 \begin_layout Plain Layout
13141 \begin_inset Index idx
13144 \begin_layout Plain Layout
13155 \begin_layout Standard
13162 a box can be super- or subscripted.
13163 But in contrary to normal super- and subscripting, the characters in the
13164 box keep their font size.
13171 is used in the following scheme:
13174 \begin_layout Standard
13179 raisebox{height}{box content}
13182 \begin_layout Standard
13183 When the box should contain a formula, an extra formula is needed like for
13194 \begin_inset Note Greyedout
13197 \begin_layout Plain Layout
13208 this extra formula is created by pressing
13212 twice instead of once because \SpecialChar LyX
13213 doesn't yet support
13227 \begin_layout Standard
13229 \begin_inset Tabular
13230 <lyxtabular version="3" rows="4" columns="2">
13231 <features booktabs="true" tabularvalignment="middle">
13232 <column alignment="center" valignment="top" width="0pt">
13233 <column alignment="center" valignment="top">
13235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13238 \begin_layout Plain Layout
13244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13247 \begin_layout Plain Layout
13255 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13258 \begin_layout Plain Layout
13262 \begin_inset Formula $\to$
13268 \begin_inset Formula $\to$
13276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13279 \begin_layout Plain Layout
13280 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13293 \begin_layout Plain Layout
13297 \begin_inset Formula $\to$
13303 \begin_inset Formula $\to$
13311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13314 \begin_layout Plain Layout
13315 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13328 \begin_layout Plain Layout
13332 \begin_inset Formula $\to$
13348 \begin_inset space \textvisiblespace{}
13356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13359 \begin_layout Plain Layout
13360 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13376 \begin_layout Standard
13401 , with the difference that there is no frame.
13404 \begin_layout Subsection
13406 \begin_inset CommandInset label
13408 name "subsec:Colored-Boxes"
13413 \begin_inset Index idx
13416 \begin_layout Plain Layout
13425 \begin_layout Standard
13426 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13435 \begin_layout Plain Layout
13436 The \SpecialChar LaTeX
13441 is part of every \SpecialChar LaTeX
13442 standard installation.
13448 \begin_inset Index idx
13451 \begin_layout Plain Layout
13457 has to be loaded in the \SpecialChar LaTeX
13458 -preamble with the line
13462 \begin_layout Plain Layout
13463 When text is colored somewhere in the document with a predefined color,
13465 loads the \SpecialChar LaTeX
13471 Thus it is possible that the package is loaded twice, but this does not
13478 \begin_inset Note Note
13481 \begin_layout Plain Layout
13482 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13491 \begin_layout Standard
13499 \begin_layout Standard
13500 \begin_inset VSpace medskip
13503 To color boxes, the command
13510 \begin_inset Index idx
13513 \begin_layout Plain Layout
13521 is used in the following scheme:
13524 \begin_layout Standard
13529 colorbox{color}{box content}
13532 \begin_layout Standard
13533 The box content can also be a box and a
13539 can also be part of another box (see the 2nd and 3rd example).
13540 When the box should contain a formula, an extra formula has to be created,
13541 the same way as for
13551 \begin_layout Plain Layout
13552 This also applies for the command
13566 \begin_layout Standard
13567 One of the following predefined colors can be chosen:
13570 \begin_layout Standard
13604 \begin_layout Standard
13606 \begin_inset Tabular
13607 <lyxtabular version="3" rows="4" columns="2">
13608 <features booktabs="true" tabularvalignment="middle">
13609 <column alignment="center" valignment="top" width="0pt">
13610 <column alignment="center" valignment="top">
13612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13615 \begin_layout Plain Layout
13621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13624 \begin_layout Plain Layout
13632 <cell alignment="center" valignment="top" leftline="true" usebox="none">
13635 \begin_layout Plain Layout
13639 \begin_inset Formula $\to$
13649 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13652 \begin_layout Plain Layout
13653 \begin_inset Formula $\colorbox{yellow}{A=B}$
13662 <row topspace="1.5mm">
13663 <cell alignment="center" valignment="top" usebox="none">
13666 \begin_layout Plain Layout
13670 \begin_inset Formula $\to$
13678 \begin_inset space \textvisiblespace{}
13686 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
13689 \begin_layout Plain Layout
13690 \begin_inset Formula $\colorbox{green}{\fbox{A=B}}$
13699 <row topspace="1.5mm" bottomspace="1mm">
13700 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
13703 \begin_layout Plain Layout
13707 \begin_inset space \textvisiblespace{}
13713 \begin_inset Formula $\to$
13729 \begin_inset space \textvisiblespace{}
13737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
13740 \begin_layout Plain Layout
13741 \begin_inset Formula $\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}$
13757 \begin_layout Standard
13764 only colors the box but not the characters in the box.
13765 To color all characters, the whole formula is highlighted and the desired
13766 color is chosen in the
13769 \begin_inset space ~
13775 The dialog can be called with the toolbar button
13778 arg "dialog-show character"
13783 Edit\SpecialChar menuseparator
13785 \begin_inset space ~
13788 Style\SpecialChar menuseparator
13792 The formula number then has the same color as the formula.
13793 When the formula number should get another color than the formula characters,
13794 the color must be changed within the formula.
13797 \begin_layout Standard
13801 \begin_layout Standard
13804 \begin_inset Formula
13806 \int A=B\label{eq:red}
13814 \begin_inset Formula
13816 \textcolor{red}{\int A=B}\label{eq:redgreen}
13824 \begin_layout Standard
13826 \begin_inset CommandInset ref
13832 is completely colored red.
13833 \begin_inset Newline newline
13837 \begin_inset CommandInset ref
13839 reference "eq:redgreen"
13843 was first completely colored green to set the color for the formula number.
13844 Subsequently the formula characters were colored red.
13847 \begin_layout Standard
13848 \begin_inset VSpace bigskip
13851 To color the frame different than the rest of the box, the command
13858 \begin_inset Index idx
13861 \begin_layout Plain Layout
13869 is used in the following scheme:
13872 \begin_layout Standard
13877 fcolorbox{frame color}{color}{box content}
13880 \begin_layout Standard
13887 is an extension of the command
13894 The frame width is set, like for
13917 \begin_layout Plain Layout
13929 \begin_inset Formula
13931 \fcolorbox{cyan}{magenta}{A=B}
13940 \begin_layout Plain Layout
13954 \begin_layout Standard
13955 This formula was created with the command
13956 \begin_inset Newline newline
13964 \begin_inset Formula $\to$
13970 \begin_inset Formula $\to$
13980 \begin_layout Standard
13981 \begin_inset VSpace bigskip
13984 To use other colors than the predefined ones, they have to be defined first.
13987 \begin_layout Standard
13988 One can for example define the color
13989 \begin_inset Quotes eld
13997 \begin_inset Quotes erd
14000 with the \SpecialChar LaTeX
14004 \begin_layout Standard
14009 definecolor{darkgreen}{cmyk}{0.5,
14024 \begin_inset Index idx
14027 \begin_layout Plain Layout
14038 \begin_layout Standard
14043 is the color space that denotes the colors
14060 The four comma separated numbers are the portion factor for the corresponding
14061 colors of the color space.
14062 The factors can be in the range of 0
14063 \begin_inset space \thinspace{}
14067 \begin_inset space \thinspace{}
14075 also the color space
14079 can be used for definitions.
14096 , so that there are in this case three portion factors for the corresponding
14098 Furthermore there is the color space
14102 with one portion factor for the gray value.
14105 \begin_layout Standard
14106 As example a framed box with the new defined color
14110 where the characters have been colored
14115 \begin_inset Formula
14117 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14125 \begin_layout Standard
14126 Self-defined colors can also be used for text with the help of the command
14134 \begin_inset Index idx
14137 \begin_layout Plain Layout
14146 \begin_layout Standard
14150 \begin_layout Plain Layout
14154 textcolor{darkgreen}{
14160 \begin_inset Quotes eld
14164 \begin_inset Quotes erd
14171 \begin_layout Plain Layout
14181 \begin_layout Standard
14189 \begin_inset Index idx
14192 \begin_layout Plain Layout
14200 is used in the scheme
14204 textcolor{color}{characters to color}
14209 \begin_layout Subsection
14211 \begin_inset CommandInset label
14213 name "subsec:Paragraph-Boxes"
14218 \begin_inset Index idx
14221 \begin_layout Plain Layout
14222 Boxes ! as paragraph
14230 \begin_layout Standard
14231 A box that can contain several lines and paragraphs, a so-called paragraph
14232 box (parbox), can be created with the menu
14234 Insert\SpecialChar menuseparator
14237 or the toolbar button
14246 \begin_layout Standard
14247 The following example shows a framed parbox in a line:
14250 \begin_layout Standard
14251 \begin_inset VSpace medskip
14255 \begin_inset Box Boxed
14265 height_special "totalheight"
14270 backgroundcolor "none"
14273 \begin_layout Plain Layout
14274 This is a paragraph box.
14276 \begin_inset space \thinspace{}
14279 cm long and can also contain formulas:
14280 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14291 \begin_layout Standard
14292 \begin_inset VSpace medskip
14298 \begin_layout Standard
14299 Such a box is created by right-clicking on the gray box inset.
14300 A dialog pops up showing the box properties.
14314 \begin_inset space \thinspace{}
14319 Vertical Box Alignment
14324 \begin_layout Standard
14325 \begin_inset VSpace medskip
14328 In \SpecialChar LaTeX
14329 a parbox is created with the command
14336 \begin_inset Index idx
14339 \begin_layout Plain Layout
14347 which has the following scheme:
14350 \begin_layout Standard
14355 parbox[position]{width}{box content}
14358 \begin_layout Standard
14373 \begin_inset Quotes eld
14377 \begin_inset Quotes erd
14380 means that the box is aligned within the surrounding text with its last
14387 \begin_inset Quotes eld
14391 \begin_inset Quotes erd
14394 this is done with the first line.
14395 When no position is given, the box will be vertically centered, see section
14403 \begin_inset space ~
14408 manual for examples.
14411 \begin_layout Standard
14412 \begin_inset VSpace bigskip
14415 To frame formulas completely, including the formula number, the formula
14416 must be set into a parbox.
14417 To do this, the command
14431 is inserted in \SpecialChar TeX
14432 mode before the formula.
14440 \begin_inset Index idx
14443 \begin_layout Plain Layout
14451 is hereby the line width set for the document.
14452 Because the frame is outside the parbox, 2
14453 \begin_inset space \thinspace{}
14456 times the frame separation and the frame thickness must be subtracted from
14458 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
14467 \begin_layout Plain Layout
14472 is part of every \SpecialChar LaTeX
14473 standard installation.
14479 \begin_inset Index idx
14482 \begin_layout Plain Layout
14488 must be loaded in the \SpecialChar LaTeX
14489 -preamble with the line
14492 \begin_layout Standard
14500 \begin_layout Standard
14501 Behind the formula both boxes are closed by entering
14505 in \SpecialChar TeX
14507 Here is an example:
14511 \begin_layout Plain Layout
14525 \begin_layout Standard
14529 \begin_layout Plain Layout
14547 \begin_inset Formula
14549 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14558 \begin_layout Plain Layout
14569 \begin_layout Plain Layout
14583 \begin_layout Standard
14584 \begin_inset VSpace medskip
14587 As a parbox is used as the argument of
14593 , there is in this case no difference between
14608 \begin_layout Standard
14609 \begin_inset VSpace bigskip
14612 Paragraph boxes are very useful to comment formulas directly.
14619 is used in combination with the command
14633 \begin_inset CommandInset ref
14635 reference "subsec:User-defined-Numbering"
14642 \begin_layout Standard
14643 An example of a formula commented with
14652 \begin_layout Standard
14656 \begin_layout Plain Layout
14669 This is a description.
14670 It is distinctly separated from the formula and multiline.
14674 \begin_layout Plain Layout
14686 \begin_layout Standard
14687 Such a formula must be inserted completely in \SpecialChar TeX
14688 mode because \SpecialChar LyX
14690 support the command
14697 The formula is created with the following command sequence:
14700 \begin_layout Standard
14713 is inserted in \SpecialChar TeX
14718 \begin_layout Plain Layout
14719 When the formula style
14731 can also be replaced by
14738 (formula styles see
14739 \begin_inset CommandInset ref
14741 reference "sec:Formula-Styles"
14750 Then the description follows as normal text and finally
14756 is inserted in \SpecialChar TeX
14770 hereby create a displayed formula.
14773 \begin_layout Standard
14780 can be seen in this example that was
14781 \begin_inset Quotes eld
14785 \begin_inset Quotes erd
14788 using the mathematical textmode:
14789 \begin_inset Formula
14791 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14799 \begin_layout Section
14801 \begin_inset Index idx
14804 \begin_layout Plain Layout
14813 \begin_layout Subsection
14815 \begin_inset CommandInset label
14817 name "subsec:Big-Operators"
14822 \begin_inset Index idx
14825 \begin_layout Plain Layout
14832 \begin_inset Index idx
14835 \begin_layout Plain Layout
14842 \begin_inset Index idx
14845 \begin_layout Plain Layout
14854 \begin_layout Standard
14855 To be able to use all integral operators listed here, the option
14857 Use esint package automatically
14859 must be set in the document settings under
14862 \begin_inset space ~
14870 \begin_layout Standard
14871 \begin_inset space \hfill{}
14875 \begin_inset Tabular
14876 <lyxtabular version="3" rows="11" columns="2">
14877 <features booktabs="true" tabularvalignment="middle">
14878 <column alignment="center" valignment="top" width="0pt">
14879 <column alignment="center" valignment="top" width="0pt">
14881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14884 \begin_layout Plain Layout
14890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14893 \begin_layout Plain Layout
14901 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14904 \begin_layout Plain Layout
14908 \begin_inset Index idx
14911 \begin_layout Plain Layout
14924 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14927 \begin_layout Plain Layout
14928 \begin_inset Formula $\int$
14938 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14941 \begin_layout Plain Layout
14949 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14952 \begin_layout Plain Layout
14953 \begin_inset Formula $\oint$
14963 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14966 \begin_layout Plain Layout
14974 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
14977 \begin_layout Plain Layout
14978 \begin_inset Formula $\ointctrclockwise$
14988 <cell alignment="center" valignment="top" leftline="true" usebox="none">
14991 \begin_layout Plain Layout
14999 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15002 \begin_layout Plain Layout
15003 \begin_inset Formula $\ointclockwise$
15013 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15016 \begin_layout Plain Layout
15024 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15027 \begin_layout Plain Layout
15028 \begin_inset Formula $\sqint$
15038 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15041 \begin_layout Plain Layout
15049 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15052 \begin_layout Plain Layout
15054 \begin_inset Formula $\fint$
15064 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15067 \begin_layout Plain Layout
15075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15078 \begin_layout Plain Layout
15080 \begin_inset Formula $\landupint$
15090 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15093 \begin_layout Plain Layout
15101 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15104 \begin_layout Plain Layout
15106 \begin_inset Formula $\landdownint$
15116 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15119 \begin_layout Plain Layout
15127 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15130 \begin_layout Plain Layout
15131 \begin_inset Formula $\bigcap$
15141 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15144 \begin_layout Plain Layout
15152 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15155 \begin_layout Plain Layout
15156 \begin_inset Formula $\bigcup$
15170 \begin_inset space \hfill{}
15174 \begin_inset Tabular
15175 <lyxtabular version="3" rows="11" columns="2">
15176 <features booktabs="true" tabularvalignment="middle">
15177 <column alignment="center" valignment="top" width="0pt">
15178 <column alignment="center" valignment="top" width="0pt">
15180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15192 \begin_layout Plain Layout
15200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15203 \begin_layout Plain Layout
15207 \begin_inset Index idx
15210 \begin_layout Plain Layout
15223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15226 \begin_layout Plain Layout
15227 \begin_inset Formula $\sum$
15237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15240 \begin_layout Plain Layout
15244 \begin_inset Index idx
15247 \begin_layout Plain Layout
15254 \begin_layout Plain Layout
15273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15276 \begin_layout Plain Layout
15277 \begin_inset Formula $\prod$
15287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15290 \begin_layout Plain Layout
15298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15301 \begin_layout Plain Layout
15302 \begin_inset Formula $\coprod$
15312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15315 \begin_layout Plain Layout
15323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15326 \begin_layout Plain Layout
15327 \begin_inset Formula $\bigodot$
15337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15340 \begin_layout Plain Layout
15348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15351 \begin_layout Plain Layout
15352 \begin_inset Formula $\bigotimes$
15362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15365 \begin_layout Plain Layout
15373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15376 \begin_layout Plain Layout
15377 \begin_inset Formula $\bigoplus$
15387 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15390 \begin_layout Plain Layout
15398 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15401 \begin_layout Plain Layout
15402 \begin_inset Formula $\bigwedge$
15412 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15415 \begin_layout Plain Layout
15423 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15426 \begin_layout Plain Layout
15427 \begin_inset Formula $\bigvee$
15437 <cell alignment="center" valignment="top" leftline="true" usebox="none">
15440 \begin_layout Plain Layout
15448 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
15451 \begin_layout Plain Layout
15452 \begin_inset Formula $\bigsqcup$
15462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
15465 \begin_layout Plain Layout
15473 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
15476 \begin_layout Plain Layout
15477 \begin_inset Formula $\biguplus$
15491 \begin_inset space \hfill{}
15497 \begin_layout Standard
15498 All big operators can also be inserted via the math toolbar button
15501 arg "math-insert \\intop"
15507 \begin_layout Standard
15508 The operators are called big because they are bigger than the sometimes
15509 equal looking binary operators.
15510 All big operators can have limits as described in the next subsection.
15513 \begin_layout Standard
15514 For all integral operators there is a second version available, ending in
15532 These operators are different from
15539 \begin_inset space \space{}
15542 in the style the operator limits are displayed, see
15543 \begin_inset CommandInset ref
15545 reference "subsec:Operator-Limits"
15553 \begin_layout Subsubsection*
15554 Advice for Integrals
15557 \begin_layout Standard
15562 in an integral is an operator, that therefore has to be set upright.
15563 This is done by highlighting the
15567 and using the keyboard shortcut
15577 \begin_layout Plain Layout
15583 \begin_inset CommandInset ref
15585 reference "subsec:Font-Styles"
15595 Finally the smallest space is inserted before the
15599 , as this is usual for operators.
15603 \begin_layout Standard
15605 \begin_inset Formula $\int A(x)dx$
15609 \begin_inset Newline newline
15613 \begin_inset Phantom HPhantom
15616 \begin_layout Plain Layout
15623 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15629 \begin_layout Standard
15630 For multiple integrals there are the following commands:
15631 \begin_inset VSpace medskip
15637 \begin_layout Standard
15638 \begin_inset space \hfill{}
15642 \begin_inset Tabular
15643 <lyxtabular version="3" rows="4" columns="2">
15644 <features booktabs="true" tabularvalignment="middle">
15645 <column alignment="center" valignment="top" width="0pt">
15646 <column alignment="center" valignment="top" width="0pt">
15648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15651 \begin_layout Plain Layout
15657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15660 \begin_layout Plain Layout
15667 <row bottomspace="1mm">
15668 <cell alignment="center" valignment="top" usebox="none">
15671 \begin_layout Plain Layout
15679 <cell alignment="center" valignment="top" usebox="none">
15682 \begin_layout Plain Layout
15683 \begin_inset Formula $\iint$
15692 <row bottomspace="1mm">
15693 <cell alignment="center" valignment="top" usebox="none">
15696 \begin_layout Plain Layout
15704 <cell alignment="center" valignment="top" usebox="none">
15707 \begin_layout Plain Layout
15708 \begin_inset Formula $\oiint$
15717 <row bottomspace="1mm">
15718 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15721 \begin_layout Plain Layout
15729 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15732 \begin_layout Plain Layout
15733 \begin_inset Formula $\sqiint$
15747 \begin_inset space \hfill{}
15751 \begin_inset Tabular
15752 <lyxtabular version="3" rows="4" columns="2">
15753 <features booktabs="true" tabularvalignment="middle">
15754 <column alignment="center" valignment="top" width="0pt">
15755 <column alignment="center" valignment="top" width="0pt">
15757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15760 \begin_layout Plain Layout
15766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15769 \begin_layout Plain Layout
15776 <row bottomspace="1mm">
15777 <cell alignment="center" valignment="top" usebox="none">
15780 \begin_layout Plain Layout
15788 <cell alignment="center" valignment="top" usebox="none">
15791 \begin_layout Plain Layout
15792 \begin_inset Formula $\iiint$
15801 <row bottomspace="1mm">
15802 <cell alignment="center" valignment="top" usebox="none">
15805 \begin_layout Plain Layout
15813 <cell alignment="center" valignment="top" usebox="none">
15816 \begin_layout Plain Layout
15817 \begin_inset Formula $\iiiint$
15826 <row bottomspace="1mm">
15827 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15830 \begin_layout Plain Layout
15838 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15841 \begin_layout Plain Layout
15842 \begin_inset Formula $\dotsint$
15856 \begin_inset space \hfill{}
15862 \begin_layout Subsection
15864 \begin_inset CommandInset label
15866 name "subsec:Operator-Limits"
15871 \begin_inset Index idx
15874 \begin_layout Plain Layout
15883 \begin_layout Standard
15884 Limits are created by super- and subscripts:
15887 \begin_layout Standard
15889 \begin_inset Tabular
15890 <lyxtabular version="3" rows="2" columns="2">
15891 <features booktabs="true" tabularvalignment="middle">
15892 <column alignment="center" valignment="top" width="0pt">
15893 <column alignment="center" valignment="top" width="0pt">
15895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15898 \begin_layout Plain Layout
15904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15907 \begin_layout Plain Layout
15915 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15918 \begin_layout Plain Layout
15924 \begin_inset space \textvisiblespace{}
15928 \begin_inset Formula $\to$
15932 \begin_inset Formula $\to$
15940 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
15943 \begin_layout Plain Layout
15944 \begin_inset Formula $\prod_{0}^{\infty}A(x)$
15960 \begin_layout Standard
15961 Limits of inline formulas are set right beside the operator.
15962 Limits in displayed formulas are set above or below the operator, except
15963 for integral limits.
15966 \begin_layout Standard
15967 To force that the limits are set beside the operator, the cursor is set
15968 directly behind the operator and the limits type is changed with the menu
15971 Edit\SpecialChar menuseparator
15972 Math\SpecialChar menuseparator
15991 \begin_layout Standard
15992 The default limits type is this:
15993 \begin_inset Formula
15995 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16000 This is how it looks when the limits type was changed to
16007 \begin_inset Formula
16009 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16014 For integrals, except those ending with
16030 etc., the limits are by default set beside the operator.
16031 But for multiple integrals the limits are often set below the operator.
16032 In the following example the limits type was therefore set to
16036 and so set below the integrals:
16037 \begin_inset Formula
16039 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16047 \begin_layout Standard
16048 \begin_inset VSpace medskip
16051 To specify conditions for limits, the commands
16058 \begin_inset Index idx
16061 \begin_layout Plain Layout
16076 \begin_inset Index idx
16079 \begin_layout Plain Layout
16088 To create for example this expression
16089 \begin_inset Formula
16091 \sum_{\begin{subarray}{c}
16095 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16103 \begin_layout Standard
16104 the following has to be done:
16105 \begin_inset Newline newline
16117 \begin_inset space \textvisiblespace{}
16123 One is now in a blue box under the summation operator and insert there
16129 \begin_inset space \textvisiblespace{}
16135 The blue box is now within a purple box and now several lines can be written
16137 A new line is created by inserting a line break (
16140 arg "newline-insert newline"
16145 \begin_inset Newline newline
16150 0<k<1000 Ctrl+Return
16151 \begin_inset Newline newline
16156 is typed in, a new box appears below for the new line.
16159 \begin_layout Standard
16160 The alignment of the lines can be changed to left aligned with the
16170 Edit\SpecialChar menuseparator
16174 To get right alignment,
16179 \begin_inset space \textvisiblespace{}
16184 is inserted at the beginning of the line.
16187 \begin_layout Standard
16200 with the difference that the lines are always centered.
16203 \begin_layout Standard
16204 \begin_inset VSpace bigskip
16208 \begin_inset CommandInset ref
16210 reference "eq:substack"
16214 there can be too much space beside an operator, because the characters
16215 following the operator are set beside the limits.
16216 To avoid this the command
16223 \begin_inset Index idx
16226 \begin_layout Plain Layout
16235 To activate it, set in the document settings under
16238 \begin_inset space ~
16248 \begin_inset Index idx
16251 \begin_layout Plain Layout
16252 Packages ! mathtools
16260 \begin_inset space ~
16272 sets the space besides the operator to 0
16273 \begin_inset space \thinspace{}
16277 \begin_inset Newline newline
16281 \begin_inset CommandInset ref
16283 reference "eq:substack"
16287 , one uses the command
16290 \begin_layout Standard
16298 \begin_layout Standard
16299 and inserts the operator with its limits into the braces.
16300 Behind the brace one continues the formula:
16301 \begin_inset Formula
16303 \smashoperator{\sum_{\begin{subarray}{c}
16307 \end{subarray}}^{n}}k^{-2}
16315 \begin_layout Standard
16316 It is possible to set the space of only one side of the operator to 0
16317 \begin_inset space \thinspace{}
16321 To do this write either
16340 stands for the left and
16344 for the right side of the operator.
16345 Here is an example of the possible
16354 \begin_layout Standard
16355 \begin_inset Formula
16357 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}
16365 \begin_layout Standard
16366 \begin_inset VSpace bigskip
16372 \begin_layout Standard
16373 When several consecutive operators have limits the typesetting of the limits
16374 looks often imperfect in the output, see this example:
16375 \begin_inset Formula
16377 \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}
16382 To improve the typesetting set in the document settings under
16385 \begin_inset space ~
16395 \begin_inset Index idx
16398 \begin_layout Plain Layout
16399 Packages ! mathtools
16407 \begin_inset space ~
16413 Then insert into your formula the command
16420 \begin_inset Index idx
16423 \begin_layout Plain Layout
16431 directly before the first operator.
16432 The example will then look like this:
16433 \begin_inset Formula
16435 \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}
16443 \begin_layout Standard
16444 \begin_inset VSpace bigskip
16447 How to use one limit for several operators is described in
16448 \begin_inset CommandInset ref
16450 reference "subsec:Self-defined-Operators"
16457 \begin_layout Subsection
16458 Decoration for Operators
16459 \begin_inset Index idx
16462 \begin_layout Plain Layout
16463 Operators ! Decoration
16471 \begin_layout Standard
16479 \begin_inset Index idx
16482 \begin_layout Plain Layout
16497 \begin_inset Index idx
16500 \begin_layout Plain Layout
16508 characters can be placed above or below an operator, respectively.
16516 \begin_inset Index idx
16519 \begin_layout Plain Layout
16527 characters can be set before and behind a big operator.
16530 \begin_layout Standard
16532 \begin_inset space ~
16544 \begin_layout Itemize
16551 is used to set characters at the corners of the operator
16554 \begin_layout Itemize
16561 is used to set characters before and/or behind the operator (this variant
16562 represents \SpecialChar LaTeX
16572 \begin_layout Itemize
16579 is used to set characters at the left corners and/or behind the operator
16582 \begin_layout Itemize
16589 is used to set characters at the right corners and/or before the operator
16592 \begin_layout Standard
16593 For example the command
16598 \begin_inset space \textvisiblespace{}
16604 \begin_inset space \textvisiblespace{}
16608 \begin_inset Formula $\to$
16612 \begin_inset Formula $\to$
16616 \begin_inset space \textvisiblespace{}
16626 \begin_inset Formula
16628 \sideset{}{'}\sum_{k=1}^{n}
16636 \begin_layout Standard
16637 \begin_inset Note Greyedout
16640 \begin_layout Plain Layout
16647 can only be used to decorate big operators, binary operators are not allowed.
16655 \begin_layout Standard
16668 can also be used to decorate symbols and characters.
16669 For example, the command
16674 \begin_inset space \textvisiblespace{}
16680 \begin_inset space \textvisiblespace{}
16686 \begin_inset Formula $\uparrow$
16694 \begin_inset Formula
16696 \overset{a}{\maltese}
16704 \begin_layout Subsection
16706 \begin_inset CommandInset label
16708 name "subsec:Binary-Operators"
16713 \begin_inset Index idx
16716 \begin_layout Plain Layout
16725 \begin_layout Standard
16726 Binary operators are surrounded by space when there is a character before
16728 \begin_inset VSpace medskip
16734 \begin_layout Standard
16735 \begin_inset Tabular
16736 <lyxtabular version="3" rows="13" columns="2">
16737 <features booktabs="true" tabularvalignment="middle">
16738 <column alignment="center" valignment="top" width="0pt">
16739 <column alignment="center" valignment="top" width="0pt">
16741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16744 \begin_layout Plain Layout
16746 \begin_inset Note Note
16749 \begin_layout Plain Layout
16756 is only used as spacer.
16766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16769 \begin_layout Plain Layout
16777 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16780 \begin_layout Plain Layout
16786 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16789 \begin_layout Plain Layout
16790 \begin_inset Formula $+$
16800 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16809 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16812 \begin_layout Plain Layout
16813 \begin_inset Formula $-$
16823 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16826 \begin_layout Plain Layout
16834 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16837 \begin_layout Plain Layout
16838 \begin_inset Formula $\pm$
16848 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16851 \begin_layout Plain Layout
16859 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16862 \begin_layout Plain Layout
16863 \begin_inset Formula $\mp$
16873 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16876 \begin_layout Plain Layout
16884 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16887 \begin_layout Plain Layout
16888 \begin_inset Formula $\cdot$
16898 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16901 \begin_layout Plain Layout
16909 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16912 \begin_layout Plain Layout
16913 \begin_inset Formula $\times$
16923 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16926 \begin_layout Plain Layout
16934 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16937 \begin_layout Plain Layout
16938 \begin_inset Formula $\div$
16948 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16951 \begin_layout Plain Layout
16955 \begin_layout Plain Layout
16968 \begin_layout Plain Layout
16980 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
16983 \begin_layout Plain Layout
16984 \begin_inset Formula $*$
16994 <cell alignment="center" valignment="top" leftline="true" usebox="none">
16997 \begin_layout Plain Layout
17005 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17008 \begin_layout Plain Layout
17009 \begin_inset Formula $\star$
17019 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17022 \begin_layout Plain Layout
17030 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17033 \begin_layout Plain Layout
17034 \begin_inset Formula $\circ$
17044 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17047 \begin_layout Plain Layout
17055 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17058 \begin_layout Plain Layout
17059 \begin_inset Formula $\diamond$
17069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17072 \begin_layout Plain Layout
17080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17083 \begin_layout Plain Layout
17084 \begin_inset Formula $\bullet$
17098 \begin_inset space \hfill{}
17102 \begin_inset Tabular
17103 <lyxtabular version="3" rows="13" columns="2">
17104 <features booktabs="true" tabularvalignment="middle">
17105 <column alignment="center" valignment="top" width="0pt">
17106 <column alignment="center" valignment="top" width="0pt">
17108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17111 \begin_layout Plain Layout
17117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17120 \begin_layout Plain Layout
17128 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17131 \begin_layout Plain Layout
17139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17142 \begin_layout Plain Layout
17143 \begin_inset Formula $\nabla$
17153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17156 \begin_layout Plain Layout
17164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17167 \begin_layout Plain Layout
17168 \begin_inset Formula $\bigtriangledown$
17178 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17181 \begin_layout Plain Layout
17189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17192 \begin_layout Plain Layout
17193 \begin_inset Formula $\bigtriangleup$
17203 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17206 \begin_layout Plain Layout
17214 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17217 \begin_layout Plain Layout
17218 \begin_inset Formula $\Box$
17228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17239 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17242 \begin_layout Plain Layout
17243 \begin_inset Formula $\cap$
17253 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17256 \begin_layout Plain Layout
17264 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17267 \begin_layout Plain Layout
17268 \begin_inset Formula $\cup$
17278 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17281 \begin_layout Plain Layout
17289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17292 \begin_layout Plain Layout
17293 \begin_inset Formula $\dagger$
17303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17306 \begin_layout Plain Layout
17314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17317 \begin_layout Plain Layout
17318 \begin_inset Formula $\ddagger$
17328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17331 \begin_layout Plain Layout
17339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17342 \begin_layout Plain Layout
17343 \begin_inset Formula $\wr$
17353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17356 \begin_layout Plain Layout
17364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17367 \begin_layout Plain Layout
17368 \begin_inset Formula $\bigcirc$
17378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17381 \begin_layout Plain Layout
17389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17392 \begin_layout Plain Layout
17393 \begin_inset Formula $\wedge$
17403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17406 \begin_layout Plain Layout
17414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17417 \begin_layout Plain Layout
17418 \begin_inset Formula $\vee$
17432 \begin_inset space \hfill{}
17436 \begin_inset Tabular
17437 <lyxtabular version="3" rows="13" columns="2">
17438 <features booktabs="true" tabularvalignment="middle">
17439 <column alignment="center" valignment="top" width="0pt">
17440 <column alignment="center" valignment="top" width="0pt">
17442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17445 \begin_layout Plain Layout
17451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17454 \begin_layout Plain Layout
17462 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17465 \begin_layout Plain Layout
17473 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17476 \begin_layout Plain Layout
17477 \begin_inset Formula $\oplus$
17487 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17490 \begin_layout Plain Layout
17498 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17501 \begin_layout Plain Layout
17502 \begin_inset Formula $\ominus$
17512 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17515 \begin_layout Plain Layout
17523 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17526 \begin_layout Plain Layout
17527 \begin_inset Formula $\otimes$
17537 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17540 \begin_layout Plain Layout
17548 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17551 \begin_layout Plain Layout
17552 \begin_inset Formula $\oslash$
17562 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17565 \begin_layout Plain Layout
17573 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17576 \begin_layout Plain Layout
17577 \begin_inset Formula $\odot$
17587 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17590 \begin_layout Plain Layout
17598 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17601 \begin_layout Plain Layout
17602 \begin_inset Formula $\amalg$
17612 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17615 \begin_layout Plain Layout
17623 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17626 \begin_layout Plain Layout
17627 \begin_inset Formula $\uplus$
17637 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17640 \begin_layout Plain Layout
17648 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17651 \begin_layout Plain Layout
17652 \begin_inset Formula $\setminus$
17662 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17665 \begin_layout Plain Layout
17673 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17676 \begin_layout Plain Layout
17677 \begin_inset Formula $\sqcap$
17687 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17690 \begin_layout Plain Layout
17698 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17701 \begin_layout Plain Layout
17702 \begin_inset Formula $\sqcup$
17712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
17715 \begin_layout Plain Layout
17723 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
17726 \begin_layout Plain Layout
17727 \begin_inset Formula $\triangleleft$
17737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
17740 \begin_layout Plain Layout
17748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
17751 \begin_layout Plain Layout
17752 \begin_inset Formula $\triangleright$
17768 \begin_layout Standard
17769 All binary operators can also be inserted via the math toolbar button
17772 arg "math-insert \\pm"
17778 \begin_layout Standard
17779 To typeset the Laplace operator also
17796 \begin_inset Formula $\nabla^{2}$
17799 ) can be used instead of
17808 \begin_layout Standard
17815 Insert\SpecialChar menuseparator
17827 \begin_layout Subsection
17828 Self-defined Operators
17829 \begin_inset CommandInset label
17831 name "subsec:Self-defined-Operators"
17836 \begin_inset Index idx
17839 \begin_layout Plain Layout
17840 Operators ! self-defined
17848 \begin_layout Standard
17849 With the help of the command
17853 DeclareMathOperator
17856 \begin_inset Index idx
17859 \begin_layout Plain Layout
17864 DeclareMathOperator
17869 custom operators can be defined in the \SpecialChar LaTeX
17871 Its command scheme is:
17874 \begin_layout Standard
17879 DeclareMathOperator{new command}{display}
17882 \begin_layout Standard
17883 Display can be characters or symbols that define how the operator looks
17885 To define a big operator a * is set behind the command.
17886 All self-defined big operators can have limits as described in
17887 \begin_inset CommandInset ref
17889 reference "subsec:Operator-Limits"
17896 \begin_layout Standard
17897 For example the \SpecialChar LaTeX
17901 \begin_layout Standard
17906 DeclareMathOperator*{
17913 \begin_layout Standard
17914 defines the command
17920 , that inserts a big operator consisting of the lozenge symbol from
17921 \begin_inset CommandInset ref
17923 reference "subsec:Miscellaneous-Symbols"
17928 \begin_inset Formula
17930 \Lozenge_{n=1}^{\infty}
17935 The command for this formula is:
17946 \begin_inset Formula $\to$
17952 \begin_layout Standard
17953 \begin_inset VSpace bigskip
17956 When self-defined operators are not used several times in the document,
17957 they can also be defined with the commands
17964 \begin_inset Index idx
17967 \begin_layout Plain Layout
17982 \begin_inset Index idx
17985 \begin_layout Plain Layout
17993 , which have the following scheme:
17996 \begin_layout Standard
18010 \begin_layout Standard
18017 defines big operators,
18026 \begin_layout Standard
18034 \begin_inset space \thinspace{}
18038 \begin_inset space \space{}
18041 be used to use one limit for several operators:
18044 \begin_layout Standard
18045 \begin_inset Formula
18047 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18055 \begin_layout Standard
18056 The command for the formula above is:
18057 \begin_inset Newline newline
18073 \begin_inset space \textvisiblespace{}
18079 \begin_inset Formula $\to$
18085 \begin_inset space \textvisiblespace{}
18093 \begin_layout Section
18095 \begin_inset Index idx
18098 \begin_layout Plain Layout
18107 \begin_layout Subsection
18109 \begin_inset CommandInset label
18111 name "subsec:Font-Styles"
18116 \begin_inset Index idx
18119 \begin_layout Plain Layout
18128 \begin_layout Standard
18129 Latin letters in formulas can be set in one of the following font styles:
18132 \begin_layout Standard
18134 \begin_inset Tabular
18135 <lyxtabular version="3" rows="6" columns="3">
18136 <features booktabs="true" tabularvalignment="middle">
18137 <column alignment="center" valignment="top" width="0pt">
18138 <column alignment="center" valignment="top">
18139 <column alignment="center" valignment="top">
18141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18144 \begin_layout Plain Layout
18150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18153 \begin_layout Plain Layout
18159 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18162 \begin_layout Plain Layout
18170 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18173 \begin_layout Plain Layout
18179 \begin_inset space \textvisiblespace{}
18189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18192 \begin_layout Plain Layout
18193 \begin_inset Formula $\mathbb{ABC}$
18201 <cell alignment="center" valignment="top" usebox="none">
18204 \begin_layout Plain Layout
18212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18215 \begin_layout Plain Layout
18221 \begin_inset space \textvisiblespace{}
18231 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18234 \begin_layout Plain Layout
18235 \begin_inset Formula $\mathbf{AbC}$
18243 <cell alignment="center" valignment="top" usebox="none">
18246 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18268 \begin_inset space \textvisiblespace{}
18278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18281 \begin_layout Plain Layout
18282 \begin_inset Formula $\boldsymbol{AbC}$
18290 <cell alignment="center" valignment="top" usebox="none">
18293 \begin_layout Plain Layout
18296 arg "font-boldsymbol"
18306 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18309 \begin_layout Plain Layout
18315 \begin_inset space \textvisiblespace{}
18325 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18328 \begin_layout Plain Layout
18329 \begin_inset Formula $\mathcal{ABC}$
18337 <cell alignment="center" valignment="top" usebox="none">
18340 \begin_layout Plain Layout
18348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18351 \begin_layout Plain Layout
18357 \begin_inset space \textvisiblespace{}
18367 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18370 \begin_layout Plain Layout
18371 \begin_inset Formula $\mathfrak{AbC}$
18379 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18382 \begin_layout Plain Layout
18396 \begin_layout Standard
18398 \begin_inset Tabular
18399 <lyxtabular version="3" rows="6" columns="3">
18400 <features booktabs="true" tabularvalignment="middle">
18401 <column alignment="center" valignment="top" width="0pt">
18402 <column alignment="center" valignment="top">
18403 <column alignment="center" valignment="top">
18405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18408 \begin_layout Plain Layout
18414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18417 \begin_layout Plain Layout
18423 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
18426 \begin_layout Plain Layout
18434 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18437 \begin_layout Plain Layout
18443 \begin_inset space \textvisiblespace{}
18453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18456 \begin_layout Plain Layout
18457 \begin_inset Formula $\mathit{AbC}$
18465 <cell alignment="center" valignment="top" usebox="none">
18468 \begin_layout Plain Layout
18476 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18479 \begin_layout Plain Layout
18485 \begin_inset space \textvisiblespace{}
18495 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18498 \begin_layout Plain Layout
18499 \begin_inset Formula $\mathrm{AbC}$
18507 <cell alignment="center" valignment="top" usebox="none">
18510 \begin_layout Plain Layout
18523 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18526 \begin_layout Plain Layout
18532 \begin_inset space \textvisiblespace{}
18542 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18545 \begin_layout Plain Layout
18546 \begin_inset Formula $\mathsf{AbC}$
18554 <cell alignment="center" valignment="top" usebox="none">
18557 \begin_layout Plain Layout
18570 <cell alignment="center" valignment="top" leftline="true" usebox="none">
18573 \begin_layout Plain Layout
18579 \begin_inset space \textvisiblespace{}
18589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
18592 \begin_layout Plain Layout
18593 \begin_inset Formula $\mathtt{AbC}$
18601 <cell alignment="center" valignment="top" usebox="none">
18604 \begin_layout Plain Layout
18607 arg "font-typewriter"
18617 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
18620 \begin_layout Plain Layout
18626 \begin_inset space \textvisiblespace{}
18636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
18639 \begin_layout Plain Layout
18640 \begin_inset Formula $\mathscr{ABC}$
18648 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
18651 \begin_layout Plain Layout
18665 \begin_layout Standard
18666 \begin_inset Note Greyedout
18669 \begin_layout Plain Layout
18692 can only be used for big letters.
18700 \begin_layout Standard
18701 Predefined is the style
18710 \begin_layout Standard
18711 The style commands work also for letters in mathematical constructs:
18712 \begin_inset Formula
18714 \mathfrak{A=\frac{b}{C}}
18722 \begin_layout Standard
18723 Characters in mathematical text don't appear in a math font style but in
18724 the text font style
18731 That their style can't be set correctly via the text style dialog is a
18732 bug in \SpecialChar LyX
18737 \begin_layout Plain Layout
18738 \begin_inset CommandInset href
18740 name "LyX-bug #4629"
18741 target "http://www.lyx.org/trac/ticket/4629"
18754 \begin_layout Standard
18755 Instead of the style commands the dialog
18757 Edit\SpecialChar menuseparator
18758 Math\SpecialChar menuseparator
18761 or the toolbar button
18764 arg "math-insert \\font"
18770 \begin_layout Subsection
18772 \begin_inset CommandInset label
18774 name "subsec:Bold-Formulas"
18779 \begin_inset Index idx
18782 \begin_layout Plain Layout
18791 \begin_layout Standard
18792 To make a complete formula bold, the command
18798 from the previous subsection cannot be used, because it doesn't work for
18799 small Greek letters.
18800 Furthermore it prints Latin letters always upright, like in the following
18804 \begin_layout Standard
18805 \begin_inset Formula
18807 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18815 \begin_layout Standard
18816 To display the formula correctly, the command
18823 \begin_inset Formula
18825 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18830 It is also possible to set the formula in a
18832 boldmath environment
18835 This environment is created by inserting the command
18842 \begin_inset Index idx
18845 \begin_layout Plain Layout
18853 in \SpecialChar TeX
18855 To end the environment, the command
18862 \begin_inset Index idx
18865 \begin_layout Plain Layout
18873 is inserted in \SpecialChar TeX
18878 \begin_layout Plain Layout
18888 \begin_inset Formula
18890 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18899 \begin_layout Plain Layout
18911 \begin_layout Subsection
18913 \begin_inset Index idx
18916 \begin_layout Plain Layout
18925 \begin_layout Standard
18926 Formulas can be colored like normal text: Highlight a formula or a formula
18932 Here is a formula in magenta:
18933 \begin_inset Formula
18935 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18943 \begin_layout Standard
18944 You can also define your own colors as described in
18945 \begin_inset CommandInset ref
18947 reference "subsec:Colored-Boxes"
18952 They can be used with the \SpecialChar TeX
18960 \begin_inset Index idx
18963 \begin_layout Plain Layout
18974 \begin_layout Standard
18979 textcolor{color}{characters or formula}
18982 \begin_layout Standard
18983 The following example was colored completely dark green and partly red:
18986 \begin_layout Standard
18990 \begin_layout Plain Layout
18994 textcolor{darkgreen}{
19000 \begin_inset Formula
19002 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19011 \begin_layout Plain Layout
19021 \begin_layout Standard
19022 Due to a bug in \SpecialChar LyX
19023 only complete formulas can be colored with self-defined
19028 \begin_layout Plain Layout
19029 \begin_inset CommandInset href
19031 name "LyX-bug #5269"
19032 target "http://www.lyx.org/trac/ticket/5269"
19045 \begin_layout Subsection
19047 \begin_inset CommandInset label
19049 name "subsec:Font-Sizes"
19054 \begin_inset Index idx
19057 \begin_layout Plain Layout
19066 \begin_layout Standard
19067 For characters in formulas there are, analog to characters in text, the
19068 following size commands:
19071 \begin_layout Standard
19115 \begin_inset Newline newline
19137 \begin_layout Standard
19138 The size produced by the commands depends on the document font size, which
19139 corresponds to the command
19146 The other commands produce smaller or larger sizes than
19153 The font size can however not exceed a certain value.
19154 Is for example the document font size 12
19155 \begin_inset space \thinspace{}
19164 switches to the same size as
19174 \begin_layout Standard
19175 A size command is inserted in \SpecialChar TeX
19176 mode before the formula and sets the size
19177 for all following formula and text characters.
19178 To switch back to the initial size, the command
19184 is inserted behind the formula in \SpecialChar TeX
19188 \begin_layout Standard
19189 Within a formula the size can be changed using the following size commands
19190 or the toolbar button
19193 arg "math-insert \\style"
19199 \begin_layout Standard
19202 \begin_inset Tabular
19203 <lyxtabular version="3" rows="5" columns="2">
19204 <features booktabs="true" tabularvalignment="middle">
19205 <column alignment="center" valignment="top" width="0pt">
19206 <column alignment="center" valignment="top">
19208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19211 \begin_layout Plain Layout
19217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19220 \begin_layout Plain Layout
19228 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19231 \begin_layout Plain Layout
19235 \begin_inset Index idx
19238 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula ${\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19264 <row topspace="1mm">
19265 <cell alignment="center" valignment="top" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula ${\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19290 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula ${\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula ${\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}$
19346 \begin_layout Standard
19347 After entering these commands, a blue box appears in which the formula parts
19351 \begin_layout Standard
19352 There is a further method to change the font size, that though only works
19353 for symbols or letters in mathematical text.
19354 To use it, one of the above text size commands is inserted in mathematical
19356 All following characters until the end of the mathematical text or until
19357 another size command will have the selected size.
19359 \begin_inset VSpace -2mm
19365 \begin_layout Standard
19369 \begin_layout Plain Layout
19379 \begin_inset Formula
19381 A=\frac{B}{c}\cdot\maltese
19387 \begin_inset Formula
19389 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19398 \begin_layout Plain Layout
19410 \begin_layout Standard
19411 \begin_inset VSpace medskip
19414 Before both formulas the command
19421 The command for the second formula is:
19422 \begin_inset Newline newline
19430 \begin_inset space \textvisiblespace{}
19436 \begin_inset space \textvisiblespace{}
19442 \begin_inset space \textvisiblespace{}
19448 \begin_inset space \textvisiblespace{}
19452 \begin_inset Formula $\to$
19456 \begin_inset Formula $\to$
19460 \begin_inset Newline newline
19464 \begin_inset space \hspace*{}
19475 \begin_inset space \textvisiblespace{}
19481 \begin_inset space \textvisiblespace{}
19487 \begin_inset space \textvisiblespace{}
19493 \begin_layout Standard
19494 If a symbol cannot be displayed in different sizes, it will always be displayed
19495 in the default size.
19498 \begin_layout Section
19500 \begin_inset Index idx
19503 \begin_layout Plain Layout
19512 \begin_layout Standard
19513 Greek letters can also be inserted via the toolbar button
19516 arg "math-insert \\alpha"
19520 All international typesetting norms purport that Greek letters in math
19521 have to be typeset italic/slanted.
19522 In some languages, like French or Russian, they are nevertheless sometimes
19526 \begin_layout Subsection
19528 \begin_inset Index idx
19531 \begin_layout Plain Layout
19532 Greek letters ! small
19540 \begin_layout Standard
19541 \begin_inset space \hfill{}
19545 \begin_inset Tabular
19546 <lyxtabular version="3" rows="11" columns="2">
19547 <features booktabs="true" tabularvalignment="middle">
19548 <column alignment="center" valignment="top" width="0pt">
19549 <column alignment="center" valignment="top" width="0pt">
19551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19554 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19563 \begin_layout Plain Layout
19571 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19574 \begin_layout Plain Layout
19582 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19585 \begin_layout Plain Layout
19586 \begin_inset Formula $\alpha$
19596 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19599 \begin_layout Plain Layout
19607 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19610 \begin_layout Plain Layout
19611 \begin_inset Formula $\beta$
19621 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\gamma$
19646 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\delta$
19671 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\epsilon$
19696 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\varepsilon$
19721 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\zeta$
19746 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\eta$
19771 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\theta$
19796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\vartheta$
19825 \begin_inset space \hfill{}
19829 \begin_inset Tabular
19830 <lyxtabular version="3" rows="12" columns="2">
19831 <features booktabs="true" tabularvalignment="middle">
19832 <column alignment="center" valignment="top" width="0pt">
19833 <column alignment="center" valignment="top" width="0pt">
19835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19838 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19855 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19858 \begin_layout Plain Layout
19866 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19869 \begin_layout Plain Layout
19870 \begin_inset Formula $\iota$
19880 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19883 \begin_layout Plain Layout
19891 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19894 \begin_layout Plain Layout
19895 \begin_inset Formula $\kappa$
19905 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19908 \begin_layout Plain Layout
19916 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19919 \begin_layout Plain Layout
19920 \begin_inset Formula $\varkappa$
19930 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19933 \begin_layout Plain Layout
19941 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19944 \begin_layout Plain Layout
19945 \begin_inset Formula $\lambda$
19955 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19969 \begin_layout Plain Layout
19970 \begin_inset Formula $\mu$
19980 <cell alignment="center" valignment="top" leftline="true" usebox="none">
19983 \begin_layout Plain Layout
19991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
19994 \begin_layout Plain Layout
19995 \begin_inset Formula $\nu$
20005 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20008 \begin_layout Plain Layout
20016 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20019 \begin_layout Plain Layout
20020 \begin_inset Formula $\xi$
20030 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20033 \begin_layout Plain Layout
20039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20042 \begin_layout Plain Layout
20043 \begin_inset Formula $o$
20053 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20056 \begin_layout Plain Layout
20064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20067 \begin_layout Plain Layout
20068 \begin_inset Formula $\pi$
20078 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20081 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20092 \begin_layout Plain Layout
20093 \begin_inset Formula $\varpi$
20103 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\rho$
20132 \begin_inset space \hfill{}
20136 \begin_inset Tabular
20137 <lyxtabular version="3" rows="11" columns="2">
20138 <features booktabs="true" tabularvalignment="middle">
20139 <column alignment="center" valignment="top" width="0pt">
20140 <column alignment="center" valignment="top" width="0pt">
20142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20154 \begin_layout Plain Layout
20162 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20173 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20176 \begin_layout Plain Layout
20177 \begin_inset Formula $\varrho$
20187 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20190 \begin_layout Plain Layout
20198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20201 \begin_layout Plain Layout
20202 \begin_inset Formula $\sigma$
20212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20215 \begin_layout Plain Layout
20223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20226 \begin_layout Plain Layout
20227 \begin_inset Formula $\varsigma$
20237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20240 \begin_layout Plain Layout
20248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20251 \begin_layout Plain Layout
20252 \begin_inset Formula $\tau$
20262 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20265 \begin_layout Plain Layout
20273 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20276 \begin_layout Plain Layout
20277 \begin_inset Formula $\upsilon$
20287 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20290 \begin_layout Plain Layout
20298 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20301 \begin_layout Plain Layout
20302 \begin_inset Formula $\phi$
20312 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20315 \begin_layout Plain Layout
20323 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20326 \begin_layout Plain Layout
20327 \begin_inset Formula $\varphi$
20337 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20351 \begin_layout Plain Layout
20352 \begin_inset Formula $\chi$
20362 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20365 \begin_layout Plain Layout
20373 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20376 \begin_layout Plain Layout
20377 \begin_inset Formula $\psi$
20387 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20390 \begin_layout Plain Layout
20398 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20401 \begin_layout Plain Layout
20402 \begin_inset Formula $\omega$
20416 \begin_inset space \hfill{}
20422 \begin_layout Standard
20423 \begin_inset VSpace medskip
20429 \begin_layout Standard
20430 How to create special upright Greek letters is explained in
20431 \begin_inset CommandInset ref
20433 reference "subsec:Upright-small-Greek"
20440 \begin_layout Subsection
20442 \begin_inset Index idx
20445 \begin_layout Plain Layout
20446 Greek letters ! big
20454 \begin_layout Standard
20455 \begin_inset space \hfill{}
20459 \begin_inset Tabular
20460 <lyxtabular version="3" rows="7" columns="2">
20461 <features booktabs="true" tabularvalignment="middle">
20462 <column alignment="center" valignment="top" width="0pt">
20463 <column alignment="center" valignment="top" width="0pt">
20465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20468 \begin_layout Plain Layout
20474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20488 \begin_layout Plain Layout
20496 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20499 \begin_layout Plain Layout
20500 \begin_inset Formula $\Gamma$
20510 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20513 \begin_layout Plain Layout
20521 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20524 \begin_layout Plain Layout
20525 \begin_inset Formula $\Delta$
20535 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20538 \begin_layout Plain Layout
20546 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20549 \begin_layout Plain Layout
20550 \begin_inset Formula $\Theta$
20560 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20563 \begin_layout Plain Layout
20571 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20574 \begin_layout Plain Layout
20575 \begin_inset Formula $\Lambda$
20585 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20588 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20600 \begin_inset Formula $\Xi$
20610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20613 \begin_layout Plain Layout
20621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20624 \begin_layout Plain Layout
20625 \begin_inset Formula $\Pi$
20639 \begin_inset space \hfill{}
20643 \begin_inset Tabular
20644 <lyxtabular version="3" rows="6" columns="2">
20645 <features booktabs="true" tabularvalignment="middle">
20646 <column alignment="center" valignment="top" width="0pt">
20647 <column alignment="center" valignment="top" width="0pt">
20649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20669 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20672 \begin_layout Plain Layout
20680 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Plain Layout
20684 \begin_inset Formula $\Sigma$
20694 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20697 \begin_layout Plain Layout
20705 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20708 \begin_layout Plain Layout
20709 \begin_inset Formula $\Upsilon$
20719 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20722 \begin_layout Plain Layout
20730 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Plain Layout
20734 \begin_inset Formula $\Phi$
20744 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20747 \begin_layout Plain Layout
20755 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Plain Layout
20759 \begin_inset Formula $\Psi$
20769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20772 \begin_layout Plain Layout
20780 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20783 \begin_layout Plain Layout
20784 \begin_inset Formula $\Omega$
20798 \begin_inset space \hfill{}
20804 \begin_layout Standard
20805 \begin_inset VSpace medskip
20808 That the big Greek letters appear upright is caused by a design bug when
20811 To get correct italic big letters, begin every command with
20816 For example the command
20823 \begin_inset Formula $\varGamma$
20827 Another way is to load the package
20835 \begin_layout Plain Layout
20840 is part of the \SpecialChar LaTeX
20846 \begin_inset Index idx
20849 \begin_layout Plain Layout
20854 \begin_layout Plain Layout
20874 \begin_inset Index idx
20877 \begin_layout Plain Layout
20883 with the \SpecialChar LaTeX
20887 \begin_layout Standard
20892 usepackage{fixmath}
20895 \begin_layout Standard
20896 Then all big Greek letters in a document will automatically be typeset italic.
20899 \begin_layout Subsection
20901 \begin_inset Index idx
20904 \begin_layout Plain Layout
20905 Greek letters ! bold
20913 \begin_layout Standard
20914 Greek letters cannot be set with different font styles like Latin letters.
20915 They can only be made bold with the command
20922 \begin_inset Index idx
20925 \begin_layout Plain Layout
20936 \begin_layout Standard
20938 \begin_inset Tabular
20939 <lyxtabular version="3" rows="3" columns="2">
20940 <features booktabs="true" tabularvalignment="middle">
20941 <column alignment="center" valignment="top" width="0pt">
20942 <column alignment="center" valignment="top">
20944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20947 \begin_layout Plain Layout
20953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20956 \begin_layout Plain Layout
20964 <cell alignment="center" valignment="top" leftline="true" usebox="none">
20967 \begin_layout Plain Layout
20979 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
20982 \begin_layout Plain Layout
20983 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20996 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21012 \begin_inset Formula $\theta\boldsymbol{\theta}$
21028 \begin_layout Section
21033 \begin_layout Plain Layout
21046 \begin_layout Plain Layout
21047 A list with all symbols of most of the \SpecialChar LaTeX
21048 -packages can be found in
21049 \begin_inset CommandInset citation
21065 \begin_layout Plain Layout
21073 \begin_inset Note Note
21076 \begin_layout Plain Layout
21079 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21082 \begin_layout Plain Layout
21085 texorpdfstring is in section
21086 \begin_inset CommandInset ref
21088 reference "subsec:Formulas-in-Section"
21098 \begin_inset Index idx
21101 \begin_layout Plain Layout
21110 \begin_layout Standard
21111 Many of the symbols listed in this section can also be inserted via the
21115 arg "math-insert \\nabla"
21121 arg "math-insert \\digamma"
21127 \begin_layout Subsection
21128 Mathematical Symbols
21129 \begin_inset CommandInset label
21131 name "subsec:Mathematical-Symbols"
21136 \begin_inset Index idx
21139 \begin_layout Plain Layout
21140 Symbols ! mathematical
21148 \begin_layout Standard
21149 \begin_inset Tabular
21150 <lyxtabular version="3" rows="10" columns="2">
21151 <features booktabs="true" tabularvalignment="middle">
21152 <column alignment="center" valignment="top" width="0pt">
21153 <column alignment="center" valignment="top" width="0pt">
21155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21158 \begin_layout Plain Layout
21164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21167 \begin_layout Plain Layout
21175 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21178 \begin_layout Plain Layout
21186 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21189 \begin_layout Plain Layout
21190 \begin_inset Formula $\neg$
21200 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21203 \begin_layout Plain Layout
21211 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21214 \begin_layout Plain Layout
21215 \begin_inset Formula $\Im$
21225 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21228 \begin_layout Plain Layout
21236 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21239 \begin_layout Plain Layout
21240 \begin_inset Formula $\Re$
21250 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21253 \begin_layout Plain Layout
21261 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21264 \begin_layout Plain Layout
21265 \begin_inset Formula $\aleph$
21275 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21278 \begin_layout Plain Layout
21286 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21289 \begin_layout Plain Layout
21290 \begin_inset Formula $\partial$
21300 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21303 \begin_layout Plain Layout
21311 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21314 \begin_layout Plain Layout
21315 \begin_inset Formula $\infty$
21325 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21328 \begin_layout Plain Layout
21336 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21339 \begin_layout Plain Layout
21340 \begin_inset Formula $\wp$
21350 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21353 \begin_layout Plain Layout
21361 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21364 \begin_layout Plain Layout
21365 \begin_inset Formula $\imath$
21375 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21378 \begin_layout Plain Layout
21386 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21389 \begin_layout Plain Layout
21390 \begin_inset Formula $\jmath$
21404 \begin_inset space \hfill{}
21408 \begin_inset Tabular
21409 <lyxtabular version="3" rows="10" columns="2">
21410 <features booktabs="true" tabularvalignment="middle">
21411 <column alignment="center" valignment="top" width="0pt">
21412 <column alignment="center" valignment="top" width="0pt">
21414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21417 \begin_layout Plain Layout
21423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21426 \begin_layout Plain Layout
21428 \begin_inset Note Note
21431 \begin_layout Plain Layout
21438 is only used as spacer.
21450 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21453 \begin_layout Plain Layout
21461 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21464 \begin_layout Plain Layout
21465 \begin_inset Formula $\forall$
21475 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21478 \begin_layout Plain Layout
21486 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21489 \begin_layout Plain Layout
21490 \begin_inset Formula $\exists$
21500 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21503 \begin_layout Plain Layout
21511 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21514 \begin_layout Plain Layout
21515 \begin_inset Formula $\nexists$
21525 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21528 \begin_layout Plain Layout
21536 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21539 \begin_layout Plain Layout
21540 \begin_inset Formula $\emptyset$
21550 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21553 \begin_layout Plain Layout
21561 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21564 \begin_layout Plain Layout
21565 \begin_inset Formula $\varnothing$
21575 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21578 \begin_layout Plain Layout
21586 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21589 \begin_layout Plain Layout
21590 \begin_inset Formula $\dag$
21600 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21603 \begin_layout Plain Layout
21611 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Plain Layout
21615 \begin_inset Formula $\ddag$
21625 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21628 \begin_layout Plain Layout
21636 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21639 \begin_layout Plain Layout
21643 \begin_layout Plain Layout
21653 \begin_inset Formula $\complement$
21660 \begin_layout Plain Layout
21674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21677 \begin_layout Plain Layout
21685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21688 \begin_layout Plain Layout
21689 \begin_inset Formula $\Bbbk$
21703 \begin_inset space \hfill{}
21707 \begin_inset Tabular
21708 <lyxtabular version="3" rows="10" columns="2">
21709 <features booktabs="true" tabularvalignment="middle">
21710 <column alignment="center" valignment="top" width="0pt">
21711 <column alignment="center" valignment="top" width="0pt">
21713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21716 \begin_layout Plain Layout
21722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21725 \begin_layout Plain Layout
21733 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21736 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21748 \begin_inset Formula $\prime$
21758 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21761 \begin_layout Plain Layout
21769 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21772 \begin_layout Plain Layout
21773 \begin_inset Formula $\backprime$
21783 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21786 \begin_layout Plain Layout
21794 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21797 \begin_layout Plain Layout
21798 \begin_inset Formula $\mho$
21808 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21811 \begin_layout Plain Layout
21819 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Plain Layout
21823 \begin_inset Formula $\triangle$
21833 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21836 \begin_layout Plain Layout
21844 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21847 \begin_layout Plain Layout
21848 \begin_inset Formula $\angle$
21858 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21861 \begin_layout Plain Layout
21869 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21872 \begin_layout Plain Layout
21873 \begin_inset Formula $\measuredangle$
21883 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21886 \begin_layout Plain Layout
21894 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Plain Layout
21898 \begin_inset Formula $\sphericalangle$
21908 <cell alignment="center" valignment="top" leftline="true" usebox="none">
21911 \begin_layout Plain Layout
21919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
21922 \begin_layout Plain Layout
21923 \begin_inset Formula $\top$
21933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21936 \begin_layout Plain Layout
21944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21947 \begin_layout Plain Layout
21948 \begin_inset Formula $\bot$
21964 \begin_layout Subsection
21965 Miscellaneous Symbols
21966 \begin_inset CommandInset label
21968 name "subsec:Miscellaneous-Symbols"
21973 \begin_inset Index idx
21976 \begin_layout Plain Layout
21977 Symbols ! miscellaneous
21985 \begin_layout Standard
21988 \begin_inset Tabular
21989 <lyxtabular version="3" rows="10" columns="2">
21990 <features booktabs="true" tabularvalignment="middle">
21991 <column alignment="center" valignment="top" width="0pt">
21992 <column alignment="center" valignment="top" width="0pt">
21994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21997 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22017 \begin_layout Plain Layout
22025 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22028 \begin_layout Plain Layout
22029 \begin_inset Formula $\flat$
22039 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22042 \begin_layout Plain Layout
22050 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22053 \begin_layout Plain Layout
22054 \begin_inset Formula $\natural$
22064 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22067 \begin_layout Plain Layout
22075 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22078 \begin_layout Plain Layout
22079 \begin_inset Formula $\sharp$
22089 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22092 \begin_layout Plain Layout
22100 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22103 \begin_layout Plain Layout
22104 \begin_inset Formula $\surd$
22114 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22117 \begin_layout Plain Layout
22125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22128 \begin_layout Plain Layout
22129 \begin_inset Formula $\checkmark$
22139 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22142 \begin_layout Plain Layout
22150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22153 \begin_layout Plain Layout
22154 \begin_inset Formula $\yen$
22164 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22167 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22178 \begin_layout Plain Layout
22179 \begin_inset Formula $\pounds$
22189 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22192 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22201 \begin_layout Plain Layout
22202 \begin_inset Formula $\$$
22212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Plain Layout
22221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Plain Layout
22225 \begin_inset Formula $§$
22239 \begin_inset space \hfill{}
22243 \begin_inset Tabular
22244 <lyxtabular version="3" rows="10" columns="2">
22245 <features booktabs="true" tabularvalignment="middle">
22246 <column alignment="center" valignment="top" width="0pt">
22247 <column alignment="center" valignment="top">
22249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22252 \begin_layout Plain Layout
22258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22272 \begin_layout Plain Layout
22280 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22283 \begin_layout Plain Layout
22284 \begin_inset Formula $\hbar$
22294 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22297 \begin_layout Plain Layout
22305 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22308 \begin_layout Plain Layout
22309 \begin_inset Formula $\hslash$
22319 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22322 \begin_layout Plain Layout
22330 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22333 \begin_layout Plain Layout
22334 \begin_inset Formula $\clubsuit$
22344 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22347 \begin_layout Plain Layout
22355 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22358 \begin_layout Plain Layout
22359 \begin_inset Formula $\spadesuit$
22369 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22372 \begin_layout Plain Layout
22380 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22383 \begin_layout Plain Layout
22384 \begin_inset Formula $\bigstar$
22394 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22397 \begin_layout Plain Layout
22405 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22408 \begin_layout Plain Layout
22409 \begin_inset Formula $\blacklozenge$
22419 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22422 \begin_layout Plain Layout
22430 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22433 \begin_layout Plain Layout
22434 \begin_inset Formula $\blacktriangle$
22444 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22447 \begin_layout Plain Layout
22455 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22458 \begin_layout Plain Layout
22459 \begin_inset Formula $\blacktriangledown$
22469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22472 \begin_layout Plain Layout
22480 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22483 \begin_layout Plain Layout
22484 \begin_inset Formula $\bullet$
22498 \begin_inset space \hfill{}
22502 \begin_inset Tabular
22503 <lyxtabular version="3" rows="10" columns="2">
22504 <features booktabs="true" tabularvalignment="middle">
22505 <column alignment="center" valignment="top" width="0pt">
22506 <column alignment="center" valignment="top" width="0pt">
22508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22511 \begin_layout Plain Layout
22517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22531 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22542 \begin_layout Plain Layout
22543 \begin_inset Formula $\diamondsuit$
22553 <cell alignment="center" valignment="top" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22567 \begin_layout Plain Layout
22568 \begin_inset Formula $\Diamond$
22578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\heartsuit$
22603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\P$
22628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22642 \begin_layout Plain Layout
22643 \begin_inset Formula $\copyright$
22653 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22656 \begin_layout Plain Layout
22664 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22667 \begin_layout Plain Layout
22668 \begin_inset Formula $\circledR$
22678 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22692 \begin_layout Plain Layout
22693 \begin_inset Formula $\maltese$
22703 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22706 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22718 \begin_inset Formula $\diagup$
22728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22742 \begin_layout Plain Layout
22743 \begin_inset Formula $\diagdown$
22759 \begin_layout Standard
22760 \begin_inset VSpace medskip
22766 \begin_layout Standard
22767 Some symbols can be displayed in different sizes, see
22768 \begin_inset CommandInset ref
22770 reference "subsec:Font-Sizes"
22777 \begin_layout Subsection
22779 \begin_inset Index idx
22782 \begin_layout Plain Layout
22783 Symbols ! Euro-symbol
22789 \begin_inset Index idx
22792 \begin_layout Plain Layout
22799 \begin_layout Plain Layout
22816 \begin_layout Standard
22817 To use the Euro symbol in formulas, the \SpecialChar LaTeX
22823 \begin_inset Index idx
22826 \begin_layout Plain Layout
22832 must be installed and loaded with the \SpecialChar LaTeX
22836 \begin_layout Standard
22841 usepackage[gennarrow]{eurosym}
22844 \begin_layout Standard
22845 The Euro symbol can now be inserted with the command
22852 \begin_inset Index idx
22855 \begin_layout Plain Layout
22866 \begin_layout Standard
22867 The Euro symbol can directly be inserted with the € key in mathematical
22868 text, without having
22883 can also be inserted in \SpecialChar TeX
22885 The official currency symbol can then be inserted with the command
22892 \begin_inset Index idx
22895 \begin_layout Plain Layout
22903 , that is only available in \SpecialChar TeX
22907 \begin_layout Standard
22911 \begin_layout Plain Layout
22921 \begin_inset Note Note
22924 \begin_layout Plain Layout
22925 The following table will only be displayed when the \SpecialChar LaTeX
22938 \begin_layout Standard
22939 An overview about the different Euro symbols:
22942 \begin_layout Standard
22944 \begin_inset Tabular
22945 <lyxtabular version="3" rows="4" columns="3">
22946 <features booktabs="true" tabularvalignment="middle">
22947 <column alignment="center" valignment="top" width="0pt">
22948 <column alignment="center" valignment="top" width="0pt">
22949 <column alignment="center" valignment="top" width="0pt">
22951 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
22954 \begin_layout Plain Layout
22958 \begin_layout Plain Layout
22962 cmidrule[0.08em]{2-3}
22972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22975 \begin_layout Plain Layout
22981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22984 \begin_layout Plain Layout
22992 <cell alignment="center" valignment="top" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23004 \begin_layout Plain Layout
23012 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23015 \begin_layout Plain Layout
23016 \begin_inset Formula $\euro$
23026 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23029 \begin_layout Plain Layout
23035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23038 \begin_layout Plain Layout
23044 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23047 \begin_layout Plain Layout
23048 \begin_inset Formula $\mbox{€}$
23058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23061 \begin_layout Plain Layout
23068 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23071 \begin_layout Plain Layout
23079 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23082 \begin_layout Plain Layout
23086 \begin_layout Plain Layout
23106 \begin_inset Note Note
23109 \begin_layout Plain Layout
23116 is used here only for table borders.
23126 manual for details.
23134 \begin_layout Standard
23138 \begin_layout Plain Layout
23148 \begin_inset Note Note
23151 \begin_layout Plain Layout
23152 The following will be displayed when the \SpecialChar LaTeX
23165 \begin_layout Standard
23166 You need to install the \SpecialChar LaTeX
23171 to see the rest of this subsection in the output.
23174 \begin_layout Standard
23178 \begin_layout Plain Layout
23190 \begin_layout Section
23192 \begin_inset CommandInset label
23194 name "sec:Relations"
23199 \begin_inset Index idx
23202 \begin_layout Plain Layout
23209 \begin_inset Index idx
23212 \begin_layout Plain Layout
23217 \begin_layout Plain Layout
23228 \begin_layout Plain Layout
23243 \begin_layout Standard
23244 All following relations can also be inserted via the toolbar button
23247 arg "math-insert \\leq"
23253 \begin_layout Standard
23254 \begin_inset Tabular
23255 <lyxtabular version="3" rows="17" columns="2">
23256 <features booktabs="true" tabularvalignment="middle">
23257 <column alignment="center" valignment="top" width="0pt">
23258 <column alignment="center" valignment="top" width="0pt">
23260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23263 \begin_layout Plain Layout
23269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23272 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23283 \begin_layout Plain Layout
23289 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23292 \begin_layout Plain Layout
23293 \begin_inset Formula $<$
23303 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23306 \begin_layout Plain Layout
23314 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23317 \begin_layout Plain Layout
23318 \begin_inset Formula $\le$
23328 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23331 \begin_layout Plain Layout
23339 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23342 \begin_layout Plain Layout
23343 \begin_inset Formula $\ll$
23353 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23356 \begin_layout Plain Layout
23364 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23367 \begin_layout Plain Layout
23368 \begin_inset Formula $\prec$
23378 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23381 \begin_layout Plain Layout
23389 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23392 \begin_layout Plain Layout
23393 \begin_inset Formula $\preceq$
23403 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23406 \begin_layout Plain Layout
23414 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23417 \begin_layout Plain Layout
23418 \begin_inset Formula $\subset$
23428 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23431 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $\subseteq$
23453 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\sqsubseteq$
23478 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\in$
23503 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\vdash$
23528 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\smile$
23553 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\lhd$
23578 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\unlhd$
23603 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\gtrless$
23628 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\mid$
23653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\nmid$
23682 \begin_inset space \hfill{}
23686 \begin_inset Tabular
23687 <lyxtabular version="3" rows="17" columns="2">
23688 <features booktabs="true" tabularvalignment="middle">
23689 <column alignment="center" valignment="top" width="0pt">
23690 <column alignment="center" valignment="top" width="0pt">
23692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23695 \begin_layout Plain Layout
23701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23704 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23721 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23724 \begin_layout Plain Layout
23725 \begin_inset Formula $=$
23735 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23738 \begin_layout Plain Layout
23746 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23749 \begin_layout Plain Layout
23750 \begin_inset Formula $\not=$
23760 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23763 \begin_layout Plain Layout
23771 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23774 \begin_layout Plain Layout
23775 \begin_inset Formula $\equiv$
23785 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23788 \begin_layout Plain Layout
23796 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23799 \begin_layout Plain Layout
23800 \begin_inset Formula $\sim$
23810 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23813 \begin_layout Plain Layout
23821 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23824 \begin_layout Plain Layout
23825 \begin_inset Formula $\simeq$
23835 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23838 \begin_layout Plain Layout
23846 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23849 \begin_layout Plain Layout
23850 \begin_inset Formula $\approx$
23860 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23863 \begin_layout Plain Layout
23871 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23874 \begin_layout Plain Layout
23875 \begin_inset Formula $\cong$
23885 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23888 \begin_layout Plain Layout
23896 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23899 \begin_layout Plain Layout
23900 \begin_inset Formula $\bowtie$
23910 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23913 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\notin$
23935 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23938 \begin_layout Plain Layout
23946 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23949 \begin_layout Plain Layout
23950 \begin_inset Formula $\perp$
23960 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23963 \begin_layout Plain Layout
23971 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23974 \begin_layout Plain Layout
23975 \begin_inset Formula $\propto$
23985 <cell alignment="center" valignment="top" leftline="true" usebox="none">
23988 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $\asymp$
24010 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24024 \begin_layout Plain Layout
24025 \begin_inset Formula $\doteq$
24035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24038 \begin_layout Plain Layout
24046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24049 \begin_layout Plain Layout
24050 \begin_inset Formula $\circeq$
24060 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $\models$
24085 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24088 \begin_layout Plain Layout
24096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24099 \begin_layout Plain Layout
24100 \begin_inset Formula $\widehat{=}$
24114 \begin_inset space \hfill{}
24118 \begin_inset Tabular
24119 <lyxtabular version="3" rows="17" columns="2">
24120 <features booktabs="true" tabularvalignment="middle">
24121 <column alignment="center" valignment="top" width="0pt">
24122 <column alignment="center" valignment="top" width="0pt">
24124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24127 \begin_layout Plain Layout
24133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24136 \begin_layout Plain Layout
24144 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24153 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24156 \begin_layout Plain Layout
24157 \begin_inset Formula $>$
24167 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24170 \begin_layout Plain Layout
24178 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24181 \begin_layout Plain Layout
24182 \begin_inset Formula $\ge$
24192 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24195 \begin_layout Plain Layout
24203 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24206 \begin_layout Plain Layout
24207 \begin_inset Formula $\gg$
24217 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24220 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24231 \begin_layout Plain Layout
24232 \begin_inset Formula $\succ$
24242 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24245 \begin_layout Plain Layout
24253 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24256 \begin_layout Plain Layout
24257 \begin_inset Formula $\succeq$
24267 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24270 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24281 \begin_layout Plain Layout
24282 \begin_inset Formula $\supset$
24292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24295 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24306 \begin_layout Plain Layout
24307 \begin_inset Formula $\supseteq$
24317 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24320 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24331 \begin_layout Plain Layout
24332 \begin_inset Formula $\sqsupseteq$
24342 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24357 \begin_inset Formula $\ni$
24367 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24370 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24381 \begin_layout Plain Layout
24382 \begin_inset Formula $\dashv$
24392 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Plain Layout
24407 \begin_inset Formula $\frown$
24417 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24431 \begin_layout Plain Layout
24432 \begin_inset Formula $\rhd$
24442 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24457 \begin_inset Formula $\unrhd$
24467 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\lessgtr$
24492 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24507 \begin_inset Formula $\parallel$
24517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24532 \begin_inset Formula $\nparallel$
24548 \begin_layout Standard
24549 \begin_inset VSpace medskip
24564 are bigger than the equal looking operators
24579 \begin_layout Standard
24581 supports also many special relations.
24582 Use the toolbar button
24585 arg "math-insert \\leqq"
24588 to see a list of these relations.
24591 \begin_layout Standard
24592 Relations are, in contrary to symbols, always surrounded by space.
24595 \begin_layout Standard
24596 Relations with labels can be created with the command
24603 \begin_inset Index idx
24606 \begin_layout Plain Layout
24617 \begin_layout Standard
24619 \begin_inset Tabular
24620 <lyxtabular version="3" rows="2" columns="2">
24621 <features booktabs="true" tabularvalignment="middle">
24622 <column alignment="center" valignment="top" width="0pt">
24623 <column alignment="center" valignment="top">
24625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24628 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24644 <row topspace="1.5mm">
24645 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24648 \begin_layout Plain Layout
24652 \begin_inset space \textvisiblespace{}
24660 \begin_inset space \textvisiblespace{}
24664 \begin_inset Formula $\downarrow$
24670 \begin_inset space \textvisiblespace{}
24674 \begin_inset space \textvisiblespace{}
24682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24685 \begin_layout Plain Layout
24686 \begin_inset Formula $A(r)\stackrel{r\to\infty}{\approx}B$
24702 \begin_layout Section
24706 \begin_layout Subsection
24707 Predefined Functions
24708 \begin_inset CommandInset label
24710 name "subsec:Predefined-Functions"
24715 \begin_inset Index idx
24718 \begin_layout Plain Layout
24719 Functions ! predefined
24727 \begin_layout Standard
24728 In general, variables are set
24732 in mathematical expressions, but not function names, because
24733 \begin_inset Formula $sin$
24736 could be misunderstood as
24737 \begin_inset Formula $s\cdot i\cdot n$
24741 Therefore there are predefined functions which are additionally a bit separated
24743 They are inserted as commands starting with a backslash before their name.
24746 \begin_layout Standard
24748 \begin_inset Tabular
24749 <lyxtabular version="3" rows="2" columns="2">
24750 <features booktabs="true" tabularvalignment="middle">
24751 <column alignment="center" valignment="top" width="0pt">
24752 <column alignment="center" valignment="top" width="0pt">
24754 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24757 \begin_layout Plain Layout
24763 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
24766 \begin_layout Plain Layout
24774 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24777 \begin_layout Plain Layout
24783 <cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
24786 \begin_layout Plain Layout
24787 \begin_inset Formula $Asin(x)+B$
24801 \begin_inset space \quad{}
24805 \begin_inset Tabular
24806 <lyxtabular version="3" rows="2" columns="2">
24807 <features booktabs="true" tabularvalignment="middle">
24808 <column alignment="center" valignment="top" width="0pt">
24809 <column alignment="center" valignment="top" width="0pt">
24811 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24814 \begin_layout Plain Layout
24820 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
24823 \begin_layout Plain Layout
24831 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24834 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
24845 \begin_layout Plain Layout
24846 \begin_inset Formula $A\sin(x)+B$
24862 \begin_layout Standard
24863 The following functions are predefined:
24866 \begin_layout Standard
24867 \begin_inset VSpace -2mm
24873 \begin_layout Standard
24875 \begin_inset Tabular
24876 <lyxtabular version="3" rows="9" columns="4">
24877 <features booktabs="true" tabularvalignment="middle">
24878 <column alignment="center" valignment="top" width="0pt">
24879 <column alignment="center" valignment="top" width="0pt">
24880 <column alignment="center" valignment="top" width="0pt">
24881 <column alignment="center" valignment="top" width="0pt">
24883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24886 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24895 \begin_layout Plain Layout
24901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24904 \begin_layout Plain Layout
24910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24913 \begin_layout Plain Layout
24921 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24924 \begin_layout Plain Layout
24932 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24935 \begin_layout Plain Layout
24943 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24946 \begin_layout Plain Layout
24954 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24957 \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" usebox="none">
24981 \begin_layout Plain Layout
24989 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24992 \begin_layout Plain Layout
25000 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25003 \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" usebox="none">
25027 \begin_layout Plain Layout
25035 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25038 \begin_layout Plain Layout
25046 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25049 \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" usebox="none">
25073 \begin_layout Plain Layout
25081 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25092 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25095 \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" usebox="none">
25119 \begin_layout Plain Layout
25127 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25130 \begin_layout Plain Layout
25138 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25141 \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" usebox="none">
25165 \begin_layout Plain Layout
25173 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25176 \begin_layout Plain Layout
25184 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25187 \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" usebox="none">
25211 \begin_layout Plain Layout
25219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25233 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25246 \begin_layout Plain Layout
25254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25268 \begin_layout Plain Layout
25276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25279 \begin_layout Plain Layout
25295 \begin_layout Standard
25296 They can also be inserted with the math toolbar button
25299 arg "math-insert \\functions"
25305 \begin_layout Subsection
25306 Self-defined Functions
25307 \begin_inset Index idx
25310 \begin_layout Plain Layout
25311 Functions ! self-defined
25319 \begin_layout Standard
25320 To use a function that is not predefined, like for example the sign function
25321 sgn(x), there are two possibilities:
25324 \begin_layout Itemize
25325 Define the function by inserting the following line to the \SpecialChar LaTeX
25330 \begin_layout Plain Layout
25335 DeclareMathOperator
25338 \begin_inset CommandInset ref
25340 reference "subsec:Self-defined-Operators"
25350 \begin_inset Newline newline
25354 \begin_inset VSpace -3mm
25358 \begin_inset Newline newline
25365 DeclareMathOperator{
25370 \begin_inset Index idx
25373 \begin_layout Plain Layout
25378 DeclareMathOperator
25384 \begin_inset Newline newline
25388 \begin_inset VSpace -2mm
25392 \begin_inset Newline newline
25395 Now the new defined function can be called with the command
25404 \begin_layout Itemize
25405 Write the formula as usual, mark the formula name, in our example the letters
25410 , and change it to mathematical text.
25411 Finally, a space is inserted between prefactor and function.
25414 \begin_layout Standard
25415 The result is the same with both methods as with a predefined function
25419 \begin_layout Plain Layout
25420 In \SpecialChar LyX
25421 self-defined functions are displayed red, predefined ones black.
25429 \begin_layout Standard
25431 \begin_inset Tabular
25432 <lyxtabular version="3" rows="3" columns="2">
25433 <features booktabs="true" tabularvalignment="middle">
25434 <column alignment="center" valignment="top" width="0pt">
25435 <column alignment="center" valignment="top" width="0pt">
25437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25440 \begin_layout Plain Layout
25446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25449 \begin_layout Plain Layout
25457 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25460 \begin_layout Plain Layout
25468 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25471 \begin_layout Plain Layout
25472 \begin_inset Formula $A\sgn(x)+B$
25482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25485 \begin_layout Plain Layout
25489 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25500 \begin_layout Plain Layout
25501 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25517 \begin_layout Standard
25518 The first method is more suitable when the self-defined function should
25519 be used several times.
25522 \begin_layout Subsection
25524 \begin_inset Index idx
25527 \begin_layout Plain Layout
25536 \begin_layout Standard
25537 For limits, in addition to the commands
25544 \begin_inset Index idx
25547 \begin_layout Plain Layout
25567 the following functions are defined:
25570 \begin_layout Standard
25572 \begin_inset Tabular
25573 <lyxtabular version="3" rows="5" columns="2">
25574 <features booktabs="true" tabularvalignment="middle">
25575 <column alignment="center" valignment="top" width="0pt">
25576 <column alignment="center" valignment="top" width="0pt">
25578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25590 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25601 \begin_layout Plain Layout
25609 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25612 \begin_layout Plain Layout
25613 \begin_inset Formula $\varliminf$
25622 <row topspace="1.5mm">
25623 <cell alignment="center" valignment="top" usebox="none">
25626 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25637 \begin_layout Plain Layout
25638 \begin_inset Formula $\varlimsup$
25647 <row topspace="1.5mm">
25648 <cell alignment="center" valignment="top" usebox="none">
25651 \begin_layout Plain Layout
25659 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25662 \begin_layout Plain Layout
25663 \begin_inset Formula $\varprojlim$
25672 <row topspace="1.5mm" bottomspace="1mm">
25673 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25676 \begin_layout Plain Layout
25684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25687 \begin_layout Plain Layout
25688 \begin_inset Formula $\varinjlim$
25704 \begin_layout Standard
25705 \begin_inset VSpace medskip
25708 The limit is created by inserting a subscript.
25709 It is set right beside the function in an inline formula:
25712 \begin_layout Standard
25714 \begin_inset Tabular
25715 <lyxtabular version="3" rows="2" columns="2">
25716 <features booktabs="true" tabularvalignment="middle">
25717 <column alignment="center" valignment="top" width="0pt">
25718 <column alignment="center" valignment="top" width="0pt">
25720 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25723 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
25732 \begin_layout Plain Layout
25740 <cell alignment="center" valignment="top" usebox="none">
25743 \begin_layout Plain Layout
25749 \begin_inset space \textvisiblespace{}
25753 \begin_inset space \textvisiblespace{}
25761 <cell alignment="center" valignment="top" usebox="none">
25764 \begin_layout Plain Layout
25765 \begin_inset Formula $\lim_{x\to A}x=B$
25781 \begin_layout Standard
25782 In a displayed formula the limit is set below the formula, as usual:
25783 \begin_inset Formula
25793 \begin_layout Standard
25794 \begin_inset VSpace medskip
25800 \begin_layout Standard
25801 How to adjust the typesetting of the limits see
25802 \begin_inset CommandInset ref
25804 reference "subsec:Operator-Limits"
25811 \begin_layout Subsection
25813 \begin_inset Index idx
25816 \begin_layout Plain Layout
25817 Functions ! modulo-
25825 \begin_layout Standard
25826 The modulo-function is special, because it exists in four variants.
25827 The variants in a displayed formula are:
25828 \begin_inset Formula
25830 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25831 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
25832 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
25833 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
25834 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
25842 \begin_layout Standard
25843 In an inline formula less space is set before the function names for all
25845 By default the modulo-functions take only the first following character
25847 To use more than one character, one has to put them into \SpecialChar TeX
25849 \begin_inset Formula
25851 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25852 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
25853 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
25861 \begin_layout Section
25863 \begin_inset Index idx
25866 \begin_layout Plain Layout
25875 \begin_layout Standard
25876 The characters ^ and _ would normally create a superscript and subscript,
25878 To get these characters you have to insert them with a leading
25883 \begin_layout Standard
25886 \begin_inset Tabular
25887 <lyxtabular version="3" rows="3" columns="2">
25888 <features booktabs="true" tabularvalignment="middle">
25889 <column alignment="left" valignment="top" width="0pt">
25890 <column alignment="block" valignment="top">
25892 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25895 \begin_layout Plain Layout
25901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25904 \begin_layout Plain Layout
25912 <cell alignment="left" valignment="top" leftline="true" usebox="none">
25915 \begin_layout Plain Layout
25919 \begin_inset space \textvisiblespace{}
25927 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25930 \begin_layout Plain Layout
25931 \begin_inset Formula $\mathcircumflex$
25941 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
25944 \begin_layout Plain Layout
25952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25955 \begin_layout Plain Layout
25956 \begin_inset Formula $\_$
25972 \begin_layout Subsection
25973 Special Characters in Mathematical Text
25976 \begin_layout Standard
25977 The following commands can only be used in mathematical text or in \SpecialChar TeX
25981 \begin_layout Standard
25982 \begin_inset space \hfill{}
25986 \begin_inset Tabular
25987 <lyxtabular version="3" rows="8" columns="2">
25988 <features booktabs="true" tabularvalignment="middle">
25989 <column alignment="left" valignment="top" width="0pt">
25990 <column alignment="block" valignment="top">
25992 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26004 \begin_layout Plain Layout
26012 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26015 \begin_layout Plain Layout
26023 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26026 \begin_layout Plain Layout
26027 \begin_inset Formula $\textrm{œ}$
26037 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26040 \begin_layout Plain Layout
26048 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26051 \begin_layout Plain Layout
26052 \begin_inset Formula $\textrm{Œ}$
26062 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26065 \begin_layout Plain Layout
26073 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26076 \begin_layout Plain Layout
26077 \begin_inset Formula $\textrm{æ}$
26087 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26090 \begin_layout Plain Layout
26098 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26101 \begin_layout Plain Layout
26102 \begin_inset Formula $\textrm{Æ}$
26112 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26115 \begin_layout Plain Layout
26123 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26126 \begin_layout Plain Layout
26127 \begin_inset Formula $\textrm{å}$
26137 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26140 \begin_layout Plain Layout
26148 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26151 \begin_layout Plain Layout
26152 \begin_inset Formula $\textrm{Å}$
26162 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26165 \begin_layout Plain Layout
26173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26176 \begin_layout Plain Layout
26177 \begin_inset Formula $\textrm{ı}$
26191 \begin_inset space \hfill{}
26195 \begin_inset Tabular
26196 <lyxtabular version="3" rows="8" columns="2">
26197 <features booktabs="true" tabularvalignment="middle">
26198 <column alignment="left" valignment="top" width="0pt">
26199 <column alignment="center" valignment="top">
26201 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26204 \begin_layout Plain Layout
26206 \begin_inset Note Note
26209 \begin_layout Plain Layout
26211 \begin_inset space \thinspace{}
26214 mm is used for separation, because otherwise the output will be ¡ and ¿
26225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26228 \begin_layout Plain Layout
26236 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26239 \begin_layout Plain Layout
26247 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26250 \begin_layout Plain Layout
26251 \begin_inset Formula $\textrm{ø}$
26261 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26264 \begin_layout Plain Layout
26272 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26275 \begin_layout Plain Layout
26276 \begin_inset Formula $\textrm{Ø}$
26286 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26289 \begin_layout Plain Layout
26297 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26300 \begin_layout Plain Layout
26301 \begin_inset Formula $\textrm{ł}$
26311 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26314 \begin_layout Plain Layout
26322 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26325 \begin_layout Plain Layout
26326 \begin_inset Formula $\textrm{Ł}$
26336 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26339 \begin_layout Plain Layout
26341 \begin_inset space \hspace{}
26346 \begin_inset space \textvisiblespace{}
26354 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26357 \begin_layout Plain Layout
26358 \begin_inset Formula $\textrm{!`}$
26368 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26371 \begin_layout Plain Layout
26373 \begin_inset space \hspace{}
26378 \begin_inset space \textvisiblespace{}
26386 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26389 \begin_layout Plain Layout
26390 \begin_inset Formula $\textrm{?`}$
26400 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26403 \begin_layout Plain Layout
26411 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26414 \begin_layout Plain Layout
26415 \begin_inset Formula $\textrm{ȷ}$
26429 \begin_inset space \hfill{}
26435 \begin_layout Standard
26437 \begin_inset Formula $\textrm{\textrm{Å}}$
26441 \begin_inset Formula $\textrm{\textrm{Ø}}$
26444 can also be inserted via the math toolbar button
26447 arg "math-insert \\digamma"
26453 \begin_layout Standard
26454 An exception are the commands
26457 \begin_inset space \hspace{}
26466 \begin_inset space \hspace{}
26472 , because they can be inserted in \SpecialChar LyX
26476 \begin_layout Subsection
26478 \begin_inset CommandInset label
26480 name "subsec:Accents-in-Text"
26485 \begin_inset Index idx
26488 \begin_layout Plain Layout
26497 \begin_layout Standard
26498 With the following commands all letters can be accented.
26499 The commands must be inserted in \SpecialChar TeX
26503 \begin_layout Standard
26504 \begin_inset space \hfill{}
26508 \begin_inset Tabular
26509 <lyxtabular version="3" rows="8" columns="2">
26510 <features booktabs="true" tabularvalignment="middle">
26511 <column alignment="left" valignment="top" width="0pt">
26512 <column alignment="block" valignment="top">
26514 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26517 \begin_layout Plain Layout
26523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26526 \begin_layout Plain Layout
26534 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26537 \begin_layout Plain Layout
26541 \begin_inset Quotes grd
26549 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26552 \begin_layout Plain Layout
26556 \begin_layout Plain Layout
26572 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26575 \begin_layout Plain Layout
26583 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26586 \begin_layout Plain Layout
26590 \begin_layout Plain Layout
26606 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26609 \begin_layout Plain Layout
26613 \begin_inset space \textvisiblespace{}
26621 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26624 \begin_layout Plain Layout
26628 \begin_layout Plain Layout
26644 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26647 \begin_layout Plain Layout
26655 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26658 \begin_layout Plain Layout
26662 \begin_layout Plain Layout
26678 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26681 \begin_layout Plain Layout
26685 \begin_inset space \textvisiblespace{}
26693 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26696 \begin_layout Plain Layout
26700 \begin_layout Plain Layout
26716 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26719 \begin_layout Plain Layout
26723 \begin_inset space \textvisiblespace{}
26731 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26734 \begin_layout Plain Layout
26738 \begin_layout Plain Layout
26754 <cell alignment="left" valignment="top" bottomline="true" leftline="true" usebox="none">
26757 \begin_layout Plain Layout
26761 \begin_inset space \textvisiblespace{}
26769 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26772 \begin_layout Plain Layout
26776 \begin_layout Plain Layout
26796 \begin_inset space \hfill{}
26800 \begin_inset Tabular
26801 <lyxtabular version="3" rows="8" columns="2">
26802 <features booktabs="true" tabularvalignment="middle">
26803 <column alignment="left" valignment="top" width="0pt">
26804 <column alignment="center" valignment="top">
26806 <cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26809 \begin_layout Plain Layout
26815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26818 \begin_layout Plain Layout
26826 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26829 \begin_layout Plain Layout
26833 \begin_inset space \textvisiblespace{}
26841 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26844 \begin_layout Plain Layout
26848 \begin_layout Plain Layout
26864 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26867 \begin_layout Plain Layout
26875 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26878 \begin_layout Plain Layout
26882 \begin_layout Plain Layout
26898 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26901 \begin_layout Plain Layout
26905 \begin_inset Index idx
26908 \begin_layout Plain Layout
26919 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26926 \begin_layout Plain Layout
26942 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26945 \begin_layout Plain Layout
26953 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26956 \begin_layout Plain Layout
26960 \begin_layout Plain Layout
26976 <cell alignment="left" valignment="top" leftline="true" usebox="none">
26979 \begin_layout Plain Layout
26983 \begin_inset space \textvisiblespace{}
26991 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26994 \begin_layout Plain Layout
26998 \begin_layout Plain Layout
27014 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27017 \begin_layout Plain Layout
27021 \begin_inset space \textvisiblespace{}
27029 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27032 \begin_layout Plain Layout
27036 \begin_layout Plain Layout
27052 <cell alignment="left" valignment="top" leftline="true" usebox="none">
27055 \begin_layout Plain Layout
27059 \begin_inset space \textvisiblespace{}
27067 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27070 \begin_layout Plain Layout
27074 \begin_layout Plain Layout
27094 \begin_inset space \hfill{}
27100 \begin_layout Standard
27101 \begin_inset VSpace medskip
27110 also two different characters can be accented.
27116 \begin_inset space \textvisiblespace{}
27125 \begin_layout Plain Layout
27137 \begin_layout Standard
27150 can in combination with vowels directly be inserted with the keyboard without
27151 using \SpecialChar TeX
27153 The same applies for the tilde
27157 \begin_layout Plain Layout
27158 This only applies for keyboards where the tilde is defined as accent.
27167 in combination with
27182 \begin_layout Standard
27225 and accents that are inserted directly with the keyboard are also available
27226 in mathematical text.
27227 For the other accents there are special math commands to be used in formulas,
27229 \begin_inset CommandInset ref
27231 reference "subsec:Accents-for-one"
27238 \begin_layout Standard
27239 \begin_inset VSpace bigskip
27242 Furthermore, with the command
27249 \begin_inset Index idx
27252 \begin_layout Plain Layout
27260 all numbers and letters can be set into a circle, quasi accented with a
27261 circle, similar to the copyright symbol.
27264 \begin_layout Standard
27266 \begin_inset Tabular
27267 <lyxtabular version="3" rows="3" columns="2">
27268 <features booktabs="true" tabularvalignment="middle">
27269 <column alignment="center" valignment="top" width="0pt">
27270 <column alignment="center" valignment="top">
27272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27275 \begin_layout Plain Layout
27281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27284 \begin_layout Plain Layout
27292 <cell alignment="center" valignment="top" leftline="true" usebox="none">
27295 \begin_layout Plain Layout
27303 <cell multicolumn="1" alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
27306 \begin_layout Plain Layout
27310 \begin_layout Plain Layout
27325 <row topspace="1mm">
27326 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
27329 \begin_layout Plain Layout
27340 raisebox{-1.5pt}{W}}
27345 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27348 \begin_layout Plain Layout
27352 \begin_layout Plain Layout
27382 \begin_layout Standard
27383 One has to take care that the character fits in the circle.
27394 \begin_layout Plain Layout
27396 \begin_inset CommandInset ref
27398 reference "subsec:Font-Sizes"
27407 specifies thereby the size of the circle.
27418 \begin_layout Plain Layout
27420 \begin_inset CommandInset ref
27422 reference "subsec:Boxes-without-Frame"
27431 the character can be centered.
27434 \begin_layout Subsection
27436 \begin_inset Index idx
27439 \begin_layout Plain Layout
27448 \begin_layout Standard
27449 Old-style figures (also known as old-style numerals) are created with the
27457 \begin_inset Index idx
27460 \begin_layout Plain Layout
27469 The command can be used in formulas and in \SpecialChar TeX
27471 The command scheme is:
27474 \begin_layout Standard
27479 oldstylenums{number}
27482 \begin_layout Standard
27487 oldstylenums{0123456789
27490 \begin_inset Formula $\oldstylenums{0123456789}$
27496 \begin_layout Section
27498 \begin_inset CommandInset label
27500 name "sec:Formula-Styles"
27505 \begin_inset Index idx
27508 \begin_layout Plain Layout
27517 \begin_layout Itemize
27518 There are two different alignment styles:
27522 \begin_layout Description
27523 Centered is the predefined standard.
27526 \begin_layout Description
27527 Indented this can be set using the menu
27529 Document\SpecialChar menuseparator
27535 \begin_inset space ~
27541 \begin_layout Standard
27546 is used, the indentation can be adjusted.
27547 The default value depends on the used document class.
27551 \begin_layout Itemize
27552 And two different numbering styles that can be set in the menu
27554 Document\SpecialChar menuseparator
27560 \begin_inset space ~
27569 \begin_layout Description
27570 Right is in most cases the default.
27573 \begin_layout Description
27578 \begin_layout Standard
27579 The chosen styles are used for all displayed formulas of the document.
27580 When both, centered and indented formulas should be created in a document,
27586 The indented formulas are then set in a flalign environment, see
27587 \begin_inset CommandInset ref
27589 reference "subsec:Flalign-Environment"
27596 \begin_layout Section
27598 \begin_inset CommandInset label
27600 name "sec:Multiline-Formulas"
27605 \begin_inset Index idx
27608 \begin_layout Plain Layout
27609 Formula ! multiline
27617 \begin_layout Subsection
27621 \begin_layout Standard
27622 In \SpecialChar LyX
27623 multiline formulas are created by pressing
27626 arg "newline-insert newline"
27630 This creates either an
27634 that is described in
27635 \begin_inset CommandInset ref
27637 reference "subsec:Standard-align-Environment"
27641 or, when automatically loading the package
27645 is disabled in the document settings, an
27647 eqnarray environment
27649 that is described in
27650 \begin_inset CommandInset ref
27652 reference "subsec:Eqnarray-Environment"
27657 The align environment is recommended because it provides in any case a
27658 typographically correct output.
27661 \begin_layout Standard
27662 There are other multiline formula environments that can be created via the
27665 Insert\SpecialChar menuseparator
27669 These environments are described in the following sections.
27672 \begin_layout Standard
27673 In all multiline formula environments a new line is created by pressing
27677 arg "newline-insert newline"
27681 To add or delete lines, the math toolbar buttons
27684 arg "tabular-feature append-row"
27690 arg "tabular-feature delete-row"
27693 , respectively, or the menu
27695 Edit\SpecialChar menuseparator
27701 \begin_layout Subsubsection
27703 \begin_inset CommandInset label
27705 name "subsec:Line-Separation"
27710 \begin_inset Index idx
27713 \begin_layout Plain Layout
27714 Formula ! multiline ! Line separation
27722 \begin_layout Standard
27723 There is sometimes not enough space in multiline formulas between the lines:
27724 \begin_inset Formula
27726 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}\\
27727 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
27735 \begin_layout Standard
27736 In \SpecialChar LaTeX
27737 additional line space is specified as optional argument of the new line
27739 This is not yet possible in \SpecialChar LyX
27744 \begin_layout Plain Layout
27746 \begin_inset CommandInset href
27748 name "LyX-bug #1505"
27749 target "http://www.lyx.org/trac/ticket/1505"
27759 , therefore the whole formula must be inserted in \SpecialChar TeX
27761 To add in our example space, the command
27769 is inserted at the end of the first line.
27774 \begin_layout Plain Layout
27781 \begin_layout Plain Layout
27783 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27786 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27793 \begin_layout Plain Layout
27797 left(B^{2}+x_{0}^{2}
27805 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27810 \begin_layout Plain Layout
27822 \begin_layout Standard
27823 \begin_inset VSpace bigskip
27826 To set the line separation for all lines in a formula, the length
27833 \begin_inset Index idx
27836 \begin_layout Plain Layout
27846 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
27857 \begin_inset space \thinspace{}
27862 \begin_inset space \thinspace{}
27865 mm additional line separation as in the previous example, the command
27868 \begin_layout Standard
27878 \begin_layout Standard
27879 is inserted in \SpecialChar TeX
27880 mode before the formula.
27881 This requires that the \SpecialChar LaTeX
27890 \begin_layout Plain Layout
27895 is part of every \SpecialChar LaTeX
27896 standard installation.
27902 \begin_inset Index idx
27905 \begin_layout Plain Layout
27911 was loaded in \SpecialChar LaTeX
27912 -preamble with the line
27915 \begin_layout Standard
27923 \begin_layout Standard
27928 \begin_layout Plain Layout
27940 \begin_inset Formula
27942 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}\\
27943 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
27951 \begin_layout Standard
27955 \begin_layout Plain Layout
27966 To get back to the predefined distance,
27972 is set to the value 3
27973 \begin_inset space \thinspace{}
27979 \begin_layout Subsubsection
27981 \begin_inset CommandInset label
27983 name "subsec:Column-Separation"
27988 \begin_inset Index idx
27991 \begin_layout Plain Layout
27992 Formula ! multiline ! Column separation
28000 \begin_layout Standard
28001 Multiline formulas form a matrix.
28002 A formula in the eqnarray environment is for example a matrix with three
28004 By changing the column separation in this environment, the space beside
28005 the relation sign can be changed.
28008 \begin_layout Standard
28009 The column separation is specified with the length
28016 \begin_inset Index idx
28019 \begin_layout Plain Layout
28028 \begin_inset Newline newline
28031 column separation = 2
28032 \begin_inset space \thinspace{}
28042 \begin_inset Newline newline
28048 \begin_layout Standard
28058 \begin_layout Standard
28059 inserted in \SpecialChar TeX
28060 mode, sets for all following formulas a column separation of
28062 \begin_inset space \thinspace{}
28066 To get back to the predefined distance,
28073 \begin_inset space \thinspace{}
28079 \begin_layout Standard
28081 \begin_inset space \thinspace{}
28084 cm column separation:
28088 \begin_layout Plain Layout
28100 \begin_inset Formula
28108 A formula with the predefined column separation for matrices of 10
28109 \begin_inset space \thinspace{}
28116 \begin_layout Plain Layout
28128 \begin_inset Formula
28139 \begin_layout Standard
28140 \begin_inset Newpage newpage
28146 \begin_layout Subsubsection
28148 \begin_inset Index idx
28151 \begin_layout Plain Layout
28160 \begin_layout Standard
28161 Long formulas can be typeset using these methods:
28164 \begin_layout Itemize
28165 When one side of the equation is much shorter than the line width, this
28166 one is chosen for the left side and the right side is typeset over two
28168 \begin_inset Formula
28170 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 \\
28171 & & -\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}
28176 The minus sign at the beginning of the second line does normally not appear
28177 as an operator because it is the first character of the line.
28178 Thus it would not be surrounded by space and could not be distinguished
28179 from the fraction bar.
28181 \begin_inset space \thinspace{}
28184 pt space was inserted behind the minus sign with the command
28194 \begin_layout Plain Layout
28202 \begin_inset CommandInset ref
28204 reference "subsec:Variable-Space"
28214 \begin_inset Index idx
28217 \begin_layout Plain Layout
28228 \begin_layout Itemize
28229 When both sides of the equation are too long, the command
28236 \begin_inset Index idx
28239 \begin_layout Plain Layout
28248 It is inserted in the first column of the first line and causes all further
28249 insertions to overwrite the following columns:
28250 \begin_inset Formula
28252 \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 \\
28253 & & -\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 \\
28254 & & =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}
28259 After the insertion of
28265 , the cursor is in a purple box that is a bit shifted to the left from the
28267 In this the formula is inserted.
28268 \begin_inset Newline newline
28271 The content of the further lines is inserted to the second or another formula
28273 The greater the column number where it was inserted, the larger the indentation.
28274 \begin_inset VSpace medskip
28278 \begin_inset Newline newline
28282 \begin_inset Note Greyedout
28285 \begin_layout Plain Layout
28286 Note the following when using
28295 \begin_layout Itemize
28296 The formula doesn't use the full page width.
28298 \begin_inset space \thinspace{}
28302 \begin_inset space \space{}
28306 \begin_inset Formula $-B^{2}$
28309 is added to the first line in the above example, it would have been outside
28311 To better use the width, negative space can be inserted at the beginning
28315 \begin_layout Itemize
28316 Due to a bug in \SpecialChar LyX
28317 the cursor cannot be set with the mouse into the first
28322 \begin_layout Plain Layout
28323 \begin_inset CommandInset href
28325 name "LyX-bug #1429"
28326 target "http://www.lyx.org/trac/ticket/1429"
28336 One can only set the cursor at the beginning of the line and move it with
28345 \begin_layout Itemize
28346 Other methods to set long formulas are offered by the environments described
28348 \begin_inset CommandInset ref
28350 reference "subsec:Multline-Environment"
28355 \begin_inset CommandInset ref
28357 reference "subsec:Multiline-Formula-Parts"
28364 \begin_layout Subsubsection
28365 Multiline Fractions
28366 \begin_inset CommandInset label
28368 name "subsec:Multiline-Fractions"
28373 \begin_inset Index idx
28376 \begin_layout Plain Layout
28377 Fractions ! multiline
28385 \begin_layout Standard
28386 There are cases where the denominator and/or the numerator of a fraction
28387 is so long that the fraction does not fit into one line.
28388 It is then necessary to add a line break within the fraction.
28389 This can be done using the command
28396 \begin_inset Index idx
28399 \begin_layout Plain Layout
28408 To activate it, set in the document settings under
28411 \begin_inset space ~
28421 \begin_inset Index idx
28424 \begin_layout Plain Layout
28425 Packages ! mathtools
28433 \begin_inset space ~
28448 \begin_layout Standard
28453 splitfrac{first line}{second line}
28456 \begin_layout Standard
28457 and is used as denominator and/or numerator:
28460 \begin_layout Standard
28461 \begin_inset Formula
28463 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}
28468 The command for the first numerator above is:
28471 \begin_layout Standard
28476 splitfrac{xy+xy+xy+xy+xy
28477 \begin_inset space \textvisiblespace{}
28485 \begin_layout Subsubsection
28487 \begin_inset CommandInset label
28489 name "subsec:Multiline-Brackets"
28494 \begin_inset Index idx
28497 \begin_layout Plain Layout
28498 Brackets ! for multiline expressions
28506 \begin_layout Standard
28507 For brackets spanning multiple lines the following problem occurs:
28508 \begin_inset Formula
28510 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28511 & & \left.\cdots+B-D\right]
28519 \begin_layout Standard
28520 The closing bracket is smaller than the opening bracket because brackets
28521 with variable size may not span multiple lines.
28524 \begin_layout Standard
28525 To set the bracket size for the second line correctly, the first line is
28533 \begin_inset Index idx
28536 \begin_layout Plain Layout
28544 and the second line with
28552 \begin_layout Plain Layout
28566 \begin_inset CommandInset ref
28568 reference "subsec:Automatic-Bracket-Size"
28580 \begin_inset Index idx
28583 \begin_layout Plain Layout
28606 \begin_inset space \textvisiblespace{}
28616 \begin_inset space \textvisiblespace{}
28626 \begin_inset space \textvisiblespace{}
28632 \begin_inset Formula $\downarrow$
28638 \begin_inset Index idx
28641 \begin_layout Plain Layout
28649 is inserted, because the multiplication operator with its limits is the
28650 largest symbol in the first line and this should be the size for the bracket
28651 in the second line.
28654 \begin_layout Standard
28655 The result is this:
28656 \begin_inset Formula
28658 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28659 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
28667 \begin_layout Subsection
28671 \begin_layout Standard
28672 Align environments can be used for every kind of multiline formulas.
28673 They are especially useful to set several formulas side by side.
28676 \begin_layout Standard
28677 Align environments consist of columns.
28678 The odd columns are right aligned, the even ones left aligned.
28679 Every line in an Align environment can be numbered.
28682 \begin_layout Standard
28683 Align environments are created via the menu
28685 Insert\SpecialChar menuseparator
28691 Edit\SpecialChar menuseparator
28692 Math\SpecialChar menuseparator
28693 Change Formula Type
28695 already existing formulas can be converted to Align environments.
28698 \begin_layout Standard
28699 To add or delete columns, the math toolbar buttons
28702 arg "tabular-feature append-column"
28708 arg "tabular-feature delete-column"
28711 , respectively, or the menu
28713 Edit\SpecialChar menuseparator
28719 \begin_layout Subsubsection
28720 Standard align Environment
28721 \begin_inset CommandInset label
28723 name "subsec:Standard-align-Environment"
28728 \begin_inset Index idx
28731 \begin_layout Plain Layout
28732 Formula ! multiline ! align environment
28740 \begin_layout Standard
28741 This Align environment is created by pressing
28744 arg "newline-insert newline"
28747 in a formula or by the menu
28749 Insert\SpecialChar menuseparator
28750 Math\SpecialChar menuseparator
28751 AMS align Environment
28756 \begin_layout Standard
28757 An example for two formulas set side by side, that are created with a four
28758 column align environment:
28759 \begin_inset Formula
28761 A & =\sin(B) & C & =D\\
28762 C & \ne A & B & \ne D
28767 As it can be seen, the formulas in this environment are placed so as if
28776 \begin_layout Plain Layout
28784 \begin_inset CommandInset ref
28786 reference "subsec:Variable-Space"
28797 before the first and after every even column.
28798 When the formula style
28804 \begin_layout Plain Layout
28806 \begin_inset CommandInset ref
28808 reference "sec:Formula-Styles"
28819 is used, the formula is set without the
28825 before the first column.
28828 \begin_layout Subsubsection
28829 Alignat Environment
28830 \begin_inset Index idx
28833 \begin_layout Plain Layout
28834 Formula ! multiline ! alignat environment
28842 \begin_layout Standard
28843 The alignat environment has no predefined column separation.
28844 It can be inserted manually with the spaces that are described
28845 \begin_inset CommandInset ref
28847 reference "subsec:Space"
28854 \begin_layout Standard
28855 The above example in the alignat environment where 1
28856 \begin_inset space \thinspace{}
28859 cm space was inserted at the beginning of the second formula:
28860 \begin_inset Formula
28861 \begin{alignat*}{2}
28862 A & =\sin(B) & \hspace{1cm}C & =D\\
28863 C & \ne A & B & \ne D
28868 Because the column separation can be set separately for every column, this
28869 environment is especially suitable to set three and more formulas side
28873 \begin_layout Subsubsection
28874 Flalign Environment
28875 \begin_inset CommandInset label
28877 name "subsec:Flalign-Environment"
28882 \begin_inset Index idx
28885 \begin_layout Plain Layout
28886 Formula ! multiline ! flalign environment
28894 \begin_layout Standard
28895 In this environment the first two columns are always set as much as possible
28896 to the left and the last two ones to the right.
28898 \begin_inset Formula
28900 A & =1 & B & =2 & C & =3\\
28901 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
28909 \begin_layout Standard
28910 By creating a flalign environment with an odd number of columns where an
28911 empty \SpecialChar TeX
28912 brace is inserted to the last column, several formulas in a document
28913 can be set to the left, although the formula style
28918 As example the indented formula
28919 \begin_inset CommandInset ref
28921 reference "eq:VolInt"
28926 \begin_inset Formula
28928 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
28933 The first two columns contain the formula.
28934 To indent it as with the formula style
28939 \begin_inset space \thinspace{}
28942 pt space was inserted at the beginning of the first column.
28945 \begin_layout Subsection
28946 Eqnarray Environment
28947 \begin_inset CommandInset label
28949 name "subsec:Eqnarray-Environment"
28954 \begin_inset Index idx
28957 \begin_layout Plain Layout
28958 Formula ! multiline ! eqnarray environment
28966 \begin_layout Standard
28967 When this environment has been created, three blue boxes appear.
28968 The content of the first box is right aligned, the content of the last
28970 The content of the middle box appears centered and a bit smaller, because
28971 it is designed to insert there only relation characters.
28972 \begin_inset Formula
28974 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28984 \begin_layout Subsection
28986 \begin_inset Index idx
28989 \begin_layout Plain Layout
28990 Formula ! multiline ! gather environment
28998 \begin_layout Standard
28999 This environment consists of only one centered column.
29000 Every line can be numbered.
29001 \begin_inset Formula
29012 \begin_layout Subsection
29013 Multline Environment
29014 \begin_inset CommandInset label
29016 name "subsec:Multline-Environment"
29021 \begin_inset Index idx
29024 \begin_layout Plain Layout
29025 Formula ! multiline ! multline environment
29033 \begin_layout Standard
29034 The multline environment consists, like the gather environment, of only
29036 But the first line is left aligned, the last one right aligned.
29037 All other lines are centered.
29038 Therefore this environment is suitable for long formulas.
29040 \begin_inset CommandInset ref
29042 reference "eq:lefteqn"
29046 in the multline environment:
29047 \begin_inset Formula
29049 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}\\
29050 -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}\\
29051 =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}}
29059 \begin_layout Standard
29060 In the output only the last (first) line of a multline environment appears
29061 numbered when the document numbering is right (left).
29065 \begin_layout Plain Layout
29066 numbering styles see
29067 \begin_inset CommandInset ref
29069 reference "sec:Formula-Styles"
29081 \begin_layout Standard
29089 \begin_inset Index idx
29092 \begin_layout Plain Layout
29107 \begin_inset Index idx
29110 \begin_layout Plain Layout
29118 a centered line can be right or left aligned, respectively.
29119 The commands are used as follows:
29122 \begin_layout Standard
29127 shoveright{line content}
29133 shoveleft{line content}
29136 \begin_layout Standard
29137 \begin_inset VSpace medskip
29147 \begin_inset Index idx
29150 \begin_layout Plain Layout
29158 specifies the distance of the first line from the left page margin.
29159 Predefined is the length 0
29160 \begin_inset space \thinspace{}
29166 \begin_layout Standard
29167 As example the above formula where the command
29170 \begin_layout Standard
29180 \begin_layout Standard
29181 was inserted in \SpecialChar TeX
29186 \begin_layout Plain Layout
29198 \begin_inset Formula
29200 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}\\
29201 \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}}\\
29202 =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}}
29211 \begin_layout Plain Layout
29222 The second line was left aligned using
29231 \begin_layout Subsection
29232 Multiline Formula Parts
29233 \begin_inset CommandInset label
29235 name "subsec:Multiline-Formula-Parts"
29240 \begin_inset Index idx
29243 \begin_layout Plain Layout
29244 Formula ! multiline ! formula parts
29252 \begin_layout Standard
29253 To display only parts of a formula with multiple lines, one of the following
29254 environments is used:
29271 They can be inserted via the menu
29273 Insert\SpecialChar menuseparator
29276 or by using the commands described in this section.
29279 \begin_layout Standard
29280 The first three have the same properties as the corresponding multiline
29281 formula environments, but it is possible to set further formula parts beside
29284 \begin_inset Formula
29286 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29287 \Delta E\Delta t & \ge\frac{\hbar}{2}
29289 \right\} \textrm{Uncertainty relations}
29297 \begin_layout Standard
29298 To get this formula, a displayed formula is created where the command
29305 \begin_inset Index idx
29308 \begin_layout Plain Layout
29317 A purple box appears around the blue formula box where now columns and
29318 lines can be added.
29319 Outside the multiline environment other formula parts can be set, like
29323 \begin_layout Standard
29324 The aligned environment is also suitable for long formulas whose lines are
29325 horizontally aligned.
29326 Using aligned in a displayed formula has the advantage that the formula
29327 number is vertically centered behind the lines.
29329 \begin_inset CommandInset ref
29331 reference "eq:shortlong"
29335 in the aligned environment:
29336 \begin_inset Formula
29338 \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}|}\\
29339 & -\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}|}
29348 \begin_layout Standard
29349 To use the environments
29368 \begin_inset Index idx
29371 \begin_layout Plain Layout
29386 \begin_inset Index idx
29389 \begin_layout Plain Layout
29404 \begin_inset Index idx
29407 \begin_layout Plain Layout
29415 are inserted, respectively.
29416 The split environment has the same properties as the aligned environment
29417 but it can only have two columns.
29420 \begin_layout Subsection
29421 Text in multiline Formulas
29422 \begin_inset CommandInset label
29424 name "subsec:Text-in-multiline"
29429 \begin_inset Index idx
29432 \begin_layout Plain Layout
29439 \begin_inset Index idx
29442 \begin_layout Plain Layout
29443 Formula ! multiline ! text
29451 \begin_layout Standard
29452 In the Align environments, and the multline and gather environment, text
29453 can be inserted that will appear in a separate line and doesn't affect
29454 the column alignment.
29455 To do this, the command
29462 \begin_inset Index idx
29465 \begin_layout Plain Layout
29473 is used in the following scheme:
29476 \begin_layout Standard
29484 \begin_layout Standard
29485 The text should not be longer than a line because it cannot be hyphenated.
29486 As \SpecialChar LyX
29487 doesn't yet support
29493 directly, the text is written as mathematical text.
29500 must hereby be at the beginning of a line and appears in the output above
29502 An example where the text was inserted at the beginning of the second line:
29503 \begin_inset Formula
29505 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29506 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29514 \begin_layout Standard
29521 always creates some vertical space between the text and the formula lines.
29522 To avoid this space, set in the document settings under
29525 \begin_inset space ~
29535 \begin_inset Index idx
29538 \begin_layout Plain Layout
29539 Packages ! mathtools
29547 \begin_inset space ~
29553 Then you can use the command
29560 \begin_inset Index idx
29563 \begin_layout Plain Layout
29580 \begin_layout Standard
29581 \begin_inset Formula
29583 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29584 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29592 \begin_layout Section
29594 \begin_inset Index idx
29597 \begin_layout Plain Layout
29604 \begin_inset Index idx
29607 \begin_layout Plain Layout
29608 Formula ! numbering|see
29612 \begin_layout Plain Layout
29623 \begin_layout Plain Layout
29638 \begin_layout Subsection
29642 \begin_layout Standard
29643 Numbered formulas can be created with the menu
29645 Insert\SpecialChar menuseparator
29646 Math\SpecialChar menuseparator
29648 \begin_inset space ~
29656 \begin_inset space ~
29662 Existing formulas can be numbered with the menu
29664 Edit\SpecialChar menuseparator
29665 Math\SpecialChar menuseparator
29667 \begin_inset space ~
29675 arg "math-number-toggle"
29679 The formula number is displayed in \SpecialChar LyX
29680 behind the formula as a number sign
29682 The number sign is replaced in the output by the formula number.
29685 \begin_layout Standard
29686 When numbering is turned on in multiline formulas, all lines will be numbered.
29687 But the numbering can be controlled with the menu
29689 Edit\SpecialChar menuseparator
29690 Math\SpecialChar menuseparator
29692 \begin_inset space ~
29696 \begin_inset space ~
29700 \begin_inset space ~
29708 arg "math-number-line-toggle"
29714 \begin_layout Standard
29715 Except for inline formulas, all formulas can be numbered with two different
29717 \begin_inset CommandInset ref
29719 reference "sec:Formula-Styles"
29726 \begin_layout Subsection
29728 \begin_inset Index idx
29731 \begin_layout Plain Layout
29732 Cross-references ! to formulas
29740 \begin_layout Standard
29741 All labeled formulas can be cross-referenced.
29742 A label is added by the menu
29744 Insert\SpecialChar menuseparator
29747 or the toolbar button
29754 The cursor must hereby be inside a displayed formula.
29755 Alternatively you can right-click on the formula and choose
29760 A dialog pops up displaying the prefix
29765 The label is inserted there behind the prefix.
29766 The predefined prefix means
29767 \begin_inset Quotes eld
29771 \begin_inset Quotes erd
29774 and makes it easier to find labels in large documents because it marks
29775 it as formula label to divide it from e.
29776 \begin_inset space \thinspace{}
29780 \begin_inset space \space{}
29784 To change a label, the menu
29786 Insert\SpecialChar menuseparator
29789 is used again or you right-click on a formula and then on
29796 \begin_layout Standard
29797 The name of the label is displayed in \SpecialChar LyX
29798 within two parentheses behind formula.
29799 A formula with a label is always numbered.
29802 \begin_layout Standard
29803 Cross-references are inserted via the menu
29805 Insert\SpecialChar menuseparator
29808 or with the toolbar button
29811 arg "dialog-show-new-inset ref"
29815 A formula cross-reference appears in the output as formula number.
29816 When in the cross-reference dialog window the format
29820 is chosen, the cross-reference appears in the output as formula number
29822 \begin_inset Newline newline
29825 By right-clicking on a cross-reference in \SpecialChar LyX
29826 , one jumps to the formula that
29830 \begin_layout Standard
29831 Here are as examples cross-references to formulas of the following subsections:
29832 \begin_inset Note Note
29835 \begin_layout Plain Layout
29836 Note the different cross-reference types.
29844 \begin_layout Standard
29846 \begin_inset CommandInset ref
29853 \begin_inset CommandInset ref
29861 \begin_inset CommandInset ref
29867 ) big Latin letters are used for the numbering in contrary to (
29868 \begin_inset CommandInset ref
29877 \begin_layout Standard
29878 \begin_inset VSpace medskip
29881 When the argument of
29889 \begin_layout Plain Layout
29897 \begin_inset CommandInset ref
29899 reference "subsec:User-defined-Numbering"
29910 contains a box like in
29911 \begin_inset CommandInset ref
29913 reference "subsec:Paragraph-Boxes"
29917 , the formula cannot be referenced.
29920 \begin_layout Subsection
29922 \begin_inset Index idx
29925 \begin_layout Plain Layout
29926 Formula numbering ! subnumbering
29934 \begin_layout Standard
29935 With the help of the commands
29939 begin{subequations}
29947 formulas can be subnumbered.
29948 Both commands are inserted in \SpecialChar TeX
29952 \begin_layout Standard
29954 \begin_inset Formula
29965 \begin_layout Plain Layout
29969 begin{subequations}
29975 \begin_inset VSpace -5mm
29979 \begin_inset Formula
29987 \begin_inset Formula
29997 \begin_layout Standard
30001 \begin_layout Plain Layout
30013 \begin_layout Standard
30014 To create the example, the following is done:
30017 \begin_layout Enumerate
30018 first formula is inserted
30021 \begin_layout Enumerate
30026 begin{subequations}
30027 \begin_inset Newline newline
30032 is inserted after the first formula
30035 \begin_layout Enumerate
30036 second formula is inserted
30039 \begin_layout Enumerate
30040 third formula is inserted
30043 \begin_layout Enumerate
30050 is inserted after the third formula
30053 \begin_layout Standard
30054 Every formula between the commands
30066 will be subnumbered with a, b, c, \SpecialChar ldots
30068 For multiline formulas every line will be subnumbered.
30071 \begin_layout Standard
30072 Referencing subequations work like for normal equations:
30073 \begin_inset CommandInset ref
30080 \begin_inset CommandInset ref
30087 If you want to reference the subequations collectively, insert a label
30092 begin{subequations}
30096 \begin_inset CommandInset ref
30098 reference "eq:Here-is-an"
30105 \begin_layout Standard
30106 By inserting commands in \SpecialChar TeX
30107 mode, a space is created between the first two
30110 \begin_inset space \thinspace{}
30113 mm vertical space is inserted after the command
30117 begin{subequations}
30120 When the formula style
30126 \begin_layout Plain Layout
30128 \begin_inset CommandInset ref
30130 reference "sec:Formula-Styles"
30142 \begin_inset space \thinspace{}
30145 mm space is inserted instead.
30148 \begin_layout Standard
30149 To get another subnumber instead of small Latin letters, insert this command
30154 begin{subequations}
30159 \begin_layout Standard
30168 theparentequation -
30173 \begin_layout Standard
30180 creates hereby the parent number and
30186 adds a small Roman number as subnumber.
30187 For more information about the customization of the numbering, see
30188 \begin_inset CommandInset ref
30190 reference "subsec:Numbering-with-Roman"
30197 \begin_layout Standard
30198 Here is an example for a multiline formula where the numbering is customized
30199 and turned off for the second line:
30203 \begin_layout Plain Layout
30207 begin{subequations}
30213 \begin_inset CommandInset label
30215 name "eq:Here-is-an"
30223 \begin_layout Plain Layout
30231 theparentequation -
30239 \begin_inset Formula
30241 A & = & (B-Z)^{2}=(B-Z)(B-Z)\\
30242 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30243 & = & B^{2}-2BZ+Z^{2}
30252 \begin_layout Plain Layout
30264 \begin_layout Subsection
30265 User-defined Numbering
30266 \begin_inset CommandInset label
30268 name "subsec:User-defined-Numbering"
30273 \begin_inset Index idx
30276 \begin_layout Plain Layout
30277 Formula numbering ! user-defined
30285 \begin_layout Standard
30286 \begin_inset Index idx
30289 \begin_layout Plain Layout
30290 Formula numbering ! self-defined delimiters
30295 With the standard numbering parentheses are set around the formula number.
30296 To replace the parentheses for example by vertical bars, the following
30297 line is added to the \SpecialChar LaTeX
30301 \begin_layout Standard
30313 \begin_inset Note Note
30316 \begin_layout Plain Layout
30317 This macro is already declared in the \SpecialChar LaTeX
30318 -preamble for testing.
30319 To activate it, remove the percent sign at the beginning.
30327 \begin_layout Standard
30328 To use other characters, the vertical bars besides the
30332 are replaced by one ore more characters.
30333 To get only the formula number the vertical bars are omitted.
30336 \begin_layout Standard
30337 \begin_inset VSpace bigskip
30340 When there should be an expression of your choice instead of the consecutive
30341 formula number in parentheses behind the formula, the command
30348 \begin_inset Index idx
30351 \begin_layout Plain Layout
30360 \begin_inset Formula
30362 A+B=C\tag{something}\label{eq:tag}
30367 In this example the command
30372 \begin_inset space \textvisiblespace{}
30377 was inserted in the formula.
30380 \begin_layout Standard
30386 \begin_inset space \textvisiblespace{}
30391 is inserted instead, the star prevents the parentheses around the expression:
30392 \begin_inset Formula
30394 A+B=C\tag*{something}
30402 \begin_layout Standard
30403 \begin_inset VSpace bigskip
30406 To restart the formula numbering with new document parts or sections, the
30407 following command is used:
30410 \begin_layout Standard
30415 @addtoreset{equation}{part}
30418 \begin_inset Index idx
30421 \begin_layout Plain Layout
30426 \begin_layout Plain Layout
30437 \begin_layout Plain Layout
30450 \begin_layout Plain Layout
30461 \begin_layout Plain Layout
30474 \begin_inset Newline newline
30478 \begin_inset Newline newline
30485 @addtoreset{equation}{section}
30488 \begin_layout Standard
30489 To be able to use these commands in \SpecialChar TeX
30491 \begin_inset Quotes eld
30495 \begin_inset Quotes erd
30498 character has to be made
30499 \begin_inset Quotes eld
30503 \begin_inset Quotes erd
30506 for \SpecialChar LaTeX
30521 So the command sequence in \SpecialChar TeX
30525 \begin_layout Standard
30531 \begin_inset Newline newline
30536 @addtoreset{equation}{section}
30537 \begin_inset Newline newline
30545 \begin_layout Standard
30546 In the \SpecialChar LaTeX
30559 can be omitted as they are automatically internally inserted by \SpecialChar LyX
30563 \begin_layout Standard
30578 \begin_layout Plain Layout
30583 is part of the \SpecialChar LaTeX
30589 \begin_inset Index idx
30592 \begin_layout Plain Layout
30593 Packages ! carlisle
30598 that is part of every \SpecialChar LaTeX
30599 standard installation.
30605 \begin_inset Index idx
30608 \begin_layout Plain Layout
30609 Packages ! remreset
30614 has to be loaded in the \SpecialChar LaTeX
30615 -preamble with the line
30618 \begin_layout Standard
30623 usepackage{remreset}
30626 \begin_layout Standard
30634 \begin_inset Index idx
30637 \begin_layout Plain Layout
30642 \begin_layout Plain Layout
30653 \begin_layout Plain Layout
30666 \begin_layout Plain Layout
30677 \begin_layout Plain Layout
30689 can be used with the same scheme as
30698 \begin_layout Standard
30699 \begin_inset VSpace bigskip
30702 Sometimes formulas should be numbered in the following form:
30705 \begin_layout Standard
30708 (section number.formula number)
30711 \begin_layout Standard
30712 The formula number should start with every section with
30713 \begin_inset Quotes eld
30717 \begin_inset Quotes erd
30723 \begin_layout Standard
30724 For this case there is the command
30731 \begin_inset Index idx
30734 \begin_layout Plain Layout
30742 , which is used with the following scheme:
30745 \begin_layout Standard
30750 numberwithin{counter}{sectioning}
30753 \begin_layout Standard
30754 Counter denotes what kind of numbering is affected, sectioning denotes what
30755 number is before the dot.
30758 \begin_layout Standard
30759 Thus in our case the following \SpecialChar LaTeX
30760 preamble or \SpecialChar TeX
30764 \begin_layout Standard
30769 numberwithin{equation}{section}
30772 \begin_layout Standard
30773 This is the result:
30777 \begin_layout Plain Layout
30781 numberwithin{equation}{section}
30787 \begin_inset Formula
30797 \begin_layout Standard
30799 \begin_inset space \thinspace{}
30803 \begin_inset space \space{}
30806 tables so that the number of the part is the sectioning,
30807 \begin_inset Newline newline
30814 numberwithin{table}{part}
30819 \begin_layout Standard
30820 To go back to the standard numbering or to prevent this kind of numbering
30821 when it is defined by the document class, the following command is inserted
30822 as \SpecialChar TeX
30823 code or to the \SpecialChar LaTeX
30827 \begin_layout Standard
30837 \begin_inset Index idx
30840 \begin_layout Plain Layout
30854 \begin_layout Plain Layout
30870 \begin_inset Newline newline
30878 \begin_inset Newline newline
30890 \begin_layout Standard
30897 uses internally the command
30903 , described above, that also needs to be reverted.
30907 \begin_layout Plain Layout
30914 \begin_layout Plain Layout
30918 @removefromreset{equation}{section}
30921 \begin_layout Plain Layout
30933 \begin_layout Standard
30934 \begin_inset Newpage newpage
30940 \begin_layout Subsection
30941 Numbering with Roman Numbers and Letters
30942 \begin_inset CommandInset label
30944 name "subsec:Numbering-with-Roman"
30949 \begin_inset Index idx
30952 \begin_layout Plain Layout
30953 Formula numbering ! with letters
30959 \begin_inset Index idx
30962 \begin_layout Plain Layout
30963 Formula numbering ! with Roman numbers
30971 \begin_layout Standard
30972 Formulas can also be numbered with Roman numbers and Latin letters.
30973 To number for example with small Roman numbers, the command
30976 \begin_layout Standard
30988 \begin_layout Standard
30989 is inserted before the formula in \SpecialChar TeX
30998 \begin_inset Index idx
31001 \begin_layout Plain Layout
31009 redefines the predefined command
31025 \begin_layout Plain Layout
31032 has the same scheme like the command
31038 that is described in
31039 \begin_inset CommandInset ref
31041 reference "subsec:The-Command-newcommand"
31054 is the formula counter.
31061 is used as prefix for a counter, the value of the counter is output as
31063 When a formula is numbered, \SpecialChar LaTeX
31064 sets internally the command
31070 behind the formula.
31076 \begin_inset Index idx
31079 \begin_layout Plain Layout
31089 outputs the counter as small Roman number.
31092 \begin_layout Standard
31093 All formulas behind the command
31103 are now numbered Roman.
31104 To switch to numbering with big Roman numbers, the command is inserted
31118 \begin_inset Index idx
31121 \begin_layout Plain Layout
31133 \begin_inset Quotes eld
31137 \begin_inset Quotes erd
31140 with small Latin letters there is the command
31147 \begin_inset Index idx
31150 \begin_layout Plain Layout
31158 , for big ones there is the command
31165 \begin_inset Index idx
31168 \begin_layout Plain Layout
31181 \begin_layout Standard
31182 \begin_inset Note Greyedout
31185 \begin_layout Plain Layout
31192 \begin_inset space ~
31195 formulas can be numbered with Latin letters in one document.
31203 \begin_layout Standard
31207 \begin_layout Plain Layout
31223 \begin_layout Standard
31224 \begin_inset Formula
31226 A=\textrm{small roman}
31235 \begin_layout Plain Layout
31249 \begin_inset Formula
31251 B=\textrm{big Roman}\label{eq:Rom}
31260 \begin_layout Plain Layout
31274 \begin_inset Formula
31276 C=\textrm{small Latin}
31285 \begin_layout Plain Layout
31299 \begin_inset Formula
31301 D=\textrm{big Latin}\label{eq:Lat}
31309 \begin_layout Standard
31310 To switch back to the default numbering, insert the command:
31313 \begin_layout Standard
31323 \begin_inset Index idx
31326 \begin_layout Plain Layout
31337 \begin_layout Standard
31341 \begin_layout Plain Layout
31355 \begin_inset Formula
31365 \begin_layout Standard
31366 \begin_inset VSpace medskip
31369 As you see, formulas are numbered serially independent from the numbering
31371 When then numbering should start with
31372 \begin_inset Quotes eld
31376 \begin_inset Quotes erd
31379 when the style is changed, new equation counters have to be defined.
31380 A description about this can be found in the file
31381 \begin_inset CommandInset href
31383 name "Formula-numbering.lyx"
31384 target "run:Formula-numbering.lyx"
31392 \begin_layout Section
31393 Chemical Symbols and Equations
31394 \begin_inset CommandInset label
31396 name "subsec:Chemical-Symbols-and"
31401 \begin_inset Index idx
31404 \begin_layout Plain Layout
31405 Chemical characters ! Symbols
31411 \begin_inset Index idx
31414 \begin_layout Plain Layout
31421 \begin_inset Index idx
31424 \begin_layout Plain Layout
31433 \begin_layout Standard
31434 An example text from chemistry:
31437 \begin_layout Quote
31439 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31442 -ion reacts with two
31443 \begin_inset Formula $\mathrm{Na^{+}}$
31446 -ions to sodium sulfate
31447 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31451 The chemical equation for this is:
31452 \begin_inset Formula
31454 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31462 \begin_layout Standard
31463 This chemical equation can directly be created as formula.
31464 To avoid that the symbols appear italic, everything is highlighted and
31465 changed by the shortcut
31471 to the upright font style.
31475 \begin_layout Plain Layout
31481 \begin_inset CommandInset ref
31483 reference "subsec:Font-Styles"
31495 \begin_layout Standard
31496 A more convenient way to typeset chemical formulas is to use the command
31504 \begin_inset Index idx
31507 \begin_layout Plain Layout
31515 that is available when the \SpecialChar LaTeX
31521 \begin_inset Index idx
31524 \begin_layout Plain Layout
31537 to a formula a new blue box appears where chemical formulas can be inserted
31538 in an intuitive way.
31541 \begin_layout Standard
31543 \begin_inset Tabular
31544 <lyxtabular version="3" rows="10" columns="2">
31545 <features booktabs="true" tabularvalignment="middle">
31546 <column alignment="center" valignment="top" width="0pt">
31547 <column alignment="center" valignment="top">
31549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31552 \begin_layout Plain Layout
31558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31561 \begin_layout Plain Layout
31569 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31572 \begin_layout Plain Layout
31576 \begin_inset space \textvisiblespace{}
31584 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31587 \begin_layout Plain Layout
31588 \begin_inset Formula $\ce{H2CO3}$
31597 <row topspace="1.5mm">
31598 <cell alignment="center" valignment="top" usebox="none">
31601 \begin_layout Plain Layout
31605 \begin_inset space \textvisiblespace{}
31613 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31616 \begin_layout Plain Layout
31617 \begin_inset Formula $\ce{SO4^{2-}}$
31626 <row topspace="1.5mm">
31627 <cell alignment="center" valignment="top" usebox="none">
31630 \begin_layout Plain Layout
31634 \begin_inset space \textvisiblespace{}
31642 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31645 \begin_layout Plain Layout
31646 \begin_inset Formula $\ce{(NH4)2S}$
31655 <row topspace="1.5mm">
31656 <cell alignment="center" valignment="top" usebox="none">
31659 \begin_layout Plain Layout
31663 \begin_inset space \textvisiblespace{}
31671 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31674 \begin_layout Plain Layout
31675 \begin_inset Formula $\ce{KCr(SO4)2.12H2O}$
31684 <row topspace="1.5mm">
31685 <cell alignment="center" valignment="top" usebox="none">
31688 \begin_layout Plain Layout
31692 \begin_inset space \textvisiblespace{}
31698 \begin_inset space \textvisiblespace{}
31704 \begin_inset space \textvisiblespace{}
31712 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31715 \begin_layout Plain Layout
31716 \begin_inset Formula $\ce{A-B\dbond C\tbond D}$
31725 <row topspace="1.5mm">
31726 <cell alignment="center" valignment="top" usebox="none">
31729 \begin_layout Plain Layout
31733 \begin_inset space \textvisiblespace{}
31737 \begin_inset Formula $\downarrow$
31741 \begin_inset Formula $\to$
31749 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31752 \begin_layout Plain Layout
31753 \begin_inset Formula $\ce{_{90}^{227}Th+}$
31763 <cell alignment="center" valignment="top" leftline="true" usebox="none">
31766 \begin_layout Plain Layout
31770 \begin_inset space \textvisiblespace{}
31776 \begin_inset space \textvisiblespace{}
31782 \begin_inset space \textvisiblespace{}
31790 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
31793 \begin_layout Plain Layout
31794 \begin_inset Formula $\ce{\ensuremath{\mu\hyphen}Cl}$
31804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31807 \begin_layout Plain Layout
31811 \begin_inset space \textvisiblespace{}
31815 \begin_inset space \textvisiblespace{}
31819 \begin_inset space \textvisiblespace{}
31823 \begin_inset space \textvisiblespace{}
31827 \begin_inset space \textvisiblespace{}
31835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31838 \begin_layout Plain Layout
31839 \begin_inset Formula $\ce{CO2 + C <=> 2CO}$
31848 <row topspace="1.5mm">
31849 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
31852 \begin_layout Plain Layout
31856 \begin_inset space \textvisiblespace{}
31860 \begin_inset space \textvisiblespace{}
31864 \begin_inset space \textvisiblespace{}
31868 \begin_inset space \textvisiblespace{}
31876 \begin_inset space \textvisiblespace{}
31884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
31887 \begin_layout Plain Layout
31888 \begin_inset Formula $\ce{CO2 + C ->[\alpha][\beta] 2CO}$
31904 \begin_layout Standard
31905 \begin_inset Note Greyedout
31908 \begin_layout Plain Layout
31914 It is not possible in \SpecialChar LyX
31915 to use the character ^ to get an up-arrow as described
31921 One instead uses a negative thin space followed by the command
31928 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
31939 \begin_layout Standard
31946 the command for equation
31947 \begin_inset space ~
31951 \begin_inset CommandInset ref
31953 reference "eq:chem-reaction"
31958 \begin_inset Newline newline
31966 \begin_inset space \textvisiblespace{}
31970 \begin_inset space \textvisiblespace{}
31974 \begin_inset space \textvisiblespace{}
31978 \begin_inset space \textvisiblespace{}
31982 \begin_inset space \textvisiblespace{}
31986 \begin_inset space \textvisiblespace{}
31992 \begin_layout Standard
31993 To create multiline chemical equations first a multiline formula is created
31995 \begin_inset CommandInset ref
31997 reference "sec:Multiline-Formulas"
32002 Afterwards the command
32008 is used in every small blue box of the formula.
32010 \begin_inset CommandInset ref
32012 reference "eq:TEOS-reaction-1"
32017 \begin_inset CommandInset ref
32019 reference "eq:TEOS-reaction-2"
32023 are an example of a multi-stage chemical reaction where every equation
32024 has its own number.
32025 \begin_inset Formula
32027 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32028 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32036 \begin_layout Standard
32047 package provides the command
32054 \begin_inset Index idx
32057 \begin_layout Plain Layout
32065 that has to be used for special cases.
32066 For more information about
32072 and more examples have a look at the documentation of
32077 \begin_inset CommandInset citation
32087 \begin_layout Section
32091 \begin_layout Standard
32093 supports two types of commutative diagrams:
32101 that are explained in the following.
32104 \begin_layout Subsection
32106 \begin_inset Index idx
32109 \begin_layout Plain Layout
32118 \begin_layout Standard
32119 Diagrams of this type visualize relations by vertical and horizontal lines
32121 \begin_inset Formula
32123 \begin{CD}A@>>>B@>>>C\\
32134 \begin_layout Standard
32135 To get them, the command
32140 \begin_inset Index idx
32143 \begin_layout Plain Layout
32153 is inserted to a formula.
32154 A blue box appears with two dashed lines where further commands can be
32159 arg "newline-insert newline"
32162 a new line is created.
32163 Horizontal relations are inserted in odd, vertical in even formula lines.
32166 \begin_layout Standard
32167 To create the relations there are the following commands:
32170 \begin_layout Itemize
32175 creates a left arrow,
32186 \begin_layout Itemize
32191 creates an up arrow,
32199 a vertical equal sign
32202 \begin_layout Itemize
32208 is a placeholder for non-existent relations
32211 \begin_layout Standard
32212 All arrows can be labeled as follows:
32215 \begin_layout Itemize
32216 If text inserted between the first and second < or >, resp., it is placed
32218 When it is inserted between the second and third one, it appears under
32222 \begin_layout Itemize
32223 When text for vertical arrows is inserted between the first and second A
32224 or V, resp., it is placed left beside the arrow.
32225 When it is inserted between the second and third one, it appears right
32227 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32231 \begin_layout Standard
32232 As example a diagram with all possible relations:
32235 \begin_layout Standard
32236 \begin_inset Formula
32238 \begin{CD}A@>j>>B@>>k>C@=F\\
32249 \begin_layout Standard
32250 The command for this is:
32251 \begin_inset Newline newline
32259 \begin_inset space \textvisiblespace{}
32262 A@>j>>B@>>k>C@=F Ctrl+Return
32263 \begin_inset Newline newline
32267 \begin_inset Phantom HPhantom
32270 \begin_layout Plain Layout
32276 \begin_inset space \textvisiblespace{}
32289 \begin_inset Formula $\to$
32295 \begin_inset Newline newline
32299 \begin_inset Phantom HPhantom
32302 \begin_layout Plain Layout
32308 \begin_inset space \textvisiblespace{}
32319 \begin_layout Subsection
32321 \begin_inset Index idx
32324 \begin_layout Plain Layout
32325 Diagrams ! xymatrix
32333 \begin_layout Standard
32334 To be able to use xymatrices, the \SpecialChar LaTeX
32340 A xymatrix is created by inserting the command
32347 Then you are able to add new matrix columns and rows like for normal matrices,
32349 \begin_inset CommandInset ref
32351 reference "sec:Matrices"
32358 \begin_layout Standard
32359 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32361 All possibilities to create commutative diagrams and decorations are explained
32366 that you find in the menu
32368 Help\SpecialChar menuseparator
32370 \begin_inset space ~
32378 \begin_layout Subsection
32384 \begin_inset Index idx
32387 \begin_layout Plain Layout
32396 \begin_layout Standard
32401 -diagrams, the \SpecialChar LaTeX
32411 -diagram is created by inserting the command
32418 Then you are able to add new matrix columns and rows like for normal matrices,
32420 \begin_inset CommandInset ref
32422 reference "sec:Matrices"
32429 \begin_layout Standard
32430 Examples how to create
32434 diagrams in \SpecialChar LyX
32437 Feynman-diagram manual
32439 that you find in the menu
32441 Help\SpecialChar menuseparator
32443 \begin_inset space ~
32451 \begin_layout Standard
32452 \begin_inset Newpage newpage
32458 \begin_layout Section
32459 User-defined Commands
32460 \begin_inset Index idx
32463 \begin_layout Plain Layout
32464 User-defined commands
32472 \begin_layout Standard
32473 \begin_inset Note Greyedout
32476 \begin_layout Plain Layout
32481 The names of user-defined commands and macros may only consist of Latin
32490 \begin_layout Subsection
32494 \begin_inset CommandInset label
32496 name "subsec:The-Command-newcommand"
32501 \begin_inset Index idx
32504 \begin_layout Plain Layout
32505 User-defined commands !
32513 \begin_inset Index idx
32516 \begin_layout Plain Layout
32527 \begin_layout Standard
32528 Many \SpecialChar LaTeX
32529 -commands are too long to be used frequently.
32530 But it is possible to define with the command
32536 new shorter commands.
32539 \begin_layout Standard
32540 The command scheme of
32549 \begin_layout Standard
32554 newcommand{new command name}[number of arguments][optional
32559 \begin_inset Newline newline
32563 \begin_inset Phantom HPhantom
32566 \begin_layout Plain Layout
32576 {command definition}
32579 \begin_layout Standard
32580 \begin_inset Note Greyedout
32583 \begin_layout Plain Layout
32588 Assure that the name of the new command is not already used in your document
32589 or by \SpecialChar LaTeX
32590 -packages that you use.
32591 When you for example define the command
32603 , you get an error message because
32609 is already defined as command for
32610 \begin_inset Quotes eld
32614 \begin_inset Formula $\le$
32618 \begin_inset Quotes erd
32629 \begin_layout Standard
32630 The number of arguments is an integer in the range 0
32631 \begin_inset space \thinspace{}
32635 \begin_inset space \thinspace{}
32638 9 and specifies how many arguments the new command should have.
32639 With the optional value a value for an optional argument can be predefined.
32640 When this is done, the
32648 rgument of the new command is automatically an optional one.
32651 \begin_layout Standard
32652 Here are some examples:
32655 \begin_layout Itemize
32656 To define the command
32668 , the \SpecialChar LaTeX
32670 \begin_inset VSpace medskip
32674 \begin_inset Newline newline
32688 \begin_layout Itemize
32689 To define the command
32701 , the argument (that should be underlined) must be taken into account.
32702 For this the preamble line is:
32703 \begin_inset VSpace medskip
32707 \begin_inset Newline newline
32721 \begin_inset VSpace medskip
32725 \begin_inset Newline newline
32732 acts as argument placeholder, the
32736 behind it denotes that it is the placeholder for the first argument.
32739 \begin_layout Itemize
32747 \begin_inset space \thinspace{}
32751 \begin_inset space \space{}
32761 \begin_inset VSpace medskip
32765 \begin_inset Newline newline
32776 framebox#1#2{$#3$}}
32779 \begin_inset VSpace medskip
32783 \begin_inset Newline newline
32786 The two Dollar signs creates the extra formula needed for
32793 \begin_inset CommandInset ref
32795 reference "subsec:Boxes-with-Frame"
32802 \begin_layout Itemize
32803 To create a new command for
32809 where the color for the box need not be specified, the argument for the
32810 color is defined optional:
32811 \begin_inset VSpace medskip
32815 \begin_inset Newline newline
32826 fcolorbox{#2}{#1}{$#3$}}
32829 \begin_inset VSpace medskip
32833 \begin_inset Newline newline
32836 When the color is not specified when using
32842 , the predefined color
32849 \begin_layout Standard
32850 A test of the new defined commands:
32853 \begin_layout Standard
32855 \begin_inset Tabular
32856 <lyxtabular version="3" rows="6" columns="2">
32857 <features booktabs="true" tabularvalignment="middle">
32858 <column alignment="center" valignment="top" width="0pt">
32859 <column alignment="center" valignment="top">
32861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32864 \begin_layout Plain Layout
32870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32873 \begin_layout Plain Layout
32881 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32884 \begin_layout Plain Layout
32888 \begin_inset space \textvisiblespace{}
32896 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32899 \begin_layout Plain Layout
32900 \begin_inset Formula $A\gr B$
32910 <cell alignment="center" valignment="top" leftline="true" usebox="none">
32913 \begin_layout Plain Layout
32921 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32924 \begin_layout Plain Layout
32925 \begin_inset Formula $\us{ABcd}$
32934 <row topspace="1mm">
32935 <cell alignment="center" valignment="top" usebox="none">
32938 \begin_layout Plain Layout
32942 \begin_inset Formula $\to$
32948 \begin_inset Formula $\to$
32956 \begin_inset space \textvisiblespace{}
32964 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
32967 \begin_layout Plain Layout
32968 \begin_inset Formula $\fb{[2cm]}{}{\int A=B}$
32977 <row topspace="1.5mm">
32978 <cell alignment="center" valignment="top" usebox="none">
32981 \begin_layout Plain Layout
32985 \begin_inset Formula $\to$
32993 \begin_inset space \textvisiblespace{}
33001 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
33004 \begin_layout Plain Layout
33005 \begin_inset Formula $\cb{red}{\int A=B}$
33014 <row topspace="1.5mm" bottomspace="1mm">
33015 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
33018 \begin_layout Plain Layout
33024 \begin_inset Formula $\to$
33032 \begin_inset space \textvisiblespace{}
33040 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
33043 \begin_layout Plain Layout
33044 \begin_inset Formula $\cb[green]{red}{\int A=B}$
33060 \begin_layout Subsection
33062 \begin_inset Index idx
33065 \begin_layout Plain Layout
33066 User-defined commands! Math macros
33072 \begin_inset Index idx
33075 \begin_layout Plain Layout
33084 \begin_layout Standard
33085 User-defined commands are especially convenient for complex expressions.
33086 When you are for example dealing with a document that has quadratic equations,
33087 the same solution type occurs several times.
33088 The general form of a quadratic equation is
33089 \begin_inset Formula
33091 0=\lambda^{2}+p\lambda+q
33096 The general form of the solution is
33097 \begin_inset Formula
33099 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33107 \begin_layout Standard
33108 To define a command for the solution formula where only the three parameters
33110 \begin_inset Formula $\lambda$
33114 \begin_inset Formula $p$
33118 \begin_inset Formula $q$
33121 need to be specified and the index of
33122 \begin_inset Formula $\lambda$
33125 can be given optionally, the \SpecialChar LaTeX
33127 \begin_inset Newline newline
33143 \begin_inset Newline newline
33147 \begin_inset Phantom HPhantom
33150 \begin_layout Plain Layout
33164 frac{#3^{2}}{4}-#4}}
33167 \begin_layout Standard
33168 To create with this the solution formula, the command
33169 \begin_inset Newline newline
33179 \begin_inset Formula $\to$
33185 \begin_inset Formula $\to$
33192 is inserted to a formula
33197 \begin_layout Standard
33198 The definition of the new command is unintuitive because one has to know
33199 the schemes of all used \SpecialChar LaTeX
33201 \begin_inset space \thinspace{}
33205 \begin_inset space \space{}
33208 that a fraction is inserted in \SpecialChar LaTeX
33213 frac{numerator}{denominator}
33216 Furthermore one can easily forget a brace in the definition and cannot
33217 see in \SpecialChar LyX
33218 what the new command is doing.
33219 To avoid these problems \SpecialChar LyX
33220 offers the possibility to use math macros instead
33230 \begin_layout Standard
33231 A math macro is created by using the menu
33233 Insert\SpecialChar menuseparator
33234 Math\SpecialChar menuseparator
33237 or the toolbar button
33240 arg "math-macro newmacroname_newcommand"
33244 The math macro toolbar appears together with the following box where the
33246 \begin_inset Newline newline
33250 \begin_inset space \hspace*{\fill}
33254 \begin_inset Graphics
33255 filename clipart/macrobox.png
33261 \begin_inset space \hspace*{\fill}
33265 \begin_inset Newline newline
33269 \begin_inset FormulaMacro
33270 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33275 newmacroname is the default name of the macro that should be changed to
33276 something sensible.
33277 The wanted formula is inserted in the first blue box.
33278 An argument placeholder is inserted with the command
33285 \begin_inset space \thinspace{}
33289 \begin_inset space \space{}
33298 or by using the macro toolbar button
33301 arg "math-macro-add-param"
33305 Argument placeholders are displayed red.
33307 \begin_inset space ~
33310 arguments are possible.
33311 Optional arguments are created with the toolbar button
33314 arg "math-macro-add-optional-param"
33318 The first non-optional argument can be transformed to an optional one with
33322 arg "math-macro-make-optional"
33326 In the second blue box the appearance of the macro in \SpecialChar LyX
33328 Normally you want to see it as it is defined, so the box is kept empty.
33329 But when you have created a macro that needs lot of space on the screen,
33330 you can insert in the box for example
33331 \begin_inset Newline newline
33361 \begin_inset Newline newline
33366 For the macro only the arguments with the macro name in front of them will
33367 then be displayed in \SpecialChar LyX
33368 , leading to a better overview.
33369 The formula appears in the output as defined in the first box.
33370 \begin_inset Newline newline
33373 The appearance of macros in formulas can furthermore be changed for single
33374 macros by setting the cursor in the macro and using the menu
33376 View\SpecialChar menuseparator
33378 \begin_inset space ~
33382 \begin_inset space ~
33390 \begin_layout Standard
33391 To use a macro, the macro name is inserted as command to a formula, in our
33399 Our macro looks in \SpecialChar LyX
33401 \begin_inset Newline newline
33405 \begin_inset space \hspace*{\fill}
33409 \begin_inset Graphics
33410 filename clipart/macrouse.png
33416 \begin_inset space \hspace*{\fill}
33420 \begin_inset Newline newline
33423 Here is our macro example with the arguments
33424 \begin_inset Formula $x$
33428 \begin_inset Formula $\ln(x)$
33432 \begin_inset Formula $B$
33438 \begin_layout Standard
33439 \begin_inset Formula
33449 \begin_layout Standard
33453 Tools\SpecialChar menuseparator
33454 Preferences\SpecialChar menuseparator
33455 Editing\SpecialChar menuseparator
33458 different styles to edit macros.
33459 To find the style that suits you the most, choose a style and set the cursor
33460 in a macro formula to see the difference.
33463 \begin_layout Standard
33464 A math macro is transformed internally to a
33470 command when exporting the document.
33477 command is not placed in the \SpecialChar LaTeX
33478 -preamble, therefore macros can only be used
33479 in formulas that are in the document below the macro definition box.
33482 \begin_layout Standard
33483 Math macros can also be directly created from a
33490 When writing for example the command
33493 \begin_inset Newline newline
33502 xleftarrow[#2]{#1}}
33503 \begin_inset Newline newline
33508 in \SpecialChar LyX
33509 as normal text, highlighting it completely and using then the shortcut
33514 , the command will be transformed to a math macro.
33515 Using this method you need to be careful that the
33521 command is typed correctly, otherwise you get a faulty macro leading to
33526 \begin_layout Standard
33527 Math macros currently have the problem that further formulas in macro definition
33528 s are handled wrongly.
33529 Therefore the example
33536 \begin_inset CommandInset ref
33538 reference "subsec:The-Command-newcommand"
33542 cannot be created as macro.
33545 \begin_layout Standard
33546 When the cursor is in a macro definition box, you will see the macro toolbar
33547 in \SpecialChar LyX
33551 \begin_layout Standard
33552 \begin_inset VSpace defskip
33558 \begin_layout Standard
33559 \begin_inset Graphics
33560 filename clipart/MacroToolbar.png
33565 \begin_inset Index idx
33568 \begin_layout Plain Layout
33577 \begin_layout Standard
33578 \begin_inset VSpace defskip
33584 \begin_layout Standard
33585 The macro toolbar contains from left to right the following buttons:
33588 \begin_layout Standard
33589 \begin_inset VSpace defskip
33595 \begin_layout Standard
33596 \begin_inset Tabular
33597 <lyxtabular version="3" rows="9" columns="2">
33598 <features islongtable="true" longtabularalignment="center">
33599 <column alignment="left" valignment="top">
33600 <column alignment="left" valignment="top" width="85col%">
33601 <row interlinespace="2.5mm">
33602 <cell alignment="center" valignment="top" usebox="none">
33605 \begin_layout Plain Layout
33608 arg "math-macro-remove-param"
33616 <cell alignment="center" valignment="top" usebox="none">
33619 \begin_layout Plain Layout
33622 Edit\SpecialChar menuseparator
33623 Math\SpecialChar menuseparator
33625 \begin_inset space ~
33628 Definition\SpecialChar menuseparator
33629 Remove Last Argument
33635 <row interlinespace="2.5mm">
33636 <cell alignment="center" valignment="top" usebox="none">
33639 \begin_layout Plain Layout
33642 arg "math-macro-add-param"
33650 <cell alignment="center" valignment="top" usebox="none">
33653 \begin_layout Plain Layout
33656 Edit\SpecialChar menuseparator
33657 Math\SpecialChar menuseparator
33659 \begin_inset space ~
33662 Definition\SpecialChar menuseparator
33669 <row interlinespace="2.5mm">
33670 <cell alignment="center" valignment="top" usebox="none">
33673 \begin_layout Plain Layout
33676 arg "math-macro-make-optional"
33684 <cell alignment="center" valignment="top" usebox="none">
33687 \begin_layout Plain Layout
33690 Edit\SpecialChar menuseparator
33691 Math\SpecialChar menuseparator
33693 \begin_inset space ~
33696 Definition\SpecialChar menuseparator
33697 Transform First Non-Optional to
33698 \begin_inset Newline newline
33702 \begin_inset Phantom HPhantom
33705 \begin_layout Plain Layout
33708 Edit\SpecialChar menuseparator
33709 Math\SpecialChar menuseparator
33711 \begin_inset space ~
33714 Definition\SpecialChar menuseparator
33726 <row interlinespace="2.5mm">
33727 <cell alignment="center" valignment="top" usebox="none">
33730 \begin_layout Plain Layout
33733 arg "math-macro-make-nonoptional"
33741 <cell alignment="center" valignment="top" usebox="none">
33744 \begin_layout Plain Layout
33747 Edit\SpecialChar menuseparator
33748 Math\SpecialChar menuseparator
33750 \begin_inset space ~
33753 Definition\SpecialChar menuseparator
33754 Transform Last Optional to
33755 \begin_inset Newline newline
33759 \begin_inset Phantom HPhantom
33762 \begin_layout Plain Layout
33765 Edit\SpecialChar menuseparator
33766 Math\SpecialChar menuseparator
33768 \begin_inset space ~
33771 Definition\SpecialChar menuseparator
33777 Non-Optional Argument
33783 <row interlinespace="2.5mm">
33784 <cell alignment="center" valignment="top" usebox="none">
33787 \begin_layout Plain Layout
33790 arg "math-macro-remove-optional-param"
33798 <cell alignment="center" valignment="top" usebox="none">
33801 \begin_layout Plain Layout
33804 Edit\SpecialChar menuseparator
33805 Math\SpecialChar menuseparator
33807 \begin_inset space ~
33810 Definition\SpecialChar menuseparator
33811 Remove Optional Argument
33817 <row interlinespace="2.5mm">
33818 <cell alignment="center" valignment="top" usebox="none">
33821 \begin_layout Plain Layout
33824 arg "math-macro-add-optional-param"
33832 <cell alignment="center" valignment="top" usebox="none">
33835 \begin_layout Plain Layout
33838 Edit\SpecialChar menuseparator
33839 Math\SpecialChar menuseparator
33841 \begin_inset space ~
33844 Definition\SpecialChar menuseparator
33845 Insert Optional Argument
33851 <row interlinespace="2.5mm">
33852 <cell alignment="center" valignment="top" usebox="none">
33855 \begin_layout Plain Layout
33858 arg "math-macro-remove-greedy-param"
33866 <cell alignment="center" valignment="top" usebox="none">
33869 \begin_layout Plain Layout
33872 Edit\SpecialChar menuseparator
33873 Math\SpecialChar menuseparator
33875 \begin_inset space ~
33878 Definition\SpecialChar menuseparator
33879 Remove Last Argument
33880 \begin_inset Newline newline
33884 \begin_inset Phantom HPhantom
33887 \begin_layout Plain Layout
33890 Edit\SpecialChar menuseparator
33891 Math\SpecialChar menuseparator
33893 \begin_inset space ~
33896 Definition\SpecialChar menuseparator
33902 Spitting Out To The Right
33908 <row interlinespace="2.5mm">
33909 <cell alignment="center" valignment="top" usebox="none">
33912 \begin_layout Plain Layout
33915 arg "math-macro-append-greedy-param"
33923 <cell alignment="center" valignment="top" usebox="none">
33926 \begin_layout Plain Layout
33929 Edit\SpecialChar menuseparator
33930 Math\SpecialChar menuseparator
33932 \begin_inset space ~
33935 Definition\SpecialChar menuseparator
33937 \begin_inset Newline newline
33941 \begin_inset Phantom HPhantom
33944 \begin_layout Plain Layout
33947 Edit\SpecialChar menuseparator
33948 Math\SpecialChar menuseparator
33950 \begin_inset space ~
33953 Definition\SpecialChar menuseparator
33959 Eating From The Right
33965 <row interlinespace="2.5mm">
33966 <cell alignment="center" valignment="top" usebox="none">
33969 \begin_layout Plain Layout
33972 arg "math-macro-add-greedy-optional-param"
33980 <cell alignment="center" valignment="top" usebox="none">
33983 \begin_layout Plain Layout
33986 Edit\SpecialChar menuseparator
33987 Math\SpecialChar menuseparator
33989 \begin_inset space ~
33992 Definition\SpecialChar menuseparator
33993 Append Optional Argument
33994 \begin_inset Newline newline
33998 \begin_inset Phantom HPhantom
34001 \begin_layout Plain Layout
34004 Edit\SpecialChar menuseparator
34005 Math\SpecialChar menuseparator
34007 \begin_inset space ~
34010 Definition\SpecialChar menuseparator
34016 Eating From The Right
34029 \begin_layout Section
34030 Computer Algebra Systems
34033 \begin_layout Standard
34035 offers the exchange between mathematical expressions written in \SpecialChar LyX
34037 editor and external applications or user defined scripts.
34038 Currently supported applications are
34055 Note that the set of supported mathematical constructs is limited only
34056 to very simple cases.
34059 \begin_layout Subsection
34063 \begin_layout Standard
34064 Write some expression in a formula, go to the
34066 Edit\SpecialChar menuseparator
34067 Math\SpecialChar menuseparator
34068 Use Computer Algebra System
34070 menu and choose the application you have installed on the computer.
34071 After that the result of computation should show on the right side of the
34072 expression together with the
34073 \begin_inset Quotes eld
34077 \begin_inset Quotes erd
34083 \begin_layout Standard
34084 Here are few simple examples (with results from
34088 ) to show what kind of computations can be performed:
34091 \begin_layout Itemize
34092 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34098 \begin_layout Itemize
34099 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34105 \begin_layout Itemize
34106 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34112 \begin_layout Itemize
34113 \begin_inset Formula $\int\left(\frac{1}{1+x^{3}}\right)dx=-\frac{\log\left(x^{2}-x+1\right)}{6}+\frac{\arctan\left(\frac{2\,x-1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\log\left(x+1\right)}{3}$
34117 \begin_inset Newline newline
34121 \begin_inset Note Greyedout
34124 \begin_layout Plain Layout
34129 One needs to use proper delimiter insets
34130 \begin_inset Formula $\left(\right)$
34133 instead of simple '(' ')' characters.
34141 \begin_layout Itemize
34142 \begin_inset Formula $\det\left[\begin{array}{ccc}
34146 \end{array}\right]=-56$
34152 \begin_layout Itemize
34153 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34159 \begin_layout Itemize
34160 \begin_inset Formula $powerseries\left(-\log\left(5-x\right),x,1\right)=\sum_{{\mathit{i}_{2}}=0}^{\infty}{\frac{4^{-{\mathit{i}_{2}}-1}\,\left(x-1\right)^{{\mathit{i}_{2}}+1}}{{\mathit{i}_{2}}+1}}-\log4$
34166 \begin_layout Itemize
34167 \begin_inset Formula $solve\left(x_{1}+y_{1}^{3}=y_{1}+x_{1}^{2},x_{1}\right)=\left[x_{1}=-\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}-1}{2},x_{1}=\frac{\sqrt{4\,y_{1}^{3}-4\,y_{1}+1}+1}{2}\right]$
34173 \begin_layout Subsection
34177 \begin_layout Standard
34178 Currently there is no keyboard shortcut for calling the algebra applications.
34179 One can easily bind a shortcut to the
34193 \begin_inset space \thinspace{}
34197 \begin_inset space \space{}
34204 key inside the math editor.
34209 one would use this shortcut definition command:
34212 \begin_layout Standard
34215 command-alternatives paragraph-break;math-extern maxima
34218 \begin_layout Section
34220 \begin_inset Index idx
34223 \begin_layout Plain Layout
34232 \begin_layout Subsection
34234 \begin_inset Index idx
34237 \begin_layout Plain Layout
34246 \begin_layout Standard
34247 Negative numbers often look ugly in formulas because the minus sign before
34248 the number is set with the same length as the minus operator sign.
34249 When writing the negative number in normal text, the minus sign appears
34253 \begin_layout Standard
34254 Thus, the problem disappears when converting the minus sign to mathematical
34258 \begin_layout Standard
34259 An example to visualize the problem:
34262 \begin_layout Standard
34264 \begin_inset Tabular
34265 <lyxtabular version="3" rows="3" columns="2">
34266 <features booktabs="true" tabularvalignment="middle">
34267 <column alignment="right" valignment="top" width="0pt">
34268 <column alignment="left" valignment="top">
34270 <cell alignment="right" valignment="top" topline="true" leftline="true" usebox="none">
34273 \begin_layout Plain Layout
34279 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34282 \begin_layout Plain Layout
34290 <cell alignment="right" valignment="top" leftline="true" usebox="none">
34293 \begin_layout Plain Layout
34299 <cell alignment="center" valignment="top" rightline="true" usebox="none">
34302 \begin_layout Plain Layout
34303 \begin_inset Formula $x=-2$
34313 <cell alignment="right" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34316 \begin_layout Plain Layout
34322 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34325 \begin_layout Plain Layout
34326 \begin_inset Formula $x=\textrm{-}2$
34342 \begin_layout Subsection
34343 Comma as decimal Separator
34344 \begin_inset Index idx
34347 \begin_layout Plain Layout
34356 \begin_layout Standard
34357 In \SpecialChar LaTeX
34358 a comma inside a formula is used, according to the English convention,
34359 as number group separator.
34360 So there will be space added behind all commas in formulas.
34363 \begin_layout Standard
34364 To avoid this, the comma is highlighted and changed to mathematical text
34374 \begin_layout Standard
34375 To use all formula commas in the document as decimal separator, the file
34384 \begin_layout Plain Layout
34389 is part of the \SpecialChar LaTeX
34395 \begin_inset Index idx
34398 \begin_layout Plain Layout
34403 \begin_layout Plain Layout
34423 \begin_inset Index idx
34426 \begin_layout Plain Layout
34432 is loaded with the \SpecialChar LaTeX
34436 \begin_layout Standard
34444 \begin_layout Subsection
34446 \begin_inset CommandInset label
34448 name "subsec:Physical-Vectors"
34453 \begin_inset Index idx
34456 \begin_layout Plain Layout
34465 \begin_layout Standard
34466 Predefined vectors are offered by the \SpecialChar LaTeX
34472 \begin_inset Index idx
34475 \begin_layout Plain Layout
34481 that is loaded with the \SpecialChar LaTeX
34485 \begin_layout Standard
34493 \begin_layout Standard
34497 \begin_layout Plain Layout
34507 \begin_inset Note Note
34510 \begin_layout Plain Layout
34511 The following table will only be displayed when the \SpecialChar LaTeX
34524 \begin_layout Standard
34525 The following commands are defined:
34528 \begin_layout Standard
34530 \begin_inset Tabular
34531 <lyxtabular version="3" rows="4" columns="2">
34532 <features booktabs="true" tabularvalignment="middle">
34533 <column alignment="center" valignment="top" width="0pt">
34534 <column alignment="center" valignment="top">
34536 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34539 \begin_layout Plain Layout
34545 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34548 \begin_layout Plain Layout
34556 <cell alignment="center" valignment="top" usebox="none">
34559 \begin_layout Plain Layout
34569 <cell alignment="center" valignment="top" usebox="none">
34572 \begin_layout Plain Layout
34573 \begin_inset Formula $\Bra{\psi}$
34583 <cell alignment="center" valignment="top" usebox="none">
34586 \begin_layout Plain Layout
34596 <cell alignment="center" valignment="top" usebox="none">
34599 \begin_layout Plain Layout
34600 \begin_inset Formula $\Ket{\psi}$
34610 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34613 \begin_layout Plain Layout
34625 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34628 \begin_layout Plain Layout
34629 \begin_inset Formula $\Braket{\psi|\phi}$
34645 \begin_layout Standard
34652 assures that all vertical bars are set in the size of the surrounding brackets:
34653 \begin_inset Formula
34655 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
34664 \begin_layout Plain Layout
34674 \begin_inset Note Note
34677 \begin_layout Plain Layout
34678 The following will be displayed when the \SpecialChar LaTeX
34691 \begin_layout Standard
34692 You need to install the \SpecialChar LaTeX
34697 to see the rest of this subsection in the output.
34700 \begin_layout Standard
34704 \begin_layout Plain Layout
34716 \begin_layout Standard
34723 can also be achieved using the command
34729 , that is described in
34730 \begin_inset CommandInset ref
34732 reference "subsec:Automatic-Bracket-Size"
34739 \begin_layout Subsection
34740 Self-defined Fractions
34741 \begin_inset CommandInset label
34743 name "subsec:Self-defined-Fractions"
34748 \begin_inset Index idx
34751 \begin_layout Plain Layout
34752 Fractions ! self-defined
34760 \begin_layout Standard
34761 To define custom commands for fractions, the command
34768 \begin_inset Index idx
34771 \begin_layout Plain Layout
34778 \begin_layout Plain Layout
34792 is used in the following scheme:
34795 \begin_layout Standard
34808 bracket}{fraction bar thickness}{style}
34809 \begin_inset Newline newline
34813 \begin_inset Phantom HPhantom
34816 \begin_layout Plain Layout
34826 {numerator}{denominator}
34829 \begin_layout Standard
34830 The style is a number in the range of 0
34831 \begin_inset space \thinspace{}
34835 \begin_inset space \thinspace{}
34841 \begin_layout Standard
34843 \begin_inset Tabular
34844 <lyxtabular version="3" rows="5" columns="2">
34845 <features booktabs="true" tabularvalignment="middle">
34846 <column alignment="center" valignment="top" width="0pt">
34847 <column alignment="center" valignment="top">
34849 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34852 \begin_layout Plain Layout
34858 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
34861 \begin_layout Plain Layout
34869 <cell alignment="center" valignment="top" usebox="none">
34872 \begin_layout Plain Layout
34878 <cell alignment="center" valignment="top" usebox="none">
34881 \begin_layout Plain Layout
34882 display style formula
34889 <cell alignment="center" valignment="top" usebox="none">
34892 \begin_layout Plain Layout
34898 <cell alignment="center" valignment="top" usebox="none">
34901 \begin_layout Plain Layout
34909 <cell alignment="center" valignment="top" usebox="none">
34912 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" usebox="none">
34921 \begin_layout Plain Layout
34929 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34932 \begin_layout Plain Layout
34938 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
34941 \begin_layout Plain Layout
34955 \begin_layout Standard
34956 When no style is given, the size is adjusted to the surrounding environment
34957 like for the command
34966 \begin_layout Standard
34967 When no fraction bar thickness is given, the predefined value of 0.4
34968 \begin_inset space \thinspace{}
34974 \begin_layout Standard
34975 \begin_inset VSpace medskip
34978 For example, the commands
34991 \begin_inset CommandInset ref
34993 reference "subsec:Fractions"
34997 are defined with the commands
35000 \begin_layout Standard
35009 genfrac{}{}{}{0}{#1}{#2}}
35012 \begin_layout Standard
35016 \begin_layout Standard
35025 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35028 \begin_layout Standard
35029 \begin_inset VSpace medskip
35032 To define a fraction where the fraction bar thickness can be given as optional
35033 argument, the following line is inserted to the \SpecialChar LaTeX
35037 \begin_layout Standard
35046 genfrac{}{}{#1}{}{#2}{#3}}
35049 \begin_layout Standard
35051 \begin_inset Formula
35053 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35054 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35059 As one can see, the distance of the numerator and the denominator to the
35060 fraction bar is round about three times the bar thickness.
35063 \begin_layout Standard
35064 \begin_inset Newpage newpage
35070 \begin_layout Subsection
35072 \begin_inset Index idx
35075 \begin_layout Plain Layout
35084 \begin_layout Standard
35085 There are four ways to cancel formulas or parts of formulas:
35088 \begin_layout Standard
35092 \begin_layout Plain Layout
35102 \begin_inset Note Note
35105 \begin_layout Plain Layout
35106 The following table will only be displayed when the \SpecialChar LaTeX
35119 \begin_layout Standard
35121 \begin_inset Tabular
35122 <lyxtabular version="3" rows="5" columns="2">
35123 <features booktabs="true" tabularvalignment="middle">
35124 <column alignment="center" valignment="top" width="0pt">
35125 <column alignment="center" valignment="top">
35127 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35130 \begin_layout Plain Layout
35136 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35139 \begin_layout Plain Layout
35147 <cell alignment="center" valignment="top" usebox="none">
35150 \begin_layout Plain Layout
35154 \begin_inset space \textvisiblespace{}
35160 \begin_inset space \textvisiblespace{}
35168 <cell alignment="center" valignment="top" usebox="none">
35171 \begin_layout Plain Layout
35172 \begin_inset Formula $\cancel{\int A=B}$
35181 <row topspace="1.5mm">
35182 <cell alignment="center" valignment="top" usebox="none">
35185 \begin_layout Plain Layout
35189 \begin_inset space \textvisiblespace{}
35195 \begin_inset space \textvisiblespace{}
35203 <cell alignment="center" valignment="top" usebox="none">
35206 \begin_layout Plain Layout
35207 \begin_inset Formula $\bcancel{\int A=B}$
35216 <row topspace="1.5mm">
35217 <cell alignment="center" valignment="top" usebox="none">
35220 \begin_layout Plain Layout
35224 \begin_inset space \textvisiblespace{}
35230 \begin_inset space \textvisiblespace{}
35238 <cell alignment="center" valignment="top" usebox="none">
35241 \begin_layout Plain Layout
35242 \begin_inset Formula $\xcancel{\int A=B}$
35252 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35255 \begin_layout Plain Layout
35259 \begin_inset space \textvisiblespace{}
35265 \begin_inset space \textvisiblespace{}
35269 \begin_inset Formula $\to$
35277 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
35280 \begin_layout Plain Layout
35281 \begin_inset Formula $\cancelto{1}{\int A=B}\hspace{3mm}$
35297 \begin_layout Standard
35304 is especially suitable to visualize the reduction of fractions within formulas:
35305 \begin_inset Formula
35307 \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}}}
35315 \begin_layout Standard
35316 To change the size of
35323 \begin_inset Quotes eld
35327 \begin_inset Quotes erd
35330 value one can add the \SpecialChar LaTeX
35334 \begin_layout Standard
35339 PassOptionsToPackage{option}{cancel}
35342 \begin_layout Standard
35351 which leads to the same size as for the canceled value, or
35355 which makes is it a bit smaller than normal.
35358 \begin_layout Standard
35359 To color the cancellation bar one adds this command as \SpecialChar TeX
35363 \begin_layout Standard
35375 \begin_layout Standard
35380 can be replaced by a color of your choice.
35383 \begin_layout Standard
35387 \begin_layout Plain Layout
35403 \begin_layout Standard
35404 \begin_inset Formula
35406 \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}}}
35414 \begin_layout Standard
35418 \begin_layout Plain Layout
35432 \begin_inset Note Note
35435 \begin_layout Plain Layout
35444 \begin_layout Standard
35445 For further customizations, see the documentation of the package
35450 \begin_inset CommandInset citation
35458 \begin_inset Index idx
35461 \begin_layout Plain Layout
35470 \begin_layout Standard
35474 \begin_layout Plain Layout
35484 \begin_inset Note Note
35487 \begin_layout Plain Layout
35488 The following will be displayed when the \SpecialChar LaTeX
35501 \begin_layout Standard
35502 You need to install the \SpecialChar LaTeX
35507 to see the rest of this subsection in the output.
35510 \begin_layout Standard
35514 \begin_layout Plain Layout
35526 \begin_layout Subsection
35527 Formulas in Section Headings
35528 \begin_inset CommandInset label
35530 name "subsec:Formulas-in-Section"
35535 \begin_inset Index idx
35538 \begin_layout Plain Layout
35539 Formula ! in section headings
35547 \begin_layout Standard
35548 When formulas are used in section headings, the following has to be taken
35552 \begin_layout Standard
35553 \begin_inset Note Greyedout
35556 \begin_layout Plain Layout
35562 \begin_inset Index idx
35565 \begin_layout Plain Layout
35566 Packages ! hyperref
35571 support is enabled in the document settings dialog under
35574 \begin_inset space ~
35579 , PDF-bookmarks are created for every section heading in the table of contents.
35580 If a section heading contains formulas, they are incorrectly displayed
35581 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35590 \begin_layout Standard
35591 Both problems can be solved by inserting at the end of the section heading
35592 a short title with the menu
35594 Insert\SpecialChar menuseparator
35596 \begin_inset space ~
35602 Short titles are used as alternative for multiline section headings to
35603 keep the table of contents clearly arranged.
35604 Only the short title appears in the table of contents and therefore also
35605 in the PDF-bookmark.
35608 \begin_layout Standard
35609 When formulas should be used in the table of contents but
35613 is used, one can use the following command in \SpecialChar TeX
35617 \begin_layout Standard
35622 texorpdfstring{part}{alternative}
35623 \begin_inset Index idx
35626 \begin_layout Plain Layout
35637 \begin_layout Standard
35638 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35639 This can be characters, formulas, footnotes, but also cross-references.
35640 The alternative is used instead of the part for the bookmark.
35643 \begin_layout Standard
35644 Here are two example headings:
35645 \begin_inset VSpace -3mm
35652 \begin_layout Plain Layout
35664 \begin_layout Subsubsection
35665 Heading without formula in table of contents
35666 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35670 \begin_inset Argument 1
35673 \begin_layout Plain Layout
35674 Heading without formula in table of contents
35682 \begin_layout Subsubsection
35683 Heading with formula in table of contents
35687 \begin_layout Plain Layout
35697 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35704 \begin_layout Plain Layout
35714 \begin_layout Standard
35718 \begin_layout Plain Layout
35727 In the first heading a short title was used, in the second one
35736 \begin_layout Standard
35737 To get the same formatting as for the other headings, the complete heading
35746 \begin_layout Plain Layout
35748 \begin_inset CommandInset ref
35750 reference "subsec:Bold-Formulas"
35762 \begin_layout Subsection
35763 Formulas in multi-column Text
35764 \begin_inset Index idx
35767 \begin_layout Plain Layout
35768 Formula ! in multi-column text
35776 \begin_layout Standard
35777 Formulas in multi-column text are often too wide to fit into a column and
35778 thus need to be set over the whole page width.
35779 This is done by using the \SpecialChar LaTeX
35788 \begin_layout Plain Layout
35793 is part of every \SpecialChar LaTeX
35794 standard installation.
35800 \begin_inset Index idx
35803 \begin_layout Plain Layout
35804 Packages ! multicol
35809 , that is loaded with the \SpecialChar LaTeX
35813 \begin_layout Standard
35818 usepackage{multicol}
35821 \begin_layout Standard
35822 \begin_inset Note Greyedout
35825 \begin_layout Plain Layout
35826 Note that in this case the setting
35829 \begin_inset space ~
35836 Document\SpecialChar menuseparator
35842 \begin_inset space ~
35862 \begin_layout Standard
35863 Before the multi-column text the command
35866 \begin_layout Standard
35871 begin{multicols}{column number}
35874 \begin_layout Standard
35875 is written in \SpecialChar TeX
35877 The column number is a number in the range of 2
35878 \begin_inset space \thinspace{}
35882 \begin_inset space \thinspace{}
35886 Before the formula the multi-column text is ended by inserting the command
35889 \begin_layout Standard
35897 \begin_layout Standard
35898 in \SpecialChar TeX
35902 \begin_layout Standard
35903 Due to the command some space is automatically added before the formula.
35905 \begin_inset space \thinspace{}
35908 mm vertical space is inserted before the formula.
35909 When the formula style
35915 \begin_layout Plain Layout
35917 \begin_inset CommandInset ref
35919 reference "sec:Formula-Styles"
35931 \begin_inset space \thinspace{}
35934 mm space is inserted instead.
35937 \begin_layout Standard
35938 As example a multi-column text with a displayed formula:
35941 \begin_layout Standard
35947 \begin_layout Plain Layout
35951 begin{multicols}{2}
35956 Das Spektrum wird fouriertransformiert.
35957 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35958 , Lösungsmittel) zu trennen.
35959 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35960 nun das Aussehen des Ausgangssignals.
35961 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35962 über alle Phasen integrieren muss.
35964 \begin_inset Formula $S$
35967 unser normiertes Ausgangssignal und
35968 \begin_inset Formula $P$
35971 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35975 \begin_layout Plain Layout
35985 \begin_inset VSpace -6mm
35989 \begin_inset Formula
35991 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36000 \begin_layout Plain Layout
36004 begin{multicols}{2}
36010 \begin_inset Formula $S_{0}$
36013 das Signal ohne Gradient ist und die Normierungsbedingung
36014 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36018 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36020 \begin_inset Formula $\nicefrac{\pi}{2}$
36024 \begin_inset space \thinspace{}
36027 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36028 das Signal zusätzlich abschwächt.
36029 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36031 \begin_inset Formula $T_{2}$
36037 \begin_layout Standard
36043 \begin_layout Plain Layout
36055 \begin_layout Subsection
36056 Formulas with Description of Variables
36057 \begin_inset Index idx
36060 \begin_layout Plain Layout
36061 Formula ! with description of variables
36069 \begin_layout Standard
36070 To describe variables within a formula, like in formula
36071 \begin_inset CommandInset ref
36073 reference "eq:within"
36082 \begin_inset Formula $n$
36086 \begin_inset space ~
36089 matrix is used with left aligned columns for the
36090 \begin_inset Formula $n$
36097 \begin_layout Plain Layout
36099 \begin_inset CommandInset ref
36101 reference "sec:Matrices"
36110 To set the description in a smaller size, before the matrix e.
36111 \begin_inset space \thinspace{}
36115 \begin_inset space \space{}
36128 \begin_layout Plain Layout
36130 \begin_inset CommandInset ref
36132 reference "subsec:Font-Sizes"
36144 \begin_layout Standard
36145 When the formula style
36151 \begin_layout Plain Layout
36153 \begin_inset CommandInset ref
36155 reference "sec:Formula-Styles"
36176 \begin_layout Plain Layout
36183 only works in formulas with the style
36188 \begin_inset CommandInset ref
36190 reference "subsec:Variable-Space"
36199 is inserted before and after the matrix to have the same separation of
36200 the matrix from the equation and the side margin.
36203 \begin_layout Standard
36204 When the formula style
36208 is used, the method described in
36209 \begin_inset CommandInset ref
36211 reference "subsec:Flalign-Environment"
36215 is used to indent formulas.
36217 \begin_inset CommandInset ref
36219 reference "eq:within"
36223 consists of five columns where in the first two columns contain the equation,
36224 the third the matrix and the last one an empty \SpecialChar TeX
36226 \begin_inset Formula
36228 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36229 \rho & \textrm{density}\\
36230 V & \textrm{volume}\\
36231 g & \textrm{gravitational acceleration}
36232 \end{array} & & {}\label{eq:within}
36240 \begin_layout Subsection
36241 Upright small Greek Letters
36242 \begin_inset CommandInset label
36244 name "subsec:Upright-small-Greek"
36249 \begin_inset Index idx
36252 \begin_layout Plain Layout
36253 Greek letters ! upright
36261 \begin_layout Standard
36262 Most of the math fonts only provide italic small Greek letters.
36263 But for symbols of elementary particles like pions and neutrinos, upright
36264 Greek letters are needed.
36273 \begin_layout Plain Layout
36278 is part of the \SpecialChar LaTeX
36284 \begin_inset Index idx
36287 \begin_layout Plain Layout
36292 \begin_layout Plain Layout
36312 \begin_inset Index idx
36315 \begin_layout Plain Layout
36321 that is loaded with the \SpecialChar LaTeX
36325 \begin_layout Standard
36330 usepackage{upgreek}
36333 \begin_layout Standard
36339 \begin_layout Plain Layout
36349 \begin_inset Note Note
36352 \begin_layout Plain Layout
36353 The following table will only be displayed when the \SpecialChar LaTeX
36363 They are created when the command for a small Greek letter is started with
36369 For example the command
36376 \begin_inset Formula $\uptau$
36382 \begin_layout Standard
36383 With these commands reactions of elementary particles can be typeset:
36384 \begin_inset Formula
36386 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36394 \begin_layout Standard
36395 The upright letters are more bold and wider than the italic ones.
36396 They should therefore not be used for units like
36397 \begin_inset Quotes eld
36401 \begin_inset Quotes erd
36407 \begin_layout Standard
36411 \begin_layout Plain Layout
36421 \begin_inset Note Note
36424 \begin_layout Plain Layout
36425 The following will be displayed when the \SpecialChar LaTeX
36438 \begin_layout Standard
36439 You need to install the \SpecialChar LaTeX
36444 to see the rest of this subsection in the output.
36447 \begin_layout Standard
36451 \begin_layout Plain Layout
36463 \begin_layout Subsection
36464 Text Characters in Formulas
36465 \begin_inset Index idx
36468 \begin_layout Plain Layout
36477 \begin_layout Standard
36478 In some cases you might want to insert text characters directly into formulas.
36479 When for example the centered dot · is often used in formulas like
36480 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36483 , one would have to insert the command
36493 \begin_layout Plain Layout
36495 \begin_inset CommandInset ref
36497 reference "subsec:Binary-Operators"
36506 all the time, because this character is defined in all encodings as text
36508 But the encoding can be changed by this \SpecialChar LaTeX
36512 \begin_layout Standard
36517 Declare Inputtext{183}{
36527 f\SpecialChar ligaturebreak
36531 \begin_layout Standard
36532 The character encoding (menu
36534 Document\SpecialChar menuseparator
36535 Settings\SpecialChar menuseparator
36538 ) specifies what character appears when a keyboard key is pressed.
36539 When the key for the character '·' is pressed, internally the command
36546 But this command is not available in a formula so that you would get \SpecialChar LaTeX
36548 With the changed encoding the right command is chosen automatically, depending
36549 on if the character was inserted into a formula or not.
36552 \begin_layout Standard
36553 The encoding of several characters is saved in definition files.
36554 For example the encoding
36558 is defined in the file
36562 which is in the installation folder of \SpecialChar LaTeX
36564 Encodings should only be changed via the \SpecialChar LaTeX
36565 -preamble and not in the definition
36567 Otherwise documents could not be edited by other \SpecialChar LyX
36568 users working on other
36572 \begin_layout Standard
36573 \begin_inset VSpace medskip
36576 Besides the centered dot, in this document the degree sign ° is defined
36577 with the following \SpecialChar LaTeX
36578 -preamble line so that it can be directly inserted into
36582 \begin_layout Standard
36587 DeclareInputtext{176}{
36597 f\SpecialChar ligaturebreak
36601 \begin_layout Subsection
36603 -comments in formulas
36604 \begin_inset Index idx
36607 \begin_layout Plain Layout
36617 \begin_layout Standard
36618 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
36620 code of your file with the menu
36622 Insert\SpecialChar menuseparator
36623 Note\SpecialChar menuseparator
36627 This is not possible in a formula but you can insert \SpecialChar LaTeX
36632 \begin_layout Standard
36640 \begin_layout Standard
36641 This creates a box in which you can write your comment.
36642 Due to a bug in \SpecialChar LyX
36647 \begin_layout Plain Layout
36648 \begin_inset CommandInset href
36650 name "LyX-bug #9002"
36651 target "http://www.lyx.org/trac/ticket/9002"
36661 you cannot write normal text inside the comment, even when you use mathematical
36662 text, you will see its \SpecialChar LaTeX
36663 -commands in the \SpecialChar LaTeX
36665 \begin_inset Newline newline
36668 This a formula with a \SpecialChar LaTeX
36670 \begin_inset Formula
36672 A=B%\text{This is the comment}
36680 \begin_layout Standard
36681 \begin_inset Newpage newpage
36687 \begin_layout Section
36690 \begin_inset Index idx
36693 \begin_layout Plain Layout
36702 \begin_layout Standard
36703 This section is a summary of the most important typographic rules, listed
36708 \begin_layout Plain Layout
36709 This collection was partly taken from the German semi-official dictionary
36711 \begin_inset Quotes eld
36715 \begin_inset Quotes erd
36719 \begin_inset CommandInset citation
36726 that lists some of the ISO rules.
36727 More rules are listed in
36728 \begin_inset CommandInset citation
36743 \begin_layout Itemize
36752 \begin_layout Plain Layout
36753 done with font styles, see
36754 \begin_inset CommandInset ref
36756 reference "subsec:Font-Styles"
36765 , no matter if they appear in italic text: 30
36766 \begin_inset space \thinspace{}
36770 \begin_inset Newline newline
36773 Between the value and the unit is the smallest space, see
36774 \begin_inset CommandInset ref
36776 reference "subsec:Predefined-Space"
36781 \begin_inset Newline newline
36784 This convention is automatically fulfilled when the command
36791 When it is entered to a formula, two boxes appear.
36792 In the first one the value is inserted, in the second one the unit, and
36794 \begin_inset Formula $\unit[30]{km/h}$
36798 \begin_inset space \thinspace{}
36808 is not a real \SpecialChar LaTeX
36809 command but the command
36815 , therefore you cannot use it in \SpecialChar TeX
36819 \begin_layout Itemize
36820 Percent and perthousand signs are set like physical units:
36821 \begin_inset Newline newline
36825 \begin_inset space \thinspace{}
36831 \begin_layout Itemize
36832 The degree sign follows directly on the value: 15°, but not when it is used
36834 \begin_inset space \thinspace{}
36840 \begin_layout Itemize
36841 In numbers with more than four digits the smallest space is inserted before
36842 every third digit to group them:
36852 \begin_inset space \thinspace{}
36856 \begin_inset space \thinspace{}
36862 \begin_layout Itemize
36863 For dimensions like 120×90×40
36864 \begin_inset space \thinspace{}
36867 cm the multiplication sign
36868 \begin_inset Quotes eld
36872 \begin_inset Quotes erd
36876 It is available either via the command
36884 Insert\SpecialChar menuseparator
36885 Special Character\SpecialChar menuseparator
36891 \begin_layout Itemize
36892 Functions with names consisting of several letters are set upright to avoid
36894 \begin_inset CommandInset ref
36896 reference "subsec:Predefined-Functions"
36903 \begin_layout Itemize
36904 Indices consisting of several letters, are set upright:
36905 \begin_inset Formula $E_{\mathrm{kin}}$
36909 \begin_inset Newline newline
36912 Components of matrices are set italic:
36913 \begin_inset Formula $\hat{H}_{kl}$
36919 \begin_layout Itemize
36920 The differentiation/integration operator 'd', the Euler's number 'e' and
36921 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36925 \begin_layout Itemize
36926 The character that denotes a
36930 transformation is inserted either by the command
36935 \begin_inset space \textvisiblespace{}
36942 Insert\SpecialChar menuseparator
36943 Special Character\SpecialChar menuseparator
36944 Symbols\SpecialChar menuseparator
36946 \begin_inset space ~
36952 \begin_inset Formula $\mathscr{F}$
36958 \begin_layout Standard
36959 \begin_inset Newpage newpage
36965 \begin_layout Section
36967 \begin_inset Index idx
36970 \begin_layout Plain Layout
36979 \begin_layout Standard
36980 Some characters and symbols can be created with several commands.
36981 Here is a list of the synonym commands:
36984 \begin_layout Standard
36985 \begin_inset VSpace bigskip
36989 \begin_inset space \hfill{}
36993 \begin_inset Tabular
36994 <lyxtabular version="3" rows="12" columns="2">
36995 <features booktabs="true" tabularvalignment="middle">
36996 <column alignment="center" valignment="top" width="0pt">
36997 <column alignment="center" valignment="top" width="0pt">
36999 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37002 \begin_layout Plain Layout
37008 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37011 \begin_layout Plain Layout
37019 <cell alignment="center" valignment="top" usebox="none">
37022 \begin_layout Plain Layout
37030 <cell alignment="center" valignment="top" usebox="none">
37033 \begin_layout Plain Layout
37041 <cell alignment="center" valignment="top" usebox="none">
37044 \begin_layout Plain Layout
37052 <cell alignment="center" valignment="top" usebox="none">
37055 \begin_layout Plain Layout
37065 <cell alignment="center" valignment="top" usebox="none">
37068 \begin_layout Plain Layout
37076 <cell alignment="center" valignment="top" usebox="none">
37079 \begin_layout Plain Layout
37089 <cell alignment="center" valignment="top" usebox="none">
37092 \begin_layout Plain Layout
37100 <cell alignment="center" valignment="top" usebox="none">
37103 \begin_layout Plain Layout
37111 <cell alignment="center" valignment="top" usebox="none">
37114 \begin_layout Plain Layout
37122 <cell alignment="center" valignment="top" usebox="none">
37125 \begin_layout Plain Layout
37133 <cell alignment="center" valignment="top" usebox="none">
37136 \begin_layout Plain Layout
37144 <cell alignment="center" valignment="top" usebox="none">
37147 \begin_layout Plain Layout
37157 <cell alignment="center" valignment="top" usebox="none">
37160 \begin_layout Plain Layout
37168 <cell alignment="center" valignment="top" usebox="none">
37171 \begin_layout Plain Layout
37181 <cell alignment="center" valignment="top" usebox="none">
37184 \begin_layout Plain Layout
37192 <cell alignment="center" valignment="top" usebox="none">
37195 \begin_layout Plain Layout
37205 <cell alignment="center" valignment="top" usebox="none">
37208 \begin_layout Plain Layout
37216 <cell alignment="center" valignment="top" usebox="none">
37219 \begin_layout Plain Layout
37229 <cell alignment="center" valignment="top" usebox="none">
37232 \begin_layout Plain Layout
37240 <cell alignment="center" valignment="top" usebox="none">
37243 \begin_layout Plain Layout
37251 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37254 \begin_layout Plain Layout
37262 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37265 \begin_layout Plain Layout
37277 \begin_inset space \hfill{}
37281 \begin_inset Tabular
37282 <lyxtabular version="3" rows="12" columns="2">
37283 <features booktabs="true" tabularvalignment="middle">
37284 <column alignment="center" valignment="top" width="0pt">
37285 <column alignment="center" valignment="top" width="0pt">
37287 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37290 \begin_layout Plain Layout
37296 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
37299 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" usebox="none">
37310 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" usebox="none">
37321 \begin_layout Plain Layout
37333 <cell alignment="center" valignment="top" usebox="none">
37336 \begin_layout Plain Layout
37344 <cell alignment="center" valignment="top" usebox="none">
37347 \begin_layout Plain Layout
37357 <cell alignment="center" valignment="top" usebox="none">
37360 \begin_layout Plain Layout
37368 <cell alignment="center" valignment="top" usebox="none">
37371 \begin_layout Plain Layout
37381 <cell alignment="center" valignment="top" usebox="none">
37384 \begin_layout Plain Layout
37392 <cell alignment="center" valignment="top" usebox="none">
37395 \begin_layout Plain Layout
37403 <cell alignment="center" valignment="top" usebox="none">
37406 \begin_layout Plain Layout
37414 <cell alignment="center" valignment="top" usebox="none">
37417 \begin_layout Plain Layout
37425 <cell alignment="center" valignment="top" usebox="none">
37428 \begin_layout Plain Layout
37436 <cell alignment="center" valignment="top" usebox="none">
37439 \begin_layout Plain Layout
37449 <cell alignment="center" valignment="top" usebox="none">
37452 \begin_layout Plain Layout
37460 <cell alignment="center" valignment="top" usebox="none">
37463 \begin_layout Plain Layout
37473 <cell alignment="center" valignment="top" usebox="none">
37476 \begin_layout Plain Layout
37484 <cell alignment="center" valignment="top" usebox="none">
37487 \begin_layout Plain Layout
37497 <cell alignment="center" valignment="top" usebox="none">
37500 \begin_layout Plain Layout
37508 <cell alignment="center" valignment="top" usebox="none">
37511 \begin_layout Plain Layout
37521 <cell alignment="center" valignment="top" usebox="none">
37524 \begin_layout Plain Layout
37532 <cell alignment="center" valignment="top" usebox="none">
37535 \begin_layout Plain Layout
37545 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37548 \begin_layout Plain Layout
37556 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
37559 \begin_layout Plain Layout
37573 \begin_inset space \hfill{}
37579 \begin_layout Standard
37580 \begin_inset Newpage newpage
37586 \begin_layout Bibliography
37587 \begin_inset CommandInset bibitem
37588 LatexCommand bibitem
37601 The \SpecialChar LaTeX
37605 Addison Wesley, 2004
37608 \begin_layout Bibliography
37609 \begin_inset CommandInset bibitem
37610 LatexCommand bibitem
37617 \begin_inset CommandInset href
37620 target "https://www.tug.org/~hvoss/PDF/mathmode.pdf"
37625 of \SpecialChar LaTeX
37629 \begin_layout Bibliography
37630 \begin_inset CommandInset bibitem
37631 LatexCommand bibitem
37638 \begin_inset CommandInset href
37641 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
37650 \begin_layout Plain Layout
37659 -\SpecialChar LaTeX
37663 \begin_layout Bibliography
37664 \begin_inset CommandInset bibitem
37665 LatexCommand bibitem
37672 \begin_inset CommandInset href
37675 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37680 of all symbols available with \SpecialChar LaTeX
37684 \begin_layout Bibliography
37685 \begin_inset CommandInset bibitem
37686 LatexCommand bibitem
37693 \begin_inset CommandInset href
37695 name "Documentation"
37696 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
37701 of the \SpecialChar LaTeX
37707 \begin_inset Index idx
37710 \begin_layout Plain Layout
37719 \begin_layout Bibliography
37720 \begin_inset CommandInset bibitem
37721 LatexCommand bibitem
37728 \begin_inset CommandInset href
37730 name "Documentation"
37731 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37736 of the \SpecialChar LaTeX
37742 \begin_inset Index idx
37745 \begin_layout Plain Layout
37746 Packages ! hyperref
37754 \begin_layout Bibliography
37755 \begin_inset CommandInset bibitem
37756 LatexCommand bibitem
37763 \begin_inset CommandInset href
37765 name "Documentation"
37766 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37771 of the \SpecialChar LaTeX
37777 \begin_inset Index idx
37780 \begin_layout Plain Layout
37789 \begin_layout Bibliography
37790 \begin_inset CommandInset bibitem
37791 LatexCommand bibitem
37803 Auflage, Duden 2001
37806 \begin_layout Bibliography
37807 \begin_inset CommandInset bibitem
37808 LatexCommand bibitem
37815 \begin_inset CommandInset href
37818 target "http://physics.nist.gov/Pubs/SP811/sec11.html"
37823 for reviewing manuscripts
37826 \begin_layout Standard
37827 \begin_inset CommandInset index_print
37828 LatexCommand printindex