1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
8 % DO NOT ALTER THIS PREAMBLE!!!
10 % This preamble is designed to ensure that the file prints
11 % out as advertised. If you mess with this preamble,
12 % parts of this document may not print out as expected. If you
13 % have problems LaTeXing this file, please contact
14 % the documentation team
15 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % solves the following problem:
28 % If the dection number consits of too many numerals the section heading
29 % will be printed in the TOC without a space between it and the section number.
30 % As solution more space between the number and the heading is inserted:
31 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
32 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
34 % increase link area for cross-references and autoname them,
35 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
36 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
37 \@ifpackageloaded{babel}{
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41 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
42 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
46 % don't load packages twice
47 % see first footnote in sec. 9.3
48 \@ifundefined{textcolor}{\usepackage{color}}{}
50 % the pages of the TOC are numbered roman
51 % and a PDF-bookmark for the TOC is added
53 \let\myTOC\tableofcontents
54 \renewcommand{\tableofcontents}{%
56 \pdfbookmark[1]{\contentsname}{}
59 \pagenumbering{arabic}}
61 % add 0.5 mm vertical space for table rows
62 \@ifundefined{extrarowheight} {\usepackage{array}}{}
63 \setlength{\extrarowheight}{0.5mm}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % makes caption labels bold
70 \setkomafont{captionlabel}{\bfseries}
72 % enables calculation of values
75 % for multiple columns used in sec. 24.7
81 % for the Fourier transformation symbol
84 % define a color, used in sec.9.3
85 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
87 % declare operators (see sec. 10.4 and sec. 15.2)
88 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
89 \DeclareMathOperator{\sgn}{sgn}
91 % example definitions for sec. 20.1
92 \newcommand{\gr}{\Longrightarrow}
93 \newcommand{\us}[1]{\underline{#1}}
94 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
95 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
96 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
98 % example macro from sec. 19.4
99 %\def\tagform@#1{\maketag@@@{|#1|}}
102 % ------------------------------------
103 % used to check for needed LaTeX packages
106 % check for package undertilde
107 % used for the command \utilde
108 \newboolean{undertilde}
109 \IfFileExists{undertilde.sty}
110 {\usepackage{undertilde}
111 \setboolean{undertilde}{true}}
112 {\setboolean{undertilde}{false}}
114 % check for package eurosym
115 % used for the Euro symbol
117 \IfFileExists{eurosym.sty}
118 {\usepackage[gennarrow]{eurosym}
119 \setboolean{eurosym}{true}}
120 {\setboolean{eurosym}{false}}
122 % check for package braket
123 % used for physical vectors
125 \IfFileExists{braket.sty}
127 \setboolean{braket}{true}}
128 {\setboolean{braket}{false}}
130 % check for package cancel
132 \IfFileExists{cancel.sty}
134 \setboolean{cancel}{true}}
135 {\setboolean{cancel}{false}}
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
145 \use_default_options false
146 \maintain_unincluded_children false
148 \language_package default
153 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
162 \default_output_format default
164 \bibtex_command default
165 \index_command default
169 \pdf_title "LyX's Math Manual"
170 \pdf_author "LyX Team, Uwe Stöhr"
171 \pdf_subject "LyX-documentation about math"
172 \pdf_keywords "LyX, Mathed"
174 \pdf_bookmarksnumbered true
175 \pdf_bookmarksopen true
176 \pdf_bookmarksopenlevel 1
177 \pdf_breaklinks false
181 \pdf_pdfusetitle false
182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
185 \use_package amsmath 2
186 \use_package amssymb 2
187 \use_package cancel 0
189 \use_package mathdots 1
190 \use_package mathtools 2
191 \use_package mhchem 1
192 \use_package stackrel 0
193 \use_package stmaryrd 0
194 \use_package undertilde 0
196 \cite_engine_type default
200 \paperorientation portrait
204 \notefontcolor #0000ff
211 \paragraph_separation skip
213 \quotes_language english
216 \paperpagestyle plain
220 \tracking_changes false
221 \output_changes false
224 \html_be_strict false
231 's detailed Math manual
235 by the \SpecialChar LyX
240 \begin_layout Plain Layout
242 If you have comments or error corrections, please send them to the \SpecialChar LyX
247 \begin_inset CommandInset href
249 name "lyx-docs@lists.lyx.org"
250 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
261 \begin_inset Note Note
264 \begin_layout Plain Layout
271 \begin_inset Newline newline
275 \begin_inset Newline newline
283 \begin_layout Standard
284 \begin_inset CommandInset toc
285 LatexCommand tableofcontents
292 \begin_layout Standard
293 \begin_inset Note Note
296 \begin_layout Plain Layout
297 To export this document to PDF, PS or DVI the \SpecialChar LaTeX
300 braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
307 If they are not installed the document can be exported anyway but the sections
308 where the packages are required will not appear in the output.
313 ; if it is not installed, this file cannot be exported.
316 \begin_layout Plain Layout
317 The latest PDF-version of this document can be found here:
318 \begin_inset Newline newline
323 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
331 \begin_layout Standard
332 \begin_inset Newpage newpage
338 \begin_layout Section
342 \begin_layout Standard
343 This document explains \SpecialChar LyX
344 's math features and is furthermore a collection
345 of \SpecialChar LaTeX
346 -commands used for mathematical characters and constructs.
347 The explanations are designed for the usage of commands.
348 It is therefore required that you have read the section
359 \begin_layout Standard
360 Most of the characters and many constructs explained in this manual are
361 also accessible via the menu
365 \SpecialChar menuseparator
381 But everybody who has to write lots of formulas will notice that it is
382 much faster to use commands instead of the math toolbar.
383 Therefore this manual is focused on commands but also mentions the correspondin
384 g toolbar buttons when available.
387 \begin_layout Standard
388 If not specially mentioned the commands are only available within formulas.
389 To be able to use all commands explained in this document, the option
393 must be checked in the document settings (menu
395 Document\SpecialChar menuseparator
396 Settings\SpecialChar menuseparator
407 \begin_layout Plain Layout
410 Use AMS math package automatically
416 \begin_layout Plain Layout
425 -math when math constructs are found that are supported by \SpecialChar LyX
434 \begin_layout Standard
435 This document doesn't list all
439 \begin_layout Plain Layout
452 \begin_layout Plain Layout
457 \begin_layout Plain Layout
466 -math commands is in the file
469 \begin_inset CommandInset href
472 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
478 , which is part of every \SpecialChar LaTeX
479 standard installation.
484 for lucidity reasons.
487 \begin_layout Section
491 \begin_layout Standard
492 To create an inline formula
493 \begin_inset Index idx
496 \begin_layout Plain Layout
502 that is embedded into a text line, use one of the shortcuts
508 or the toolbar button
515 \begin_inset Newline newline
518 To create a display style formula
519 \begin_inset Index idx
522 \begin_layout Plain Layout
523 Formula ! display style
528 which will appear bigger, has a different format, and will be in a separate
529 paragraph, use one of these shortcuts:
538 \begin_layout Standard
539 To change a display style formula to an inline formula, set the cursor into
540 the formula and use one of the shortcuts
548 Edit\SpecialChar menuseparator
549 Math\SpecialChar menuseparator
553 The same way is used to change an inline formula to a display style formula.
556 \begin_layout Standard
557 To display parts of an inline formula in the size of a display style formula,
565 \begin_inset Index idx
568 \begin_layout Plain Layout
577 Then a new blue box appears in which the desired formula part is inserted.
580 \begin_layout Standard
581 Only inline formulas are allowed inside tables.
584 \begin_layout Standard
589 can be turned on in the menu
591 View\SpecialChar menuseparator
595 When you click there on
596 \begin_inset Quotes eld
600 \begin_inset Quotes erd
603 the toolbar will be shown permanently at the bottom; this state is visualized
608 menu with a checkmark.
609 When you click in this state again on
610 \begin_inset Quotes eld
614 \begin_inset Quotes erd
625 is only shown when the cursor is within a formula; this state is visualized
626 by the renaming of the menu entry from
627 \begin_inset Quotes eld
631 \begin_inset Quotes erd
635 \begin_inset Quotes eld
643 \begin_inset Quotes erd
649 \begin_layout Standard
652 \begin_inset Index idx
655 \begin_layout Plain Layout
662 is invoked by pressing the toolbar button
670 Insert\SpecialChar menuseparator
682 \begin_layout Standard
683 To change the \SpecialChar LaTeX
685 \begin_inset Index idx
688 \begin_layout Plain Layout
697 Document\SpecialChar menuseparator
698 Settings\SpecialChar menuseparator
708 \begin_layout Standard
709 To edit matrices, case differentiations and multiline formulas subsequently,
712 Edit\SpecialChar menuseparator
717 Edit\SpecialChar menuseparator
719 \begin_inset space \thinspace{}
723 \begin_inset space \thinspace{}
733 When lines and columns are swapped via the menu, the column or line where
734 the cursor is in is exchanged with the column to the right or the line
736 Is the cursor in the last column or row, the exchange is done with the
737 column to the left or the line above.
740 \begin_layout Standard
741 To write text in formulas
745 \begin_layout Plain Layout
746 For multiline formulas the command
753 \begin_inset CommandInset ref
755 reference "subsec:Text-in-multiline"
769 \begin_inset Index idx
772 \begin_layout Plain Layout
779 \begin_inset Index idx
782 \begin_layout Plain Layout
789 This mode is invoked with the shortcut
795 or by the insertion of the command
802 \begin_inset Index idx
805 \begin_layout Plain Layout
814 The text appears black in \SpecialChar LyX
815 and can therefore be distinguished from the
816 other formula parts which appear blue.
817 In the output mathematical text is set upright, in contrary to other formula
821 \begin_layout Subsection*
825 \begin_layout Standard
826 Most of the \SpecialChar LaTeX
827 -commands for math constructs have the following scheme:
830 \begin_layout Standard
846 \begin_layout Standard
847 A command always starts with a backslash
848 \begin_inset Quotes gld
858 \begin_inset Quotes grd
862 To omit optional arguments, also omit the associated brackets.
863 The braces around the required arguments are named in this document as
866 \begin_inset Index idx
869 \begin_layout Plain Layout
877 If you add in a formula a left brace to a command name, \SpecialChar LyX
879 creates a \SpecialChar TeX
881 In all other cases \SpecialChar TeX
882 braces are created in formulas with the command
890 braces appear red in \SpecialChar LyX
891 , in contrary to normal braces which appear blue.
893 mode no command is needed to get \SpecialChar TeX
896 braces don't appear in the output.
899 \begin_layout Standard
900 When commands without arguments, like commands for symbols are entered in
902 mode, a space character must
906 be behind the command to end it.
907 This space doesn't appear in the output.
908 When the space should appear in the output, the space must be followed
909 by a protected space in normal text.
912 \begin_layout Standard
913 A protected space is inserted with
916 arg "command-alternatives space-insert protected ; math-space"
922 \begin_layout Subsection*
923 \begin_inset Newpage newpage
929 \begin_layout Itemize
931 \begin_inset space \textvisiblespace{}
934 denotes a space character to be input.
937 \begin_layout Itemize
939 \begin_inset Formula $\to$
942 denotes the usage of the corresponding arrow key on the keyboard.
947 key can often be used instead of
948 \begin_inset Formula $\to$
952 \begin_inset Formula $\downarrow$
960 \begin_inset Formula $\leftarrow$
964 \begin_inset Formula $\uparrow$
970 \begin_layout Subsection*
974 \begin_layout Standard
976 \begin_inset Float table
982 \begin_layout Plain Layout
984 \begin_inset Caption Standard
986 \begin_layout Plain Layout
987 \begin_inset CommandInset label
989 name "tab:Available-units"
1001 \begin_layout Plain Layout
1003 \begin_inset Tabular
1004 <lyxtabular version="3" rows="13" columns="2">
1005 <features booktabs="true" tabularvalignment="middle">
1006 <column alignment="center" valignment="top">
1007 <column alignment="center" valignment="top" width="0pt">
1009 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1012 \begin_layout Plain Layout
1018 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1021 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1032 \begin_layout Plain Layout
1038 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1041 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1052 \begin_layout Plain Layout
1058 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1061 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1072 \begin_layout Plain Layout
1078 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1081 \begin_layout Plain Layout
1083 \begin_inset space \thinspace{}
1087 \begin_inset space \thinspace{}
1097 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1100 \begin_layout Plain Layout
1106 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1109 \begin_layout Plain Layout
1111 \begin_inset space \thinspace{}
1115 \begin_inset space \thinspace{}
1125 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1128 \begin_layout Plain Layout
1134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1137 \begin_layout Plain Layout
1139 \begin_inset space \thinspace{}
1143 \begin_inset space \thinspace{}
1153 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1156 \begin_layout Plain Layout
1162 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1165 \begin_layout Plain Layout
1167 \begin_inset space \thinspace{}
1171 \begin_inset space \thinspace{}
1181 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1184 \begin_layout Plain Layout
1190 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1193 \begin_layout Plain Layout
1195 \begin_inset space \thinspace{}
1199 \begin_inset space \thinspace{}
1209 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1212 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1221 \begin_layout Plain Layout
1223 \begin_inset space \thinspace{}
1227 \begin_inset Formula $\approx$
1231 \begin_inset space \thinspace{}
1241 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1244 \begin_layout Plain Layout
1250 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1253 \begin_layout Plain Layout
1255 \begin_inset space \thinspace{}
1259 \begin_inset space \thinspace{}
1269 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1272 \begin_layout Plain Layout
1278 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1281 \begin_layout Plain Layout
1285 \begin_inset Quotes eld
1291 \begin_inset Quotes erd
1301 <cell alignment="center" valignment="top" leftline="true" usebox="none">
1304 \begin_layout Plain Layout
1310 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
1313 \begin_layout Plain Layout
1315 \begin_inset Quotes eld
1323 \begin_inset Quotes erd
1333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
1336 \begin_layout Plain Layout
1342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
1345 \begin_layout Plain Layout
1347 \begin_inset space \thinspace{}
1351 \begin_inset Formula $\nicefrac{1}{18}$
1355 \begin_inset space \thinspace{}
1376 \begin_layout Standard
1377 \begin_inset Newpage newpage
1383 \begin_layout Section
1387 \begin_layout Subsection
1389 \begin_inset Index idx
1392 \begin_layout Plain Layout
1399 \begin_inset Index idx
1402 \begin_layout Plain Layout
1409 \begin_inset Index idx
1412 \begin_layout Plain Layout
1417 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1441 \begin_inset Index idx
1444 \begin_layout Plain Layout
1449 \begin_layout Plain Layout
1460 \begin_layout Plain Layout
1475 \begin_layout Standard
1476 Indices are created with an underscore
1477 \begin_inset Quotes eld
1481 \begin_inset Quotes erd
1484 or via the math toolbar button
1487 arg "math-subscript"
1490 , exponents with a caret
1491 \begin_inset Quotes eld
1495 \begin_inset Quotes erd
1498 or via the math toolbar button
1501 arg "math-superscript"
1505 \begin_inset Separator parbreak
1511 \begin_layout Standard
1513 \begin_inset Tabular
1514 <lyxtabular version="3" rows="4" columns="2">
1515 <features booktabs="true" tabularvalignment="middle">
1516 <column alignment="center" valignment="top" width="0pt">
1517 <column alignment="center" valignment="top" width="0pt">
1519 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1522 \begin_layout Plain Layout
1528 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1531 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1548 <cell alignment="center" valignment="top" usebox="none">
1551 \begin_layout Plain Layout
1552 \begin_inset Formula $B_{V}$
1561 <row topspace="1.5mm">
1562 <cell alignment="center" valignment="top" usebox="none">
1565 \begin_layout Plain Layout
1571 <cell alignment="center" valignment="top" usebox="none">
1574 \begin_layout Plain Layout
1575 \begin_inset Formula $B^{V}$
1584 <row topspace="1.5mm">
1585 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1588 \begin_layout Plain Layout
1590 \begin_inset space \textvisiblespace{}
1598 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $B^{A}$
1618 \begin_layout Standard
1619 As the caret is in some languages an accent, vowels will be accentuated
1620 in this case and not set as exponents
1624 \begin_layout Plain Layout
1625 Depending on the used keyboard settings this can also happen for characters
1632 To get exponents in this case, press
1636 after the caret as in the last example.
1639 \begin_layout Subsection
1641 \begin_inset CommandInset label
1643 name "subsec:Fractions"
1648 \begin_inset Index idx
1651 \begin_layout Plain Layout
1660 \begin_layout Standard
1661 Fractions are generated with the command
1668 \begin_inset Index idx
1671 \begin_layout Plain Layout
1679 or via the math toolbar button
1682 arg "math-insert \\frac"
1686 The font size is adjusted automatically, depending on whether the fraction
1687 is in an inline or display style formula.
1688 With the math toolbar button
1691 arg "math-insert \\frac-square"
1694 you can select different fraction types.
1697 \begin_layout Standard
1705 \begin_inset Index idx
1708 \begin_layout Plain Layout
1716 a fraction can be created that always has the size of a display style formula.
1724 \begin_inset Index idx
1727 \begin_layout Plain Layout
1735 the fraction appears always with the size of an inline formula.
1739 \begin_layout Standard
1740 A line with the fraction
1741 \begin_inset Formula $\frac{1}{2}$
1744 that was created with the command
1753 \begin_layout Standard
1754 A line with the fraction
1755 \begin_inset Formula $\dfrac{1}{2}$
1758 that was created with the command
1765 \begin_inset Separator parbreak
1771 \begin_layout Standard
1773 \begin_inset Tabular
1774 <lyxtabular version="3" rows="4" columns="2">
1775 <features booktabs="true" tabularvalignment="middle">
1776 <column alignment="center" valignment="top" width="0pt">
1777 <column alignment="center" valignment="top" width="0pt">
1779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1782 \begin_layout Plain Layout
1788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
1791 \begin_layout Plain Layout
1798 <row topspace="1.5mm">
1799 <cell alignment="center" valignment="top" usebox="none">
1802 \begin_layout Plain Layout
1806 \begin_inset space \textvisiblespace{}
1810 \begin_inset Formula $\downarrow$
1818 <cell alignment="center" valignment="top" usebox="none">
1821 \begin_layout Plain Layout
1822 \begin_inset Formula $\frac{A}{B}$
1831 <row topspace="2mm">
1832 <cell alignment="center" valignment="top" usebox="none">
1835 \begin_layout Plain Layout
1839 \begin_inset space \textvisiblespace{}
1843 \begin_inset Formula $\downarrow$
1851 <cell alignment="center" valignment="top" usebox="none">
1854 \begin_layout Plain Layout
1855 \begin_inset Formula $\dfrac{A}{B}$
1864 <row topspace="2mm" bottomspace="1mm">
1865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1868 \begin_layout Plain Layout
1872 \begin_inset space \textvisiblespace{}
1878 \begin_inset space \textvisiblespace{}
1882 \begin_inset Formula $\downarrow$
1886 \begin_inset Formula $\downarrow\downarrow$
1894 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1897 \begin_layout Plain Layout
1898 \begin_inset Formula $\dfrac{e^{\frac{1}{2}}}{3}$
1914 \begin_layout Standard
1915 \begin_inset VSpace bigskip
1919 \begin_inset Newpage newpage
1922 For nested fractions the command
1929 \begin_inset Index idx
1932 \begin_layout Plain Layout
1942 \begin_inset VSpace -3mm
1948 \begin_layout Standard
1949 \begin_inset Formula
1951 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
1952 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
1960 \begin_layout Standard
1961 The command for the example above is:
1964 \begin_layout Standard
1970 \begin_inset space \textvisiblespace{}
1974 \begin_inset Formula $\downarrow$
1980 \begin_inset space \textvisiblespace{}
1986 \begin_inset space \textvisiblespace{}
1990 \begin_inset Formula $\downarrow$
1994 \begin_inset Formula $\downarrow$
2000 \begin_layout Standard
2001 \begin_inset VSpace medskip
2007 \begin_layout Standard
2014 sets the fraction always in the size of a displayed formula, also when
2015 it is part of another fraction.
2018 \begin_layout Standard
2019 It is possible to specify the alignment of the numerator.
2026 is used to left align it, the command
2039 centers the numerator.
2040 These fractions demonstrate the different alignments:
2043 \begin_layout Standard
2046 \begin_inset Formula
2048 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2056 \begin_layout Standard
2057 \begin_inset Note Greyedout
2060 \begin_layout Plain Layout
2077 are no real \SpecialChar LaTeX
2078 commands but represent the command
2082 cfrac[alignment]{numerator}{denominator}
2085 Therefore you cannot use them in \SpecialChar TeX
2094 \begin_layout Standard
2095 \begin_inset VSpace medskip
2098 It is often advantageous to combine
2111 \begin_inset Formula
2113 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2121 \begin_layout Standard
2122 For inline fractions with a sloped fraction stroke you can use the command
2130 \begin_inset Index idx
2133 \begin_layout Plain Layout
2142 \begin_inset Formula $\nicefrac{5}{31}$
2152 \begin_inset Index idx
2155 \begin_layout Plain Layout
2164 \begin_inset Formula $\unitfrac{5}{31}$
2167 There is furthermore the command
2173 that offers to write a fraction in combination with a number:
2174 \begin_inset Formula $\unitfrac[2]{1}{3}$
2180 \begin_layout Standard
2181 \begin_inset Note Greyedout
2184 \begin_layout Plain Layout
2195 is not a real \SpecialChar LaTeX
2196 command but the command
2197 \begin_inset Newline newline
2204 unitfrac[number]{numerator}{denominator}
2207 Therefore you cannot use it in \SpecialChar TeX
2216 \begin_layout Standard
2217 How to define own fractions where the fraction stroke can be changed, is
2219 \begin_inset CommandInset ref
2221 reference "subsec:Self-defined-Fractions"
2228 \begin_layout Standard
2229 Multiline fractions are explained in
2230 \begin_inset CommandInset ref
2232 reference "subsec:Multiline-Fractions"
2239 \begin_layout Subsection
2241 \begin_inset Index idx
2244 \begin_layout Plain Layout
2253 \begin_layout Standard
2254 Square roots are created with
2261 \begin_inset Index idx
2264 \begin_layout Plain Layout
2272 or the math toolbar button
2275 arg "math-insert \\sqrt"
2278 , all other roots with the command
2285 \begin_inset Index idx
2288 \begin_layout Plain Layout
2296 or with the math toolbar button
2299 arg "math-insert \\root"
2303 \begin_inset Separator parbreak
2309 \begin_layout Standard
2311 \begin_inset Tabular
2312 <lyxtabular version="3" rows="3" columns="2">
2313 <features booktabs="true" tabularvalignment="middle">
2314 <column alignment="center" valignment="top" width="0pt">
2315 <column alignment="center" valignment="top" width="0pt">
2317 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2320 \begin_layout Plain Layout
2326 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2329 \begin_layout Plain Layout
2336 <row topspace="1mm">
2337 <cell alignment="center" valignment="top" usebox="none">
2340 \begin_layout Plain Layout
2344 \begin_inset space \textvisiblespace{}
2352 <cell alignment="center" valignment="top" usebox="none">
2355 \begin_layout Plain Layout
2356 \begin_inset Formula $\sqrt{A-B}$
2365 <row topspace="1mm">
2366 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2369 \begin_layout Plain Layout
2373 \begin_inset space \textvisiblespace{}
2377 \begin_inset Formula $\downarrow$
2385 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2388 \begin_layout Plain Layout
2389 \begin_inset Formula $\sqrt[3]{A-B}$
2405 \begin_layout Standard
2406 A square root can also be created with
2412 when the root index field is left empty.
2415 \begin_layout Standard
2416 With certain indices the distance to the root is too small, like in this
2418 \begin_inset Formula $\sqrt[\beta]{B}$
2422 \begin_inset Newline newline
2426 \begin_inset Formula $\beta$
2430 To avoid this, the commands
2437 \begin_inset Index idx
2440 \begin_layout Plain Layout
2455 \begin_inset Index idx
2458 \begin_layout Plain Layout
2466 are used with the following scheme:
2469 \begin_layout Standard
2483 \begin_layout Standard
2484 Distance is the number of Big Points (unit bp;
2485 \begin_inset Formula $\mathrm{72\,bp=1\,inch}$
2488 ), that the index should be moved to the left or top, resp..
2489 The commands are written to the index.
2490 This way the command
2491 \begin_inset Newline newline
2501 \begin_inset Formula $\to$
2507 \begin_inset Formula $\to$
2513 \begin_inset space \textvisiblespace{}
2517 \begin_inset Formula $\to$
2521 \begin_inset Newline newline
2526 produces a correct typeset formula:
2527 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2533 \begin_layout Subsection
2534 Binomial Coefficients
2535 \begin_inset Index idx
2538 \begin_layout Plain Layout
2539 Binomial coefficients
2547 \begin_layout Standard
2548 Binomial coefficients are inserted with the command
2555 \begin_inset Index idx
2558 \begin_layout Plain Layout
2566 or with the submenu of the math toolbar button
2569 arg "math-insert \\frac-square"
2585 there are the commands
2592 \begin_inset Index idx
2595 \begin_layout Plain Layout
2610 \begin_inset Index idx
2613 \begin_layout Plain Layout
2622 For other brackets around binomial coeficients there are the commands
2629 \begin_inset Index idx
2632 \begin_layout Plain Layout
2647 \begin_inset Index idx
2650 \begin_layout Plain Layout
2659 \begin_inset Separator parbreak
2665 \begin_layout Standard
2667 \begin_inset Tabular
2668 <lyxtabular version="3" rows="6" columns="2">
2669 <features booktabs="true" tabularvalignment="middle">
2670 <column alignment="center" valignment="top" width="0pt">
2671 <column alignment="center" valignment="top" width="0pt">
2673 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2676 \begin_layout Plain Layout
2682 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2685 \begin_layout Plain Layout
2692 <row topspace="1mm">
2693 <cell alignment="center" valignment="top" usebox="none">
2696 \begin_layout Plain Layout
2700 \begin_inset space \textvisiblespace{}
2704 \begin_inset Formula $\downarrow$
2712 <cell alignment="center" valignment="top" usebox="none">
2715 \begin_layout Plain Layout
2716 \begin_inset Formula $\binom{A}{B}$
2725 <row topspace="2mm">
2726 <cell alignment="center" valignment="top" usebox="none">
2729 \begin_layout Plain Layout
2733 \begin_inset space \textvisiblespace{}
2737 \begin_inset Formula $\downarrow$
2745 <cell alignment="center" valignment="top" usebox="none">
2748 \begin_layout Plain Layout
2749 \begin_inset Formula $\dbinom{A}{B}$
2758 <row topspace="2mm" bottomspace="0.5mm">
2759 <cell alignment="center" valignment="top" usebox="none">
2762 \begin_layout Plain Layout
2766 \begin_inset space \textvisiblespace{}
2770 \begin_inset Formula $\downarrow$
2778 <cell alignment="center" valignment="top" usebox="none">
2781 \begin_layout Plain Layout
2782 \begin_inset Formula $\tbinom{A}{B}$
2791 <row topspace="1mm">
2792 <cell alignment="center" valignment="top" topline="true" usebox="none">
2795 \begin_layout Plain Layout
2799 \begin_inset space \textvisiblespace{}
2803 \begin_inset Formula $\downarrow$
2811 <cell alignment="center" valignment="top" topline="true" usebox="none">
2814 \begin_layout Plain Layout
2815 \begin_inset Formula ${A \brack B}$
2824 <row topspace="2mm" bottomspace="0.5mm">
2825 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2828 \begin_layout Plain Layout
2832 \begin_inset space \textvisiblespace{}
2836 \begin_inset Formula $\downarrow$
2844 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2847 \begin_layout Plain Layout
2848 \begin_inset Formula ${A \brace B}$
2864 \begin_layout Subsection
2865 Case Differentiations
2866 \begin_inset Index idx
2869 \begin_layout Plain Layout
2870 Case differentiations
2878 \begin_layout Standard
2880 \begin_inset Tabular
2881 <lyxtabular version="3" rows="3" columns="2">
2882 <features booktabs="true" tabularvalignment="middle">
2883 <column alignment="center" valignment="top" width="0pt">
2884 <column alignment="center" valignment="top" width="0pt">
2886 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2889 \begin_layout Plain Layout
2895 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
2898 \begin_layout Plain Layout
2906 <cell alignment="center" valignment="top" usebox="none">
2909 \begin_layout Plain Layout
2913 \begin_inset space \textvisiblespace{}
2917 \begin_inset Formula $\to$
2921 \begin_inset Index idx
2924 \begin_layout Plain Layout
2937 <cell alignment="center" valignment="top" usebox="none">
2940 \begin_layout Plain Layout
2941 \begin_inset Formula $\begin{cases}
2951 <row topspace="1.5mm">
2952 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2955 \begin_layout Plain Layout
2959 \begin_inset space \textvisiblespace{}
2965 arg "newline-insert newline"
2973 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
2976 \begin_layout Plain Layout
2977 \begin_inset Formula $\begin{cases}
2978 A & \textrm{for }x>0\\
2979 B & \textrm{for }x=0
2996 \begin_layout Standard
3003 or pressing the math toolbar button
3006 arg "math-insert \\cases"
3009 you can create new lines with the shortcut
3012 arg "newline-insert newline"
3015 or the table toolbar button
3018 arg "inset-modify tabular append-row"
3024 \begin_layout Standard
3031 is also available via the menu
3033 Insert\SpecialChar menuseparator
3034 Math\SpecialChar menuseparator
3040 \begin_layout Subsection
3042 \begin_inset Index idx
3045 \begin_layout Plain Layout
3054 \begin_layout Standard
3062 \begin_inset Index idx
3065 \begin_layout Plain Layout
3073 every character can be displayed canceled.
3074 The characters are quasi accentuated by a slash.
3075 \begin_inset Separator parbreak
3081 \begin_layout Standard
3083 \begin_inset Tabular
3084 <lyxtabular version="3" rows="4" columns="2">
3085 <features booktabs="true" tabularvalignment="middle">
3086 <column alignment="center" valignment="top" width="0pt">
3087 <column alignment="center" valignment="top" width="0pt">
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3092 \begin_layout Plain Layout
3098 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3101 \begin_layout Plain Layout
3109 <cell alignment="center" valignment="top" usebox="none">
3112 \begin_layout Plain Layout
3120 <cell alignment="center" valignment="top" usebox="none">
3123 \begin_layout Plain Layout
3124 \begin_inset Formula $\not=$
3134 <cell alignment="center" valignment="top" usebox="none">
3137 \begin_layout Plain Layout
3147 <cell alignment="center" valignment="top" usebox="none">
3150 \begin_layout Plain Layout
3151 \begin_inset Formula $\not\le$
3161 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3164 \begin_layout Plain Layout
3174 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3177 \begin_layout Plain Layout
3178 \begin_inset Formula $\not\parallel$
3194 \begin_layout Standard
3195 The last example shows that not all negations look good.
3196 Therefore there are special commands for some negations (see
3197 \begin_inset CommandInset ref
3199 reference "subsec:Mathematical-Symbols"
3204 \begin_inset CommandInset ref
3206 reference "sec:Relations"
3213 \begin_layout Subsection
3215 \begin_inset CommandInset label
3217 name "subsec:Placeholders"
3222 \begin_inset Index idx
3225 \begin_layout Plain Layout
3232 \begin_inset Index idx
3235 \begin_layout Plain Layout
3236 Chemical characters ! Isotopes
3242 \begin_inset Index idx
3245 \begin_layout Plain Layout
3250 \begin_layout Plain Layout
3261 \begin_layout Plain Layout
3276 \begin_layout Standard
3278 \begin_inset space \thinspace{}
3282 \begin_inset space \space{}
3289 \begin_layout Plain Layout
3290 Typesetting isotopes and chemical symbols is described in
3291 \begin_inset CommandInset ref
3293 reference "subsec:Chemical-Symbols-and"
3302 the following problem occurs:
3303 \begin_inset Separator parbreak
3309 \begin_layout Standard
3311 \begin_inset Tabular
3312 <lyxtabular version="3" rows="2" columns="2">
3313 <features booktabs="true" tabularvalignment="middle">
3314 <column alignment="center" valignment="top" width="0pt">
3315 <column alignment="center" valignment="top" width="0pt">
3317 <cell alignment="center" valignment="top" usebox="none">
3320 \begin_layout Plain Layout
3321 Indices created with sub- and superscripts:
3326 <cell alignment="center" valignment="top" usebox="none">
3329 \begin_layout Plain Layout
3330 \begin_inset Formula $_{9}^{19}\mathrm{F}$
3339 <row topspace="1.5mm">
3340 <cell alignment="center" valignment="top" usebox="none">
3343 \begin_layout Plain Layout
3349 <cell alignment="center" valignment="top" usebox="none">
3352 \begin_layout Plain Layout
3353 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3369 \begin_layout Standard
3370 The shorter index is by default placed below or above the first character
3371 of the longer index.
3372 To avoid this there is the command
3379 \begin_inset Index idx
3382 \begin_layout Plain Layout
3390 or the math toolbar button
3391 \begin_inset space \thinspace{}
3398 \begin_layout Plain Layout
3399 can be found in the submenu of the toolbar button
3402 arg "math-insert \\space"
3411 \begin_inset Graphics
3412 filename ../images/math/phantom.png
3417 that creates one or more phantom characters.
3424 a small blue box appears that is superposed with two red arrows.
3425 The arrows indicate that the complete width and height of the box content
3426 will be created as placeholder.
3427 Phantom characters are accordingly placeholders with the size of the characters.
3428 \begin_inset Separator parbreak
3434 \begin_layout Standard
3436 \begin_inset Tabular
3437 <lyxtabular version="3" rows="4" columns="2">
3438 <features booktabs="true" tabularvalignment="middle">
3439 <column alignment="center" valignment="top" width="0pt">
3440 <column alignment="center" valignment="top" width="0pt">
3442 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3445 \begin_layout Plain Layout
3451 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3454 \begin_layout Plain Layout
3461 <row topspace="1.5mm">
3462 <cell alignment="center" valignment="top" usebox="none">
3465 \begin_layout Plain Layout
3467 \begin_inset space \textvisiblespace{}
3473 \begin_inset space \textvisiblespace{}
3477 \begin_inset Formula $\to$
3481 \begin_inset space \textvisiblespace{}
3489 <cell alignment="center" valignment="top" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3502 <row topspace="1.5mm" bottomspace="0.5mm">
3503 <cell alignment="center" valignment="top" usebox="none">
3506 \begin_layout Plain Layout
3508 \begin_inset space \textvisiblespace{}
3514 \begin_inset space \textvisiblespace{}
3518 \begin_inset Formula $\to$
3522 \begin_inset space \textvisiblespace{}
3530 <cell alignment="center" valignment="top" usebox="none">
3533 \begin_layout Plain Layout
3534 \begin_inset Formula $_{\phantom{23}9}^{235}\mathrm{F}$
3543 <row topspace="1.5mm" bottomspace="0.5mm">
3544 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3547 \begin_layout Plain Layout
3551 \begin_inset space \textvisiblespace{}
3557 \begin_inset space \textvisiblespace{}
3561 \begin_inset Formula $\to$
3565 \begin_inset space \textvisiblespace{}
3573 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3576 \begin_layout Plain Layout
3577 \begin_inset Formula $\Lambda_{MMt}^{\phantom{ii}t}$
3593 \begin_layout Standard
3594 Furthermore there are the commands
3601 \begin_inset Index idx
3604 \begin_layout Plain Layout
3613 \begin_inset space ~
3617 \begin_inset Graphics
3618 filename ../images/math/vphantom.png
3630 \begin_inset Index idx
3633 \begin_layout Plain Layout
3642 \begin_inset space ~
3646 \begin_inset Graphics
3647 filename ../images/math/hphantom.png
3659 creates only space for the maximal height of the characters in the box
3660 but not for its width.
3667 creates only space for the width of the box content.
3668 Therefore the boxes of both commands have only one red arrow.
3671 \begin_layout Standard
3672 For example the command
3677 \begin_inset space \textvisiblespace{}
3684 creates space for the height of the integral sign,
3688 \begin_layout Plain Layout
3695 creates an integral sign, see
3696 \begin_inset CommandInset ref
3698 reference "subsec:Big-Operators"
3707 because this is the larger character.
3708 An example application is in
3709 \begin_inset CommandInset ref
3711 reference "subsec:Multiline-Brackets"
3718 \begin_layout Standard
3719 Placeholders can also be used for text when they are inserted via the menu
3722 Insert\SpecialChar menuseparator
3723 Formatting\SpecialChar menuseparator
3729 \begin_layout Standard
3731 \begin_inset Newline newline
3735 \begin_inset Phantom Phantom
3738 \begin_layout Plain Layout
3747 \begin_layout Subsection
3749 \begin_inset Index idx
3752 \begin_layout Plain Layout
3759 \begin_inset Index idx
3762 \begin_layout Plain Layout
3763 Formula ! underlined
3771 \begin_layout Standard
3773 \begin_inset Tabular
3774 <lyxtabular version="3" rows="4" columns="2">
3775 <features booktabs="true" tabularvalignment="middle">
3776 <column alignment="center" valignment="top" width="0pt">
3777 <column alignment="center" valignment="top" width="0pt">
3779 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3782 \begin_layout Plain Layout
3788 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3791 \begin_layout Plain Layout
3798 <row topspace="2mm">
3799 <cell alignment="center" valignment="top" usebox="none">
3802 \begin_layout Plain Layout
3806 \begin_inset space \textvisiblespace{}
3810 \begin_inset Index idx
3813 \begin_layout Plain Layout
3826 <cell alignment="center" valignment="top" usebox="none">
3829 \begin_layout Plain Layout
3830 \begin_inset Formula $\overline{A+B}$
3839 <row bottomspace="1mm">
3840 <cell alignment="center" valignment="top" usebox="none">
3843 \begin_layout Plain Layout
3847 \begin_inset space \textvisiblespace{}
3851 \begin_inset Index idx
3854 \begin_layout Plain Layout
3867 <cell alignment="center" valignment="top" usebox="none">
3870 \begin_layout Plain Layout
3871 \begin_inset Formula $\underline{A+B}$
3880 <row topspace="2mm" bottomspace="1mm">
3881 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3884 \begin_layout Plain Layout
3888 \begin_inset space \textvisiblespace{}
3894 \begin_inset space \textvisiblespace{}
3902 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
3905 \begin_layout Plain Layout
3906 \begin_inset Formula $\overline{\underline{A+B}}$
3922 \begin_layout Standard
3923 In the last example it doesn't matter if first
3938 \begin_layout Standard
3939 To double underline use
3948 \begin_layout Standard
3949 It is possible to place up to 6 lines above or below characters.
3952 \begin_layout Standard
3953 \begin_inset VSpace bigskip
3956 Custom lines can be created using the command
3963 \begin_inset Index idx
3966 \begin_layout Plain Layout
3974 which has the following scheme:
3977 \begin_layout Standard
3982 rule[vertical offset]{length}{thickness}
3985 \begin_layout Standard
3986 The optional vertical offset shifts the line upwards (or downwards, when
3987 the value is negative).
3989 \begin_inset CommandInset ref
3991 reference "tab:Available-units"
3995 can be used for the values.
3996 Here are two example lines created with the commands
3997 \begin_inset Newline newline
4004 rule[-2ex]{3cm}{2pt}
4015 \begin_layout Standard
4017 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4023 \begin_layout Standard
4030 can also be used for text when a line is inserted via the menu
4032 Insert\SpecialChar menuseparator
4033 Formatting\SpecialChar menuseparator
4035 \begin_inset space ~
4043 \begin_layout Standard
4045 \begin_inset CommandInset line
4056 \begin_layout Subsection
4058 \begin_inset CommandInset label
4060 name "subsec:Ellipses"
4065 \begin_inset Index idx
4068 \begin_layout Plain Layout
4077 \begin_layout Standard
4078 There are different types of ellipses available.
4082 \begin_layout Plain Layout
4083 In the math toolbar in the submenu of the button
4086 arg "math-insert \\ldots"
4094 For listings dots at the baseline are used (
4101 \begin_inset Index idx
4104 \begin_layout Plain Layout
4112 ), while for operations dots are needed that are on the same height as the
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4132 When using the command
4139 \begin_inset Index idx
4142 \begin_layout Plain Layout
4150 , \SpecialChar LaTeX
4151 decides on the basis of the next character what type is used.
4152 \begin_inset Separator parbreak
4158 \begin_layout Standard
4160 \begin_inset Tabular
4161 <lyxtabular version="3" rows="9" columns="2">
4162 <features booktabs="true" tabularvalignment="middle">
4163 <column alignment="center" valignment="top" width="0pt">
4164 <column alignment="center" valignment="top" width="0pt">
4166 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4169 \begin_layout Plain Layout
4175 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4178 \begin_layout Plain Layout
4186 <cell alignment="center" valignment="top" usebox="none">
4189 \begin_layout Plain Layout
4191 \begin_inset space \textvisiblespace{}
4197 \begin_inset space \textvisiblespace{}
4205 <cell alignment="center" valignment="top" usebox="none">
4208 \begin_layout Plain Layout
4209 \begin_inset Formula $A_{1},\dots,A_{n}$
4219 <cell alignment="center" valignment="top" usebox="none">
4222 \begin_layout Plain Layout
4224 \begin_inset space \textvisiblespace{}
4230 \begin_inset space \textvisiblespace{}
4238 <cell alignment="center" valignment="top" usebox="none">
4241 \begin_layout Plain Layout
4242 \begin_inset Formula $A_{1}+\dots+A_{n}$
4252 <cell alignment="center" valignment="top" usebox="none">
4255 \begin_layout Plain Layout
4257 \begin_inset space \textvisiblespace{}
4263 \begin_inset space \textvisiblespace{}
4271 <cell alignment="center" valignment="top" usebox="none">
4274 \begin_layout Plain Layout
4275 \begin_inset Formula $A_{1},\ldots,A_{n}$
4285 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4288 \begin_layout Plain Layout
4290 \begin_inset space \textvisiblespace{}
4296 \begin_inset space \textvisiblespace{}
4304 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
4307 \begin_layout Plain Layout
4308 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4318 <cell alignment="center" valignment="top" usebox="none">
4321 \begin_layout Plain Layout
4329 <cell alignment="center" valignment="top" usebox="none">
4332 \begin_layout Plain Layout
4333 \begin_inset Formula $\vdots$
4343 <cell alignment="center" valignment="top" usebox="none">
4346 \begin_layout Plain Layout
4354 <cell alignment="center" valignment="top" usebox="none">
4357 \begin_layout Plain Layout
4358 \begin_inset Formula $\ddots$
4368 <cell alignment="center" valignment="top" usebox="none">
4371 \begin_layout Plain Layout
4379 <cell alignment="center" valignment="top" usebox="none">
4382 \begin_layout Plain Layout
4383 \begin_inset Formula $\iddots$
4393 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4396 \begin_layout Plain Layout
4398 \begin_inset space \thinspace{}
4401 matrix with the different dots
4406 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4409 \begin_layout Plain Layout
4410 \begin_inset Formula $\begin{array}{ccc}
4411 A_{11} & \cdots & A_{1m}\\
4412 \vdots & \ddots & \vdots\\
4413 A_{n1} & \cdots & A_{nm}
4430 \begin_layout Standard
4431 The ellipses available in menu
4433 Insert\SpecialChar menuseparator
4435 \begin_inset space ~
4449 \begin_layout Standard
4450 \begin_inset VSpace medskip
4459 , one of the options
4461 Use mathdots package (automatically)
4463 must be set in the document settings under
4466 \begin_inset space ~
4472 \begin_inset Newline newline
4477 Use mathdots package
4479 will improve the appearance of all dots in the documents if their font
4480 style or size is not the default.
4483 \begin_layout Standard
4484 \begin_inset VSpace medskip
4487 Specially for matrices there are ellipses that span over several columns.
4488 They are created with the command
4495 \begin_inset Index idx
4498 \begin_layout Plain Layout
4506 , that has the following scheme:
4509 \begin_layout Standard
4514 hdotsfor[distance]{number of columns}
4517 \begin_layout Standard
4518 The number of columns specifies how many columns should be spanned.
4519 Distance is a factor for the distance between the dots.
4522 \begin_layout Standard
4523 In the following matrix the command
4529 was inserted in the first box of the second line, to get an ellipsis with
4530 a dot distance twice as long as with the command
4537 \begin_inset Formula
4539 \left(\begin{array}{cccc}
4548 Note that the matrix fields that should be spanned must be empty, otherwise
4549 you get \SpecialChar LaTeX
4553 \begin_layout Standard
4554 \begin_inset VSpace bigskip
4557 Furthermore you can fill with the command
4564 \begin_inset Index idx
4567 \begin_layout Plain Layout
4575 the rest of a line with dots.
4576 The effect of these commands is the same as with
4583 \begin_inset CommandInset ref
4585 reference "subsec:Variable-Space"
4592 \begin_layout Standard
4593 For example the command
4598 \begin_inset space \textvisiblespace{}
4606 \begin_layout Standard
4607 \begin_inset Formula $A\dotfill B$
4613 \begin_layout Standard
4620 there is for a line the command
4627 \begin_inset Index idx
4630 \begin_layout Plain Layout
4641 \begin_layout Standard
4642 \begin_inset Formula $A\hrulefill B$
4648 \begin_layout Standard
4649 To use the commands for text, they have to be inserted in \SpecialChar TeX
4653 \begin_layout Section
4655 \begin_inset CommandInset label
4662 \begin_inset Index idx
4665 \begin_layout Plain Layout
4674 \begin_layout Standard
4675 Matrices can be inserted via the math toolbar button
4678 arg "dialog-show mathmatrix"
4683 Insert\SpecialChar menuseparator
4684 Math\SpecialChar menuseparator
4688 In the matrix dialog you can specify the number of columns and rows, the
4689 alignment and the decoration.
4690 The vertical alignment is only of importance for matrices in inline formulas:
4693 \begin_layout Standard
4694 The first matrix is top
4695 \begin_inset Formula $\begin{array}[t]{cccc}
4703 \begin_inset Formula $\begin{array}{cccc}
4710 and the third bottom
4711 \begin_inset Formula $\begin{array}[b]{cccc}
4721 \begin_layout Standard
4722 The horizontal alignment specifies how the column entries should be aligned.
4723 It is set by entering a letter for every column.
4728 denotes left aligned,
4737 To create for example a 4
4742 \begin_inset space ~
4745 matrix where the first column is left aligned, the second and third are
4746 centered and the last one is right aligned, one enters for the horizontal
4752 Normally in a matrix all columns are centered, therefore the default for
4760 \begin_layout Standard
4761 Horizontal alignment:
4764 \begin_layout Standard
4770 \begin_inset Formula $\begin{array}{lll}
4782 \begin_inset Formula $\begin{array}{ccc}
4794 \begin_inset Formula $\begin{array}{rrr}
4804 \begin_layout Standard
4805 To add or delete rows and columns subsequently, the math toolbar buttons
4809 arg "inset-modify tabular append-row"
4815 arg "inset-modify tabular delete-row"
4819 \begin_inset space \thinspace{}
4824 Edit\SpecialChar menuseparator
4828 New rows can also be created with
4831 arg "newline-insert newline"
4837 \begin_layout Standard
4838 \begin_inset VSpace bigskip
4845 adds parentheses in the selected style around the matrix.
4846 Alternatively, parentheses can can either be created with the commands
4854 \begin_inset Index idx
4857 \begin_layout Plain Layout
4872 \begin_inset Index idx
4875 \begin_layout Plain Layout
4886 \begin_inset space ~
4892 \begin_inset CommandInset ref
4894 reference "subsec:Automatic-Bracket-Size"
4898 , or by using the following commands:
4899 \begin_inset VSpace medskip
4905 \begin_layout Standard
4906 \begin_inset space \hfill{}
4910 \begin_inset Tabular
4911 <lyxtabular version="3" rows="4" columns="2">
4912 <features booktabs="true" tabularvalignment="middle">
4913 <column alignment="center" valignment="top" width="0pt">
4914 <column alignment="center" valignment="top">
4916 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4919 \begin_layout Plain Layout
4925 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
4928 \begin_layout Plain Layout
4935 <row topspace="1.5mm">
4936 <cell alignment="center" valignment="top" usebox="none">
4939 \begin_layout Plain Layout
4943 \begin_inset space \textvisiblespace{}
4951 \begin_inset space \thinspace{}
4959 <cell alignment="center" valignment="top" usebox="none">
4962 \begin_layout Plain Layout
4963 \begin_inset Formula $\begin{bmatrix}\begin{array}{cc}
4964 0 & \textrm{-}\mathrm{i}\\
4966 \end{array}\end{bmatrix}$
4975 <row topspace="1.5mm" bottomspace="0.5mm">
4976 <cell alignment="center" valignment="top" usebox="none">
4979 \begin_layout Plain Layout
4983 \begin_inset space \textvisiblespace{}
4991 \begin_inset space \thinspace{}
4999 <cell alignment="center" valignment="top" usebox="none">
5002 \begin_layout Plain Layout
5003 \begin_inset Formula $\begin{Bmatrix}\begin{array}{cc}
5004 0 & \textrm{-}\mathrm{i}\\
5006 \end{array}\end{Bmatrix}$
5016 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5019 \begin_layout Plain Layout
5023 \begin_inset space \textvisiblespace{}
5031 \begin_inset space \thinspace{}
5039 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5042 \begin_layout Plain Layout
5043 \begin_inset Formula $\begin{pmatrix}\begin{array}{cc}
5044 0 & \textrm{-}\mathrm{i}\\
5046 \end{array}\end{pmatrix}$
5060 \begin_inset space \hfill{}
5064 \begin_inset Tabular
5065 <lyxtabular version="3" rows="4" columns="2">
5066 <features booktabs="true" tabularvalignment="middle">
5067 <column alignment="center" valignment="top" width="0pt">
5068 <column alignment="center" valignment="top">
5070 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5073 \begin_layout Plain Layout
5079 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5082 \begin_layout Plain Layout
5089 <row topspace="1.5mm">
5090 <cell alignment="center" valignment="top" usebox="none">
5093 \begin_layout Plain Layout
5097 \begin_inset space \textvisiblespace{}
5105 \begin_inset space \thinspace{}
5113 <cell alignment="center" valignment="top" usebox="none">
5116 \begin_layout Plain Layout
5117 \begin_inset Formula $\begin{vmatrix}\begin{array}{cc}
5118 0 & \textrm{-}\mathrm{i}\\
5120 \end{array}\end{vmatrix}$
5129 <row topspace="1.5mm" bottomspace="0.5mm">
5130 <cell alignment="center" valignment="top" usebox="none">
5133 \begin_layout Plain Layout
5137 \begin_inset space \textvisiblespace{}
5145 \begin_inset space \thinspace{}
5153 <cell alignment="center" valignment="top" usebox="none">
5156 \begin_layout Plain Layout
5157 \begin_inset Formula $\begin{Vmatrix}\begin{array}{cc}
5158 0 & \textrm{-}\mathrm{i}\\
5160 \end{array}\end{Vmatrix}$
5170 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5173 \begin_layout Plain Layout
5177 \begin_inset space \textvisiblespace{}
5185 \begin_inset space \thinspace{}
5193 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5196 \begin_layout Plain Layout
5197 \begin_inset Formula $\begin{matrix}\begin{array}{cc}
5198 0 & \textrm{-}\mathrm{i}\\
5200 \end{array}\end{matrix}$
5214 \begin_inset space \hfill{}
5220 \begin_layout Standard
5221 \begin_inset VSpace medskip
5225 \begin_inset space \thinspace{}
5229 \begin_inset space \space{}
5238 is inserted, a blue box appears between two vertical lines where the matrix
5240 \begin_inset Newline newline
5243 Note that decorated matrices ignore the vertical alignment.
5246 \begin_layout Standard
5247 \begin_inset VSpace bigskip
5250 As all multiline formulas are matrices, the length
5257 \begin_inset Index idx
5260 \begin_layout Plain Layout
5268 that is described in
5269 \begin_inset CommandInset ref
5271 reference "subsec:Column-Separation"
5275 can also be used to change the column separation of matrices.
5278 \begin_layout Standard
5279 To change the row separation, the command
5286 \begin_inset Index idx
5289 \begin_layout Plain Layout
5298 It is used as follows:
5301 \begin_layout Standard
5308 arraystretch}{stretch factor}
5309 \begin_inset Index idx
5312 \begin_layout Plain Layout
5323 \begin_layout Standard
5330 assigns the stretch factor to the predefined command
5338 \begin_inset space \thinspace{}
5342 \begin_inset space \space{}
5345 the row separation, use the factor 2.
5346 This is then used for all following matrices.
5347 To go back to the original separation, assign the factor 1 to
5356 \begin_layout Standard
5357 To set matrices into a text line, the command
5364 \begin_inset Index idx
5367 \begin_layout Plain Layout
5376 When it is inserted a blue box with two dashed lines appears.
5377 In this box the matrix is inserted.
5380 \begin_layout Standard
5382 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5384 \end{smallmatrix}\right)$
5390 \begin_layout Section
5391 Brackets and Delimiters
5392 \begin_inset Index idx
5395 \begin_layout Plain Layout
5402 \begin_inset Index idx
5405 \begin_layout Plain Layout
5414 \begin_layout Subsection
5415 Vertical Brackets and Delimiters
5416 \begin_inset Index idx
5419 \begin_layout Plain Layout
5428 \begin_layout Standard
5429 \begin_inset space \hfill{}
5433 \begin_inset Tabular
5434 <lyxtabular version="3" rows="9" columns="2">
5435 <features booktabs="true" tabularvalignment="middle">
5436 <column alignment="center" valignment="top" width="0pt">
5437 <column alignment="center" valignment="top" width="0pt">
5439 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5442 \begin_layout Plain Layout
5448 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5451 \begin_layout Plain Layout
5459 <cell alignment="center" valignment="top" usebox="none">
5462 \begin_layout Plain Layout
5468 <cell alignment="center" valignment="top" usebox="none">
5471 \begin_layout Plain Layout
5472 \begin_inset Formula $($
5482 <cell alignment="center" valignment="top" usebox="none">
5485 \begin_layout Plain Layout
5491 <cell alignment="center" valignment="top" usebox="none">
5494 \begin_layout Plain Layout
5495 \begin_inset Formula $\{$
5505 <cell alignment="center" valignment="top" usebox="none">
5508 \begin_layout Plain Layout
5514 <cell alignment="center" valignment="top" usebox="none">
5517 \begin_layout Plain Layout
5518 \begin_inset Formula $[$
5528 <cell alignment="center" valignment="top" usebox="none">
5531 \begin_layout Plain Layout
5539 <cell alignment="center" valignment="top" usebox="none">
5542 \begin_layout Plain Layout
5543 \begin_inset Formula $\langle$
5553 <cell alignment="center" valignment="top" usebox="none">
5556 \begin_layout Plain Layout
5564 <cell alignment="center" valignment="top" usebox="none">
5567 \begin_layout Plain Layout
5568 \begin_inset Formula $\lceil$
5578 <cell alignment="center" valignment="top" usebox="none">
5581 \begin_layout Plain Layout
5589 <cell alignment="center" valignment="top" usebox="none">
5592 \begin_layout Plain Layout
5593 \begin_inset Formula $\lfloor$
5603 <cell alignment="center" valignment="top" usebox="none">
5606 \begin_layout Plain Layout
5612 <cell alignment="center" valignment="top" usebox="none">
5615 \begin_layout Plain Layout
5616 \begin_inset Formula $/$
5626 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5629 \begin_layout Plain Layout
5635 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5638 \begin_layout Plain Layout
5639 \begin_inset Formula $|$
5653 \begin_inset space \hfill{}
5657 \begin_inset Tabular
5658 <lyxtabular version="3" rows="9" columns="2">
5659 <features booktabs="true" tabularvalignment="middle">
5660 <column alignment="center" valignment="top" width="0pt">
5661 <column alignment="center" valignment="top" width="0pt">
5663 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5666 \begin_layout Plain Layout
5672 <cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
5675 \begin_layout Plain Layout
5683 <cell alignment="center" valignment="top" usebox="none">
5686 \begin_layout Plain Layout
5692 <cell alignment="center" valignment="top" usebox="none">
5695 \begin_layout Plain Layout
5696 \begin_inset Formula $)$
5706 <cell alignment="center" valignment="top" usebox="none">
5709 \begin_layout Plain Layout
5715 <cell alignment="center" valignment="top" usebox="none">
5718 \begin_layout Plain Layout
5719 \begin_inset Formula $\}$
5729 <cell alignment="center" valignment="top" usebox="none">
5732 \begin_layout Plain Layout
5738 <cell alignment="center" valignment="top" usebox="none">
5741 \begin_layout Plain Layout
5742 \begin_inset Formula $]$
5752 <cell alignment="center" valignment="top" usebox="none">
5755 \begin_layout Plain Layout
5763 <cell alignment="center" valignment="top" usebox="none">
5766 \begin_layout Plain Layout
5767 \begin_inset Formula $\rangle$
5777 <cell alignment="center" valignment="top" usebox="none">
5780 \begin_layout Plain Layout
5788 <cell alignment="center" valignment="top" usebox="none">
5791 \begin_layout Plain Layout
5792 \begin_inset Formula $\rceil$
5802 <cell alignment="center" valignment="top" usebox="none">
5805 \begin_layout Plain Layout
5813 <cell alignment="center" valignment="top" usebox="none">
5816 \begin_layout Plain Layout
5817 \begin_inset Formula $\rfloor$
5827 <cell alignment="center" valignment="top" usebox="none">
5830 \begin_layout Plain Layout
5840 <cell alignment="center" valignment="top" usebox="none">
5843 \begin_layout Plain Layout
5844 \begin_inset Formula $\backslash$
5854 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5857 \begin_layout Plain Layout
5865 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
5868 \begin_layout Plain Layout
5869 \begin_inset Formula $\|$
5883 \begin_inset space \hfill{}
5889 \begin_layout Standard
5892 \begin_inset Note Greyedout
5895 \begin_layout Plain Layout
5908 \begin_inset Index idx
5911 \begin_layout Plain Layout
5919 must be used for the backslash, because the command
5927 produces a line break there.
5935 \begin_layout Standard
5936 For all characters listed above the size can be adjusted with the commands
5937 described in the following two subsections.
5938 When using these commands, the characters < and > can directly be used
5939 instead of the commands
5954 \begin_layout Subsubsection
5956 \begin_inset CommandInset label
5958 name "subsec:Manual-Bracket-Size"
5963 \begin_inset Index idx
5966 \begin_layout Plain Layout
5967 Bracket size ! manual
5975 \begin_layout Standard
5976 The bracket size can be specified manually by the \SpecialChar LaTeX
5984 \begin_inset Index idx
5987 \begin_layout Plain Layout
6020 denotes the smallest and
6026 the largest bracket size.
6029 \begin_layout Standard
6030 These commands are used to emphasize levels of brackets:
6031 \begin_inset Separator parbreak
6037 \begin_layout Standard
6039 \begin_inset Tabular
6040 <lyxtabular version="3" rows="2" columns="2">
6041 <features tabularvalignment="middle">
6042 <column alignment="center" valignment="top" width="0pt">
6043 <column alignment="center" valignment="top" width="0pt">
6045 <cell alignment="center" valignment="top" usebox="none">
6048 \begin_layout Plain Layout
6049 all brackets in the same size:
6054 <cell alignment="center" valignment="top" usebox="none">
6057 \begin_layout Plain Layout
6058 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6068 <cell alignment="center" valignment="top" usebox="none">
6071 \begin_layout Plain Layout
6077 <cell alignment="center" valignment="top" usebox="none">
6080 \begin_layout Plain Layout
6081 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6095 \begin_inset Note Note
6098 \begin_layout Plain Layout
6105 is only used as spacer.
6113 \begin_layout Standard
6114 For the second formula the command
6121 \begin_inset space \textvisiblespace{}
6129 \begin_layout Standard
6130 Here is an overview about all bracket sizes:
6131 \begin_inset Separator parbreak
6137 \begin_layout Standard
6154 \begin_inset space \textvisiblespace{}
6162 \begin_inset space \textvisiblespace{}
6166 \begin_inset space \textvisiblespace{}
6176 \begin_layout Standard
6178 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6184 \begin_layout Standard
6191 -commands there is the variant
6198 \begin_inset Index idx
6201 \begin_layout Plain Layout
6209 that adds a bit more space between the bracket and its content, and the
6223 \begin_inset Index idx
6226 \begin_layout Plain Layout
6236 , that don't add additional space.
6241 at the end of the command
6247 is for a left bracket; for a right bracket this will be replaced by an
6253 A left or right bracket can each be an opening or closing bracket.
6256 \begin_layout Standard
6257 In the following table is a comparison of the variants:
6258 \begin_inset Separator parbreak
6264 \begin_layout Standard
6266 \begin_inset Tabular
6267 <lyxtabular version="3" rows="5" columns="2">
6268 <features tabularvalignment="middle">
6269 <column alignment="center" valignment="middle">
6270 <column alignment="center" valignment="middle">
6272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6275 \begin_layout Plain Layout
6281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6284 \begin_layout Plain Layout
6286 \begin_inset Note Note
6289 \begin_layout Plain Layout
6296 is only used as spacer.
6308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6311 \begin_layout Plain Layout
6321 \begin_inset space \textvisiblespace{}
6331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6334 \begin_layout Plain Layout
6335 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6348 \begin_layout Plain Layout
6358 \begin_inset space \textvisiblespace{}
6368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6371 \begin_layout Plain Layout
6372 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6385 \begin_layout Plain Layout
6395 \begin_inset space \textvisiblespace{}
6405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6422 \begin_layout Plain Layout
6434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6437 \begin_layout Plain Layout
6438 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6454 \begin_layout Subsubsection
6455 Automatic Bracket Size
6456 \begin_inset CommandInset label
6458 name "subsec:Automatic-Bracket-Size"
6463 \begin_inset Index idx
6466 \begin_layout Plain Layout
6467 Bracket size ! automatic
6475 \begin_layout Standard
6476 Brackets with variable size can be inserted with the commands
6483 \begin_inset Index idx
6486 \begin_layout Plain Layout
6501 \begin_inset Index idx
6504 \begin_layout Plain Layout
6512 or via the math toolbar button
6515 arg "dialog-show mathdelimiter"
6531 the wanted bracket must be inserted.
6532 The bracket size will then automatically be calculated for the output.
6533 \begin_inset Separator parbreak
6539 \begin_layout Standard
6541 normal bracket: The command
6548 \begin_inset space \textvisiblespace{}
6552 \begin_inset Formula $\downarrow$
6556 \begin_inset space \textvisiblespace{}
6562 \begin_inset Formula
6572 \begin_layout Standard
6574 multiline bracket: The command
6583 \begin_inset space \textvisiblespace{}
6587 \begin_inset Formula $\downarrow$
6591 \begin_inset space \textvisiblespace{}
6599 \begin_inset Formula
6601 \ln\left(\frac{A}{C}\right)
6609 \begin_layout Standard
6625 \begin_inset space ~
6631 This has the advantage that you can see in \SpecialChar LyX
6632 immediately the real bracket
6633 size and that the matching right bracket will be created too.
6634 \begin_inset Newline newline
6637 The command for the last example would then be:
6648 \begin_inset space \textvisiblespace{}
6652 \begin_inset Formula $\downarrow$
6658 \begin_layout Standard
6659 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6660 For example the command
6667 \begin_inset space \textvisiblespace{}
6671 \begin_inset Formula $\downarrow$
6675 \begin_inset space \textvisiblespace{}
6685 \begin_inset Formula
6687 \left.\frac{A}{B}\right\}
6706 will be converted by \SpecialChar LyX
6707 to brackets in the right size when the document is
6708 reloaded and an omitted bracket will appear as dashed line.
6711 \begin_layout Standard
6712 \begin_inset VSpace bigskip
6715 Because all popular \SpecialChar LaTeX
6716 distributions use e\SpecialChar TeX
6717 , an extension to \SpecialChar LaTeX
6726 \begin_inset Index idx
6729 \begin_layout Plain Layout
6737 is additionally available for all brackets and limits.
6738 With this command the height of the following character is adapted to the
6739 one of the surrounding brackets, what is e.
6740 \begin_inset space \thinspace{}
6744 \begin_inset space \space{}
6747 needed for physical vectors:
6748 \begin_inset Formula
6750 \left\langle \phi\:\middle|\:J=\frac{3}{2}\,,\,M_{J}\right\rangle
6755 For physical vectors there is a special \SpecialChar LaTeX
6756 -package, described in
6757 \begin_inset CommandInset ref
6759 reference "subsec:Physical-Vectors"
6766 \begin_layout Subsection
6768 \begin_inset Index idx
6771 \begin_layout Plain Layout
6772 Brackets ! horizontal
6780 \begin_layout Standard
6782 \begin_inset Tabular
6783 <lyxtabular version="3" rows="4" columns="2">
6784 <features tabularvalignment="middle">
6785 <column alignment="center" valignment="top" width="0pt">
6786 <column alignment="center" valignment="top" width="0pt">
6788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6791 \begin_layout Plain Layout
6793 \begin_inset Note Note
6796 \begin_layout Plain Layout
6803 is only used as spacer.
6813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6816 \begin_layout Plain Layout
6824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6827 \begin_layout Plain Layout
6831 \begin_layout Plain Layout
6843 \begin_inset space \textvisiblespace{}
6847 \begin_inset space \textvisiblespace{}
6854 \begin_layout Plain Layout
6862 \begin_inset Index idx
6865 \begin_layout Plain Layout
6878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6881 \begin_layout Plain Layout
6882 \begin_inset Formula $\overbrace{A+B}^{3}$
6892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6895 \begin_layout Plain Layout
6899 \begin_layout Plain Layout
6911 \begin_inset space \textvisiblespace{}
6915 \begin_inset space \textvisiblespace{}
6922 \begin_layout Plain Layout
6930 \begin_inset Index idx
6933 \begin_layout Plain Layout
6946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6949 \begin_layout Plain Layout
6950 \begin_inset Formula $\underbrace{A+B}_{5}$
6960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6963 \begin_layout Plain Layout
6967 \begin_inset space \textvisiblespace{}
6973 \begin_inset space \textvisiblespace{}
6977 \begin_inset space \textvisiblespace{}
6981 \begin_inset space \textvisiblespace{}
6985 \begin_inset space \textvisiblespace{}
6989 \begin_inset space \textvisiblespace{}
6993 \begin_inset space \textvisiblespace{}
7001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7004 \begin_layout Plain Layout
7005 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7021 \begin_layout Standard
7022 In the last example it doesn't matter if
7034 is inserted at first.
7037 \begin_layout Standard
7038 \begin_inset VSpace medskip
7044 \begin_layout Standard
7045 If you set in the document settings under
7048 \begin_inset space ~
7058 \begin_inset Index idx
7061 \begin_layout Plain Layout
7062 Packages ! mathtools
7070 \begin_inset space ~
7075 , you have access to square backets:
7076 \begin_inset Separator parbreak
7082 \begin_layout Standard
7084 \begin_inset Tabular
7085 <lyxtabular version="3" rows="4" columns="2">
7086 <features tabularvalignment="middle">
7087 <column alignment="center" valignment="top" width="0pt">
7088 <column alignment="center" valignment="top" width="0pt">
7090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7093 \begin_layout Plain Layout
7095 \begin_inset Note Note
7098 \begin_layout Plain Layout
7105 is only used as spacer.
7115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7118 \begin_layout Plain Layout
7126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7129 \begin_layout Plain Layout
7133 \begin_layout Plain Layout
7169 \begin_inset space \textvisiblespace{}
7176 \begin_layout Plain Layout
7184 \begin_inset Index idx
7187 \begin_layout Plain Layout
7200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7203 \begin_layout Plain Layout
7204 \begin_inset Formula $\overbracket{A+B}^{3}$
7214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7217 \begin_layout Plain Layout
7221 \begin_layout Plain Layout
7257 \begin_inset space \textvisiblespace{}
7264 \begin_layout Plain Layout
7272 \begin_inset Index idx
7275 \begin_layout Plain Layout
7300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7303 \begin_layout Plain Layout
7304 \begin_inset Formula $\underbracket{A+B}_{5}$
7314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7317 \begin_layout Plain Layout
7323 \begin_inset space \textvisiblespace{}
7327 \begin_inset space \textvisiblespace{}
7331 \begin_inset space \textvisiblespace{}
7335 \begin_inset space \textvisiblespace{}
7339 \begin_inset space \textvisiblespace{}
7347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7350 \begin_layout Plain Layout
7351 \begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
7367 \begin_layout Standard
7380 you can change the thickness of the bracket's stroke by specifying the
7381 desired thickness in square brackets behind the command:
7382 \begin_inset Separator parbreak
7388 \begin_layout Standard
7390 \begin_inset Tabular
7391 <lyxtabular version="3" rows="3" columns="2">
7392 <features tabularvalignment="middle">
7393 <column alignment="center" valignment="top" width="0pt">
7394 <column alignment="center" valignment="top" width="0pt">
7396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7399 \begin_layout Plain Layout
7401 \begin_inset Note Note
7404 \begin_layout Plain Layout
7411 is only used as spacer.
7421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7424 \begin_layout Plain Layout
7432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7435 \begin_layout Plain Layout
7439 \begin_layout Plain Layout
7477 \begin_inset space \textvisiblespace{}
7484 \begin_layout Plain Layout
7496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7499 \begin_layout Plain Layout
7500 \begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
7510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7513 \begin_layout Plain Layout
7517 \begin_layout Plain Layout
7555 \begin_inset space \textvisiblespace{}
7562 \begin_layout Plain Layout
7574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7577 \begin_layout Plain Layout
7578 \begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
7594 \begin_layout Standard
7595 \begin_inset VSpace bigskip
7598 When brackets should overlap each other, multiline formulas, as described
7600 \begin_inset CommandInset ref
7602 reference "sec:Multiline-Formulas"
7607 \begin_inset Formula
7609 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd\\
7610 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7615 In the first row the formula is inserted together with the first brace.
7616 It is hereby important that the space command
7620 \begin_layout Plain Layout
7621 Space commands are explained in
7622 \begin_inset CommandInset ref
7624 reference "subsec:Predefined-Space"
7639 is inserted before the first
7640 \begin_inset Formula $d$
7643 , because the brace that ends behind the
7644 \begin_inset Formula $q$
7647 prevents that the following
7648 \begin_inset Quotes eld
7652 \begin_inset Quotes erd
7655 is surrounded by space.
7659 \begin_layout Plain Layout
7660 because a bracket is not handled as a character, see
7661 \begin_inset CommandInset ref
7663 reference "subsec:Binary-Operators"
7672 In the second row the second brace is inserted.
7673 As it should begin before the
7674 \begin_inset Formula $b$
7689 \begin_layout Plain Layout
7697 \begin_inset CommandInset ref
7699 reference "subsec:Placeholders"
7708 This space is needed because the
7709 \begin_inset Quotes eld
7713 \begin_inset Quotes erd
7716 is also surrounded by space in the formula.
7717 The brace is placed under the command
7726 \begin_layout Standard
7727 It gets more complicated when brackets overlap each other above and under
7728 the formula, like in the following example:
7732 \begin_layout Plain Layout
7744 \begin_inset Formula
7746 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7747 A & = & \underbrace{gggg+bbqq}_{r}+\:dddd
7756 \begin_layout Plain Layout
7767 The first formula row is the same as the second row of the previous example,
7768 with the difference that the brace is above.
7769 The second row contains the formula together with the second brace.
7770 To avoid that there is space between the upper brace in the first row and
7771 the formula, the row spacing needs to be reduced.
7772 This is not easily possible due to a bug in \SpecialChar LyX
7777 \begin_layout Plain Layout
7778 \begin_inset CommandInset href
7780 name "LyX-bug #1505"
7781 target "http://www.lyx.org/trac/ticket/1505"
7790 As a solution for the problem, the global formula row separation
7797 \begin_inset Index idx
7800 \begin_layout Plain Layout
7808 must be changed to -6
7809 \begin_inset space \thinspace{}
7812 pt before the formula with the command
7828 is set back after the formula to the standard value of 3
7829 \begin_inset space \thinspace{}
7832 pt using the same command.
7833 More about the row separation in formulas is explained in
7834 \begin_inset CommandInset ref
7836 reference "subsec:Line-Separation"
7843 \begin_layout Section
7845 \begin_inset Index idx
7848 \begin_layout Plain Layout
7857 \begin_layout Standard
7858 Arrows can be inserted via the math toolbar button
7861 arg "math-insert \\leftarrow"
7864 or the commands listed in the following subsections.
7867 \begin_layout Subsection
7869 \begin_inset Index idx
7872 \begin_layout Plain Layout
7881 \begin_layout Standard
7882 \begin_inset space \hfill{}
7886 \begin_inset Tabular
7887 <lyxtabular version="3" rows="8" columns="2">
7888 <features tabularvalignment="middle">
7889 <column alignment="center" valignment="top" width="0pt">
7890 <column alignment="center" valignment="top" width="0pt">
7892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7895 \begin_layout Plain Layout
7901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7904 \begin_layout Plain Layout
7912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7915 \begin_layout Plain Layout
7923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7926 \begin_layout Plain Layout
7927 \begin_inset Formula $\gets$
7937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7940 \begin_layout Plain Layout
7948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7951 \begin_layout Plain Layout
7952 \begin_inset Formula $\Leftarrow$
7962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7965 \begin_layout Plain Layout
7973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7976 \begin_layout Plain Layout
7977 \begin_inset Formula $\longleftarrow$
7987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7990 \begin_layout Plain Layout
7998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8001 \begin_layout Plain Layout
8002 \begin_inset Formula $\Longleftarrow$
8012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8015 \begin_layout Plain Layout
8023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8026 \begin_layout Plain Layout
8027 \begin_inset Formula $\leftharpoonup$
8037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8040 \begin_layout Plain Layout
8048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8051 \begin_layout Plain Layout
8052 \begin_inset Formula $\leftharpoondown$
8062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8065 \begin_layout Plain Layout
8073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8076 \begin_layout Plain Layout
8077 \begin_inset Formula $\hookleftarrow$
8091 \begin_inset space \hfill{}
8095 \begin_inset Tabular
8096 <lyxtabular version="3" rows="8" columns="2">
8097 <features tabularvalignment="middle">
8098 <column alignment="center" valignment="top" width="0pt">
8099 <column alignment="center" valignment="top" width="0pt">
8101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8104 \begin_layout Plain Layout
8110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8113 \begin_layout Plain Layout
8121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8124 \begin_layout Plain Layout
8132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8135 \begin_layout Plain Layout
8136 \begin_inset Formula $\to$
8146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8149 \begin_layout Plain Layout
8157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8160 \begin_layout Plain Layout
8161 \begin_inset Formula $\Rightarrow$
8171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8174 \begin_layout Plain Layout
8182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8185 \begin_layout Plain Layout
8186 \begin_inset Formula $\longrightarrow$
8196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8199 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8210 \begin_layout Plain Layout
8211 \begin_inset Formula $\Longrightarrow$
8221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8224 \begin_layout Plain Layout
8232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8235 \begin_layout Plain Layout
8236 \begin_inset Formula $\rightharpoonup$
8246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8249 \begin_layout Plain Layout
8257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8260 \begin_layout Plain Layout
8261 \begin_inset Formula $\rightharpoondown$
8271 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8274 \begin_layout Plain Layout
8282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8285 \begin_layout Plain Layout
8286 \begin_inset Formula $\hookrightarrow$
8300 \begin_inset space \hfill{}
8306 \begin_layout Standard
8307 \begin_inset space \hfill{}
8311 \begin_inset Tabular
8312 <lyxtabular version="3" rows="6" columns="2">
8313 <features tabularvalignment="middle">
8314 <column alignment="center" valignment="top" width="0pt">
8315 <column alignment="center" valignment="top" width="0pt">
8317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8320 \begin_layout Plain Layout
8326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8329 \begin_layout Plain Layout
8337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8340 \begin_layout Plain Layout
8348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8351 \begin_layout Plain Layout
8352 \begin_inset Formula $\leftrightarrow$
8362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8365 \begin_layout Plain Layout
8373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8376 \begin_layout Plain Layout
8377 \begin_inset Formula $\Leftrightarrow$
8387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8390 \begin_layout Plain Layout
8398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8401 \begin_layout Plain Layout
8402 \begin_inset Formula $\longleftrightarrow$
8412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8415 \begin_layout Plain Layout
8423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8426 \begin_layout Plain Layout
8427 \begin_inset Formula $\Longleftrightarrow$
8437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8440 \begin_layout Plain Layout
8448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8451 \begin_layout Plain Layout
8452 \begin_inset Formula $\rightleftharpoons$
8466 \begin_inset space \hspace{}
8471 \begin_inset space \hfill{}
8475 \begin_inset Tabular
8476 <lyxtabular version="3" rows="5" columns="2">
8477 <features tabularvalignment="middle">
8478 <column alignment="center" valignment="top" width="0pt">
8479 <column alignment="center" valignment="top" width="0pt">
8481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8484 \begin_layout Plain Layout
8490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8493 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8504 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8515 \begin_layout Plain Layout
8516 \begin_inset Formula $\mapsto$
8526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8529 \begin_layout Plain Layout
8537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8540 \begin_layout Plain Layout
8541 \begin_inset Formula $\longmapsto$
8551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8554 \begin_layout Plain Layout
8562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8565 \begin_layout Plain Layout
8566 \begin_inset Formula $\leadsto$
8576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8579 \begin_layout Plain Layout
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8590 \begin_layout Plain Layout
8591 \begin_inset Formula $\dasharrow$
8605 \begin_inset space \hfill{}
8611 \begin_layout Standard
8612 \begin_inset VSpace medskip
8615 Arrows used as accents like e.
8616 \begin_inset space \thinspace{}
8620 \begin_inset space \space{}
8623 vector arrows are listed in
8624 \begin_inset CommandInset ref
8626 reference "sec:Accents"
8633 \begin_layout Standard
8634 \begin_inset VSpace bigskip
8637 Furthermore there are the labeled arrows
8638 \begin_inset Index idx
8641 \begin_layout Plain Layout
8654 \begin_inset Index idx
8657 \begin_layout Plain Layout
8672 \begin_inset Index idx
8675 \begin_layout Plain Layout
8682 \begin_layout Plain Layout
8697 When inserting one of these commands in a formula, an arrow with two blue
8698 boxes appear where the label can be inserted.
8699 The length of the arrow adapts to the label width.
8702 \begin_layout Standard
8704 \begin_inset Tabular
8705 <lyxtabular version="3" rows="3" columns="2">
8706 <features tabularvalignment="middle">
8707 <column alignment="center" valignment="top" width="0pt">
8708 <column alignment="center" valignment="top" width="0pt">
8710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8713 \begin_layout Plain Layout
8719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8722 \begin_layout Plain Layout
8724 \begin_inset Note Note
8727 \begin_layout Plain Layout
8734 is only used as spacer.
8746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8749 \begin_layout Plain Layout
8753 \begin_inset space \textvisiblespace{}
8757 \begin_inset Formula $\downarrow$
8761 \begin_inset Formula $\to$
8769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8772 \begin_layout Plain Layout
8773 \begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8786 \begin_layout Plain Layout
8790 \begin_inset space \textvisiblespace{}
8794 \begin_inset Formula $\downarrow$
8798 \begin_inset Formula $\to$
8806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8809 \begin_layout Plain Layout
8810 \begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8826 \begin_layout Standard
8827 \begin_inset VSpace medskip
8833 \begin_layout Standard
8834 If you set in the document settings under
8837 \begin_inset space ~
8847 \begin_inset Index idx
8850 \begin_layout Plain Layout
8851 Packages ! mathtools
8859 \begin_inset space ~
8864 , you have access to the following labeled arrows:
8867 \begin_layout Standard
8868 \begin_inset Newpage newpage
8872 \begin_inset Separator parbreak
8878 \begin_layout Standard
8880 \begin_inset space \hspace*{\fill}
8884 \begin_inset Tabular
8885 <lyxtabular version="3" rows="7" columns="2">
8886 <features tabularvalignment="middle">
8887 <column alignment="center" valignment="top" width="0pt">
8888 <column alignment="center" valignment="top" width="0pt">
8890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8893 \begin_layout Plain Layout
8899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8902 \begin_layout Plain Layout
8904 \begin_inset Note Note
8907 \begin_layout Plain Layout
8914 is only used as spacer.
8926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8929 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8952 \begin_layout Plain Layout
8953 \begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
8963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8966 \begin_layout Plain Layout
8986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8989 \begin_layout Plain Layout
8990 \begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9003 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9040 \begin_layout Plain Layout
9060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9063 \begin_layout Plain Layout
9064 \begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9077 \begin_layout Plain Layout
9097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9100 \begin_layout Plain Layout
9101 \begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
9111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9114 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9138 \begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
9152 \begin_inset space \hspace*{\fill}
9156 \begin_inset Tabular
9157 <lyxtabular version="3" rows="7" columns="2">
9158 <features tabularvalignment="middle">
9159 <column alignment="center" valignment="top" width="0pt">
9160 <column alignment="center" valignment="top" width="0pt">
9162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9165 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9174 \begin_layout Plain Layout
9176 \begin_inset Note Note
9179 \begin_layout Plain Layout
9186 is only used as spacer.
9198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9201 \begin_layout Plain Layout
9221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9224 \begin_layout Plain Layout
9225 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9238 \begin_layout Plain Layout
9258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9261 \begin_layout Plain Layout
9262 \begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9275 \begin_layout Plain Layout
9295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9298 \begin_layout Plain Layout
9299 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
9309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9312 \begin_layout Plain Layout
9332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9335 \begin_layout Plain Layout
9336 \begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
9346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9349 \begin_layout Plain Layout
9369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9372 \begin_layout Plain Layout
9373 \begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9386 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9410 \begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
9424 \begin_inset space \hspace*{\fill}
9430 \begin_layout Standard
9431 The command scheme is for all these arrows:
9432 \begin_inset Separator parbreak
9438 \begin_layout Standard
9440 \begin_inset Tabular
9441 <lyxtabular version="3" rows="2" columns="2">
9442 <features tabularvalignment="middle">
9443 <column alignment="center" valignment="top" width="0pt">
9444 <column alignment="center" valignment="top" width="0pt">
9446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9449 \begin_layout Plain Layout
9455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9458 \begin_layout Plain Layout
9460 \begin_inset Note Note
9463 \begin_layout Plain Layout
9470 is only used as spacer.
9482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9485 \begin_layout Plain Layout
9488 xleftrightarrow[x=a]
9491 \begin_inset Formula $\to$
9499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9502 \begin_layout Plain Layout
9503 \begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
9519 \begin_layout Subsection
9520 Vertical and diagonal Arrows
9521 \begin_inset Index idx
9524 \begin_layout Plain Layout
9531 \begin_inset Index idx
9534 \begin_layout Plain Layout
9543 \begin_layout Standard
9544 \begin_inset space \hfill{}
9548 \begin_inset Tabular
9549 <lyxtabular version="3" rows="7" columns="2">
9550 <features tabularvalignment="middle">
9551 <column alignment="center" valignment="top" width="0pt">
9552 <column alignment="center" valignment="top" width="0pt">
9554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9557 \begin_layout Plain Layout
9563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9566 \begin_layout Plain Layout
9574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9577 \begin_layout Plain Layout
9585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9588 \begin_layout Plain Layout
9589 \begin_inset Formula $\uparrow$
9599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9602 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Plain Layout
9614 \begin_inset Formula $\Uparrow$
9624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9638 \begin_layout Plain Layout
9639 \begin_inset Formula $\updownarrow$
9649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9652 \begin_layout Plain Layout
9660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9663 \begin_layout Plain Layout
9664 \begin_inset Formula $\Updownarrow$
9674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9677 \begin_layout Plain Layout
9685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9688 \begin_layout Plain Layout
9689 \begin_inset Formula $\Downarrow$
9699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9702 \begin_layout Plain Layout
9710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9713 \begin_layout Plain Layout
9714 \begin_inset Formula $\downarrow$
9728 \begin_inset space \hfill{}
9732 \begin_inset Tabular
9733 <lyxtabular version="3" rows="5" columns="2">
9734 <features tabularvalignment="middle">
9735 <column alignment="center" valignment="top" width="0pt">
9736 <column alignment="center" valignment="top" width="0pt">
9738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9741 \begin_layout Plain Layout
9747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9750 \begin_layout Plain Layout
9758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9761 \begin_layout Plain Layout
9769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9772 \begin_layout Plain Layout
9773 \begin_inset Formula $\nearrow$
9783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9786 \begin_layout Plain Layout
9794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9797 \begin_layout Plain Layout
9798 \begin_inset Formula $\searrow$
9808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9811 \begin_layout Plain Layout
9819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9822 \begin_layout Plain Layout
9823 \begin_inset Formula $\swarrow$
9833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9836 \begin_layout Plain Layout
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9847 \begin_layout Plain Layout
9848 \begin_inset Formula $\nwarrow$
9862 \begin_inset space \hfill{}
9868 \begin_layout Standard
9869 \begin_inset VSpace medskip
9872 Vertical arrows can be used also as delimiters together with the commands
9874 \begin_inset CommandInset ref
9876 reference "subsec:Manual-Bracket-Size"
9881 \begin_inset CommandInset ref
9883 reference "subsec:Automatic-Bracket-Size"
9890 \begin_layout Section
9892 \begin_inset CommandInset label
9899 \begin_inset Index idx
9902 \begin_layout Plain Layout
9911 \begin_layout Standard
9912 Accents can be inserted via the math toolbar button
9915 arg "math-insert \\hat"
9918 or the commands listed in the following subsections.
9921 \begin_layout Subsection
9922 Accents for one Character
9926 \begin_layout Plain Layout
9939 \begin_layout Plain Layout
9941 \begin_inset CommandInset ref
9943 reference "subsec:Accents-in-Text"
9956 \begin_layout Plain Layout
9964 \begin_inset Note Note
9967 \begin_layout Plain Layout
9974 is used to avoid that the footnote appears in the PDF-bookmark.
9977 \begin_layout Plain Layout
9985 \begin_inset CommandInset ref
9987 reference "subsec:Formulas-in-Section"
9997 \begin_inset CommandInset label
9999 name "subsec:Accents-for-one"
10004 \begin_inset Index idx
10007 \begin_layout Plain Layout
10008 Accents ! for one character
10016 \begin_layout Standard
10017 \begin_inset space \hfill{}
10021 \begin_inset Tabular
10022 <lyxtabular version="3" rows="8" columns="2">
10023 <features tabularvalignment="middle">
10024 <column alignment="center" valignment="top" width="0pt">
10025 <column alignment="center" valignment="top" width="0pt">
10027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10030 \begin_layout Plain Layout
10036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10039 \begin_layout Plain Layout
10041 \begin_inset Note Note
10044 \begin_layout Plain Layout
10051 is only used as spacer.
10063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10066 \begin_layout Plain Layout
10070 \begin_inset space \textvisiblespace{}
10078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10081 \begin_layout Plain Layout
10082 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
10092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10095 \begin_layout Plain Layout
10099 \begin_inset space \textvisiblespace{}
10107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10110 \begin_layout Plain Layout
10111 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
10121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10124 \begin_layout Plain Layout
10128 \begin_inset space \textvisiblespace{}
10136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10139 \begin_layout Plain Layout
10140 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
10150 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10153 \begin_layout Plain Layout
10157 \begin_inset space \textvisiblespace{}
10165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10168 \begin_layout Plain Layout
10169 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
10179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10182 \begin_layout Plain Layout
10186 \begin_inset space \textvisiblespace{}
10190 \begin_inset Index idx
10193 \begin_layout Plain Layout
10204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10207 \begin_layout Plain Layout
10208 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
10218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10221 \begin_layout Plain Layout
10225 \begin_inset space \textvisiblespace{}
10233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10236 \begin_layout Plain Layout
10237 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
10247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10250 \begin_layout Plain Layout
10254 \begin_inset space \textvisiblespace{}
10262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10265 \begin_layout Plain Layout
10266 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
10280 \begin_inset space \hfill{}
10284 \begin_inset Tabular
10285 <lyxtabular version="3" rows="7" columns="2">
10286 <features tabularvalignment="middle">
10287 <column alignment="center" valignment="top" width="0pt">
10288 <column alignment="center" valignment="top" width="0pt">
10290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10293 \begin_layout Plain Layout
10299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10302 \begin_layout Plain Layout
10310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10313 \begin_layout Plain Layout
10317 \begin_inset space \textvisiblespace{}
10325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10328 \begin_layout Plain Layout
10329 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
10339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10342 \begin_layout Plain Layout
10346 \begin_inset space \textvisiblespace{}
10354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10357 \begin_layout Plain Layout
10358 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10371 \begin_layout Plain Layout
10375 \begin_inset space \textvisiblespace{}
10383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10386 \begin_layout Plain Layout
10387 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10400 \begin_layout Plain Layout
10404 \begin_inset space \textvisiblespace{}
10412 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10415 \begin_layout Plain Layout
10416 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10429 \begin_layout Plain Layout
10433 \begin_inset space \textvisiblespace{}
10441 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10444 \begin_layout Plain Layout
10445 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10458 \begin_layout Plain Layout
10462 \begin_inset space \textvisiblespace{}
10470 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10473 \begin_layout Plain Layout
10474 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10488 \begin_inset space \hfill{}
10494 \begin_layout Standard
10495 \begin_inset VSpace bigskip
10501 \begin_layout Standard
10502 You can directly insert accents like é to formulas.
10504 will transform them to the corresponding accent command.
10506 \begin_inset Index idx
10509 \begin_layout Plain Layout
10515 it is better to insert a quotation mark before the vowel.
10516 These two characters are then treated by \SpecialChar LaTeX
10521 character when the formula part with the umlaut is marked as German.
10529 \begin_inset Quotes eld
10533 \begin_inset Quotes erd
10536 umlauts are created as demonstrated in the following example:
10539 \begin_layout Standard
10540 \begin_inset VSpace -2mm
10546 \begin_layout Standard
10548 \begin_inset Tabular
10549 <lyxtabular version="3" rows="3" columns="2">
10550 <features tabularvalignment="middle">
10551 <column alignment="center" valignment="top">
10552 <column alignment="center" valignment="top">
10554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10557 \begin_layout Plain Layout
10563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10566 \begin_layout Plain Layout
10568 \begin_inset Note Note
10571 \begin_layout Plain Layout
10579 \begin_inset space \thinspace{}
10582 pt space are only used as spacer.
10594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10597 \begin_layout Plain Layout
10600 \begin_inset Quotes grd
10608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10611 \begin_layout Plain Layout
10612 \begin_inset space \hspace{}
10619 \begin_inset Formula $"i$
10629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10632 \begin_layout Plain Layout
10636 \begin_inset space \textvisiblespace{}
10644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10647 \begin_layout Plain Layout
10648 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10664 \begin_layout Standard
10665 Another advantage to
10671 is that umlauts can directly be converted to mathematical text because
10672 the accent commands above are
10678 in mathematical text
10681 To convert an accented character to mathematical text, only the character
10682 under the accent may be converted.
10683 This applies also for all other conversions, e.
10684 \begin_inset space \thinspace{}
10688 \begin_inset space \space{}
10694 \begin_layout Standard
10695 In mathematical text, umlauts and other accented characters can directly
10699 \begin_layout Standard
10700 \begin_inset VSpace bigskip
10706 \begin_layout Standard
10708 also supports a tilde under the character if the \SpecialChar LaTeX
10714 \begin_inset Index idx
10717 \begin_layout Plain Layout
10718 Packages ! undertilde
10723 is installed on your system:
10726 \begin_layout Standard
10730 \begin_layout Plain Layout
10740 \begin_inset Note Note
10743 \begin_layout Plain Layout
10744 The following table will only be displayed when the \SpecialChar LaTeX
10755 \begin_inset Separator parbreak
10761 \begin_layout Standard
10764 \begin_inset Tabular
10765 <lyxtabular version="3" rows="2" columns="2">
10766 <features tabularvalignment="middle">
10767 <column alignment="center" valignment="top" width="0pt">
10768 <column alignment="center" valignment="top" width="0pt">
10770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10773 \begin_layout Plain Layout
10779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10782 \begin_layout Plain Layout
10790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10793 \begin_layout Plain Layout
10797 \begin_inset space \textvisiblespace{}
10805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10808 \begin_layout Plain Layout
10809 \begin_inset Formula $\raisebox{5mm}{}\utilde{A}$
10825 \begin_layout Standard
10829 \begin_layout Plain Layout
10839 \begin_inset Note Note
10842 \begin_layout Plain Layout
10843 The following will be displayed when the \SpecialChar LaTeX
10856 \begin_layout Standard
10857 You need to install the \SpecialChar LaTeX
10862 to see the rest of this subsection in the output.
10865 \begin_layout Standard
10869 \begin_layout Plain Layout
10881 \begin_layout Standard
10882 \begin_inset Newpage newpage
10888 \begin_layout Subsection
10889 Accents for several Characters
10890 \begin_inset Index idx
10893 \begin_layout Plain Layout
10894 Accents ! for several characters
10902 \begin_layout Standard
10903 \begin_inset space \hfill{}
10907 \begin_inset Tabular
10908 <lyxtabular version="3" rows="5" columns="2">
10909 <features tabularvalignment="middle">
10910 <column alignment="center" valignment="top" width="0pt">
10911 <column alignment="center" valignment="top" width="0pt">
10913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10916 \begin_layout Plain Layout
10922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10925 \begin_layout Plain Layout
10927 \begin_inset Note Note
10930 \begin_layout Plain Layout
10937 is only used as spacer.
10949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10952 \begin_layout Plain Layout
10956 \begin_inset space \textvisiblespace{}
10964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10967 \begin_layout Plain Layout
10968 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10981 \begin_layout Plain Layout
10985 \begin_inset space \textvisiblespace{}
10993 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10996 \begin_layout Plain Layout
10997 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
11007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11014 \begin_inset space \textvisiblespace{}
11022 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11025 \begin_layout Plain Layout
11026 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
11036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11042 underleftrightarrow
11043 \begin_inset space \textvisiblespace{}
11051 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11054 \begin_layout Plain Layout
11055 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
11069 \begin_inset space \hfill{}
11073 \begin_inset Tabular
11074 <lyxtabular version="3" rows="5" columns="2">
11075 <features tabularvalignment="middle">
11076 <column alignment="center" valignment="top" width="0pt">
11077 <column alignment="center" valignment="top" width="0pt">
11079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11082 \begin_layout Plain Layout
11088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11091 \begin_layout Plain Layout
11099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11106 \begin_inset space \textvisiblespace{}
11114 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11117 \begin_layout Plain Layout
11118 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
11128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11135 \begin_inset space \textvisiblespace{}
11143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11146 \begin_layout Plain Layout
11147 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
11157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11164 \begin_inset space \textvisiblespace{}
11172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11175 \begin_layout Plain Layout
11176 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
11186 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11189 \begin_layout Plain Layout
11193 \begin_inset space \textvisiblespace{}
11201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11204 \begin_layout Plain Layout
11205 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11219 \begin_inset space \hfill{}
11225 \begin_layout Standard
11226 \begin_inset VSpace medskip
11229 With these commands as many characters as you like can be accented.
11242 will only be set in the output with a length of three characters, as shown
11243 in the following example:
11244 \begin_inset Formula
11246 \widetilde{A+B=C-D}
11254 \begin_layout Standard
11262 \begin_inset Index idx
11265 \begin_layout Plain Layout
11280 \begin_inset Index idx
11283 \begin_layout Plain Layout
11291 described in the previous subsection it is also possible to accent several
11298 \begin_inset space \textvisiblespace{}
11302 \begin_inset Formula $\downarrow$
11308 \begin_inset Formula
11310 \underset{***}{A=B}
11318 \begin_layout Section
11320 \begin_inset CommandInset label
11322 name "subsec:Space"
11327 \begin_inset Index idx
11330 \begin_layout Plain Layout
11339 \begin_layout Subsection
11341 \begin_inset CommandInset label
11343 name "subsec:Predefined-Space"
11348 \begin_inset Index idx
11351 \begin_layout Plain Layout
11352 Space ! horizontal ! predefined
11360 \begin_layout Standard
11361 Sometimes it is necessary to insert horizontal space into a formula.
11362 This is done by inserting a protected space (shortcut
11365 arg "command-alternatives space-insert protected ; math-space"
11370 \begin_inset Quotes eld
11376 \begin_inset space \textvisiblespace{}
11382 \begin_inset Quotes erd
11385 appears and by pressing
11389 several times one can select one of eight different space sizes.
11390 The spaces can also be inserted using the math toolbar button
11393 arg "math-insert \\space"
11396 or special commands.
11397 Independent from the inserted command, one can select the size again by
11403 \begin_inset Separator parbreak
11409 \begin_layout Standard
11412 \begin_inset Tabular
11413 <lyxtabular version="3" rows="6" columns="3">
11414 <features tabularvalignment="middle">
11415 <column alignment="center" valignment="top">
11416 <column alignment="center" valignment="top" width="15col%">
11417 <column alignment="center" valignment="top">
11419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11422 \begin_layout Plain Layout
11428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11431 \begin_layout Plain Layout
11441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11444 \begin_layout Plain Layout
11452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11455 \begin_layout Plain Layout
11463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11475 \begin_layout Plain Layout
11476 \begin_inset Formula $A\,B$
11486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11489 \begin_layout Plain Layout
11497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11500 \begin_layout Plain Layout
11506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11509 \begin_layout Plain Layout
11510 \begin_inset Formula $A\:B$
11520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11523 \begin_layout Plain Layout
11531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11534 \begin_layout Plain Layout
11540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11543 \begin_layout Plain Layout
11544 \begin_inset Formula $A\;B$
11554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11557 \begin_layout Plain Layout
11565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11568 \begin_layout Plain Layout
11574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11577 \begin_layout Plain Layout
11578 \begin_inset Formula $A\quad B$
11588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11591 \begin_layout Plain Layout
11599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11602 \begin_layout Plain Layout
11608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11611 \begin_layout Plain Layout
11612 \begin_inset Formula $A\qquad B$
11626 \begin_inset space \hfill{}
11630 \begin_inset Tabular
11631 <lyxtabular version="3" rows="6" columns="3">
11632 <features tabularvalignment="middle">
11633 <column alignment="center" valignment="top">
11634 <column alignment="center" valignment="top" width="15col%">
11635 <column alignment="center" valignment="top">
11637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11640 \begin_layout Plain Layout
11646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11649 \begin_layout Plain Layout
11659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11662 \begin_layout Plain Layout
11670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11673 \begin_layout Plain Layout
11681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11684 \begin_layout Plain Layout
11690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11693 \begin_layout Plain Layout
11694 \begin_inset Formula $A\hfill B$
11704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11707 \begin_layout Plain Layout
11715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11718 \begin_layout Plain Layout
11724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11727 \begin_layout Plain Layout
11728 \begin_inset Formula $A\hspace*{1em}B$
11738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11741 \begin_layout Plain Layout
11749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11752 \begin_layout Plain Layout
11758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11761 \begin_layout Plain Layout
11762 \begin_inset Formula $A\hspace{1em}B$
11772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11775 \begin_layout Plain Layout
11779 \begin_inset space \textvisiblespace{}
11787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11790 \begin_layout Plain Layout
11796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11799 \begin_layout Plain Layout
11800 \begin_inset Formula $A\ B$
11810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11813 \begin_layout Plain Layout
11821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11824 \begin_layout Plain Layout
11830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11833 \begin_layout Plain Layout
11834 \begin_inset Formula $A\!B$
11850 \begin_layout Standard
11852 \begin_inset space ~
11856 \begin_inset space \thinspace{}
11860 \begin_inset space \thinspace{}
11863 7 are variable spaces which are explained in
11864 \begin_inset CommandInset ref
11866 reference "subsec:Variable-Space"
11872 \begin_inset space ~
11875 9 seems to produce no space.
11876 It is displayed red in \SpecialChar LyX
11877 contrary to the other sizes, because it is a negative
11879 There are two more negative spaces:
11880 \begin_inset Separator parbreak
11886 \begin_layout Standard
11888 \begin_inset Tabular
11889 <lyxtabular version="3" rows="3" columns="3">
11890 <features tabularvalignment="middle">
11891 <column alignment="center" valignment="middle" width="6.8cm">
11892 <column alignment="center" valignment="top" width="0pt">
11893 <column alignment="center" valignment="top" width="0pt">
11895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11898 \begin_layout Plain Layout
11904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11907 \begin_layout Plain Layout
11915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11918 \begin_layout Plain Layout
11928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11931 \begin_layout Plain Layout
11936 keystrokes after inserting the protected space
11941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11944 \begin_layout Plain Layout
11950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11953 \begin_layout Plain Layout
11961 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11964 \begin_layout Plain Layout
11970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11973 \begin_layout Plain Layout
11974 \begin_inset Formula $A\negmedspace B$
11982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11985 \begin_layout Plain Layout
11986 \begin_inset Formula $A\negthickspace B$
12002 \begin_layout Standard
12003 Negative spaces can lead to characters overlapping each other.
12004 Thus they can be used to enforce ligatures, which are e.
12005 \begin_inset space \thinspace{}
12009 \begin_inset space \space{}
12012 useful for summation operators:
12013 \begin_inset Separator parbreak
12019 \begin_layout Standard
12021 \begin_inset Tabular
12022 <lyxtabular version="3" rows="3" columns="2">
12023 <features tabularvalignment="middle">
12024 <column alignment="center" valignment="top">
12025 <column alignment="center" valignment="top">
12027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12030 \begin_layout Plain Layout
12036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12039 \begin_layout Plain Layout
12041 \begin_inset Note Note
12044 \begin_layout Plain Layout
12051 is only used as spacer.
12063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12066 \begin_layout Plain Layout
12072 \begin_inset space \textvisiblespace{}
12080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12083 \begin_layout Plain Layout
12084 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
12094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12097 \begin_layout Plain Layout
12105 \begin_inset space \textvisiblespace{}
12113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12116 \begin_layout Plain Layout
12117 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
12133 \begin_layout Standard
12135 \begin_inset VSpace medskip
12141 \begin_layout Standard
12143 Relations like for example equal signs, are always surrounded by space.
12144 To suppress this, the equal sign is placed into a \SpecialChar TeX
12146 The following example demonstrates this:
12147 \begin_inset Separator parbreak
12153 \begin_layout Standard
12155 \begin_inset Tabular
12156 <lyxtabular version="3" rows="2" columns="2">
12157 <features tabularvalignment="middle">
12158 <column alignment="center" valignment="top" width="0pt">
12159 <column alignment="center" valignment="top" width="0pt">
12161 <cell alignment="center" valignment="top" usebox="none">
12164 \begin_layout Plain Layout
12170 <cell alignment="center" valignment="top" usebox="none">
12173 \begin_layout Plain Layout
12174 \begin_inset Formula $A=B$
12184 <cell alignment="center" valignment="top" usebox="none">
12187 \begin_layout Plain Layout
12188 \begin_inset Note Note
12191 \begin_layout Plain Layout
12198 is only used as spacer.
12204 \begin_inset Formula $\raisebox{5mm}{}$
12207 equation without space
12212 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
12215 \begin_layout Plain Layout
12216 \begin_inset Formula $A{=}B$
12232 \begin_layout Standard
12234 The command for the last formula is:
12239 \begin_inset Formula $\to$
12245 \begin_layout Standard
12246 \begin_inset VSpace bigskip
12252 \begin_layout Standard
12253 Spaces are needed for physical units, because the space between the value
12254 and the unit is the smallest one and not a normal space.
12255 For units in text, the smallest space is inserted via the menu
12257 Insert\SpecialChar menuseparator
12258 Formatting\SpecialChar menuseparator
12260 \begin_inset space ~
12268 arg "space-insert thin"
12274 \begin_layout Standard
12275 An example to visualize the difference:
12278 \begin_layout Standard
12279 \begin_inset Tabular
12280 <lyxtabular version="3" rows="2" columns="2">
12281 <features tabularvalignment="middle">
12282 <column alignment="left" valignment="top">
12283 <column alignment="left" valignment="top">
12285 <cell alignment="center" valignment="top" usebox="none">
12288 \begin_layout Plain Layout
12290 \begin_inset Formula $\cdot$
12298 <cell alignment="center" valignment="top" usebox="none">
12301 \begin_layout Plain Layout
12302 space between value and unit
12309 <cell alignment="center" valignment="top" usebox="none">
12312 \begin_layout Plain Layout
12314 \begin_inset space \thinspace{}
12318 \begin_inset Formula $\cdot$
12326 <cell alignment="center" valignment="top" usebox="none">
12329 \begin_layout Plain Layout
12330 smallest space between value and unit
12343 \begin_layout Subsection
12348 \begin_layout Plain Layout
12361 \begin_layout Plain Layout
12362 for vertical space in formulas see
12363 \begin_inset CommandInset ref
12365 reference "subsec:Line-Separation"
12378 \begin_layout Plain Layout
12386 \begin_inset Note Note
12389 \begin_layout Plain Layout
12392 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12395 \begin_layout Plain Layout
12398 texorpdfstring is in section
12399 \begin_inset CommandInset ref
12401 reference "subsec:Formulas-in-Section"
12411 \begin_inset CommandInset label
12413 name "subsec:Variable-Space"
12418 \begin_inset Index idx
12421 \begin_layout Plain Layout
12422 Space ! horizontal ! variable
12430 \begin_layout Standard
12431 Space with a defined length can be inserted with the command
12438 \begin_inset Index idx
12441 \begin_layout Plain Layout
12451 \begin_inset Quotes eld
12457 \begin_inset space \textvisiblespace{}
12463 \begin_inset Quotes erd
12467 The length can be specified by left-clicking on the
12468 \begin_inset Quotes eld
12474 \begin_inset space \textvisiblespace{}
12480 \begin_inset Quotes erd
12484 The length may also be negative.
12485 When a space would be the first character in a line it would be omitted.
12486 To force its output use the command
12498 or left-click on the
12499 \begin_inset Quotes eld
12505 \begin_inset space \textvisiblespace{}
12511 \begin_inset Quotes erd
12514 and check the option
12519 \begin_inset Newline newline
12522 To insert as much space as is available, the command
12529 \begin_inset Index idx
12532 \begin_layout Plain Layout
12543 \begin_layout Standard
12544 \begin_inset VSpace -1mm
12550 \begin_layout Standard
12552 \begin_inset Tabular
12553 <lyxtabular version="3" rows="4" columns="2">
12554 <features tabularvalignment="middle">
12555 <column alignment="center" valignment="top">
12556 <column alignment="center" valignment="top">
12558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12561 \begin_layout Plain Layout
12569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12572 \begin_layout Plain Layout
12580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12583 \begin_layout Plain Layout
12587 \begin_inset space \textvisiblespace{}
12593 \begin_inset space \thinspace{}
12601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12604 \begin_layout Plain Layout
12605 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12618 \begin_layout Plain Layout
12622 \begin_inset space \textvisiblespace{}
12628 \begin_inset space \thinspace{}
12636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12639 \begin_layout Plain Layout
12640 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12653 \begin_layout Plain Layout
12657 \begin_inset space \textvisiblespace{}
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12668 \begin_layout Plain Layout
12669 \begin_inset Formula $A=A\hfill B=B$
12685 \begin_layout Standard
12686 In the last example the available space is given by the longest column entry
12688 In an inline formula the space depends on the length of the line in which
12696 Thus, when the line uses the full width, no space will be created.
12703 only has an effect on displayed formulas when the formula style
12708 (Formula styles are explained in
12709 \begin_inset CommandInset ref
12711 reference "sec:Formula-Styles"
12718 \begin_layout Standard
12725 , there are the commands
12737 that fill the space with a pattern, see
12738 \begin_inset CommandInset ref
12740 reference "subsec:Ellipses"
12747 \begin_layout Standard
12748 For text, variable space can be inserted via the menu
12750 Insert\SpecialChar menuseparator
12751 Formatting\SpecialChar menuseparator
12753 \begin_inset space ~
12761 \begin_layout Standard
12762 This is a line with
12763 \begin_inset space \hspace{}
12768 \begin_inset space \thinspace{}
12774 \begin_layout Standard
12775 This is a line with
12776 \begin_inset space \hfill{}
12782 \begin_layout Subsection
12783 Space besides inline Formulas
12784 \begin_inset Index idx
12787 \begin_layout Plain Layout
12788 Space ! besides inline formulas
12796 \begin_layout Standard
12797 The space that surrounds inline formulas can be adjusted with the length
12805 \begin_inset Index idx
12808 \begin_layout Plain Layout
12817 The value of a length is set with the command
12824 \begin_inset Index idx
12827 \begin_layout Plain Layout
12835 which has the following scheme:
12838 \begin_layout Standard
12843 setlength{length name}{value}
12846 \begin_layout Standard
12854 \begin_inset space \thinspace{}
12860 \begin_layout Standard
12870 \begin_layout Standard
12871 is inserted in \SpecialChar TeX
12874 \begin_inset space \thinspace{}
12877 mm space will now be set around all inline formulas:
12881 \begin_layout Plain Layout
12895 \begin_layout Standard
12896 This is a line with an inline formula
12897 \begin_inset Formula $A=B$
12901 \begin_inset space \thinspace{}
12904 mm surrounding space.
12908 \begin_layout Plain Layout
12922 \begin_layout Standard
12923 To return to the predefined value,
12929 is set to the value 0
12930 \begin_inset space \thinspace{}
12936 \begin_layout Section
12938 \begin_inset Index idx
12941 \begin_layout Plain Layout
12948 \begin_inset Index idx
12951 \begin_layout Plain Layout
12956 \begin_layout Plain Layout
12967 \begin_layout Plain Layout
12982 \begin_layout Standard
12983 Boxes for text are described in chapter
12990 \begin_inset space ~
12998 \begin_layout Subsection
13000 \begin_inset CommandInset label
13002 name "subsec:Boxes-with-Frame"
13007 \begin_inset Index idx
13010 \begin_layout Plain Layout
13019 \begin_layout Standard
13020 It is possible to frame a formula or part of one with the commands
13027 \begin_inset Index idx
13030 \begin_layout Plain Layout
13045 \begin_inset Index idx
13048 \begin_layout Plain Layout
13059 \begin_layout Standard
13060 When one of these commands is inserted in a formula, a blue box appears
13061 within a frame to enter formula parts.
13068 an additional formula has to be created by
13072 within this box, because the box content will otherwise be treated as mathemati
13080 is used, a new formula is automatically created inside the frame.
13083 \begin_layout Standard
13090 is not suitable to frame displayed formulas because the formula will always
13091 be set in the size of the text.
13098 is in contrary not suitable to frame inline formulas, because the formula
13099 will always be set in the size of a displayed formula.
13102 \begin_layout Standard
13116 \begin_inset Index idx
13119 \begin_layout Plain Layout
13127 where additionally the frame width and the alignment can be specified.
13134 is used in the following scheme:
13137 \begin_layout Standard
13142 framebox[frame width][position]{box content}
13145 \begin_layout Standard
13146 The position can either be
13163 right aligns the formula in the box.
13164 When no position is given, the formula will be centered.
13165 \begin_inset Newline newline
13168 If no width is given, also no position can be given.
13169 In this case the frame width is adjusted to the box content like for
13178 \begin_layout Standard
13185 is inserted, a box appears containing three blue boxes.
13186 The first two boxes are surrounded by brackets and denote the two optional
13188 The third box is for formula parts like for
13195 \begin_inset Separator parbreak
13201 \begin_layout Standard
13203 \begin_inset Tabular
13204 <lyxtabular version="3" rows="5" columns="2">
13205 <features tabularvalignment="middle">
13206 <column alignment="center" valignment="top">
13207 <column alignment="center" valignment="top">
13209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13212 \begin_layout Plain Layout
13218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13221 \begin_layout Plain Layout
13223 \begin_inset Note Note
13226 \begin_layout Plain Layout
13233 is only used as spacer.
13245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13248 \begin_layout Plain Layout
13252 \begin_inset space \textvisiblespace{}
13262 \begin_inset space \textvisiblespace{}
13270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13273 \begin_layout Plain Layout
13274 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
13284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13287 \begin_layout Plain Layout
13291 \begin_inset space \textvisiblespace{}
13297 \begin_inset space \textvisiblespace{}
13305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13308 \begin_layout Plain Layout
13309 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
13319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13322 \begin_layout Plain Layout
13326 \begin_inset space \textvisiblespace{}
13334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13337 \begin_layout Plain Layout
13338 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13351 \begin_layout Plain Layout
13355 \begin_inset space \textvisiblespace{}
13359 \begin_inset Formula $\to$
13363 \begin_inset Formula $\to$
13373 \begin_inset space \textvisiblespace{}
13377 \begin_inset Formula $\downarrow$
13385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13388 \begin_layout Plain Layout
13389 \begin_inset Formula $\raisebox{6mm}{}$
13393 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13397 \begin_inset Formula $\raisebox{-4mm}{}$
13413 \begin_layout Standard
13414 The frame thickness can also be adjusted.
13415 To do this the following commands have to be inserted in \SpecialChar TeX
13420 \begin_layout Standard
13430 \begin_inset Quotes eld
13434 \begin_inset Quotes erd
13448 \begin_inset Quotes eld
13452 \begin_inset Quotes erd
13458 \begin_layout Standard
13459 \begin_inset Quotes eld
13463 \begin_inset Quotes erd
13466 specifies the minimal distance between the frame and the first character
13468 An example for this is the following framed formula:
13472 \begin_layout Plain Layout
13484 \begin_inset Formula
13491 Before this formula the commands
13494 \begin_layout Standard
13516 \begin_layout Standard
13517 were inserted in \SpecialChar TeX
13519 The given values are used for all following boxes.
13522 \begin_layout Standard
13523 To return to the standard frame size, the command
13526 \begin_layout Standard
13551 \begin_layout Plain Layout
13565 \begin_layout Standard
13566 is inserted in \SpecialChar TeX
13567 mode before the next formula.
13570 \begin_layout Subsection
13571 Boxes without Frame
13572 \begin_inset CommandInset label
13574 name "subsec:Boxes-without-Frame"
13579 \begin_inset Index idx
13582 \begin_layout Plain Layout
13583 Boxes ! without frame
13591 \begin_layout Standard
13592 For boxes without a frame there are the following box commands:
13599 \begin_inset Index idx
13602 \begin_layout Plain Layout
13617 \begin_inset Index idx
13620 \begin_layout Plain Layout
13635 \begin_inset Index idx
13638 \begin_layout Plain Layout
13649 \begin_layout Standard
13656 a box can be super- or subscripted.
13657 But in contrary to normal super- and subscripting, the characters in the
13658 box keep their font size.
13665 is used in the following scheme:
13668 \begin_layout Standard
13673 raisebox{height}{box content}
13676 \begin_layout Standard
13677 When the box should contain a formula, an extra formula is needed like for
13688 \begin_inset Note Greyedout
13691 \begin_layout Plain Layout
13702 this extra formula is created by pressing
13706 twice instead of once because \SpecialChar LyX
13707 doesn't yet support
13721 \begin_inset Separator parbreak
13727 \begin_layout Standard
13729 \begin_inset Tabular
13730 <lyxtabular version="3" rows="4" columns="2">
13731 <features tabularvalignment="middle">
13732 <column alignment="center" valignment="top">
13733 <column alignment="center" valignment="top">
13735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13738 \begin_layout Plain Layout
13744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13747 \begin_layout Plain Layout
13755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13758 \begin_layout Plain Layout
13762 \begin_inset Formula $\to$
13768 \begin_inset Formula $\to$
13776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13779 \begin_layout Plain Layout
13780 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13793 \begin_layout Plain Layout
13797 \begin_inset Formula $\to$
13803 \begin_inset Formula $\to$
13811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13814 \begin_layout Plain Layout
13815 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13825 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13828 \begin_layout Plain Layout
13832 \begin_inset Formula $\to$
13848 \begin_inset space \textvisiblespace{}
13856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13859 \begin_layout Plain Layout
13860 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13876 \begin_layout Standard
13901 , with the difference that there is no frame.
13904 \begin_layout Subsection
13906 \begin_inset CommandInset label
13908 name "subsec:Colored-Boxes"
13913 \begin_inset Index idx
13916 \begin_layout Plain Layout
13925 \begin_layout Standard
13926 To be able to use all commands explained in this section, the \SpecialChar LaTeX
13935 \begin_layout Plain Layout
13936 The \SpecialChar LaTeX
13941 is part of every \SpecialChar LaTeX
13942 standard installation.
13948 \begin_inset Index idx
13951 \begin_layout Plain Layout
13957 has to be loaded in the \SpecialChar LaTeX
13958 -preamble with the line
13962 \begin_layout Plain Layout
13963 When text is colored somewhere in the document with a predefined color,
13965 loads the \SpecialChar LaTeX
13971 Thus it is possible that the package is loaded twice, but this does not
13978 \begin_inset Note Note
13981 \begin_layout Plain Layout
13982 To avoid that the package is loaded twice, a macro was inserted to the \SpecialChar LaTeX
13991 \begin_layout Standard
13999 \begin_layout Standard
14000 \begin_inset VSpace medskip
14003 To color boxes, the command
14010 \begin_inset Index idx
14013 \begin_layout Plain Layout
14021 is used in the following scheme:
14024 \begin_layout Standard
14029 colorbox{color}{box content}
14032 \begin_layout Standard
14033 The box content can also be a box and a
14039 can also be part of another box (see the 2nd and 3rd example).
14040 When the box should contain a formula, an extra formula has to be created,
14041 the same way as for
14051 \begin_layout Plain Layout
14052 This also applies for the command
14066 \begin_layout Standard
14067 One of the following predefined colors can be chosen:
14070 \begin_layout Standard
14104 \begin_inset Separator parbreak
14110 \begin_layout Standard
14112 \begin_inset Tabular
14113 <lyxtabular version="3" rows="4" columns="2">
14114 <features tabularvalignment="middle">
14115 <column alignment="center" valignment="top">
14116 <column alignment="center" valignment="top">
14118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14121 \begin_layout Plain Layout
14127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14130 \begin_layout Plain Layout
14132 \begin_inset Note Note
14135 \begin_layout Plain Layout
14142 is only used as spacer.
14154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14157 \begin_layout Plain Layout
14161 \begin_inset Formula $\to$
14171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14174 \begin_layout Plain Layout
14175 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
14185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14188 \begin_layout Plain Layout
14192 \begin_inset Formula $\to$
14200 \begin_inset space \textvisiblespace{}
14208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14211 \begin_layout Plain Layout
14212 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
14222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14225 \begin_layout Plain Layout
14229 \begin_inset space \textvisiblespace{}
14235 \begin_inset Formula $\to$
14251 \begin_inset space \textvisiblespace{}
14259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14262 \begin_layout Plain Layout
14263 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
14279 \begin_layout Standard
14286 only colors the box but not the characters in the box.
14287 To color all characters, the whole formula is highlighted and the desired
14288 color is chosen in the
14291 \begin_inset space ~
14297 The dialog can be called with the toolbar button
14300 arg "dialog-show character"
14305 Edit\SpecialChar menuseparator
14307 \begin_inset space ~
14310 Style\SpecialChar menuseparator
14314 The formula number then has the same color as the formula.
14315 When the formula number should get another color than the formula characters,
14316 the color must be changed within the formula.
14319 \begin_layout Standard
14323 \begin_layout Standard
14326 \begin_inset Formula
14328 \int A=B\label{eq:red}
14336 \begin_inset Formula
14338 \textcolor{red}{\int A=B}\label{eq:redgreen}
14346 \begin_layout Standard
14348 \begin_inset CommandInset ref
14354 is completely colored red.
14355 \begin_inset Newline newline
14359 \begin_inset CommandInset ref
14361 reference "eq:redgreen"
14365 was first completely colored green to set the color for the formula number.
14366 Subsequently the formula characters were colored red.
14369 \begin_layout Standard
14370 \begin_inset VSpace bigskip
14373 To color the frame different than the rest of the box, the command
14380 \begin_inset Index idx
14383 \begin_layout Plain Layout
14391 is used in the following scheme:
14394 \begin_layout Standard
14399 fcolorbox{frame color}{color}{box content}
14402 \begin_layout Standard
14409 is an extension of the command
14416 The frame width is set, like for
14439 \begin_layout Plain Layout
14451 \begin_inset Formula
14453 \fcolorbox{cyan}{magenta}{A=B}
14462 \begin_layout Plain Layout
14476 \begin_layout Standard
14477 This formula was created with the command
14478 \begin_inset Newline newline
14486 \begin_inset Formula $\to$
14492 \begin_inset Formula $\to$
14502 \begin_layout Standard
14503 \begin_inset VSpace bigskip
14506 To use other colors than the predefined ones, they have to be defined first.
14509 \begin_layout Standard
14510 One can for example define the color
14511 \begin_inset Quotes eld
14519 \begin_inset Quotes erd
14522 with the \SpecialChar LaTeX
14526 \begin_layout Standard
14531 definecolor{darkgreen}{cmyk}{0.5,
14546 \begin_inset Index idx
14549 \begin_layout Plain Layout
14560 \begin_layout Standard
14565 is the color space that denotes the colors
14582 The four comma separated numbers are the portion factor for the corresponding
14583 colors of the color space.
14584 The factors can be in the range of 0
14585 \begin_inset space \thinspace{}
14589 \begin_inset space \thinspace{}
14597 also the color space
14601 can be used for definitions.
14618 , so that there are in this case three portion factors for the corresponding
14620 Furthermore there is the color space
14624 with one portion factor for the gray value.
14627 \begin_layout Standard
14628 As example a framed box with the new defined color
14632 where the characters have been colored
14637 \begin_inset Formula
14639 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14647 \begin_layout Standard
14648 Self-defined colors can also be used for text with the help of the command
14656 \begin_inset Index idx
14659 \begin_layout Plain Layout
14668 \begin_layout Standard
14672 \begin_layout Plain Layout
14676 textcolor{darkgreen}{
14682 \begin_inset Quotes eld
14686 \begin_inset Quotes erd
14693 \begin_layout Plain Layout
14703 \begin_layout Standard
14711 \begin_inset Index idx
14714 \begin_layout Plain Layout
14722 is used in the scheme
14726 textcolor{color}{characters to color}
14731 \begin_layout Subsection
14733 \begin_inset CommandInset label
14735 name "subsec:Paragraph-Boxes"
14740 \begin_inset Index idx
14743 \begin_layout Plain Layout
14744 Boxes ! as paragraph
14752 \begin_layout Standard
14753 A box that can contain several lines and paragraphs, a so-called paragraph
14754 box (parbox), can be created with the menu
14756 Insert\SpecialChar menuseparator
14759 or the toolbar button
14768 \begin_layout Standard
14769 The following example shows a framed parbox in a line:
14772 \begin_layout Standard
14773 \begin_inset VSpace medskip
14777 \begin_inset Box Boxed
14787 height_special "totalheight"
14792 backgroundcolor "none"
14795 \begin_layout Plain Layout
14796 This is a paragraph box.
14798 \begin_inset space \thinspace{}
14801 cm long and can also contain formulas:
14802 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14813 \begin_layout Standard
14814 \begin_inset VSpace medskip
14820 \begin_layout Standard
14821 Such a box is created by right-clicking on the gray box inset.
14822 A dialog pops up showing the box properties.
14836 \begin_inset space \thinspace{}
14841 Vertical Box Alignment
14846 \begin_layout Standard
14847 \begin_inset VSpace medskip
14850 In \SpecialChar LaTeX
14851 a parbox is created with the command
14858 \begin_inset Index idx
14861 \begin_layout Plain Layout
14869 which has the following scheme:
14872 \begin_layout Standard
14877 parbox[position]{width}{box content}
14880 \begin_layout Standard
14895 \begin_inset Quotes eld
14899 \begin_inset Quotes erd
14902 means that the box is aligned within the surrounding text with its last
14909 \begin_inset Quotes eld
14913 \begin_inset Quotes erd
14916 this is done with the first line.
14917 When no position is given, the box will be vertically centered, see section
14925 \begin_inset space ~
14930 manual for examples.
14933 \begin_layout Standard
14934 \begin_inset VSpace bigskip
14937 To frame formulas completely, including the formula number, the formula
14938 must be set into a parbox.
14939 To do this, the command
14953 is inserted in \SpecialChar TeX
14954 mode before the formula.
14962 \begin_inset Index idx
14965 \begin_layout Plain Layout
14973 is hereby the line width set for the document.
14974 Because the frame is outside the parbox, 2
14975 \begin_inset space \thinspace{}
14978 times the frame separation and the frame thickness must be subtracted from
14980 As this is not automatically done by \SpecialChar LyX
14985 \begin_layout Plain Layout
14986 \begin_inset CommandInset href
14988 name "LyX-bug #4483"
14989 target "http://www.lyx.org/trac/ticket/4483"
14999 mode has to be used.
15000 To be able to multiply and subtract in arguments, the \SpecialChar LaTeX
15009 \begin_layout Plain Layout
15014 is part of every \SpecialChar LaTeX
15015 standard installation.
15021 \begin_inset Index idx
15024 \begin_layout Plain Layout
15030 must be loaded in the \SpecialChar LaTeX
15031 -preamble with the line
15034 \begin_layout Standard
15042 \begin_layout Standard
15043 Behind the formula both boxes are closed by entering
15047 in \SpecialChar TeX
15049 Here is an example:
15053 \begin_layout Plain Layout
15067 \begin_layout Standard
15071 \begin_layout Plain Layout
15089 \begin_inset Formula
15091 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
15100 \begin_layout Plain Layout
15111 \begin_layout Plain Layout
15125 \begin_layout Standard
15126 \begin_inset VSpace medskip
15129 As a parbox is used as the argument of
15135 , there is in this case no difference between
15150 \begin_layout Standard
15151 \begin_inset VSpace bigskip
15154 Paragraph boxes are very useful to comment formulas directly.
15161 is used in combination with the command
15175 \begin_inset CommandInset ref
15177 reference "subsec:User-defined-Numbering"
15184 \begin_layout Standard
15185 An example of a formula commented with
15194 \begin_layout Standard
15198 \begin_layout Plain Layout
15211 This is a description.
15212 It is distinctly separated from the formula and multiline.
15216 \begin_layout Plain Layout
15228 \begin_layout Standard
15229 Such a formula must be inserted completely in \SpecialChar TeX
15230 mode because \SpecialChar LyX
15232 support the command
15239 The formula is created with the following command sequence:
15242 \begin_layout Standard
15255 is inserted in \SpecialChar TeX
15260 \begin_layout Plain Layout
15261 When the formula style
15273 can also be replaced by
15280 (formula styles see
15281 \begin_inset CommandInset ref
15283 reference "sec:Formula-Styles"
15292 Then the description follows as normal text and finally
15298 is inserted in \SpecialChar TeX
15312 hereby create a displayed formula.
15315 \begin_layout Standard
15322 can be seen in this example that was
15323 \begin_inset Quotes eld
15327 \begin_inset Quotes erd
15330 using the mathematical textmode:
15331 \begin_inset Formula
15333 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15341 \begin_layout Section
15343 \begin_inset Index idx
15346 \begin_layout Plain Layout
15355 \begin_layout Subsection
15357 \begin_inset CommandInset label
15359 name "subsec:Big-Operators"
15364 \begin_inset Index idx
15367 \begin_layout Plain Layout
15374 \begin_inset Index idx
15377 \begin_layout Plain Layout
15384 \begin_inset Index idx
15387 \begin_layout Plain Layout
15396 \begin_layout Standard
15397 To be able to use all integral operators listed here, the option
15399 Use esint package automatically
15401 must be set in the document settings under
15404 \begin_inset space ~
15412 \begin_layout Standard
15413 \begin_inset space \hfill{}
15417 \begin_inset Tabular
15418 <lyxtabular version="3" rows="11" columns="2">
15419 <features tabularvalignment="middle">
15420 <column alignment="center" valignment="top" width="0pt">
15421 <column alignment="center" valignment="top" width="0pt">
15423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15426 \begin_layout Plain Layout
15432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15435 \begin_layout Plain Layout
15443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15446 \begin_layout Plain Layout
15450 \begin_inset Index idx
15453 \begin_layout Plain Layout
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15469 \begin_layout Plain Layout
15470 \begin_inset Formula $\int$
15480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15483 \begin_layout Plain Layout
15491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15494 \begin_layout Plain Layout
15495 \begin_inset Formula $\oint$
15505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15508 \begin_layout Plain Layout
15516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15519 \begin_layout Plain Layout
15520 \begin_inset Formula $\ointctrclockwise$
15530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15533 \begin_layout Plain Layout
15541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15544 \begin_layout Plain Layout
15545 \begin_inset Formula $\ointclockwise$
15555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15558 \begin_layout Plain Layout
15566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15569 \begin_layout Plain Layout
15570 \begin_inset Formula $\sqint$
15580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15583 \begin_layout Plain Layout
15591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15594 \begin_layout Plain Layout
15596 \begin_inset Formula $\fint$
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15609 \begin_layout Plain Layout
15617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15620 \begin_layout Plain Layout
15622 \begin_inset Formula $\landupint$
15632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15635 \begin_layout Plain Layout
15643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15646 \begin_layout Plain Layout
15648 \begin_inset Formula $\landdownint$
15658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15661 \begin_layout Plain Layout
15669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15672 \begin_layout Plain Layout
15673 \begin_inset Formula $\bigcap$
15683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15686 \begin_layout Plain Layout
15694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15697 \begin_layout Plain Layout
15698 \begin_inset Formula $\bigcup$
15712 \begin_inset space \hfill{}
15716 \begin_inset Tabular
15717 <lyxtabular version="3" rows="11" columns="2">
15718 <features tabularvalignment="middle">
15719 <column alignment="center" valignment="top" width="0pt">
15720 <column alignment="center" valignment="top" width="0pt">
15722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15725 \begin_layout Plain Layout
15731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15734 \begin_layout Plain Layout
15742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15745 \begin_layout Plain Layout
15749 \begin_inset Index idx
15752 \begin_layout Plain Layout
15765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15768 \begin_layout Plain Layout
15769 \begin_inset Formula $\sum$
15779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15782 \begin_layout Plain Layout
15786 \begin_inset Index idx
15789 \begin_layout Plain Layout
15796 \begin_layout Plain Layout
15815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15818 \begin_layout Plain Layout
15819 \begin_inset Formula $\prod$
15829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15832 \begin_layout Plain Layout
15840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15843 \begin_layout Plain Layout
15844 \begin_inset Formula $\coprod$
15854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15857 \begin_layout Plain Layout
15865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15868 \begin_layout Plain Layout
15869 \begin_inset Formula $\bigodot$
15879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15882 \begin_layout Plain Layout
15890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15893 \begin_layout Plain Layout
15894 \begin_inset Formula $\bigotimes$
15904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15907 \begin_layout Plain Layout
15915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15918 \begin_layout Plain Layout
15919 \begin_inset Formula $\bigoplus$
15929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15932 \begin_layout Plain Layout
15940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15943 \begin_layout Plain Layout
15944 \begin_inset Formula $\bigwedge$
15954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15957 \begin_layout Plain Layout
15965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15968 \begin_layout Plain Layout
15969 \begin_inset Formula $\bigvee$
15979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15982 \begin_layout Plain Layout
15990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15993 \begin_layout Plain Layout
15994 \begin_inset Formula $\bigsqcup$
16004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16007 \begin_layout Plain Layout
16015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16018 \begin_layout Plain Layout
16019 \begin_inset Formula $\biguplus$
16033 \begin_inset space \hfill{}
16039 \begin_layout Standard
16040 All big operators can also be inserted via the math toolbar button
16043 arg "math-insert \\intop"
16049 \begin_layout Standard
16050 The operators are called big because they are bigger than the sometimes
16051 equal looking binary operators.
16052 All big operators can have limits as described in the next subsection.
16055 \begin_layout Standard
16056 For all integral operators there is a second version available, ending in
16074 These operators are different from
16081 \begin_inset space \space{}
16084 in the style the operator limits are displayed, see
16085 \begin_inset CommandInset ref
16087 reference "subsec:Operator-Limits"
16095 \begin_layout Subsubsection*
16096 Advice for Integrals
16099 \begin_layout Standard
16104 in an integral is an operator, that therefore has to be set upright.
16105 This is done by highlighting the
16109 and using the keyboard shortcut
16119 \begin_layout Plain Layout
16125 \begin_inset CommandInset ref
16127 reference "subsec:Font-Styles"
16137 Finally the smallest space is inserted before the
16141 , as this is usual for operators.
16145 \begin_layout Standard
16147 \begin_inset Formula $\int A(x)dx$
16151 \begin_inset Newline newline
16155 \begin_inset Phantom HPhantom
16158 \begin_layout Plain Layout
16165 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
16171 \begin_layout Standard
16172 For multiple integrals there are the following commands:
16173 \begin_inset VSpace medskip
16179 \begin_layout Standard
16180 \begin_inset space \hfill{}
16184 \begin_inset Tabular
16185 <lyxtabular version="3" rows="4" columns="2">
16186 <features tabularvalignment="middle">
16187 <column alignment="center" valignment="top">
16188 <column alignment="center" valignment="top">
16190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16193 \begin_layout Plain Layout
16199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16202 \begin_layout Plain Layout
16204 \begin_inset Note Note
16207 \begin_layout Plain Layout
16214 is only used as spacer.
16226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16229 \begin_layout Plain Layout
16237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16240 \begin_layout Plain Layout
16241 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
16251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16254 \begin_layout Plain Layout
16262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16265 \begin_layout Plain Layout
16266 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
16276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16279 \begin_layout Plain Layout
16287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16290 \begin_layout Plain Layout
16291 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
16305 \begin_inset space \hfill{}
16309 \begin_inset Tabular
16310 <lyxtabular version="3" rows="4" columns="2">
16311 <features tabularvalignment="middle">
16312 <column alignment="center" valignment="top">
16313 <column alignment="center" valignment="top">
16315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16318 \begin_layout Plain Layout
16324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16327 \begin_layout Plain Layout
16335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16338 \begin_layout Plain Layout
16346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16349 \begin_layout Plain Layout
16350 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16363 \begin_layout Plain Layout
16371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16374 \begin_layout Plain Layout
16375 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16388 \begin_layout Plain Layout
16396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16399 \begin_layout Plain Layout
16400 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16414 \begin_inset space \hfill{}
16420 \begin_layout Subsection
16422 \begin_inset CommandInset label
16424 name "subsec:Operator-Limits"
16429 \begin_inset Index idx
16432 \begin_layout Plain Layout
16441 \begin_layout Standard
16442 Limits are created by super- and subscripts:
16443 \begin_inset Separator parbreak
16449 \begin_layout Standard
16451 \begin_inset Tabular
16452 <lyxtabular version="3" rows="2" columns="2">
16453 <features tabularvalignment="middle">
16454 <column alignment="center" valignment="top" width="0pt">
16455 <column alignment="center" valignment="top" width="0pt">
16457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16460 \begin_layout Plain Layout
16466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16469 \begin_layout Plain Layout
16471 \begin_inset Note Note
16474 \begin_layout Plain Layout
16481 is only used as spacer.
16493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16496 \begin_layout Plain Layout
16502 \begin_inset space \textvisiblespace{}
16506 \begin_inset Formula $\to$
16510 \begin_inset Formula $\to$
16518 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16521 \begin_layout Plain Layout
16522 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16538 \begin_layout Standard
16539 Limits of inline formulas are set right beside the operator.
16540 Limits in displayed formulas are set above or below the operator, except
16541 for integral limits.
16544 \begin_layout Standard
16545 To force that the limits are set beside the operator, the cursor is set
16546 directly behind the operator and the limits type is changed with the menu
16549 Edit\SpecialChar menuseparator
16550 Math\SpecialChar menuseparator
16569 \begin_layout Standard
16570 The default limits type is this:
16571 \begin_inset Formula
16573 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16578 This is how it looks when the limits type was changed to
16585 \begin_inset Formula
16587 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16592 For integrals, except those ending with
16608 etc., the limits are by default set beside the operator.
16609 But for multiple integrals the limits are often set below the operator.
16610 In the following example the limits type was therefore set to
16614 and so set below the integrals:
16615 \begin_inset Formula
16617 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16625 \begin_layout Standard
16626 \begin_inset VSpace medskip
16629 To specify conditions for limits, the commands
16636 \begin_inset Index idx
16639 \begin_layout Plain Layout
16654 \begin_inset Index idx
16657 \begin_layout Plain Layout
16666 To create for example this expression
16667 \begin_inset Formula
16669 \sum_{\begin{subarray}{c}
16673 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16681 \begin_layout Standard
16682 the following has to be done:
16683 \begin_inset Newline newline
16695 \begin_inset space \textvisiblespace{}
16701 One is now in a blue box under the summation operator and insert there
16707 \begin_inset space \textvisiblespace{}
16713 The blue box is now within a purple box and now several lines can be written
16715 A new line is created by inserting a line break (
16718 arg "newline-insert newline"
16723 \begin_inset Newline newline
16728 0<k<1000 Ctrl+Return
16729 \begin_inset Newline newline
16734 is typed in, a new box appears below for the new line.
16737 \begin_layout Standard
16738 The alignment of the lines can be changed to left aligned with the
16748 Edit\SpecialChar menuseparator
16752 To get right alignment,
16757 \begin_inset space \textvisiblespace{}
16762 is inserted at the beginning of the line.
16765 \begin_layout Standard
16778 with the difference that the lines are always centered.
16781 \begin_layout Standard
16782 \begin_inset VSpace bigskip
16786 \begin_inset CommandInset ref
16788 reference "eq:substack"
16792 there can be too much space beside an operator, because the characters
16793 following the operator are set beside the limits.
16794 To avoid this the command
16801 \begin_inset Index idx
16804 \begin_layout Plain Layout
16813 To activate it, set in the document settings under
16816 \begin_inset space ~
16826 \begin_inset Index idx
16829 \begin_layout Plain Layout
16830 Packages ! mathtools
16838 \begin_inset space ~
16850 sets the space besides the operator to 0
16851 \begin_inset space \thinspace{}
16855 \begin_inset Newline newline
16859 \begin_inset CommandInset ref
16861 reference "eq:substack"
16865 , one uses the command
16868 \begin_layout Standard
16876 \begin_layout Standard
16877 and inserts the operator with its limits into the braces.
16878 Behind the brace one continues the formula:
16879 \begin_inset Formula
16881 \smashoperator{\sum_{\begin{subarray}{c}
16885 \end{subarray}}^{n}}k^{-2}
16893 \begin_layout Standard
16894 It is possible to set the space of only one side of the operator to 0
16895 \begin_inset space \thinspace{}
16899 To do this write either
16918 stands for the left and
16922 for the right side of the operator.
16923 Here is an example of the possible
16932 \begin_layout Standard
16933 \begin_inset Formula
16935 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}
16943 \begin_layout Standard
16944 \begin_inset VSpace bigskip
16950 \begin_layout Standard
16951 When several consecutive operators have limits the typesetting of the limits
16952 looks often imperfect in the output, see this example:
16953 \begin_inset Formula
16955 \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}
16960 To improve the typesetting set in the document settings under
16963 \begin_inset space ~
16973 \begin_inset Index idx
16976 \begin_layout Plain Layout
16977 Packages ! mathtools
16985 \begin_inset space ~
16991 Then insert into your formula the command
16998 \begin_inset Index idx
17001 \begin_layout Plain Layout
17009 directly before the first operator.
17010 The example will then look like this:
17011 \begin_inset Formula
17013 \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}
17021 \begin_layout Standard
17022 \begin_inset VSpace bigskip
17025 How to use one limit for several operators is described in
17026 \begin_inset CommandInset ref
17028 reference "subsec:Self-defined-Operators"
17035 \begin_layout Subsection
17036 Decoration for Operators
17037 \begin_inset Index idx
17040 \begin_layout Plain Layout
17041 Operators ! Decoration
17049 \begin_layout Standard
17057 \begin_inset Index idx
17060 \begin_layout Plain Layout
17075 \begin_inset Index idx
17078 \begin_layout Plain Layout
17086 characters can be placed above or below an operator, respectively.
17094 \begin_inset Index idx
17097 \begin_layout Plain Layout
17105 characters can be set before and behind a big operator.
17108 \begin_layout Standard
17110 \begin_inset space ~
17122 \begin_layout Itemize
17129 is used to set characters at the corners of the operator
17132 \begin_layout Itemize
17139 is used to set characters before and/or behind the operator (this variant
17140 represents \SpecialChar LaTeX
17150 \begin_layout Itemize
17157 is used to set characters at the left corners and/or behind the operator
17160 \begin_layout Itemize
17167 is used to set characters at the right corners and/or before the operator
17170 \begin_layout Standard
17171 For example the command
17176 \begin_inset space \textvisiblespace{}
17182 \begin_inset space \textvisiblespace{}
17186 \begin_inset Formula $\to$
17190 \begin_inset Formula $\to$
17194 \begin_inset space \textvisiblespace{}
17204 \begin_inset Formula
17206 \sideset{}{'}\sum_{k=1}^{n}
17214 \begin_layout Standard
17215 \begin_inset Note Greyedout
17218 \begin_layout Plain Layout
17225 can only be used to decorate big operators, binary operators are not allowed.
17233 \begin_layout Standard
17246 can also be used to decorate symbols and characters.
17247 For example, the command
17252 \begin_inset space \textvisiblespace{}
17258 \begin_inset space \textvisiblespace{}
17264 \begin_inset Formula $\uparrow$
17272 \begin_inset Formula
17274 \overset{a}{\maltese}
17282 \begin_layout Subsection
17284 \begin_inset CommandInset label
17286 name "subsec:Binary-Operators"
17291 \begin_inset Index idx
17294 \begin_layout Plain Layout
17303 \begin_layout Standard
17304 Binary operators are surrounded by space when there is a character before
17306 \begin_inset VSpace medskip
17312 \begin_layout Standard
17313 \begin_inset space \hfill{}
17317 \begin_inset Tabular
17318 <lyxtabular version="3" rows="13" columns="2">
17319 <features tabularvalignment="middle">
17320 <column alignment="center" valignment="top" width="0pt">
17321 <column alignment="center" valignment="top" width="0pt">
17323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17328 \begin_inset Note Note
17331 \begin_layout Plain Layout
17338 is only used as spacer.
17348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17362 \begin_layout Plain Layout
17368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17371 \begin_layout Plain Layout
17372 \begin_inset Formula $+$
17382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17385 \begin_layout Plain Layout
17391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17394 \begin_layout Plain Layout
17395 \begin_inset Formula $-$
17405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17408 \begin_layout Plain Layout
17416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17419 \begin_layout Plain Layout
17420 \begin_inset Formula $\pm$
17430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17433 \begin_layout Plain Layout
17441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17444 \begin_layout Plain Layout
17445 \begin_inset Formula $\mp$
17455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17458 \begin_layout Plain Layout
17466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17469 \begin_layout Plain Layout
17470 \begin_inset Formula $\cdot$
17480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17483 \begin_layout Plain Layout
17491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17494 \begin_layout Plain Layout
17495 \begin_inset Formula $\times$
17505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17508 \begin_layout Plain Layout
17516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17519 \begin_layout Plain Layout
17520 \begin_inset Formula $\div$
17530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17533 \begin_layout Plain Layout
17537 \begin_layout Plain Layout
17550 \begin_layout Plain Layout
17562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17565 \begin_layout Plain Layout
17566 \begin_inset Formula $*$
17576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17579 \begin_layout Plain Layout
17587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17590 \begin_layout Plain Layout
17591 \begin_inset Formula $\star$
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17604 \begin_layout Plain Layout
17612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17615 \begin_layout Plain Layout
17616 \begin_inset Formula $\circ$
17626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17629 \begin_layout Plain Layout
17637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17640 \begin_layout Plain Layout
17641 \begin_inset Formula $\diamond$
17651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17654 \begin_layout Plain Layout
17662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17665 \begin_layout Plain Layout
17666 \begin_inset Formula $\bullet$
17680 \begin_inset space \hfill{}
17684 \begin_inset Tabular
17685 <lyxtabular version="3" rows="13" columns="2">
17686 <features tabularvalignment="middle">
17687 <column alignment="center" valignment="top" width="0pt">
17688 <column alignment="center" valignment="top" width="0pt">
17690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17702 \begin_layout Plain Layout
17710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17713 \begin_layout Plain Layout
17721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17724 \begin_layout Plain Layout
17725 \begin_inset Formula $\nabla$
17735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17738 \begin_layout Plain Layout
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17750 \begin_inset Formula $\bigtriangledown$
17760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17763 \begin_layout Plain Layout
17771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17774 \begin_layout Plain Layout
17775 \begin_inset Formula $\bigtriangleup$
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17799 \begin_layout Plain Layout
17800 \begin_inset Formula $\Box$
17810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17813 \begin_layout Plain Layout
17821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17824 \begin_layout Plain Layout
17825 \begin_inset Formula $\cap$
17835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17838 \begin_layout Plain Layout
17846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17849 \begin_layout Plain Layout
17850 \begin_inset Formula $\cup$
17860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17863 \begin_layout Plain Layout
17871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17874 \begin_layout Plain Layout
17875 \begin_inset Formula $\dagger$
17885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17888 \begin_layout Plain Layout
17896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17899 \begin_layout Plain Layout
17900 \begin_inset Formula $\ddagger$
17910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17913 \begin_layout Plain Layout
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17924 \begin_layout Plain Layout
17925 \begin_inset Formula $\wr$
17935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17938 \begin_layout Plain Layout
17946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17949 \begin_layout Plain Layout
17950 \begin_inset Formula $\bigcirc$
17960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17963 \begin_layout Plain Layout
17971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17974 \begin_layout Plain Layout
17975 \begin_inset Formula $\wedge$
17985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17988 \begin_layout Plain Layout
17996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17999 \begin_layout Plain Layout
18000 \begin_inset Formula $\vee$
18014 \begin_inset space \hfill{}
18018 \begin_inset Tabular
18019 <lyxtabular version="3" rows="13" columns="2">
18020 <features tabularvalignment="middle">
18021 <column alignment="center" valignment="top" width="0pt">
18022 <column alignment="center" valignment="top" width="0pt">
18024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18027 \begin_layout Plain Layout
18033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18036 \begin_layout Plain Layout
18044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18047 \begin_layout Plain Layout
18055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18058 \begin_layout Plain Layout
18059 \begin_inset Formula $\oplus$
18069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18072 \begin_layout Plain Layout
18080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18083 \begin_layout Plain Layout
18084 \begin_inset Formula $\ominus$
18094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18097 \begin_layout Plain Layout
18105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18108 \begin_layout Plain Layout
18109 \begin_inset Formula $\otimes$
18119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18122 \begin_layout Plain Layout
18130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18133 \begin_layout Plain Layout
18134 \begin_inset Formula $\oslash$
18144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18147 \begin_layout Plain Layout
18155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18158 \begin_layout Plain Layout
18159 \begin_inset Formula $\odot$
18169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18183 \begin_layout Plain Layout
18184 \begin_inset Formula $\amalg$
18194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18197 \begin_layout Plain Layout
18205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18208 \begin_layout Plain Layout
18209 \begin_inset Formula $\uplus$
18219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18222 \begin_layout Plain Layout
18230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18233 \begin_layout Plain Layout
18234 \begin_inset Formula $\setminus$
18244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18247 \begin_layout Plain Layout
18255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18258 \begin_layout Plain Layout
18259 \begin_inset Formula $\sqcap$
18269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18272 \begin_layout Plain Layout
18280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18283 \begin_layout Plain Layout
18284 \begin_inset Formula $\sqcup$
18294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18297 \begin_layout Plain Layout
18305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18308 \begin_layout Plain Layout
18309 \begin_inset Formula $\triangleleft$
18319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18322 \begin_layout Plain Layout
18330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18333 \begin_layout Plain Layout
18334 \begin_inset Formula $\triangleright$
18348 \begin_inset space \hfill{}
18354 \begin_layout Standard
18355 All binary operators can also be inserted via the math toolbar button
18358 arg "math-insert \\pm"
18364 \begin_layout Standard
18365 To typeset the Laplace operator also
18382 \begin_inset Formula $\nabla^{2}$
18385 ) can be used instead of
18394 \begin_layout Standard
18401 Insert\SpecialChar menuseparator
18413 \begin_layout Subsection
18414 Self-defined Operators
18415 \begin_inset CommandInset label
18417 name "subsec:Self-defined-Operators"
18422 \begin_inset Index idx
18425 \begin_layout Plain Layout
18426 Operators ! self-defined
18434 \begin_layout Standard
18435 With the help of the command
18439 DeclareMathOperator
18442 \begin_inset Index idx
18445 \begin_layout Plain Layout
18450 DeclareMathOperator
18455 custom operators can be defined in the \SpecialChar LaTeX
18457 Its command scheme is:
18460 \begin_layout Standard
18465 DeclareMathOperator{new command}{display}
18468 \begin_layout Standard
18469 Display can be characters or symbols that define how the operator looks
18471 To define a big operator a * is set behind the command.
18472 All self-defined big operators can have limits as described in
18473 \begin_inset CommandInset ref
18475 reference "subsec:Operator-Limits"
18482 \begin_layout Standard
18483 For example the \SpecialChar LaTeX
18487 \begin_layout Standard
18492 DeclareMathOperator*{
18499 \begin_layout Standard
18500 defines the command
18506 , that inserts a big operator consisting of the lozenge symbol from
18507 \begin_inset CommandInset ref
18509 reference "subsec:Miscellaneous-Symbols"
18514 \begin_inset Formula
18516 \Lozenge_{n=1}^{\infty}
18521 The command for this formula is:
18532 \begin_inset Formula $\to$
18538 \begin_layout Standard
18539 \begin_inset VSpace bigskip
18542 When self-defined operators are not used several times in the document,
18543 they can also be defined with the commands
18550 \begin_inset Index idx
18553 \begin_layout Plain Layout
18568 \begin_inset Index idx
18571 \begin_layout Plain Layout
18579 , which have the following scheme:
18582 \begin_layout Standard
18596 \begin_layout Standard
18603 defines big operators,
18612 \begin_layout Standard
18620 \begin_inset space \thinspace{}
18624 \begin_inset space \space{}
18627 be used to use one limit for several operators:
18630 \begin_layout Standard
18631 \begin_inset Formula
18633 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18641 \begin_layout Standard
18642 The command for the formula above is:
18643 \begin_inset Newline newline
18659 \begin_inset space \textvisiblespace{}
18665 \begin_inset Formula $\to$
18671 \begin_inset space \textvisiblespace{}
18679 \begin_layout Section
18681 \begin_inset Index idx
18684 \begin_layout Plain Layout
18693 \begin_layout Subsection
18695 \begin_inset CommandInset label
18697 name "subsec:Font-Styles"
18702 \begin_inset Index idx
18705 \begin_layout Plain Layout
18714 \begin_layout Standard
18715 Latin letters in formulas can be set in one of the following font styles:
18718 \begin_layout Standard
18720 \begin_inset space \hfill{}
18724 \begin_inset Tabular
18725 <lyxtabular version="3" rows="6" columns="2">
18726 <features tabularvalignment="middle">
18727 <column alignment="center" valignment="top">
18728 <column alignment="center" valignment="top">
18730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18733 \begin_layout Plain Layout
18739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18742 \begin_layout Plain Layout
18750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18753 \begin_layout Plain Layout
18759 \begin_inset space \textvisiblespace{}
18769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18772 \begin_layout Plain Layout
18773 \begin_inset Formula $\mathbb{ABC}$
18783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18786 \begin_layout Plain Layout
18792 \begin_inset space \textvisiblespace{}
18802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18805 \begin_layout Plain Layout
18806 \begin_inset Formula $\mathbf{AbC}$
18816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18819 \begin_layout Plain Layout
18825 \begin_inset space \textvisiblespace{}
18835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18838 \begin_layout Plain Layout
18839 \begin_inset Formula $\boldsymbol{AbC}$
18849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18852 \begin_layout Plain Layout
18858 \begin_inset space \textvisiblespace{}
18868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18871 \begin_layout Plain Layout
18872 \begin_inset Formula $\mathcal{ABC}$
18882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18885 \begin_layout Plain Layout
18891 \begin_inset space \textvisiblespace{}
18901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18904 \begin_layout Plain Layout
18905 \begin_inset Formula $\mathfrak{AbC}$
18919 \begin_inset space \hfill{}
18923 \begin_inset Tabular
18924 <lyxtabular version="3" rows="6" columns="2">
18925 <features tabularvalignment="middle">
18926 <column alignment="center" valignment="top">
18927 <column alignment="center" valignment="top">
18929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18932 \begin_layout Plain Layout
18938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18941 \begin_layout Plain Layout
18949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18952 \begin_layout Plain Layout
18958 \begin_inset space \textvisiblespace{}
18968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18971 \begin_layout Plain Layout
18972 \begin_inset Formula $\mathit{AbC}$
18982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18985 \begin_layout Plain Layout
18991 \begin_inset space \textvisiblespace{}
19001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19004 \begin_layout Plain Layout
19005 \begin_inset Formula $\mathrm{AbC}$
19015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19018 \begin_layout Plain Layout
19024 \begin_inset space \textvisiblespace{}
19034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19037 \begin_layout Plain Layout
19038 \begin_inset Formula $\mathsf{AbC}$
19048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19051 \begin_layout Plain Layout
19057 \begin_inset space \textvisiblespace{}
19067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19070 \begin_layout Plain Layout
19071 \begin_inset Formula $\mathtt{AbC}$
19081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19084 \begin_layout Plain Layout
19090 \begin_inset space \textvisiblespace{}
19100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19103 \begin_layout Plain Layout
19104 \begin_inset Formula $\mathscr{ABC}$
19118 \begin_inset space \hfill{}
19124 \begin_layout Standard
19125 \begin_inset Note Greyedout
19128 \begin_layout Plain Layout
19151 can only be used for big letters.
19159 \begin_layout Standard
19160 Predefined is the style
19169 \begin_layout Standard
19170 The style commands work also for letters in mathematical constructs:
19171 \begin_inset Formula
19173 \mathfrak{A=\frac{b}{C}}
19181 \begin_layout Standard
19182 Characters in mathematical text don't appear in a math font style but in
19183 the text font style
19190 That their style can't be set correctly via the text style dialog is a
19191 bug in \SpecialChar LyX
19196 \begin_layout Plain Layout
19197 \begin_inset CommandInset href
19199 name "LyX-bug #4629"
19200 target "http://www.lyx.org/trac/ticket/4629"
19212 \begin_layout Standard
19213 Instead of the style commands the dialog
19215 Edit\SpecialChar menuseparator
19216 Math\SpecialChar menuseparator
19219 or the toolbar button
19222 arg "math-insert \\font"
19228 \begin_layout Subsection
19230 \begin_inset CommandInset label
19232 name "subsec:Bold-Formulas"
19237 \begin_inset Index idx
19240 \begin_layout Plain Layout
19249 \begin_layout Standard
19250 To make a complete formula bold, the command
19256 from the previous subsection cannot be used, because it doesn't work for
19257 small Greek letters.
19258 Furthermore it prints Latin letters always upright, like in the following
19262 \begin_layout Standard
19263 \begin_inset Formula
19265 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
19273 \begin_layout Standard
19274 To display the formula correctly, the command
19281 \begin_inset Formula
19283 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
19288 It is also possible to set the formula in a
19290 boldmath environment
19293 This environment is created by inserting the command
19300 \begin_inset Index idx
19303 \begin_layout Plain Layout
19311 in \SpecialChar TeX
19313 To end the environment, the command
19320 \begin_inset Index idx
19323 \begin_layout Plain Layout
19331 is inserted in \SpecialChar TeX
19336 \begin_layout Plain Layout
19346 \begin_inset Formula
19348 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19357 \begin_layout Plain Layout
19369 \begin_layout Subsection
19371 \begin_inset Index idx
19374 \begin_layout Plain Layout
19383 \begin_layout Standard
19384 Formulas can be colored like normal text: Highlight a formula or a formula
19390 Here is a formula in magenta:
19391 \begin_inset Formula
19393 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19401 \begin_layout Standard
19402 You can also define your own colors as described in
19403 \begin_inset CommandInset ref
19405 reference "subsec:Colored-Boxes"
19410 They can be used with the \SpecialChar TeX
19418 \begin_inset Index idx
19421 \begin_layout Plain Layout
19432 \begin_layout Standard
19437 textcolor{color}{characters or formula}
19440 \begin_layout Standard
19441 The following example was colored completely dark green and partly red:
19444 \begin_layout Standard
19448 \begin_layout Plain Layout
19452 textcolor{darkgreen}{
19458 \begin_inset Formula
19460 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19469 \begin_layout Plain Layout
19479 \begin_layout Standard
19480 Due to a bug in \SpecialChar LyX
19481 only complete formulas can be colored with self-defined
19486 \begin_layout Plain Layout
19487 \begin_inset CommandInset href
19489 name "LyX-bug #5269"
19490 target "http://www.lyx.org/trac/ticket/5269"
19502 \begin_layout Subsection
19504 \begin_inset CommandInset label
19506 name "subsec:Font-Sizes"
19511 \begin_inset Index idx
19514 \begin_layout Plain Layout
19523 \begin_layout Standard
19524 For characters in formulas there are, analog to characters in text, the
19525 following size commands:
19528 \begin_layout Standard
19572 \begin_inset Newline newline
19594 \begin_layout Standard
19595 The size produced by the commands depends on the document font size, which
19596 corresponds to the command
19603 The other commands produce smaller or larger sizes than
19610 The font size can however not exceed a certain value.
19611 Is for example the document font size 12
19612 \begin_inset space \thinspace{}
19621 switches to the same size as
19631 \begin_layout Standard
19632 A size command is inserted in \SpecialChar TeX
19633 mode before the formula and sets the size
19634 for all following formula and text characters.
19635 To switch back to the initial size, the command
19641 is inserted behind the formula in \SpecialChar TeX
19645 \begin_layout Standard
19646 Within a formula the size can be changed using the following size commands
19647 or the toolbar button
19650 arg "math-insert \\style"
19654 \begin_inset Separator parbreak
19660 \begin_layout Standard
19663 \begin_inset Tabular
19664 <lyxtabular version="3" rows="5" columns="2">
19665 <features tabularvalignment="middle">
19666 <column alignment="center" valignment="top">
19667 <column alignment="center" valignment="top">
19669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19672 \begin_layout Plain Layout
19678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19681 \begin_layout Plain Layout
19683 \begin_inset Note Note
19686 \begin_layout Plain Layout
19693 is only used as spacer.
19705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19708 \begin_layout Plain Layout
19712 \begin_inset Index idx
19715 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19732 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19795 \begin_layout Plain Layout
19803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19806 \begin_layout Plain Layout
19807 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19823 \begin_layout Standard
19824 After entering these commands, a blue box appears in which the formula parts
19828 \begin_layout Standard
19829 There is a further method to change the font size, that though only works
19830 for symbols or letters in mathematical text.
19831 To use it, one of the above text size commands is inserted in mathematical
19833 All following characters until the end of the mathematical text or until
19834 another size command will have the selected size.
19836 \begin_inset VSpace -2mm
19842 \begin_layout Standard
19846 \begin_layout Plain Layout
19856 \begin_inset Formula
19858 A=\frac{B}{c}\cdot\maltese
19864 \begin_inset Formula
19866 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19875 \begin_layout Plain Layout
19887 \begin_layout Standard
19888 \begin_inset VSpace medskip
19891 Before both formulas the command
19898 The command for the second formula is:
19899 \begin_inset Newline newline
19907 \begin_inset space \textvisiblespace{}
19913 \begin_inset space \textvisiblespace{}
19919 \begin_inset space \textvisiblespace{}
19925 \begin_inset space \textvisiblespace{}
19929 \begin_inset Formula $\to$
19933 \begin_inset Formula $\to$
19937 \begin_inset Newline newline
19941 \begin_inset space \hspace*{}
19952 \begin_inset space \textvisiblespace{}
19958 \begin_inset space \textvisiblespace{}
19964 \begin_inset space \textvisiblespace{}
19970 \begin_layout Standard
19971 If a symbol cannot be displayed in different sizes, it will always be displayed
19972 in the default size.
19975 \begin_layout Section
19977 \begin_inset Index idx
19980 \begin_layout Plain Layout
19989 \begin_layout Standard
19990 Greek letters can also be inserted via the toolbar button
19993 arg "math-insert \\alpha"
19997 All international typesetting norms purport that Greek letters in math
19998 have to be typeset italic/slanted.
19999 In some languages, like French or Russian, they are nevertheless sometimes
20003 \begin_layout Subsection
20005 \begin_inset Index idx
20008 \begin_layout Plain Layout
20009 Greek letters ! small
20017 \begin_layout Standard
20018 \begin_inset space \hfill{}
20022 \begin_inset Tabular
20023 <lyxtabular version="3" rows="11" columns="2">
20024 <features tabularvalignment="middle">
20025 <column alignment="center" valignment="top" width="0pt">
20026 <column alignment="center" valignment="top" width="0pt">
20028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20031 \begin_layout Plain Layout
20037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20040 \begin_layout Plain Layout
20048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\alpha$
20073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20076 \begin_layout Plain Layout
20084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20087 \begin_layout Plain Layout
20088 \begin_inset Formula $\beta$
20098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20101 \begin_layout Plain Layout
20109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20112 \begin_layout Plain Layout
20113 \begin_inset Formula $\gamma$
20123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20126 \begin_layout Plain Layout
20134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20137 \begin_layout Plain Layout
20138 \begin_inset Formula $\delta$
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20151 \begin_layout Plain Layout
20159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20162 \begin_layout Plain Layout
20163 \begin_inset Formula $\epsilon$
20173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20176 \begin_layout Plain Layout
20184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20187 \begin_layout Plain Layout
20188 \begin_inset Formula $\varepsilon$
20198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20201 \begin_layout Plain Layout
20209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20212 \begin_layout Plain Layout
20213 \begin_inset Formula $\zeta$
20223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20226 \begin_layout Plain Layout
20234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20237 \begin_layout Plain Layout
20238 \begin_inset Formula $\eta$
20248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20251 \begin_layout Plain Layout
20259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20262 \begin_layout Plain Layout
20263 \begin_inset Formula $\theta$
20273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20276 \begin_layout Plain Layout
20284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20287 \begin_layout Plain Layout
20288 \begin_inset Formula $\vartheta$
20302 \begin_inset space \hfill{}
20306 \begin_inset Tabular
20307 <lyxtabular version="3" rows="12" columns="2">
20308 <features tabularvalignment="middle">
20309 <column alignment="center" valignment="top" width="0pt">
20310 <column alignment="center" valignment="top" width="0pt">
20312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20315 \begin_layout Plain Layout
20321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20324 \begin_layout Plain Layout
20332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20335 \begin_layout Plain Layout
20343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20346 \begin_layout Plain Layout
20347 \begin_inset Formula $\iota$
20357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20360 \begin_layout Plain Layout
20368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20371 \begin_layout Plain Layout
20372 \begin_inset Formula $\kappa$
20382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20385 \begin_layout Plain Layout
20393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20396 \begin_layout Plain Layout
20397 \begin_inset Formula $\varkappa$
20407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20410 \begin_layout Plain Layout
20418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20421 \begin_layout Plain Layout
20422 \begin_inset Formula $\lambda$
20432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20435 \begin_layout Plain Layout
20443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20446 \begin_layout Plain Layout
20447 \begin_inset Formula $\mu$
20457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20460 \begin_layout Plain Layout
20468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20471 \begin_layout Plain Layout
20472 \begin_inset Formula $\nu$
20482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20485 \begin_layout Plain Layout
20493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20496 \begin_layout Plain Layout
20497 \begin_inset Formula $\xi$
20507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20510 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $o$
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\pi$
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\varpi$
20580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\rho$
20609 \begin_inset space \hfill{}
20613 \begin_inset Tabular
20614 <lyxtabular version="3" rows="11" columns="2">
20615 <features tabularvalignment="middle">
20616 <column alignment="center" valignment="top" width="0pt">
20617 <column alignment="center" valignment="top" width="0pt">
20619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20622 \begin_layout Plain Layout
20628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20631 \begin_layout Plain Layout
20639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20642 \begin_layout Plain Layout
20650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Plain Layout
20654 \begin_inset Formula $\varrho$
20664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20667 \begin_layout Plain Layout
20675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20678 \begin_layout Plain Layout
20679 \begin_inset Formula $\sigma$
20689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20692 \begin_layout Plain Layout
20700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20703 \begin_layout Plain Layout
20704 \begin_inset Formula $\varsigma$
20714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20717 \begin_layout Plain Layout
20725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20728 \begin_layout Plain Layout
20729 \begin_inset Formula $\tau$
20739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20753 \begin_layout Plain Layout
20754 \begin_inset Formula $\upsilon$
20764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20767 \begin_layout Plain Layout
20775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20778 \begin_layout Plain Layout
20779 \begin_inset Formula $\phi$
20789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20792 \begin_layout Plain Layout
20800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20803 \begin_layout Plain Layout
20804 \begin_inset Formula $\varphi$
20814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20817 \begin_layout Plain Layout
20825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20828 \begin_layout Plain Layout
20829 \begin_inset Formula $\chi$
20839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20842 \begin_layout Plain Layout
20850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20853 \begin_layout Plain Layout
20854 \begin_inset Formula $\psi$
20864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20867 \begin_layout Plain Layout
20875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20878 \begin_layout Plain Layout
20879 \begin_inset Formula $\omega$
20893 \begin_inset space \hfill{}
20899 \begin_layout Standard
20900 \begin_inset VSpace medskip
20906 \begin_layout Standard
20907 How to create special upright Greek letters is explained in
20908 \begin_inset CommandInset ref
20910 reference "subsec:Upright-small-Greek"
20917 \begin_layout Subsection
20919 \begin_inset Index idx
20922 \begin_layout Plain Layout
20923 Greek letters ! big
20931 \begin_layout Standard
20932 \begin_inset space \hfill{}
20936 \begin_inset Tabular
20937 <lyxtabular version="3" rows="7" columns="2">
20938 <features tabularvalignment="middle">
20939 <column alignment="center" valignment="top" width="0pt">
20940 <column alignment="center" valignment="top" width="0pt">
20942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20945 \begin_layout Plain Layout
20951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20954 \begin_layout Plain Layout
20962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20965 \begin_layout Plain Layout
20973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20976 \begin_layout Plain Layout
20977 \begin_inset Formula $\Gamma$
20987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
20998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21001 \begin_layout Plain Layout
21002 \begin_inset Formula $\Delta$
21012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21015 \begin_layout Plain Layout
21023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21026 \begin_layout Plain Layout
21027 \begin_inset Formula $\Theta$
21037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21040 \begin_layout Plain Layout
21048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21051 \begin_layout Plain Layout
21052 \begin_inset Formula $\Lambda$
21062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21065 \begin_layout Plain Layout
21073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21076 \begin_layout Plain Layout
21077 \begin_inset Formula $\Xi$
21087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21090 \begin_layout Plain Layout
21098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21101 \begin_layout Plain Layout
21102 \begin_inset Formula $\Pi$
21116 \begin_inset space \hfill{}
21120 \begin_inset Tabular
21121 <lyxtabular version="3" rows="6" columns="2">
21122 <features tabularvalignment="middle">
21123 <column alignment="center" valignment="top" width="0pt">
21124 <column alignment="center" valignment="top" width="0pt">
21126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21129 \begin_layout Plain Layout
21135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21138 \begin_layout Plain Layout
21146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21149 \begin_layout Plain Layout
21157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21160 \begin_layout Plain Layout
21161 \begin_inset Formula $\Sigma$
21171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21174 \begin_layout Plain Layout
21182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21185 \begin_layout Plain Layout
21186 \begin_inset Formula $\Upsilon$
21196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21199 \begin_layout Plain Layout
21207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21210 \begin_layout Plain Layout
21211 \begin_inset Formula $\Phi$
21221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21224 \begin_layout Plain Layout
21232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21235 \begin_layout Plain Layout
21236 \begin_inset Formula $\Psi$
21246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21249 \begin_layout Plain Layout
21257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21260 \begin_layout Plain Layout
21261 \begin_inset Formula $\Omega$
21275 \begin_inset space \hfill{}
21281 \begin_layout Standard
21282 \begin_inset VSpace medskip
21285 That the big Greek letters appear upright is caused by a design bug when
21288 To get correct italic big letters, begin every command with
21293 For example the command
21300 \begin_inset Formula $\varGamma$
21304 Another way is to load the package
21312 \begin_layout Plain Layout
21317 is part of the \SpecialChar LaTeX
21323 \begin_inset Index idx
21326 \begin_layout Plain Layout
21331 \begin_layout Plain Layout
21351 \begin_inset Index idx
21354 \begin_layout Plain Layout
21360 with the \SpecialChar LaTeX
21364 \begin_layout Standard
21369 usepackage{fixmath}
21372 \begin_layout Standard
21373 Then all big Greek letters in a document will automatically be typeset italic.
21376 \begin_layout Subsection
21378 \begin_inset Index idx
21381 \begin_layout Plain Layout
21382 Greek letters ! bold
21390 \begin_layout Standard
21391 Greek letters cannot be set with different font styles like Latin letters.
21392 They can only be made bold with the command
21399 \begin_inset Index idx
21402 \begin_layout Plain Layout
21411 \begin_inset Separator parbreak
21417 \begin_layout Standard
21419 \begin_inset Tabular
21420 <lyxtabular version="3" rows="3" columns="2">
21421 <features tabularvalignment="middle">
21422 <column alignment="center" valignment="top">
21423 <column alignment="center" valignment="top">
21425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21428 \begin_layout Plain Layout
21434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21437 \begin_layout Plain Layout
21445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21448 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21492 \begin_layout Plain Layout
21493 \begin_inset Formula $\theta\boldsymbol{\theta}$
21509 \begin_layout Section
21514 \begin_layout Plain Layout
21527 \begin_layout Plain Layout
21528 A list with all symbols of most of the \SpecialChar LaTeX
21529 -packages can be found in
21530 \begin_inset CommandInset citation
21545 \begin_layout Plain Layout
21553 \begin_inset Note Note
21556 \begin_layout Plain Layout
21559 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21562 \begin_layout Plain Layout
21565 texorpdfstring is in section
21566 \begin_inset CommandInset ref
21568 reference "subsec:Formulas-in-Section"
21578 \begin_inset Index idx
21581 \begin_layout Plain Layout
21590 \begin_layout Standard
21591 Many of the symbols listed in this section can also be inserted via the
21595 arg "math-insert \\nabla"
21601 arg "math-insert \\digamma"
21607 \begin_layout Subsection
21608 Mathematical Symbols
21609 \begin_inset CommandInset label
21611 name "subsec:Mathematical-Symbols"
21616 \begin_inset Index idx
21619 \begin_layout Plain Layout
21620 Symbols ! mathematical
21628 \begin_layout Standard
21629 \begin_inset space \hfill{}
21633 \begin_inset Tabular
21634 <lyxtabular version="3" rows="10" columns="2">
21635 <features tabularvalignment="middle">
21636 <column alignment="center" valignment="top" width="0pt">
21637 <column alignment="center" valignment="top" width="0pt">
21639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21642 \begin_layout Plain Layout
21648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21651 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21662 \begin_layout Plain Layout
21670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21673 \begin_layout Plain Layout
21674 \begin_inset Formula $\neg$
21684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21687 \begin_layout Plain Layout
21695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21698 \begin_layout Plain Layout
21699 \begin_inset Formula $\Im$
21709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21712 \begin_layout Plain Layout
21720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21723 \begin_layout Plain Layout
21724 \begin_inset Formula $\Re$
21734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21737 \begin_layout Plain Layout
21745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21748 \begin_layout Plain Layout
21749 \begin_inset Formula $\aleph$
21759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21762 \begin_layout Plain Layout
21770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21773 \begin_layout Plain Layout
21774 \begin_inset Formula $\partial$
21784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21787 \begin_layout Plain Layout
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21798 \begin_layout Plain Layout
21799 \begin_inset Formula $\infty$
21809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21812 \begin_layout Plain Layout
21820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21823 \begin_layout Plain Layout
21824 \begin_inset Formula $\wp$
21834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21837 \begin_layout Plain Layout
21845 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21848 \begin_layout Plain Layout
21849 \begin_inset Formula $\imath$
21859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21862 \begin_layout Plain Layout
21870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21873 \begin_layout Plain Layout
21874 \begin_inset Formula $\jmath$
21888 \begin_inset space \hfill{}
21892 \begin_inset Tabular
21893 <lyxtabular version="3" rows="10" columns="2">
21894 <features tabularvalignment="middle">
21895 <column alignment="center" valignment="top" width="0pt">
21896 <column alignment="center" valignment="top" width="0pt">
21898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21901 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21912 \begin_inset Note Note
21915 \begin_layout Plain Layout
21922 is only used as spacer.
21934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21937 \begin_layout Plain Layout
21945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21948 \begin_layout Plain Layout
21949 \begin_inset Formula $\forall$
21959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21962 \begin_layout Plain Layout
21970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21973 \begin_layout Plain Layout
21974 \begin_inset Formula $\exists$
21984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21987 \begin_layout Plain Layout
21995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21998 \begin_layout Plain Layout
21999 \begin_inset Formula $\nexists$
22009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22012 \begin_layout Plain Layout
22020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22023 \begin_layout Plain Layout
22024 \begin_inset Formula $\emptyset$
22034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22037 \begin_layout Plain Layout
22045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22048 \begin_layout Plain Layout
22049 \begin_inset Formula $\varnothing$
22059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\dag$
22084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22087 \begin_layout Plain Layout
22095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22099 \begin_inset Formula $\ddag$
22109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22112 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22127 \begin_layout Plain Layout
22137 \begin_inset Formula $\complement$
22144 \begin_layout Plain Layout
22158 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22161 \begin_layout Plain Layout
22169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22173 \begin_inset Formula $\Bbbk$
22187 \begin_inset space \hfill{}
22191 \begin_inset Tabular
22192 <lyxtabular version="3" rows="10" columns="2">
22193 <features tabularvalignment="middle">
22194 <column alignment="center" valignment="top" width="0pt">
22195 <column alignment="center" valignment="top" width="0pt">
22197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22200 \begin_layout Plain Layout
22206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22209 \begin_layout Plain Layout
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22220 \begin_layout Plain Layout
22228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22231 \begin_layout Plain Layout
22232 \begin_inset Formula $\prime$
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22245 \begin_layout Plain Layout
22253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22256 \begin_layout Plain Layout
22257 \begin_inset Formula $\backprime$
22267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22270 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22281 \begin_layout Plain Layout
22282 \begin_inset Formula $\mho$
22292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22295 \begin_layout Plain Layout
22303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22306 \begin_layout Plain Layout
22307 \begin_inset Formula $\triangle$
22317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22320 \begin_layout Plain Layout
22328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22331 \begin_layout Plain Layout
22332 \begin_inset Formula $\angle$
22342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22345 \begin_layout Plain Layout
22353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22356 \begin_layout Plain Layout
22357 \begin_inset Formula $\measuredangle$
22367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22370 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22381 \begin_layout Plain Layout
22382 \begin_inset Formula $\sphericalangle$
22392 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22395 \begin_layout Plain Layout
22403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22406 \begin_layout Plain Layout
22407 \begin_inset Formula $\top$
22417 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22420 \begin_layout Plain Layout
22428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22431 \begin_layout Plain Layout
22432 \begin_inset Formula $\bot$
22446 \begin_inset space \hfill{}
22452 \begin_layout Standard
22453 \begin_inset Newpage newpage
22459 \begin_layout Subsection
22460 Miscellaneous Symbols
22461 \begin_inset CommandInset label
22463 name "subsec:Miscellaneous-Symbols"
22468 \begin_inset Index idx
22471 \begin_layout Plain Layout
22472 Symbols ! miscellaneous
22480 \begin_layout Standard
22483 \begin_inset Tabular
22484 <lyxtabular version="3" rows="10" columns="2">
22485 <features tabularvalignment="middle">
22486 <column alignment="center" valignment="top" width="0pt">
22487 <column alignment="center" valignment="top" width="0pt">
22489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22501 \begin_layout Plain Layout
22509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22512 \begin_layout Plain Layout
22520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22523 \begin_layout Plain Layout
22524 \begin_inset Formula $\flat$
22534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22537 \begin_layout Plain Layout
22545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22548 \begin_layout Plain Layout
22549 \begin_inset Formula $\natural$
22559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22562 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22573 \begin_layout Plain Layout
22574 \begin_inset Formula $\sharp$
22584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22587 \begin_layout Plain Layout
22595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22598 \begin_layout Plain Layout
22599 \begin_inset Formula $\surd$
22609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22612 \begin_layout Plain Layout
22620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22623 \begin_layout Plain Layout
22624 \begin_inset Formula $\checkmark$
22634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22637 \begin_layout Plain Layout
22645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22648 \begin_layout Plain Layout
22649 \begin_inset Formula $\yen$
22659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22662 \begin_layout Plain Layout
22670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22673 \begin_layout Plain Layout
22674 \begin_inset Formula $\pounds$
22684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22687 \begin_layout Plain Layout
22693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22696 \begin_layout Plain Layout
22697 \begin_inset Formula $\$$
22707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22710 \begin_layout Plain Layout
22716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22719 \begin_layout Plain Layout
22720 \begin_inset Formula $§$
22734 \begin_inset Tabular
22735 <lyxtabular version="3" rows="10" columns="2">
22736 <features tabularvalignment="middle">
22737 <column alignment="center" valignment="top">
22738 <column alignment="center" valignment="top">
22740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22743 \begin_layout Plain Layout
22749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22752 \begin_layout Plain Layout
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\hbar$
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\hslash$
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22825 \begin_inset Formula $\clubsuit$
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Plain Layout
22846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22849 \begin_layout Plain Layout
22850 \begin_inset Formula $\spadesuit$
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22863 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22874 \begin_layout Plain Layout
22875 \begin_inset Formula $\bigstar$
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22888 \begin_layout Plain Layout
22896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22900 \begin_inset Formula $\blacklozenge$
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22913 \begin_layout Plain Layout
22921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22924 \begin_layout Plain Layout
22925 \begin_inset Formula $\blacktriangle$
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22938 \begin_layout Plain Layout
22946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22949 \begin_layout Plain Layout
22950 \begin_inset Formula $\blacktriangledown$
22960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22963 \begin_layout Plain Layout
22971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22974 \begin_layout Plain Layout
22975 \begin_inset Formula $\bullet$
22989 \begin_inset Tabular
22990 <lyxtabular version="3" rows="10" columns="2">
22991 <features tabularvalignment="middle">
22992 <column alignment="center" valignment="top" width="0pt">
22993 <column alignment="center" valignment="top" width="0pt">
22995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23007 \begin_layout Plain Layout
23015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23018 \begin_layout Plain Layout
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23029 \begin_layout Plain Layout
23030 \begin_inset Formula $\diamondsuit$
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23054 \begin_layout Plain Layout
23055 \begin_inset Formula $\Diamond$
23065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23068 \begin_layout Plain Layout
23076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23079 \begin_layout Plain Layout
23080 \begin_inset Formula $\heartsuit$
23090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23093 \begin_layout Plain Layout
23101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23104 \begin_layout Plain Layout
23105 \begin_inset Formula $\P$
23115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23118 \begin_layout Plain Layout
23126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23129 \begin_layout Plain Layout
23130 \begin_inset Formula $\copyright$
23140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23143 \begin_layout Plain Layout
23151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23154 \begin_layout Plain Layout
23155 \begin_inset Formula $\circledR$
23165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23168 \begin_layout Plain Layout
23176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23179 \begin_layout Plain Layout
23180 \begin_inset Formula $\maltese$
23190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23193 \begin_layout Plain Layout
23201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23204 \begin_layout Plain Layout
23205 \begin_inset Formula $\diagup$
23215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
23218 \begin_layout Plain Layout
23226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
23229 \begin_layout Plain Layout
23230 \begin_inset Formula $\diagdown$
23246 \begin_layout Standard
23247 \begin_inset VSpace medskip
23253 \begin_layout Standard
23254 Some symbols can be displayed in different sizes, see
23255 \begin_inset CommandInset ref
23257 reference "subsec:Font-Sizes"
23264 \begin_layout Subsection
23266 \begin_inset Index idx
23269 \begin_layout Plain Layout
23270 Symbols ! Euro-symbol
23276 \begin_inset Index idx
23279 \begin_layout Plain Layout
23286 \begin_layout Plain Layout
23303 \begin_layout Standard
23304 To use the Euro symbol in formulas, the \SpecialChar LaTeX
23310 \begin_inset Index idx
23313 \begin_layout Plain Layout
23319 must be installed and loaded with the \SpecialChar LaTeX
23323 \begin_layout Standard
23328 usepackage[gennarrow]{eurosym}
23331 \begin_layout Standard
23332 The Euro symbol can now be inserted with the command
23339 \begin_inset Index idx
23342 \begin_layout Plain Layout
23353 \begin_layout Standard
23354 The Euro symbol can directly be inserted with the € key in mathematical
23355 text, without having
23370 can also be inserted in \SpecialChar TeX
23372 The official currency symbol can then be inserted with the command
23379 \begin_inset Index idx
23382 \begin_layout Plain Layout
23390 , that is only available in \SpecialChar TeX
23394 \begin_layout Standard
23398 \begin_layout Plain Layout
23408 \begin_inset Note Note
23411 \begin_layout Plain Layout
23412 The following table will only be displayed when the \SpecialChar LaTeX
23425 \begin_layout Standard
23426 An overview about the different Euro symbols:
23427 \begin_inset Separator parbreak
23433 \begin_layout Standard
23435 \begin_inset Tabular
23436 <lyxtabular version="3" rows="4" columns="3">
23437 <features tabularvalignment="middle">
23438 <column alignment="center" valignment="top" width="0pt">
23439 <column alignment="center" valignment="top" width="0pt">
23440 <column alignment="center" valignment="top" width="0pt">
23442 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23445 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23454 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23474 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23483 \begin_layout Plain Layout
23491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23494 \begin_layout Plain Layout
23495 \begin_inset Formula $\euro$
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23508 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23517 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\mbox{€}$
23537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23550 \begin_layout Plain Layout
23558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23561 \begin_layout Plain Layout
23565 \begin_layout Plain Layout
23587 \begin_layout Standard
23591 \begin_layout Plain Layout
23601 \begin_inset Note Note
23604 \begin_layout Plain Layout
23605 The following will be displayed when the \SpecialChar LaTeX
23618 \begin_layout Standard
23619 You need to install the \SpecialChar LaTeX
23624 to see the rest of this subsection in the output.
23627 \begin_layout Standard
23631 \begin_layout Plain Layout
23643 \begin_layout Standard
23644 \begin_inset Newpage newpage
23650 \begin_layout Section
23652 \begin_inset CommandInset label
23654 name "sec:Relations"
23659 \begin_inset Index idx
23662 \begin_layout Plain Layout
23669 \begin_inset Index idx
23672 \begin_layout Plain Layout
23677 \begin_layout Plain Layout
23688 \begin_layout Plain Layout
23703 \begin_layout Standard
23704 All following relations can also be inserted via the toolbar button
23707 arg "math-insert \\leq"
23713 \begin_layout Standard
23714 \begin_inset space \hfill{}
23718 \begin_inset Tabular
23719 <lyxtabular version="3" rows="17" columns="2">
23720 <features tabularvalignment="middle">
23721 <column alignment="center" valignment="top" width="0pt">
23722 <column alignment="center" valignment="top" width="0pt">
23724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23747 \begin_layout Plain Layout
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23756 \begin_layout Plain Layout
23757 \begin_inset Formula $<$
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23770 \begin_layout Plain Layout
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23781 \begin_layout Plain Layout
23782 \begin_inset Formula $\le$
23792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23795 \begin_layout Plain Layout
23803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23806 \begin_layout Plain Layout
23807 \begin_inset Formula $\ll$
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23820 \begin_layout Plain Layout
23828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23831 \begin_layout Plain Layout
23832 \begin_inset Formula $\prec$
23842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23845 \begin_layout Plain Layout
23853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23856 \begin_layout Plain Layout
23857 \begin_inset Formula $\preceq$
23867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23870 \begin_layout Plain Layout
23878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23881 \begin_layout Plain Layout
23882 \begin_inset Formula $\subset$
23892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23895 \begin_layout Plain Layout
23903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23906 \begin_layout Plain Layout
23907 \begin_inset Formula $\subseteq$
23917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23920 \begin_layout Plain Layout
23928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23931 \begin_layout Plain Layout
23932 \begin_inset Formula $\sqsubseteq$
23942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23945 \begin_layout Plain Layout
23953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23956 \begin_layout Plain Layout
23957 \begin_inset Formula $\in$
23967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23970 \begin_layout Plain Layout
23978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23981 \begin_layout Plain Layout
23982 \begin_inset Formula $\vdash$
23992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23995 \begin_layout Plain Layout
24003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24006 \begin_layout Plain Layout
24007 \begin_inset Formula $\smile$
24017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24020 \begin_layout Plain Layout
24028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24031 \begin_layout Plain Layout
24032 \begin_inset Formula $\lhd$
24042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24045 \begin_layout Plain Layout
24053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24056 \begin_layout Plain Layout
24057 \begin_inset Formula $\unlhd$
24067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24070 \begin_layout Plain Layout
24078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24081 \begin_layout Plain Layout
24082 \begin_inset Formula $\gtrless$
24092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24095 \begin_layout Plain Layout
24103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24106 \begin_layout Plain Layout
24107 \begin_inset Formula $\mid$
24117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24120 \begin_layout Plain Layout
24128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24131 \begin_layout Plain Layout
24132 \begin_inset Formula $\nmid$
24146 \begin_inset space \hfill{}
24150 \begin_inset Tabular
24151 <lyxtabular version="3" rows="17" columns="2">
24152 <features tabularvalignment="middle">
24153 <column alignment="center" valignment="top" width="0pt">
24154 <column alignment="center" valignment="top" width="0pt">
24156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24159 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24168 \begin_layout Plain Layout
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24179 \begin_layout Plain Layout
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24188 \begin_layout Plain Layout
24189 \begin_inset Formula $=$
24199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24213 \begin_layout Plain Layout
24214 \begin_inset Formula $\not=$
24224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24227 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24238 \begin_layout Plain Layout
24239 \begin_inset Formula $\equiv$
24249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24252 \begin_layout Plain Layout
24260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24263 \begin_layout Plain Layout
24264 \begin_inset Formula $\sim$
24274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24277 \begin_layout Plain Layout
24285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24288 \begin_layout Plain Layout
24289 \begin_inset Formula $\simeq$
24299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24302 \begin_layout Plain Layout
24310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24313 \begin_layout Plain Layout
24314 \begin_inset Formula $\approx$
24324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24327 \begin_layout Plain Layout
24335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24338 \begin_layout Plain Layout
24339 \begin_inset Formula $\cong$
24349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24352 \begin_layout Plain Layout
24360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24363 \begin_layout Plain Layout
24364 \begin_inset Formula $\bowtie$
24374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24388 \begin_layout Plain Layout
24389 \begin_inset Formula $\notin$
24399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24402 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24413 \begin_layout Plain Layout
24414 \begin_inset Formula $\perp$
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24427 \begin_layout Plain Layout
24435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24438 \begin_layout Plain Layout
24439 \begin_inset Formula $\propto$
24449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24452 \begin_layout Plain Layout
24460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24463 \begin_layout Plain Layout
24464 \begin_inset Formula $\asymp$
24474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24488 \begin_layout Plain Layout
24489 \begin_inset Formula $\doteq$
24499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24502 \begin_layout Plain Layout
24510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24513 \begin_layout Plain Layout
24514 \begin_inset Formula $\circeq$
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24539 \begin_inset Formula $\models$
24549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24552 \begin_layout Plain Layout
24560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24563 \begin_layout Plain Layout
24564 \begin_inset Formula $\widehat{=}$
24578 \begin_inset space \hfill{}
24582 \begin_inset Tabular
24583 <lyxtabular version="3" rows="17" columns="2">
24584 <features tabularvalignment="middle">
24585 <column alignment="center" valignment="top" width="0pt">
24586 <column alignment="center" valignment="top" width="0pt">
24588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24591 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24600 \begin_layout Plain Layout
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24611 \begin_layout Plain Layout
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24620 \begin_layout Plain Layout
24621 \begin_inset Formula $>$
24631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24634 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24645 \begin_layout Plain Layout
24646 \begin_inset Formula $\ge$
24656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24659 \begin_layout Plain Layout
24667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24670 \begin_layout Plain Layout
24671 \begin_inset Formula $\gg$
24681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24695 \begin_layout Plain Layout
24696 \begin_inset Formula $\succ$
24706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24709 \begin_layout Plain Layout
24717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24720 \begin_layout Plain Layout
24721 \begin_inset Formula $\succeq$
24731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24734 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24745 \begin_layout Plain Layout
24746 \begin_inset Formula $\supset$
24756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24759 \begin_layout Plain Layout
24767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24770 \begin_layout Plain Layout
24771 \begin_inset Formula $\supseteq$
24781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24784 \begin_layout Plain Layout
24792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24795 \begin_layout Plain Layout
24796 \begin_inset Formula $\sqsupseteq$
24806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24809 \begin_layout Plain Layout
24817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24820 \begin_layout Plain Layout
24821 \begin_inset Formula $\ni$
24831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24834 \begin_layout Plain Layout
24842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24845 \begin_layout Plain Layout
24846 \begin_inset Formula $\dashv$
24856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24871 \begin_inset Formula $\frown$
24881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24884 \begin_layout Plain Layout
24892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24895 \begin_layout Plain Layout
24896 \begin_inset Formula $\rhd$
24906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24909 \begin_layout Plain Layout
24917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24920 \begin_layout Plain Layout
24921 \begin_inset Formula $\unrhd$
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24945 \begin_layout Plain Layout
24946 \begin_inset Formula $\lessgtr$
24956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24959 \begin_layout Plain Layout
24967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24970 \begin_layout Plain Layout
24971 \begin_inset Formula $\parallel$
24981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24984 \begin_layout Plain Layout
24992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24995 \begin_layout Plain Layout
24996 \begin_inset Formula $\nparallel$
25010 \begin_inset space \hfill{}
25016 \begin_layout Standard
25017 \begin_inset VSpace medskip
25032 are bigger than the equal looking operators
25047 \begin_layout Standard
25049 supports also many special relations.
25050 Use the toolbar button
25053 arg "math-insert \\leqq"
25056 to see a list of these relations.
25059 \begin_layout Standard
25060 Relations are, in contrary to symbols, always surrounded by space.
25063 \begin_layout Standard
25064 Relations with labels can be created with the command
25071 \begin_inset Index idx
25074 \begin_layout Plain Layout
25083 \begin_inset Separator parbreak
25089 \begin_layout Standard
25091 \begin_inset Tabular
25092 <lyxtabular version="3" rows="2" columns="2">
25093 <features tabularvalignment="middle">
25094 <column alignment="center" valignment="top">
25095 <column alignment="center" valignment="top">
25097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25100 \begin_layout Plain Layout
25106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25109 \begin_layout Plain Layout
25111 \begin_inset Note Note
25114 \begin_layout Plain Layout
25121 is only used as spacer.
25133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25136 \begin_layout Plain Layout
25140 \begin_inset space \textvisiblespace{}
25148 \begin_inset space \textvisiblespace{}
25152 \begin_inset Formula $\downarrow$
25158 \begin_inset space \textvisiblespace{}
25162 \begin_inset space \textvisiblespace{}
25170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25173 \begin_layout Plain Layout
25174 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
25190 \begin_layout Section
25194 \begin_layout Subsection
25195 Predefined Functions
25196 \begin_inset CommandInset label
25198 name "subsec:Predefined-Functions"
25203 \begin_inset Index idx
25206 \begin_layout Plain Layout
25207 Functions ! predefined
25215 \begin_layout Standard
25216 In general, variables are set
25220 in mathematical expressions, but not function names, because
25221 \begin_inset Formula $sin$
25224 could be misunderstood as
25225 \begin_inset Formula $s\cdot i\cdot n$
25229 Therefore there are predefined functionswhich are additionally a bit separated
25231 They are inserted as commands starting with a backslash before their name.
25232 \begin_inset Separator parbreak
25238 \begin_layout Standard
25240 \begin_inset Tabular
25241 <lyxtabular version="3" rows="2" columns="4">
25242 <features tabularvalignment="middle">
25243 <column alignment="center" valignment="top" width="0pt">
25244 <column alignment="center" valignment="top" width="0pt">
25245 <column alignment="center" valignment="top" width="0pt">
25246 <column alignment="center" valignment="top" width="0pt">
25248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25251 \begin_layout Plain Layout
25257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25260 \begin_layout Plain Layout
25266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25269 \begin_layout Plain Layout
25275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25278 \begin_layout Plain Layout
25286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25289 \begin_layout Plain Layout
25295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25298 \begin_layout Plain Layout
25299 \begin_inset Formula $Asin(x)+B$
25307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25310 \begin_layout Plain Layout
25318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25321 \begin_layout Plain Layout
25322 \begin_inset Formula $A\sin(x)+B$
25338 \begin_layout Standard
25339 The following functions are predefined:
25342 \begin_layout Standard
25343 \begin_inset VSpace -2mm
25349 \begin_layout Standard
25351 \begin_inset Tabular
25352 <lyxtabular version="3" rows="9" columns="4">
25353 <features tabularvalignment="middle">
25354 <column alignment="center" valignment="top" width="0pt">
25355 <column alignment="center" valignment="top" width="0pt">
25356 <column alignment="center" valignment="top" width="0pt">
25357 <column alignment="center" valignment="top" width="0pt">
25359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25371 \begin_layout Plain Layout
25377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25380 \begin_layout Plain Layout
25386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25389 \begin_layout Plain Layout
25397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25400 \begin_layout Plain Layout
25408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25411 \begin_layout Plain Layout
25419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25422 \begin_layout Plain Layout
25430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25433 \begin_layout Plain Layout
25443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25446 \begin_layout Plain Layout
25454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25457 \begin_layout Plain Layout
25465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25468 \begin_layout Plain Layout
25476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25479 \begin_layout Plain Layout
25489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25492 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25503 \begin_layout Plain Layout
25511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25514 \begin_layout Plain Layout
25522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25525 \begin_layout Plain Layout
25535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25538 \begin_layout Plain Layout
25546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25549 \begin_layout Plain Layout
25557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25560 \begin_layout Plain Layout
25568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25571 \begin_layout Plain Layout
25581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25584 \begin_layout Plain Layout
25592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25595 \begin_layout Plain Layout
25603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25606 \begin_layout Plain Layout
25614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25617 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25630 \begin_layout Plain Layout
25638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25641 \begin_layout Plain Layout
25649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25652 \begin_layout Plain Layout
25660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25663 \begin_layout Plain Layout
25673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25676 \begin_layout Plain Layout
25684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25687 \begin_layout Plain Layout
25695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25698 \begin_layout Plain Layout
25706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25709 \begin_layout Plain Layout
25719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25722 \begin_layout Plain Layout
25730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25733 \begin_layout Plain Layout
25741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25744 \begin_layout Plain Layout
25752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25755 \begin_layout Plain Layout
25771 \begin_layout Standard
25772 They can also be inserted with the math toolbar button
25775 arg "math-insert \\functions"
25781 \begin_layout Subsection
25782 Self-defined Functions
25783 \begin_inset Index idx
25786 \begin_layout Plain Layout
25787 Functions ! self-defined
25795 \begin_layout Standard
25796 To use a function that is not predefined, like for example the sign function
25797 sgn(x), there are two possibilities:
25800 \begin_layout Itemize
25801 Define the function by inserting the following line to the \SpecialChar LaTeX
25806 \begin_layout Plain Layout
25811 DeclareMathOperator
25814 \begin_inset CommandInset ref
25816 reference "subsec:Self-defined-Operators"
25826 \begin_inset Newline newline
25830 \begin_inset VSpace -3mm
25834 \begin_inset Newline newline
25841 DeclareMathOperator{
25846 \begin_inset Index idx
25849 \begin_layout Plain Layout
25854 DeclareMathOperator
25860 \begin_inset Newline newline
25864 \begin_inset VSpace -2mm
25868 \begin_inset Newline newline
25871 Now the new defined function can be called with the command
25880 \begin_layout Itemize
25881 Write the formula as usual, mark the formula name, in our example the letters
25886 , and change it to mathematical text.
25887 Finally, a space is inserted between prefactor and function.
25890 \begin_layout Standard
25891 The result is the same with both methods as with a predefined function
25895 \begin_layout Plain Layout
25896 In \SpecialChar LyX
25897 self-defined functions are displayed red, predefined ones black.
25903 \begin_inset Separator parbreak
25909 \begin_layout Standard
25911 \begin_inset Tabular
25912 <lyxtabular version="3" rows="3" columns="2">
25913 <features tabularvalignment="middle">
25914 <column alignment="center" valignment="top" width="0pt">
25915 <column alignment="center" valignment="top" width="0pt">
25917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25920 \begin_layout Plain Layout
25926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25929 \begin_layout Plain Layout
25937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25940 \begin_layout Plain Layout
25948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25951 \begin_layout Plain Layout
25952 \begin_inset Formula $A\sgn(x)+B$
25962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25965 \begin_layout Plain Layout
25969 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25980 \begin_layout Plain Layout
25981 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25997 \begin_layout Standard
25998 The first method is more suitable when the self-defined function should
25999 be used several times.
26002 \begin_layout Subsection
26004 \begin_inset Index idx
26007 \begin_layout Plain Layout
26016 \begin_layout Standard
26017 For limits, in addition to the commands
26024 \begin_inset Index idx
26027 \begin_layout Plain Layout
26047 the following functions are defined:
26048 \begin_inset Separator parbreak
26054 \begin_layout Standard
26056 \begin_inset Tabular
26057 <lyxtabular version="3" rows="5" columns="2">
26058 <features tabularvalignment="middle">
26059 <column alignment="center" valignment="top">
26060 <column alignment="center" valignment="top">
26062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26065 \begin_layout Plain Layout
26071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26074 \begin_layout Plain Layout
26076 \begin_inset Note Note
26079 \begin_layout Plain Layout
26086 is only used as spacer.
26098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26101 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26113 \begin_inset Formula $\varliminf$
26123 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26138 \begin_inset Formula $\varlimsup$
26148 <cell alignment="center" valignment="top" leftline="true" usebox="none">
26151 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
26162 \begin_layout Plain Layout
26163 \begin_inset Formula $\varprojlim$
26173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26176 \begin_layout Plain Layout
26184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26187 \begin_layout Plain Layout
26188 \begin_inset Formula $\varinjlim$
26192 \begin_inset Formula $\raisebox{-2.5mm}{}$
26208 \begin_layout Standard
26209 \begin_inset VSpace medskip
26212 The limit is created by inserting a subscript.
26213 It is set right beside the function in an inline formula:
26216 \begin_layout Standard
26218 \begin_inset Tabular
26219 <lyxtabular version="3" rows="2" columns="2">
26220 <features tabularvalignment="middle">
26221 <column alignment="center" valignment="top" width="0pt">
26222 <column alignment="center" valignment="top" width="0pt">
26224 <cell alignment="center" valignment="top" usebox="none">
26227 \begin_layout Plain Layout
26233 <cell alignment="center" valignment="top" usebox="none">
26236 \begin_layout Plain Layout
26237 \begin_inset space \hspace{}
26242 \begin_inset Note Note
26245 \begin_layout Plain Layout
26252 are used here as spacer.
26264 <cell alignment="center" valignment="top" usebox="none">
26267 \begin_layout Plain Layout
26273 \begin_inset space \textvisiblespace{}
26277 \begin_inset space \textvisiblespace{}
26285 <cell alignment="center" valignment="top" usebox="none">
26288 \begin_layout Plain Layout
26289 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26305 \begin_layout Standard
26306 In a displayed formula the limit is set below the formula, as usual:
26307 \begin_inset Formula
26317 \begin_layout Standard
26318 \begin_inset VSpace medskip
26324 \begin_layout Standard
26325 How to adjust the typesetting of the limits see
26326 \begin_inset CommandInset ref
26328 reference "subsec:Operator-Limits"
26335 \begin_layout Subsection
26337 \begin_inset Index idx
26340 \begin_layout Plain Layout
26341 Functions ! modulo-
26349 \begin_layout Standard
26350 The modulo-function is special, because it exists in four variants.
26351 The variants in a displayed formula are:
26352 \begin_inset Formula
26354 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26355 \mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\
26356 \mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\
26357 \mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\
26358 \mathrm{a\backslash pod\textrm{␣}b} & & a\pod b
26366 \begin_layout Standard
26367 In an inline formula less space is set before the function names for all
26369 By default the modulo-functions take only the first following character
26371 To use more than one character, one has to put them into \SpecialChar TeX
26373 \begin_inset Formula
26375 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26376 \mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\
26377 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26385 \begin_layout Section
26387 \begin_inset Index idx
26390 \begin_layout Plain Layout
26399 \begin_layout Standard
26400 The characters ^ and _ would normally create a superscript and subscript,
26402 To get these characters you have to insert them with a leading
26405 \begin_inset Separator parbreak
26411 \begin_layout Standard
26414 \begin_inset Tabular
26415 <lyxtabular version="3" rows="3" columns="2">
26416 <features tabularvalignment="middle">
26417 <column alignment="block" valignment="top">
26418 <column alignment="block" valignment="top">
26420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26423 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26432 \begin_layout Plain Layout
26440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26443 \begin_layout Plain Layout
26447 \begin_inset space \textvisiblespace{}
26455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26458 \begin_layout Plain Layout
26459 \begin_inset Formula $\mathcircumflex$
26469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26483 \begin_layout Plain Layout
26484 \begin_inset Formula $\_$
26500 \begin_layout Subsection
26501 Special Characters in Mathematical Text
26504 \begin_layout Standard
26505 The following commands can only be used in mathematical text or in \SpecialChar TeX
26509 \begin_layout Standard
26510 \begin_inset space \hfill{}
26514 \begin_inset Tabular
26515 <lyxtabular version="3" rows="8" columns="2">
26516 <features tabularvalignment="middle">
26517 <column alignment="block" valignment="top">
26518 <column alignment="block" valignment="top">
26520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26523 \begin_layout Plain Layout
26529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26532 \begin_layout Plain Layout
26540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26543 \begin_layout Plain Layout
26551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26554 \begin_layout Plain Layout
26555 \begin_inset Formula $\textrm{œ}$
26565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26568 \begin_layout Plain Layout
26576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26579 \begin_layout Plain Layout
26580 \begin_inset Formula $\textrm{Œ}$
26590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26593 \begin_layout Plain Layout
26601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26604 \begin_layout Plain Layout
26605 \begin_inset Formula $\textrm{æ}$
26615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26618 \begin_layout Plain Layout
26626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26629 \begin_layout Plain Layout
26630 \begin_inset Formula $\textrm{Æ}$
26640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26643 \begin_layout Plain Layout
26651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26654 \begin_layout Plain Layout
26655 \begin_inset Formula $\textrm{\aa}$
26665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26668 \begin_layout Plain Layout
26672 \begin_inset Index idx
26675 \begin_layout Plain Layout
26682 \begin_layout Plain Layout
26703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26706 \begin_layout Plain Layout
26707 \begin_inset Formula $\textrm{Å}$
26717 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26720 \begin_layout Plain Layout
26728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26731 \begin_layout Plain Layout
26732 \begin_inset Formula $\textrm{ı}$
26746 \begin_inset space \hfill{}
26750 \begin_inset Tabular
26751 <lyxtabular version="3" rows="8" columns="2">
26752 <features tabularvalignment="middle">
26753 <column alignment="block" valignment="top">
26754 <column alignment="center" valignment="top">
26756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26759 \begin_layout Plain Layout
26761 \begin_inset Note Note
26764 \begin_layout Plain Layout
26766 \begin_inset space \thinspace{}
26769 mm is used for separation, because otherwise the output will be ¡ and ¿
26780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26783 \begin_layout Plain Layout
26791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26794 \begin_layout Plain Layout
26802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26805 \begin_layout Plain Layout
26806 \begin_inset Formula $\textrm{ø}$
26816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26819 \begin_layout Plain Layout
26827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26830 \begin_layout Plain Layout
26831 \begin_inset Formula $\textrm{Ø}$
26841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26844 \begin_layout Plain Layout
26852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26855 \begin_layout Plain Layout
26856 \begin_inset Formula $\textrm{ł}$
26866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26869 \begin_layout Plain Layout
26877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26880 \begin_layout Plain Layout
26881 \begin_inset Formula $\textrm{Ł}$
26891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26894 \begin_layout Plain Layout
26896 \begin_inset space \hspace{}
26901 \begin_inset space \textvisiblespace{}
26909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26912 \begin_layout Plain Layout
26913 \begin_inset Formula $\textrm{!`}$
26923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26926 \begin_layout Plain Layout
26928 \begin_inset space \hspace{}
26933 \begin_inset space \textvisiblespace{}
26941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26944 \begin_layout Plain Layout
26945 \begin_inset Formula $\textrm{?`}$
26955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26958 \begin_layout Plain Layout
26966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26969 \begin_layout Plain Layout
26970 \begin_inset Formula $\textrm{ȷ}$
26984 \begin_inset space \hfill{}
26990 \begin_layout Standard
26992 \begin_inset Formula $\textrm{\textrm{Å}}$
26996 \begin_inset Formula $\textrm{\textrm{Ø}}$
26999 can also be inserted via the math toolbar button
27002 arg "math-insert \\digamma"
27008 \begin_layout Standard
27009 An exception are the commands
27012 \begin_inset space \hspace{}
27021 \begin_inset space \hspace{}
27027 , because they can be inserted in \SpecialChar LyX
27031 \begin_layout Subsection
27033 \begin_inset CommandInset label
27035 name "subsec:Accents-in-Text"
27040 \begin_inset Index idx
27043 \begin_layout Plain Layout
27052 \begin_layout Standard
27053 With the following commands all letters can be accented.
27054 The commands must be inserted in \SpecialChar TeX
27058 \begin_layout Standard
27059 \begin_inset space \hfill{}
27063 \begin_inset Tabular
27064 <lyxtabular version="3" rows="8" columns="2">
27065 <features tabularvalignment="middle">
27066 <column alignment="block" valignment="top">
27067 <column alignment="block" valignment="top">
27069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27072 \begin_layout Plain Layout
27078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27081 \begin_layout Plain Layout
27089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27092 \begin_layout Plain Layout
27096 \begin_inset Quotes grd
27104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27107 \begin_layout Plain Layout
27111 \begin_layout Plain Layout
27127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27130 \begin_layout Plain Layout
27138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27141 \begin_layout Plain Layout
27145 \begin_layout Plain Layout
27161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27164 \begin_layout Plain Layout
27168 \begin_inset space \textvisiblespace{}
27176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27179 \begin_layout Plain Layout
27183 \begin_layout Plain Layout
27199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27202 \begin_layout Plain Layout
27210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27213 \begin_layout Plain Layout
27217 \begin_layout Plain Layout
27233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27236 \begin_layout Plain Layout
27240 \begin_inset space \textvisiblespace{}
27248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27251 \begin_layout Plain Layout
27255 \begin_layout Plain Layout
27271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27274 \begin_layout Plain Layout
27278 \begin_inset space \textvisiblespace{}
27286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27289 \begin_layout Plain Layout
27293 \begin_layout Plain Layout
27309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27312 \begin_layout Plain Layout
27316 \begin_inset space \textvisiblespace{}
27324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27327 \begin_layout Plain Layout
27331 \begin_layout Plain Layout
27351 \begin_inset space \hfill{}
27355 \begin_inset Tabular
27356 <lyxtabular version="3" rows="8" columns="2">
27357 <features tabularvalignment="middle">
27358 <column alignment="block" valignment="top">
27359 <column alignment="center" valignment="top">
27361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27364 \begin_layout Plain Layout
27370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27373 \begin_layout Plain Layout
27381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27384 \begin_layout Plain Layout
27388 \begin_inset space \textvisiblespace{}
27396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27399 \begin_layout Plain Layout
27403 \begin_layout Plain Layout
27419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27422 \begin_layout Plain Layout
27430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27433 \begin_layout Plain Layout
27437 \begin_layout Plain Layout
27453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27456 \begin_layout Plain Layout
27460 \begin_inset Index idx
27463 \begin_layout Plain Layout
27474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27477 \begin_layout Plain Layout
27481 \begin_layout Plain Layout
27497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27500 \begin_layout Plain Layout
27508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27511 \begin_layout Plain Layout
27515 \begin_layout Plain Layout
27531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27534 \begin_layout Plain Layout
27538 \begin_inset space \textvisiblespace{}
27546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27549 \begin_layout Plain Layout
27553 \begin_layout Plain Layout
27569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27572 \begin_layout Plain Layout
27576 \begin_inset space \textvisiblespace{}
27584 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27587 \begin_layout Plain Layout
27591 \begin_layout Plain Layout
27607 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27610 \begin_layout Plain Layout
27614 \begin_inset space \textvisiblespace{}
27622 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27625 \begin_layout Plain Layout
27629 \begin_layout Plain Layout
27649 \begin_inset space \hfill{}
27655 \begin_layout Standard
27656 \begin_inset VSpace medskip
27665 also two different characters can be accented.
27671 \begin_inset space \textvisiblespace{}
27680 \begin_layout Plain Layout
27692 \begin_layout Standard
27705 can in combination with vowels directly be inserted with the keyboard without
27706 using \SpecialChar TeX
27708 The same applies for the tilde
27712 \begin_layout Plain Layout
27713 This only applies for keyboards where the tilde is defined as accent.
27722 in combination with
27737 \begin_layout Standard
27780 and accents that are inserted directly with the keyboard are also available
27781 in mathematical text.
27782 For the other accents there are special math commands to be used in formulas,
27784 \begin_inset CommandInset ref
27786 reference "subsec:Accents-for-one"
27793 \begin_layout Standard
27794 \begin_inset VSpace bigskip
27797 Furthermore, with the command
27804 \begin_inset Index idx
27807 \begin_layout Plain Layout
27815 all numbers and letters can be set into a circle, quasi accented with a
27816 circle, similar to the copyright symbol.
27819 \begin_layout Standard
27821 \begin_inset Tabular
27822 <lyxtabular version="3" rows="3" columns="2">
27823 <features tabularvalignment="middle">
27824 <column alignment="center" valignment="top">
27825 <column alignment="center" valignment="top">
27827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27830 \begin_layout Plain Layout
27836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27839 \begin_layout Plain Layout
27841 \begin_inset Note Note
27844 \begin_layout Plain Layout
27851 is only used as spacer.
27863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27866 \begin_layout Plain Layout
27874 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27877 \begin_layout Plain Layout
27881 \begin_layout Plain Layout
27897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27900 \begin_layout Plain Layout
27911 raisebox{-1.5pt}{W}}
27916 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27919 \begin_layout Plain Layout
27920 \begin_inset Formula $\raisebox{4.5mm}{}$
27927 \begin_layout Plain Layout
27945 \begin_inset Formula $\raisebox{-2mm}{}$
27961 \begin_layout Standard
27962 One has to take care that the character fits in the circle.
27973 \begin_layout Plain Layout
27975 \begin_inset CommandInset ref
27977 reference "subsec:Font-Sizes"
27986 specifies thereby the size of the circle.
27997 \begin_layout Plain Layout
27999 \begin_inset CommandInset ref
28001 reference "subsec:Boxes-without-Frame"
28010 the character can be centered.
28013 \begin_layout Subsection
28015 \begin_inset Index idx
28018 \begin_layout Plain Layout
28027 \begin_layout Standard
28028 Old-style figures (also known as old-style numerals) are created with the
28036 \begin_inset Index idx
28039 \begin_layout Plain Layout
28048 The command can be used in formulas and in \SpecialChar TeX
28050 The command scheme is:
28053 \begin_layout Standard
28058 oldstylenums{number}
28061 \begin_layout Standard
28066 oldstylenums{0123456789
28069 \begin_inset Formula $\oldstylenums{0123456789}$
28075 \begin_layout Section
28077 \begin_inset CommandInset label
28079 name "sec:Formula-Styles"
28084 \begin_inset Index idx
28087 \begin_layout Plain Layout
28096 \begin_layout Itemize
28097 There are two different alignment styles:
28098 \begin_inset Separator parbreak
28105 \begin_layout Description
28106 Centered is the predefined standard
28109 \begin_layout Description
28110 Indented for this the option
28114 must be inserted in the menu
28116 Document\SpecialChar menuseparator
28122 \begin_inset space ~
28128 \begin_layout Standard
28133 is used, the indentation can be adjusted with the length
28140 \begin_inset Index idx
28143 \begin_layout Plain Layout
28152 Should the distance be 15
28153 \begin_inset space \thinspace{}
28156 mm, the following command line is inserted in the \SpecialChar LaTeX
28160 \begin_layout Standard
28170 \begin_layout Standard
28171 When no length is specified, the predefined value of 30
28172 \begin_inset space \thinspace{}
28179 \begin_layout Itemize
28180 And two different numbering styles:
28181 \begin_inset Separator parbreak
28188 \begin_layout Description
28189 Right is the predefined standard
28192 \begin_layout Description
28193 Left for this the option
28197 must be inserted in the menu
28199 Document\SpecialChar menuseparator
28205 \begin_inset space ~
28212 \begin_layout Standard
28221 can also be used together.
28222 In this case both options are inserted, separated by a comma.
28225 \begin_layout Standard
28226 The chosen styles are used for all displayed formulas of the document.
28227 When both, centered and indented formulas should be created in a document,
28233 The indented formulas are then set in a flalign environment, see
28234 \begin_inset CommandInset ref
28236 reference "subsec:Flalign-Environment"
28243 \begin_layout Section
28245 \begin_inset CommandInset label
28247 name "sec:Multiline-Formulas"
28252 \begin_inset Index idx
28255 \begin_layout Plain Layout
28256 Formula ! multiline
28264 \begin_layout Subsection
28268 \begin_layout Standard
28269 In \SpecialChar LyX
28270 multiline formulas are created by pressing
28273 arg "newline-insert newline"
28277 This creates either an
28279 eqnarray environment
28281 that is described in
28282 \begin_inset CommandInset ref
28284 reference "subsec:Eqnarray-Environment"
28288 or, when the option
28290 Use AMS math package
28292 in the document settings is selected, an
28296 that is described in
28297 \begin_inset CommandInset ref
28299 reference "subsec:Standard-align-Environment"
28304 The align environment is recommended because it provides in any case a
28305 typographically correct output.
28308 \begin_layout Standard
28309 There are other multiline formula environments that can be created via the
28312 Insert\SpecialChar menuseparator
28316 These environments are described in the following sections.
28319 \begin_layout Standard
28320 In all multiline formula environments a new line is created by pressing
28324 arg "newline-insert newline"
28328 To add or delete lines, the math toolbar buttons
28331 arg "inset-modify tabular append-row"
28337 arg "inset-modify tabular delete-row"
28340 , respectively, or the menu
28342 Edit\SpecialChar menuseparator
28348 \begin_layout Subsubsection
28350 \begin_inset CommandInset label
28352 name "subsec:Line-Separation"
28357 \begin_inset Index idx
28360 \begin_layout Plain Layout
28361 Formula ! multiline ! Line separation
28369 \begin_layout Standard
28370 There is sometimes not enough space in multiline formulas between the lines:
28371 \begin_inset Formula
28373 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}\\
28374 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
28382 \begin_layout Standard
28383 In \SpecialChar LaTeX
28384 additional line space is specified as optional argument of the new line
28386 This is not yet possible in \SpecialChar LyX
28391 \begin_layout Plain Layout
28393 \begin_inset CommandInset href
28395 name "LyX-bug #1505"
28396 target "http://www.lyx.org/trac/ticket/1505"
28405 , therefore the whole formula must be inserted in \SpecialChar TeX
28407 To add in our example space, the command
28415 is inserted at the end of the first line.
28420 \begin_layout Plain Layout
28427 \begin_layout Plain Layout
28429 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28432 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28439 \begin_layout Plain Layout
28443 left(B^{2}+x_{0}^{2}
28451 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28456 \begin_layout Plain Layout
28468 \begin_layout Standard
28469 \begin_inset VSpace bigskip
28472 To set the line separation for all lines in a formula, the length
28479 \begin_inset Index idx
28482 \begin_layout Plain Layout
28492 \begin_inset Formula $\mbox{line separation}=\mathrm{6\,pt+\backslash jot}$
28503 \begin_inset space \thinspace{}
28508 \begin_inset space \thinspace{}
28511 mm additional line separation as in the previous example, the command
28514 \begin_layout Standard
28524 \begin_layout Standard
28525 is inserted in \SpecialChar TeX
28526 mode before the formula.
28527 This requires that the \SpecialChar LaTeX
28536 \begin_layout Plain Layout
28541 is part of every \SpecialChar LaTeX
28542 standard installation.
28548 \begin_inset Index idx
28551 \begin_layout Plain Layout
28557 was loaded in \SpecialChar LaTeX
28558 -preamble with the line
28561 \begin_layout Standard
28569 \begin_layout Standard
28574 \begin_layout Plain Layout
28586 \begin_inset Formula
28588 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}\\
28589 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
28597 \begin_layout Standard
28601 \begin_layout Plain Layout
28612 To get back to the predefined distance,
28618 is set to the value 3
28619 \begin_inset space \thinspace{}
28625 \begin_layout Subsubsection
28627 \begin_inset CommandInset label
28629 name "subsec:Column-Separation"
28634 \begin_inset Index idx
28637 \begin_layout Plain Layout
28638 Formula ! multiline ! Column separation
28646 \begin_layout Standard
28647 Multiline formulas form a matrix.
28648 A formula in the eqnarray environment is for example a matrix with three
28650 By changing the column separation in this environment, the space beside
28651 the relation sign can be changed.
28654 \begin_layout Standard
28655 The column separation is specified with the length
28662 \begin_inset Index idx
28665 \begin_layout Plain Layout
28674 \begin_inset Newline newline
28677 column separation = 2
28678 \begin_inset space \thinspace{}
28688 \begin_inset Newline newline
28694 \begin_layout Standard
28704 \begin_layout Standard
28705 inserted in \SpecialChar TeX
28706 mode, sets for all following formulas a column separation of
28708 \begin_inset space \thinspace{}
28712 To get back to the predefined distance,
28719 \begin_inset space \thinspace{}
28725 \begin_layout Standard
28727 \begin_inset space \thinspace{}
28730 cm column separation:
28734 \begin_layout Plain Layout
28746 \begin_inset Formula
28754 A formula with the predefined column separation for matrices of 10
28755 \begin_inset space \thinspace{}
28762 \begin_layout Plain Layout
28774 \begin_inset Formula
28785 \begin_layout Subsubsection
28787 \begin_inset Index idx
28790 \begin_layout Plain Layout
28799 \begin_layout Standard
28800 Long formulas can be typeset using these methods:
28803 \begin_layout Itemize
28804 When one side of the equation is much shorter than the line width, this
28805 one is chosen for the left side and the right side is typeset over two
28807 \begin_inset Formula
28809 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 \\
28810 & & -\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}
28815 The minus sign at the beginning of the second line does normally not appear
28816 as an operator because it is the first character of the line.
28817 Thus it would not be surrounded by space and could not be distinguished
28818 from the fraction bar.
28820 \begin_inset space \thinspace{}
28823 pt space was inserted behind the minus sign with the command
28833 \begin_layout Plain Layout
28841 \begin_inset CommandInset ref
28843 reference "subsec:Variable-Space"
28853 \begin_inset Index idx
28856 \begin_layout Plain Layout
28867 \begin_layout Itemize
28868 When both sides of the equation are too long, the command
28875 \begin_inset Index idx
28878 \begin_layout Plain Layout
28887 It is inserted in the first column of the first line and causes all further
28888 insertions to overwrite the following columns:
28889 \begin_inset Formula
28891 \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 \\
28892 & & -\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 \\
28893 & & =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}
28898 After the insertion of
28904 , the cursor is in a purple box that is a bit shifted to the left from the
28906 In this the formula is inserted.
28907 \begin_inset Newline newline
28910 The content of the further lines is inserted to the second or another formula
28912 The greater the column number where it was inserted, the larger the indentation.
28913 \begin_inset VSpace medskip
28917 \begin_inset Newline newline
28921 \begin_inset Note Greyedout
28924 \begin_layout Plain Layout
28925 Note the following when using
28934 \begin_layout Itemize
28935 The formula doesn't use the full page width.
28937 \begin_inset space \thinspace{}
28941 \begin_inset space \space{}
28945 \begin_inset Formula $-B^{2}$
28948 is added to the first line in the above example, it would have been outside
28950 To better use the width, negative space can be inserted at the beginning
28954 \begin_layout Itemize
28955 Due to a bug in \SpecialChar LyX
28956 the cursor cannot be set with the mouse into the first
28961 \begin_layout Plain Layout
28962 \begin_inset CommandInset href
28964 name "LyX-bug #1429"
28965 target "http://www.lyx.org/trac/ticket/1429"
28974 One can only set the cursor at the beginning of the line and move it with
28983 \begin_layout Itemize
28984 Other methods to set long formulas are offered by the environments described
28986 \begin_inset CommandInset ref
28988 reference "subsec:Multline-Environment"
28993 \begin_inset CommandInset ref
28995 reference "subsec:Multiline-Formula-Parts"
29002 \begin_layout Subsubsection
29003 Multiline Fractions
29004 \begin_inset CommandInset label
29006 name "subsec:Multiline-Fractions"
29011 \begin_inset Index idx
29014 \begin_layout Plain Layout
29015 Fractions ! multiline
29023 \begin_layout Standard
29024 There are cases where the denominator and/or the numerator of a fraction
29025 is so long that the fraction does not fit into one line.
29026 It is then necessary to add a line break within the fraction.
29027 This can be done using the command
29034 \begin_inset Index idx
29037 \begin_layout Plain Layout
29046 To activate it, set in the document settings under
29049 \begin_inset space ~
29059 \begin_inset Index idx
29062 \begin_layout Plain Layout
29063 Packages ! mathtools
29071 \begin_inset space ~
29086 \begin_layout Standard
29091 splitfrac{first line}{second line}
29094 \begin_layout Standard
29095 and is used as denominator and/or numerator:
29098 \begin_layout Standard
29099 \begin_inset Formula
29101 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}
29106 The command for the first numerator above is:
29109 \begin_layout Standard
29114 splitfrac{xy+xy+xy+xy+xy
29115 \begin_inset space \textvisiblespace{}
29123 \begin_layout Subsubsection
29125 \begin_inset CommandInset label
29127 name "subsec:Multiline-Brackets"
29132 \begin_inset Index idx
29135 \begin_layout Plain Layout
29136 Brackets ! for multiline expressions
29144 \begin_layout Standard
29145 For brackets spanning multiple lines the following problem occurs:
29146 \begin_inset Formula
29148 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29149 & & \left.\cdots+B-D\right]
29157 \begin_layout Standard
29158 The closing bracket is smaller than the opening bracket because brackets
29159 with variable size may not span multiple lines.
29162 \begin_layout Standard
29163 To set the bracket size for the second line correctly, the first line is
29171 \begin_inset Index idx
29174 \begin_layout Plain Layout
29182 and the second line with
29190 \begin_layout Plain Layout
29204 \begin_inset CommandInset ref
29206 reference "subsec:Automatic-Bracket-Size"
29218 \begin_inset Index idx
29221 \begin_layout Plain Layout
29244 \begin_inset space \textvisiblespace{}
29254 \begin_inset space \textvisiblespace{}
29264 \begin_inset space \textvisiblespace{}
29270 \begin_inset Formula $\downarrow$
29276 \begin_inset Index idx
29279 \begin_layout Plain Layout
29287 is inserted, because the multiplication operator with its limits is the
29288 largest symbol in the first line and this should be the size for the bracket
29289 in the second line.
29292 \begin_layout Standard
29293 The result is this:
29294 \begin_inset Formula
29296 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29297 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29305 \begin_layout Subsection
29309 \begin_layout Standard
29310 Align environments can be used for every kind of multiline formulas.
29311 They are especially useful to set several formulas side by side.
29314 \begin_layout Standard
29315 Align environments consist of columns.
29316 The odd columns are right aligned, the even ones left aligned.
29317 Every line in an Align environment can be numbered.
29320 \begin_layout Standard
29321 Align environments are created via the menu
29323 Insert\SpecialChar menuseparator
29329 Edit\SpecialChar menuseparator
29330 Math\SpecialChar menuseparator
29331 Change Formula Type
29333 already existing formulas can be converted to Align environments.
29336 \begin_layout Standard
29337 To add or delete columns, the math toolbar buttons
29340 arg "inset-modify tabular append-column"
29346 arg "inset-modify tabular delete-column"
29349 , respectively, or the menu
29351 Edit\SpecialChar menuseparator
29357 \begin_layout Subsubsection
29358 Standard align Environment
29359 \begin_inset CommandInset label
29361 name "subsec:Standard-align-Environment"
29366 \begin_inset Index idx
29369 \begin_layout Plain Layout
29370 Formula ! multiline ! align environment
29378 \begin_layout Standard
29379 This Align environment is created by pressing
29382 arg "newline-insert newline"
29385 in a formula or by the menu
29387 Insert\SpecialChar menuseparator
29388 Math\SpecialChar menuseparator
29389 AMS align Environment
29394 \begin_layout Standard
29395 An example for two formulas set side by side, that are created with a four
29396 column align environment:
29397 \begin_inset Formula
29399 A & =\sin(B) & C & =D\\
29400 C & \ne A & B & \ne D
29405 As it can be seen, the formulas in this environment are placed so as if
29414 \begin_layout Plain Layout
29422 \begin_inset CommandInset ref
29424 reference "subsec:Variable-Space"
29435 before the first and after every even column.
29436 When the formula style
29442 \begin_layout Plain Layout
29444 \begin_inset CommandInset ref
29446 reference "sec:Formula-Styles"
29457 is used, the formula is set without the
29463 before the first column.
29466 \begin_layout Subsubsection
29467 Alignat Environment
29468 \begin_inset Index idx
29471 \begin_layout Plain Layout
29472 Formula ! multiline ! alignat environment
29480 \begin_layout Standard
29481 The alignat environment has no predefined column separation.
29482 It can be inserted manually with the spaces that are described
29483 \begin_inset CommandInset ref
29485 reference "subsec:Space"
29492 \begin_layout Standard
29493 The above example in the alignat environment where 1
29494 \begin_inset space \thinspace{}
29497 cm space was inserted at the beginning of the second formula:
29498 \begin_inset Formula
29499 \begin{alignat*}{2}
29500 A & =\sin(B) & \hspace{1cm}C & =D\\
29501 C & \ne A & B & \ne D
29506 Because the column separation can be set separately for every column, this
29507 environment is especially suitable to set three and more formulas side
29511 \begin_layout Subsubsection
29512 Flalign Environment
29513 \begin_inset CommandInset label
29515 name "subsec:Flalign-Environment"
29520 \begin_inset Index idx
29523 \begin_layout Plain Layout
29524 Formula ! multiline ! flalign environment
29532 \begin_layout Standard
29533 In this environment the first two columns are always set as much as possible
29534 to the left and the last two ones to the right.
29536 \begin_inset Formula
29538 A & =1 & B & =2 & C & =3\\
29539 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29547 \begin_layout Standard
29548 By creating a flalign environment with an odd number of columns where an
29549 empty \SpecialChar TeX
29550 brace is inserted to the last column, several formulas in a document
29551 can be set to the left, although the formula style
29556 As example the indented formula
29557 \begin_inset CommandInset ref
29559 reference "eq:VolInt"
29564 \begin_inset Formula
29566 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29571 The first two columns contain the formula.
29572 To indent it as with the formula style
29577 \begin_inset space \thinspace{}
29580 pt space was inserted at the beginning of the first column.
29583 \begin_layout Subsection
29584 Eqnarray Environment
29585 \begin_inset CommandInset label
29587 name "subsec:Eqnarray-Environment"
29592 \begin_inset Index idx
29595 \begin_layout Plain Layout
29596 Formula ! multiline ! eqnarray environment
29604 \begin_layout Standard
29605 When this environment has been created, three blue boxes appear.
29606 The content of the first box is right aligned, the content of the last
29608 The content of the middle box appears centered and a bit smaller, because
29609 it is designed to insert there only relation characters.
29610 \begin_inset Formula
29612 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29622 \begin_layout Subsection
29624 \begin_inset Index idx
29627 \begin_layout Plain Layout
29628 Formula ! multiline ! gather environment
29636 \begin_layout Standard
29637 This environment consists of only one centered column.
29638 Every line can be numbered.
29639 \begin_inset Formula
29650 \begin_layout Subsection
29651 Multline Environment
29652 \begin_inset CommandInset label
29654 name "subsec:Multline-Environment"
29659 \begin_inset Index idx
29662 \begin_layout Plain Layout
29663 Formula ! multiline ! multline environment
29671 \begin_layout Standard
29672 The multline environment consists, like the gather environment, of only
29674 But the first line is left aligned, the last one right aligned.
29675 All other lines are centered.
29676 Therefore this environment is suitable for long formulas.
29678 \begin_inset CommandInset ref
29680 reference "eq:lefteqn"
29684 in the multline environment:
29685 \begin_inset Formula
29687 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}\\
29688 -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}\\
29689 =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}}
29697 \begin_layout Standard
29698 In the output only the last (first) line of a multline environment appears
29699 numbered when the document numbering is right (left).
29703 \begin_layout Plain Layout
29704 numbering styles see
29705 \begin_inset CommandInset ref
29707 reference "sec:Formula-Styles"
29719 \begin_layout Standard
29727 \begin_inset Index idx
29730 \begin_layout Plain Layout
29745 \begin_inset Index idx
29748 \begin_layout Plain Layout
29756 a centered line can be right or left aligned, respectively.
29757 The commands are used as follows:
29760 \begin_layout Standard
29765 shoveright{line content}
29771 shoveleft{line content}
29774 \begin_layout Standard
29775 \begin_inset VSpace medskip
29785 \begin_inset Index idx
29788 \begin_layout Plain Layout
29796 specifies the distance of the first line from the left page margin.
29797 Predefined is the length 0
29798 \begin_inset space \thinspace{}
29804 \begin_layout Standard
29805 As example the above formula where the command
29808 \begin_layout Standard
29818 \begin_layout Standard
29819 was inserted in \SpecialChar TeX
29824 \begin_layout Plain Layout
29836 \begin_inset Formula
29838 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}\\
29839 \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}}\\
29840 =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}}
29849 \begin_layout Plain Layout
29860 The second line was left aligned using
29869 \begin_layout Subsection
29870 Multiline Formula Parts
29871 \begin_inset CommandInset label
29873 name "subsec:Multiline-Formula-Parts"
29878 \begin_inset Index idx
29881 \begin_layout Plain Layout
29882 Formula ! multiline ! formula parts
29890 \begin_layout Standard
29891 To display only parts of a formula with multiple lines, one of the following
29892 environments is used:
29909 They can be inserted via the menu
29911 Insert\SpecialChar menuseparator
29914 or by using the commands described in this section.
29917 \begin_layout Standard
29918 The first three have the same properties as the corresponding multiline
29919 formula environments, but it is possible to set further formula parts beside
29922 \begin_inset Formula
29924 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29925 \Delta E\Delta t & \ge\frac{\hbar}{2}
29927 \right\} \textrm{Uncertainty relations}
29935 \begin_layout Standard
29936 To get this formula, a displayed formula is created where the command
29943 \begin_inset Index idx
29946 \begin_layout Plain Layout
29955 A purple box appears around the blue formula box where now columns and
29956 lines can be added.
29957 Outside the multiline environment other formula parts can be set, like
29961 \begin_layout Standard
29962 The aligned environment is also suitable for long formulas whose lines are
29963 horizontally aligned.
29964 Using aligned in a displayed formula has the advantage that the formula
29965 number is vertically centered behind the lines.
29967 \begin_inset CommandInset ref
29969 reference "eq:shortlong"
29973 in the aligned environment:
29974 \begin_inset Formula
29976 \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}|}\\
29977 & -\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}|}
29986 \begin_layout Standard
29987 To use the environments
30006 \begin_inset Index idx
30009 \begin_layout Plain Layout
30024 \begin_inset Index idx
30027 \begin_layout Plain Layout
30042 \begin_inset Index idx
30045 \begin_layout Plain Layout
30053 are inserted, respectively.
30054 The split environment has the same properties as the aligned environment
30055 but it can only have two columns.
30058 \begin_layout Subsection
30059 Text in multiline Formulas
30060 \begin_inset CommandInset label
30062 name "subsec:Text-in-multiline"
30067 \begin_inset Index idx
30070 \begin_layout Plain Layout
30077 \begin_inset Index idx
30080 \begin_layout Plain Layout
30081 Formula ! multiline ! text
30089 \begin_layout Standard
30090 In the Align environments, and the multline and gather environment, text
30091 can be inserted that will appear in a separate line and doesn't affect
30092 the column alignment.
30093 To do this, the command
30100 \begin_inset Index idx
30103 \begin_layout Plain Layout
30111 is used in the following scheme:
30114 \begin_layout Standard
30122 \begin_layout Standard
30123 The text should not be longer than a line because it cannot be hyphenated.
30124 As \SpecialChar LyX
30125 doesn't yet support
30131 directly, the text is written as mathematical text.
30138 must hereby be at the beginning of a line and appears in the output above
30140 An example where the text was inserted at the beginning of the second line:
30141 \begin_inset Formula
30143 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30144 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30152 \begin_layout Standard
30159 always creates some vertical space between the text and the formula lines.
30160 To avoid this space, set in the document settings under
30163 \begin_inset space ~
30173 \begin_inset Index idx
30176 \begin_layout Plain Layout
30177 Packages ! mathtools
30185 \begin_inset space ~
30191 Then you can use the command
30198 \begin_inset Index idx
30201 \begin_layout Plain Layout
30218 \begin_layout Standard
30219 \begin_inset Formula
30221 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
30222 \shortintertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
30230 \begin_layout Section
30232 \begin_inset Index idx
30235 \begin_layout Plain Layout
30242 \begin_inset Index idx
30245 \begin_layout Plain Layout
30246 Formula ! numbering|see
30250 \begin_layout Plain Layout
30261 \begin_layout Plain Layout
30276 \begin_layout Subsection
30280 \begin_layout Standard
30281 Numbered formulas can be created with the menu
30283 Insert\SpecialChar menuseparator
30284 Math\SpecialChar menuseparator
30286 \begin_inset space ~
30294 \begin_inset space ~
30300 Existing formulas can be numbered with the menu
30302 Edit\SpecialChar menuseparator
30303 Math\SpecialChar menuseparator
30305 \begin_inset space ~
30313 arg "math-number-toggle"
30317 The formula number is displayed in \SpecialChar LyX
30318 behind the formula as a number sign
30320 The number sign is replaced in the output by the formula number.
30323 \begin_layout Standard
30324 When numbering is turned on in multiline formulas, all lines will be numbered.
30325 But the numbering can be controlled with the menu
30327 Edit\SpecialChar menuseparator
30328 Math\SpecialChar menuseparator
30330 \begin_inset space ~
30334 \begin_inset space ~
30338 \begin_inset space ~
30346 arg "math-number-line-toggle"
30352 \begin_layout Standard
30353 Except for inline formulas, all formulas can be numbered with two different
30355 \begin_inset CommandInset ref
30357 reference "sec:Formula-Styles"
30364 \begin_layout Subsection
30366 \begin_inset Index idx
30369 \begin_layout Plain Layout
30370 Cross-references ! to formulas
30378 \begin_layout Standard
30379 All labeled formulas can be cross-referenced.
30380 A label is added by the menu
30382 Insert\SpecialChar menuseparator
30385 or the toolbar button
30392 The cursor must hereby be inside a displayed formula.
30393 Alternatively you can right-click on the formula and choose
30398 A dialog pops up displaying the prefix
30403 The label is inserted there behind the prefix.
30404 The predefined prefix means
30405 \begin_inset Quotes eld
30409 \begin_inset Quotes erd
30412 and makes it easier to find labels in large documents because it marks
30413 it as formula label to divide it from e.
30414 \begin_inset space \thinspace{}
30418 \begin_inset space \space{}
30422 To change a label, the menu
30424 Insert\SpecialChar menuseparator
30427 is used again or you right-click on a formula and then on
30434 \begin_layout Standard
30435 The name of the label is displayed in \SpecialChar LyX
30436 within two parentheses behind formula.
30437 A formula with a label is always numbered.
30440 \begin_layout Standard
30441 Cross-references are inserted via the menu
30443 Insert\SpecialChar menuseparator
30446 or with the toolbar button
30449 arg "dialog-show-new-inset ref"
30453 A formula cross-reference appears in the output as formula number.
30454 When in the cross-reference dialog window the format
30458 is chosen, the cross-reference appears in the output as formula number
30460 \begin_inset Newline newline
30463 By right-clicking on a cross-reference in \SpecialChar LyX
30464 , one jumps to the formula that
30468 \begin_layout Standard
30469 Here are as examples cross-references to formulas of the following subsections:
30470 \begin_inset Note Note
30473 \begin_layout Plain Layout
30474 Note the different cross-reference types.
30482 \begin_layout Standard
30484 \begin_inset CommandInset ref
30491 \begin_inset CommandInset ref
30499 \begin_inset CommandInset ref
30505 ) big Latin letters are used for the numbering in contrary to (
30506 \begin_inset CommandInset ref
30515 \begin_layout Standard
30516 \begin_inset VSpace medskip
30519 When the argument of
30527 \begin_layout Plain Layout
30535 \begin_inset CommandInset ref
30537 reference "subsec:User-defined-Numbering"
30548 contains a box like in
30549 \begin_inset CommandInset ref
30551 reference "subsec:Paragraph-Boxes"
30555 , the formula cannot be referenced.
30558 \begin_layout Subsection
30560 \begin_inset Index idx
30563 \begin_layout Plain Layout
30564 Formula numbering ! subnumbering
30572 \begin_layout Standard
30573 With the help of the commands
30577 begin{subequations}
30585 formulas can be subnumbered.
30586 Both commands are inserted in \SpecialChar TeX
30590 \begin_layout Standard
30592 \begin_inset Formula
30603 \begin_layout Plain Layout
30607 addtocounter{equation}{-1}
30616 \begin_layout Plain Layout
30620 begin{subequations}
30626 \begin_inset VSpace -5mm
30630 \begin_inset Formula
30638 \begin_inset Formula
30648 \begin_layout Standard
30652 \begin_layout Plain Layout
30664 \begin_layout Standard
30665 To create the example, the following is done:
30668 \begin_layout Enumerate
30669 first formula is inserted
30672 \begin_layout Enumerate
30677 addtocounter{equation}{-1}
30679 begin{subequations}
30680 \begin_inset Index idx
30683 \begin_layout Plain Layout
30692 \begin_inset Newline newline
30697 is inserted after the first formula
30700 \begin_layout Enumerate
30701 second formula is inserted
30704 \begin_layout Enumerate
30705 third formula is inserted
30708 \begin_layout Enumerate
30715 is inserted after the third formula
30718 \begin_layout Standard
30719 Every formula between the commands
30731 is subnumbered as a, b,
30732 \begin_inset Newline linebreak
30735 c, \SpecialChar ldots
30736 For multiline formulas every line will be subnumbered.
30737 All subnumbered formulas are treated as
30742 But as every numbered formula increases the counter
30746 by one, the command
30752 is needed to decrease it.
30753 Otherwise the formulas
30754 \begin_inset CommandInset ref
30761 \begin_inset CommandInset ref
30768 \begin_inset CommandInset ref
30774 would be numbered as
30775 \begin_inset CommandInset ref
30782 \begin_inset CommandInset ref
30789 \begin_inset CommandInset ref
30798 \begin_layout Standard
30799 By inserting the commands in \SpecialChar TeX
30800 mode, a space is created between the first
30803 \begin_inset space \thinspace{}
30806 mm vertical space is inserted after the command
30810 begin{subequations}
30813 When the formula style
30819 \begin_layout Plain Layout
30821 \begin_inset CommandInset ref
30823 reference "sec:Formula-Styles"
30835 \begin_inset space \thinspace{}
30838 mm space is inserted instead.
30841 \begin_layout Standard
30842 Here is an example for a multiline formula where the numbering was turned
30843 off for the second line:
30847 \begin_layout Plain Layout
30851 begin{subequations}
30857 \begin_inset Formula
30859 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30860 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30861 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30870 \begin_layout Plain Layout
30882 \begin_layout Subsection
30883 User-defined Numbering
30884 \begin_inset CommandInset label
30886 name "subsec:User-defined-Numbering"
30891 \begin_inset Index idx
30894 \begin_layout Plain Layout
30895 Formula numbering ! user-defined
30903 \begin_layout Standard
30904 \begin_inset Index idx
30907 \begin_layout Plain Layout
30908 Formula numbering ! self-defined delimiters
30913 With the standard numbering parentheses are set around the formula number.
30914 To replace the parentheses for example by vertical bars, the following
30915 line is added to the \SpecialChar LaTeX
30919 \begin_layout Standard
30931 \begin_inset Note Note
30934 \begin_layout Plain Layout
30935 This macro is already declared in the \SpecialChar LaTeX
30936 -preamble for testing.
30937 To activate it, remove the percent sign at the beginning.
30945 \begin_layout Standard
30946 To use other characters, the vertical bars besides the
30950 are replaced by one ore more characters.
30951 To get only the formula number the vertical bars are omitted.
30954 \begin_layout Standard
30955 \begin_inset VSpace bigskip
30958 When there should be an expression of your choice instead of the consecutive
30959 formula number in parentheses behind the formula, the command
30966 \begin_inset Index idx
30969 \begin_layout Plain Layout
30978 \begin_inset Formula
30980 A+B=C\tag{something}\label{eq:tag}
30985 In this example the command
30990 \begin_inset space \textvisiblespace{}
30995 was inserted in the formula.
30998 \begin_layout Standard
31004 \begin_inset space \textvisiblespace{}
31009 is inserted instead, the star prevents the parentheses around the expression:
31010 \begin_inset Formula
31012 A+B=C\tag*{something}
31020 \begin_layout Standard
31021 \begin_inset VSpace bigskip
31024 To restart the formula numbering with new document parts or sections, the
31025 following command is used:
31028 \begin_layout Standard
31033 @addtoreset{equation}{part}
31036 \begin_inset Index idx
31039 \begin_layout Plain Layout
31044 \begin_layout Plain Layout
31055 \begin_layout Plain Layout
31068 \begin_layout Plain Layout
31079 \begin_layout Plain Layout
31092 \begin_inset Newline newline
31096 \begin_inset Newline newline
31103 @addtoreset{equation}{section}
31106 \begin_layout Standard
31107 To be able to use these commands in \SpecialChar TeX
31109 \begin_inset Quotes eld
31113 \begin_inset Quotes erd
31116 character has to be made
31117 \begin_inset Quotes eld
31121 \begin_inset Quotes erd
31124 for \SpecialChar LaTeX
31139 So the command sequence in \SpecialChar TeX
31143 \begin_layout Standard
31149 \begin_inset Newline newline
31154 @addtoreset{equation}{section}
31155 \begin_inset Newline newline
31163 \begin_layout Standard
31164 In the \SpecialChar LaTeX
31177 can be omitted as they are automatically internally inserted by \SpecialChar LyX
31181 \begin_layout Standard
31196 \begin_layout Plain Layout
31201 is part of the \SpecialChar LaTeX
31207 \begin_inset Index idx
31210 \begin_layout Plain Layout
31211 Packages ! carlisle
31216 that is part of every \SpecialChar LaTeX
31217 standard installation.
31223 \begin_inset Index idx
31226 \begin_layout Plain Layout
31227 Packages ! remreset
31232 has to be loaded in the \SpecialChar LaTeX
31233 -preamble with the line
31236 \begin_layout Standard
31241 usepackage{remreset}
31244 \begin_layout Standard
31252 \begin_inset Index idx
31255 \begin_layout Plain Layout
31260 \begin_layout Plain Layout
31271 \begin_layout Plain Layout
31284 \begin_layout Plain Layout
31295 \begin_layout Plain Layout
31307 can be used with the same scheme as
31316 \begin_layout Standard
31317 \begin_inset VSpace bigskip
31320 Sometimes formulas should be numbered in the following form:
31323 \begin_layout Standard
31326 (section number.formula number)
31329 \begin_layout Standard
31330 The formula number should start with every section with
31331 \begin_inset Quotes eld
31335 \begin_inset Quotes erd
31341 \begin_layout Standard
31342 For this case there is the command
31349 \begin_inset Index idx
31352 \begin_layout Plain Layout
31360 , which is used with the following scheme:
31363 \begin_layout Standard
31368 numberwithin{counter}{sectioning}
31371 \begin_layout Standard
31372 Counter denotes what kind of numbering is affected, sectioning denotes what
31373 number is before the dot.
31376 \begin_layout Standard
31377 Thus in our case the following \SpecialChar LaTeX
31378 preamble or \SpecialChar TeX
31382 \begin_layout Standard
31387 numberwithin{equation}{section}
31390 \begin_layout Standard
31391 This is the result:
31395 \begin_layout Plain Layout
31399 numberwithin{equation}{section}
31405 \begin_inset Formula
31415 \begin_layout Standard
31417 \begin_inset space \thinspace{}
31421 \begin_inset space \space{}
31424 tables so that the number of the part is the sectioning,
31425 \begin_inset Newline newline
31432 numberwithin{table}{part}
31437 \begin_layout Standard
31438 To go back to the standard numbering or to prevent this kind of numbering
31439 when it is defined by the document class, the following command is inserted
31440 as \SpecialChar TeX
31441 code or to the \SpecialChar LaTeX
31445 \begin_layout Standard
31455 \begin_inset Index idx
31458 \begin_layout Plain Layout
31472 \begin_layout Plain Layout
31488 \begin_inset Newline newline
31496 \begin_inset Newline newline
31508 \begin_layout Standard
31515 uses internally the command
31521 , described above, that also needs to be reverted.
31525 \begin_layout Plain Layout
31532 \begin_layout Plain Layout
31536 @removefromreset{equation}{section}
31539 \begin_layout Plain Layout
31551 \begin_layout Subsection
31552 Numbering with Roman Numbers and Letters
31553 \begin_inset Index idx
31556 \begin_layout Plain Layout
31557 Formula numbering ! with letters
31563 \begin_inset Index idx
31566 \begin_layout Plain Layout
31567 Formula numbering ! with Roman numbers
31575 \begin_layout Standard
31576 Formulas can also be numbered with Roman numbers and Latin letters.
31577 To number for example with small Roman numbers, the command
31580 \begin_layout Standard
31592 \begin_layout Standard
31593 is inserted before the formula in \SpecialChar TeX
31602 \begin_inset Index idx
31605 \begin_layout Plain Layout
31613 redefines the predefined command
31629 \begin_layout Plain Layout
31636 has the same scheme like the command
31642 that is described in
31643 \begin_inset CommandInset ref
31645 reference "subsec:The-Command-newcommand"
31658 is the formula counter.
31665 is used as prefix for a counter, the value of the counter is output as
31667 When a formula is numbered, \SpecialChar LaTeX
31668 sets internally the command
31674 behind the formula.
31680 \begin_inset Index idx
31683 \begin_layout Plain Layout
31693 outputs the counter as small Roman number.
31696 \begin_layout Standard
31697 All formulas behind the command
31707 are now numbered Roman.
31708 To switch to numbering with big Roman numbers, the command is inserted
31722 \begin_inset Index idx
31725 \begin_layout Plain Layout
31737 \begin_inset Quotes eld
31741 \begin_inset Quotes erd
31744 with small Latin letters there is the command
31751 \begin_inset Index idx
31754 \begin_layout Plain Layout
31762 , for big ones there is the command
31769 \begin_inset Index idx
31772 \begin_layout Plain Layout
31785 \begin_layout Standard
31786 \begin_inset Note Greyedout
31789 \begin_layout Plain Layout
31796 \begin_inset space ~
31799 formulas can be numbered with Latin letters in one document.
31807 \begin_layout Standard
31811 \begin_layout Plain Layout
31827 \begin_layout Standard
31828 \begin_inset Formula
31830 A=\textrm{small roman}
31839 \begin_layout Plain Layout
31853 \begin_inset Formula
31855 B=\textrm{big Roman}\label{eq:Rom}
31864 \begin_layout Plain Layout
31878 \begin_inset Formula
31880 C=\textrm{small Latin}
31889 \begin_layout Plain Layout
31903 \begin_inset Formula
31905 D=\textrm{big Latin}\label{eq:Lat}
31913 \begin_layout Standard
31914 To switch back to the default numbering, insert the command:
31917 \begin_layout Standard
31927 \begin_inset Index idx
31930 \begin_layout Plain Layout
31941 \begin_layout Standard
31945 \begin_layout Plain Layout
31959 \begin_inset Formula
31969 \begin_layout Standard
31970 \begin_inset VSpace medskip
31973 As you see, formulas are numbered serially independent from the numbering
31975 When then numbering should start with
31976 \begin_inset Quotes eld
31980 \begin_inset Quotes erd
31983 when the style is changed, new equation counters have to be defined.
31984 A description about this can be found in the file
31985 \begin_inset CommandInset href
31987 name "Formula-numbering.lyx"
31988 target "run:Formula-numbering.lyx"
31995 \begin_layout Section
31996 Chemical Symbols and Equations
31997 \begin_inset CommandInset label
31999 name "subsec:Chemical-Symbols-and"
32004 \begin_inset Index idx
32007 \begin_layout Plain Layout
32008 Chemical characters ! Symbols
32014 \begin_inset Index idx
32017 \begin_layout Plain Layout
32024 \begin_inset Index idx
32027 \begin_layout Plain Layout
32036 \begin_layout Standard
32037 An example text from chemistry:
32040 \begin_layout Quote
32042 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32045 -ion reacts with two
32046 \begin_inset Formula $\mathrm{Na^{+}}$
32049 -ions to sodium sulfate
32050 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32054 The chemical equation for this is:
32055 \begin_inset Formula
32057 \mathrm{2\,Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
32065 \begin_layout Standard
32066 This chemical equation can directly be created as formula.
32067 To avoid that the symbols appear italic, everything is highlighted and
32068 changed by the shortcut
32074 to the upright font style.
32078 \begin_layout Plain Layout
32084 \begin_inset CommandInset ref
32086 reference "subsec:Font-Styles"
32098 \begin_layout Standard
32099 A more convenient way to typeset chemical formulas is to use the command
32107 \begin_inset Index idx
32110 \begin_layout Plain Layout
32118 that is available when the \SpecialChar LaTeX
32124 \begin_inset Index idx
32127 \begin_layout Plain Layout
32140 to a formula a new blue box appears where chemical formulas can be inserted
32141 in an intuitive way.
32142 \begin_inset Separator parbreak
32148 \begin_layout Standard
32150 \begin_inset Tabular
32151 <lyxtabular version="3" rows="10" columns="2">
32152 <features tabularvalignment="middle">
32153 <column alignment="center" valignment="top">
32154 <column alignment="center" valignment="top">
32156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32159 \begin_layout Plain Layout
32165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32168 \begin_layout Plain Layout
32170 \begin_inset Note Note
32173 \begin_layout Plain Layout
32180 is only used as spacer.
32192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32195 \begin_layout Plain Layout
32199 \begin_inset space \textvisiblespace{}
32207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32210 \begin_layout Plain Layout
32211 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
32221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32224 \begin_layout Plain Layout
32228 \begin_inset space \textvisiblespace{}
32236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32239 \begin_layout Plain Layout
32240 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
32250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32253 \begin_layout Plain Layout
32257 \begin_inset space \textvisiblespace{}
32265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32268 \begin_layout Plain Layout
32269 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32282 \begin_layout Plain Layout
32286 \begin_inset space \textvisiblespace{}
32294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32297 \begin_layout Plain Layout
32298 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32311 \begin_layout Plain Layout
32315 \begin_inset space \textvisiblespace{}
32321 \begin_inset space \textvisiblespace{}
32327 \begin_inset space \textvisiblespace{}
32335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32338 \begin_layout Plain Layout
32339 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32352 \begin_layout Plain Layout
32356 \begin_inset space \textvisiblespace{}
32360 \begin_inset Formula $\downarrow$
32364 \begin_inset Formula $\to$
32372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32375 \begin_layout Plain Layout
32376 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32389 \begin_layout Plain Layout
32393 \begin_inset space \textvisiblespace{}
32399 \begin_inset space \textvisiblespace{}
32405 \begin_inset space \textvisiblespace{}
32413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32416 \begin_layout Plain Layout
32417 \begin_inset Formula $\raisebox{4.5mm}{}\ce{\ensuremath{\mu\hyphen}Cl}\raisebox{-2mm}{}$
32427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32430 \begin_layout Plain Layout
32434 \begin_inset space \textvisiblespace{}
32438 \begin_inset space \textvisiblespace{}
32442 \begin_inset space \textvisiblespace{}
32446 \begin_inset space \textvisiblespace{}
32450 \begin_inset space \textvisiblespace{}
32458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32461 \begin_layout Plain Layout
32462 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32475 \begin_layout Plain Layout
32479 \begin_inset space \textvisiblespace{}
32483 \begin_inset space \textvisiblespace{}
32487 \begin_inset space \textvisiblespace{}
32491 \begin_inset space \textvisiblespace{}
32499 \begin_inset space \textvisiblespace{}
32507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32510 \begin_layout Plain Layout
32511 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32527 \begin_layout Standard
32528 \begin_inset Note Greyedout
32531 \begin_layout Plain Layout
32537 It is not possible in \SpecialChar LyX
32538 to use the character ^ to get an up-arrow as described
32544 One instead uses a negative thin space followed by the command
32551 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32562 \begin_layout Standard
32569 the command for equation
32570 \begin_inset space ~
32574 \begin_inset CommandInset ref
32576 reference "eq:chem-reaction"
32581 \begin_inset Newline newline
32589 \begin_inset space \textvisiblespace{}
32593 \begin_inset space \textvisiblespace{}
32597 \begin_inset space \textvisiblespace{}
32601 \begin_inset space \textvisiblespace{}
32605 \begin_inset space \textvisiblespace{}
32609 \begin_inset space \textvisiblespace{}
32615 \begin_layout Standard
32616 To create multiline chemical equations first a multiline formula is created
32618 \begin_inset CommandInset ref
32620 reference "sec:Multiline-Formulas"
32625 Afterwards the command
32631 is used in every small blue box of the formula.
32633 \begin_inset CommandInset ref
32635 reference "eq:TEOS-reaction-1"
32640 \begin_inset CommandInset ref
32642 reference "eq:TEOS-reaction-2"
32646 are an example of a multi-stage chemical reaction where every equation
32647 has its own number.
32648 \begin_inset Formula
32650 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32651 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32659 \begin_layout Standard
32670 package provides the command
32677 \begin_inset Index idx
32680 \begin_layout Plain Layout
32688 that has to be used for special cases.
32689 For more information about
32695 and more examples have a look at the documentation of
32700 \begin_inset CommandInset citation
32709 \begin_layout Section
32713 \begin_layout Standard
32715 supports two types of commutative diagrams:
32723 that are explained in the following.
32726 \begin_layout Subsection
32728 \begin_inset Index idx
32731 \begin_layout Plain Layout
32740 \begin_layout Standard
32741 Diagrams of this type visualize relations by vertical and horizontal lines
32743 \begin_inset Formula
32745 \begin{CD}A@>>>B@>>>C\\
32756 \begin_layout Standard
32757 To get them, the command
32762 \begin_inset Index idx
32765 \begin_layout Plain Layout
32775 is inserted to a formula.
32776 A blue box appears with two dashed lines where further commands can be
32781 arg "newline-insert newline"
32784 a new line is created.
32785 Horizontal relations are inserted in odd, vertical in even formula lines.
32788 \begin_layout Standard
32789 To create the relations there are the following commands:
32792 \begin_layout Itemize
32797 creates a left arrow,
32808 \begin_layout Itemize
32813 creates an up arrow,
32821 a vertical equal sign
32824 \begin_layout Itemize
32830 is a placeholder for non-existent relations
32833 \begin_layout Standard
32834 All arrows can be labeled as follows:
32837 \begin_layout Itemize
32838 If text inserted between the first and second < or >, resp., it is placed
32840 When it is inserted between the second and third one, it appears under
32844 \begin_layout Itemize
32845 When text for vertical arrows is inserted between the first and second A
32846 or V, resp., it is placed left beside the arrow.
32847 When it is inserted between the second and third one, it appears right
32849 If the text contains an A or V, these letters must be set into a \SpecialChar TeX
32853 \begin_layout Standard
32854 As example a diagram with all possible relations:
32857 \begin_layout Standard
32858 \begin_inset Formula
32860 \begin{CD}A@>j>>B@>>k>C@=F\\
32871 \begin_layout Standard
32872 The command for this is:
32873 \begin_inset Newline newline
32881 \begin_inset space \textvisiblespace{}
32884 A@>j>>B@>>k>C@=F Ctrl+Return
32885 \begin_inset Newline newline
32889 \begin_inset Phantom HPhantom
32892 \begin_layout Plain Layout
32898 \begin_inset space \textvisiblespace{}
32911 \begin_inset Formula $\to$
32917 \begin_inset Newline newline
32921 \begin_inset Phantom HPhantom
32924 \begin_layout Plain Layout
32930 \begin_inset space \textvisiblespace{}
32941 \begin_layout Subsection
32943 \begin_inset Index idx
32946 \begin_layout Plain Layout
32947 Diagrams ! xymatrix
32955 \begin_layout Standard
32956 To be able to use xymatrices, the \SpecialChar LaTeX
32962 A xymatrix is created by inserting the command
32969 Then you are able to add new matrix columns and rows like for normal matrices,
32971 \begin_inset CommandInset ref
32973 reference "sec:Matrices"
32980 \begin_layout Standard
32981 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32983 All possibilities to create commutative diagrams and decorations are explained
32988 that you find in the menu
32990 Help\SpecialChar menuseparator
32992 \begin_inset space ~
33000 \begin_layout Subsection
33006 \begin_inset Index idx
33009 \begin_layout Plain Layout
33018 \begin_layout Standard
33023 -diagrams, the \SpecialChar LaTeX
33033 -diagram is created by inserting the command
33040 Then you are able to add new matrix columns and rows like for normal matrices,
33042 \begin_inset CommandInset ref
33044 reference "sec:Matrices"
33051 \begin_layout Standard
33052 Examples how to create
33056 diagrams in \SpecialChar LyX
33059 Feynman-diagram manual
33061 that you find in the menu
33063 Help\SpecialChar menuseparator
33065 \begin_inset space ~
33073 \begin_layout Standard
33074 \begin_inset Newpage newpage
33080 \begin_layout Section
33081 User-defined Commands
33082 \begin_inset Index idx
33085 \begin_layout Plain Layout
33086 User-defined commands
33094 \begin_layout Standard
33095 \begin_inset Note Greyedout
33098 \begin_layout Plain Layout
33103 The names of user-defined commands and macros may only consist of Latin
33112 \begin_layout Subsection
33116 \begin_inset CommandInset label
33118 name "subsec:The-Command-newcommand"
33123 \begin_inset Index idx
33126 \begin_layout Plain Layout
33127 User-defined commands !
33135 \begin_inset Index idx
33138 \begin_layout Plain Layout
33149 \begin_layout Standard
33150 Many \SpecialChar LaTeX
33151 -commands are too long to be used frequently.
33152 But it is possible to define with the command
33158 new shorter commands.
33161 \begin_layout Standard
33162 The command scheme of
33171 \begin_layout Standard
33176 newcommand{new command name}[number of arguments][optional
33181 \begin_inset Newline newline
33185 \begin_inset Phantom HPhantom
33188 \begin_layout Plain Layout
33198 {command definition}
33201 \begin_layout Standard
33202 \begin_inset Note Greyedout
33205 \begin_layout Plain Layout
33210 Assure that the name of the new command is not already used in your document
33211 or by \SpecialChar LaTeX
33212 -packages that you use.
33213 When you for example define the command
33225 , you get an error message because
33231 is already defined as command for
33232 \begin_inset Quotes eld
33236 \begin_inset Formula $\le$
33240 \begin_inset Quotes erd
33251 \begin_layout Standard
33252 The number of arguments is an integer in the range 0
33253 \begin_inset space \thinspace{}
33257 \begin_inset space \thinspace{}
33260 9 and specifies how many arguments the new command should have.
33261 With the optional value a value for an optional argument can be predefined.
33262 When this is done, the
33270 rgument of the new command is automatically an optional one.
33273 \begin_layout Standard
33274 Here are some examples:
33277 \begin_layout Itemize
33278 To define the command
33290 , the \SpecialChar LaTeX
33292 \begin_inset VSpace medskip
33296 \begin_inset Newline newline
33310 \begin_layout Itemize
33311 To define the command
33323 , the argument (that should be underlined) must be taken into account.
33324 For this the preamble line is:
33325 \begin_inset VSpace medskip
33329 \begin_inset Newline newline
33343 \begin_inset VSpace medskip
33347 \begin_inset Newline newline
33354 acts as argument placeholder, the
33358 behind it denotes that it is the placeholder for the first argument.
33361 \begin_layout Itemize
33369 \begin_inset space \thinspace{}
33373 \begin_inset space \space{}
33383 \begin_inset VSpace medskip
33387 \begin_inset Newline newline
33398 framebox#1#2{$#3$}}
33401 \begin_inset VSpace medskip
33405 \begin_inset Newline newline
33408 The two Dollar signs creates the extra formula needed for
33415 \begin_inset CommandInset ref
33417 reference "subsec:Boxes-with-Frame"
33424 \begin_layout Itemize
33425 To create a new command for
33431 where the color for the box need not be specified, the argument for the
33432 color is defined optional:
33433 \begin_inset VSpace medskip
33437 \begin_inset Newline newline
33448 fcolorbox{#2}{#1}{$#3$}}
33451 \begin_inset VSpace medskip
33455 \begin_inset Newline newline
33458 When the color is not specified when using
33464 , the predefined color
33471 \begin_layout Standard
33472 A test of the new defined commands:
33473 \begin_inset Separator parbreak
33479 \begin_layout Standard
33481 \begin_inset Tabular
33482 <lyxtabular version="3" rows="6" columns="2">
33483 <features tabularvalignment="middle">
33484 <column alignment="center" valignment="top">
33485 <column alignment="center" valignment="top">
33487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33490 \begin_layout Plain Layout
33496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33499 \begin_layout Plain Layout
33501 \begin_inset Note Note
33504 \begin_layout Plain Layout
33511 is only used as spacer.
33523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33526 \begin_layout Plain Layout
33530 \begin_inset space \textvisiblespace{}
33538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33541 \begin_layout Plain Layout
33542 \begin_inset Formula $A\gr B$
33552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33555 \begin_layout Plain Layout
33563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33566 \begin_layout Plain Layout
33567 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33580 \begin_layout Plain Layout
33584 \begin_inset Formula $\to$
33590 \begin_inset Formula $\to$
33598 \begin_inset space \textvisiblespace{}
33606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33609 \begin_layout Plain Layout
33610 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33623 \begin_layout Plain Layout
33627 \begin_inset Formula $\to$
33635 \begin_inset space \textvisiblespace{}
33643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33646 \begin_layout Plain Layout
33647 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33660 \begin_layout Plain Layout
33666 \begin_inset Formula $\to$
33674 \begin_inset space \textvisiblespace{}
33682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33685 \begin_layout Plain Layout
33686 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33702 \begin_layout Subsection
33704 \begin_inset Index idx
33707 \begin_layout Plain Layout
33708 User-defined commands! Math macros
33714 \begin_inset Index idx
33717 \begin_layout Plain Layout
33726 \begin_layout Standard
33727 User-defined commands are especially convenient for complex expressions.
33728 When you are for example dealing with a document that has quadratic equations,
33729 the same solution type occurs several times.
33730 The general form of a quadratic equation is
33731 \begin_inset Formula
33733 0=\lambda^{2}+p\lambda+q
33738 The general form of the solution is
33739 \begin_inset Formula
33741 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33749 \begin_layout Standard
33750 To define a command for the solution formula where only the three parameters
33752 \begin_inset Formula $\lambda$
33756 \begin_inset Formula $p$
33760 \begin_inset Formula $q$
33763 need to be specified and the index of
33764 \begin_inset Formula $\lambda$
33767 can be given optionally, the \SpecialChar LaTeX
33769 \begin_inset Newline newline
33785 \begin_inset Newline newline
33789 \begin_inset Phantom HPhantom
33792 \begin_layout Plain Layout
33806 frac{#3^{2}}{4}-#4}}
33809 \begin_layout Standard
33810 To create with this the solution formula, the command
33811 \begin_inset Newline newline
33821 \begin_inset Formula $\to$
33827 \begin_inset Formula $\to$
33834 is inserted to a formula
33839 \begin_layout Standard
33840 The definition of the new command is unintuitive because one has to know
33841 the schemes of all used \SpecialChar LaTeX
33843 \begin_inset space \thinspace{}
33847 \begin_inset space \space{}
33850 that a fraction is inserted in \SpecialChar LaTeX
33855 frac{numerator}{denominator}
33858 Furthermore one can easily forget a brace in the definition and cannot
33859 see in \SpecialChar LyX
33860 what the new command is doing.
33861 To avoid these problems \SpecialChar LyX
33862 offers the possibility to use math macros instead
33872 \begin_layout Standard
33873 A math macro is created by using the menu
33875 Insert\SpecialChar menuseparator
33876 Math\SpecialChar menuseparator
33879 or the toolbar button
33882 arg "math-macro newmacroname_newcommand"
33886 The math macro toolbar appears together with the following box where the
33888 \begin_inset Newline newline
33892 \begin_inset space \hspace*{\fill}
33896 \begin_inset Graphics
33897 filename clipart/macrobox.png
33903 \begin_inset space \hspace*{\fill}
33907 \begin_inset Newline newline
33911 \begin_inset FormulaMacro
33912 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33917 newmacroname is the default name of the macro that should be changed to
33918 something sensible.
33919 The wanted formula is inserted in the first blue box.
33920 An argument placeholder is inserted with the command
33927 \begin_inset space \thinspace{}
33931 \begin_inset space \space{}
33940 or by using the macro toolbar button
33943 arg "math-macro-add-param"
33947 Argument placeholders are displayed red.
33949 \begin_inset space ~
33952 arguments are possible.
33953 Optional arguments are created with the toolbar button
33956 arg "math-macro-add-optional-param"
33960 The first non-optional argument can be transformed to an optional one with
33964 arg "math-macro-make-optional"
33968 In the second blue box the appearance of the macro in \SpecialChar LyX
33970 Normally you want to see it as it is defined, so the box is kept empty.
33971 But when you have created a macro that needs lot of space on the screen,
33972 you can insert in the box for example
33973 \begin_inset Newline newline
34003 \begin_inset Newline newline
34008 For the macro only the arguments with the macro name in front of them will
34009 then be displayed in \SpecialChar LyX
34010 , leading to a better overview.
34011 The formula appears in the output as defined in the first box.
34012 \begin_inset Newline newline
34015 The appearance of macros in formulas can furthermore be changed for single
34016 macros by setting the cursor in the macro and using the menu
34018 View\SpecialChar menuseparator
34020 \begin_inset space ~
34024 \begin_inset space ~
34032 \begin_layout Standard
34033 To use a macro, the macro name is inserted as command to a formula, in our
34041 Our macro looks in \SpecialChar LyX
34043 \begin_inset Newline newline
34047 \begin_inset space \hspace*{\fill}
34051 \begin_inset Graphics
34052 filename clipart/macrouse.png
34058 \begin_inset space \hspace*{\fill}
34062 \begin_inset Newline newline
34065 Here is our macro example with the arguments
34066 \begin_inset Formula $x$
34070 \begin_inset Formula $\ln(x)$
34074 \begin_inset Formula $B$
34080 \begin_layout Standard
34081 \begin_inset Formula
34091 \begin_layout Standard
34095 Tools\SpecialChar menuseparator
34096 Preferences\SpecialChar menuseparator
34097 Editing\SpecialChar menuseparator
34100 different styles to edit macros.
34101 To find the style that suits you the most, choose a style and set the cursor
34102 in a macro formula to see the difference.
34105 \begin_layout Standard
34106 A math macro is transformed internally to a
34112 command when exporting the document.
34119 command is not placed in the \SpecialChar LaTeX
34120 -preamble, therefore macros can only be used
34121 in formulas that are in the document below the macro definition box.
34124 \begin_layout Standard
34125 Math macros can also be directly created from a
34132 When writing for example the command
34135 \begin_inset Newline newline
34144 xleftarrow[#2]{#1}}
34145 \begin_inset Newline newline
34150 in \SpecialChar LyX
34151 as normal text, highlighting it completely and using then the shortcut
34156 , the command will be transformed to a math macro.
34157 Using this method you need to be careful that the
34163 command is typed correctly, otherwise you get a faulty macro leading to
34168 \begin_layout Standard
34169 Math macros currently have the problem that further formulas in macro definition
34170 s are handled wrongly.
34171 Therefore the example
34178 \begin_inset CommandInset ref
34180 reference "subsec:The-Command-newcommand"
34184 cannot be created as macro.
34187 \begin_layout Standard
34188 When the cursor is in a macro definition box, you will see the macro toolbar
34189 in \SpecialChar LyX
34193 \begin_layout Standard
34194 \begin_inset VSpace defskip
34200 \begin_layout Standard
34201 \begin_inset Graphics
34202 filename clipart/MacroToolbar.png
34207 \begin_inset Index idx
34210 \begin_layout Plain Layout
34219 \begin_layout Standard
34220 \begin_inset VSpace defskip
34226 \begin_layout Standard
34227 The macro toolbar contains from left to right the following buttons:
34230 \begin_layout Standard
34231 \begin_inset VSpace defskip
34237 \begin_layout Standard
34238 \begin_inset Tabular
34239 <lyxtabular version="3" rows="9" columns="2">
34240 <features islongtable="true" longtabularalignment="center">
34241 <column alignment="left" valignment="top">
34242 <column alignment="left" valignment="top" width="85col%">
34243 <row interlinespace="2.5mm">
34244 <cell alignment="center" valignment="top" usebox="none">
34247 \begin_layout Plain Layout
34250 arg "math-macro-remove-param"
34258 <cell alignment="center" valignment="top" usebox="none">
34261 \begin_layout Plain Layout
34264 Edit\SpecialChar menuseparator
34265 Math\SpecialChar menuseparator
34267 \begin_inset space ~
34270 Definition\SpecialChar menuseparator
34271 Remove Last Argument
34277 <row interlinespace="2.5mm">
34278 <cell alignment="center" valignment="top" usebox="none">
34281 \begin_layout Plain Layout
34284 arg "math-macro-add-param"
34292 <cell alignment="center" valignment="top" usebox="none">
34295 \begin_layout Plain Layout
34298 Edit\SpecialChar menuseparator
34299 Math\SpecialChar menuseparator
34301 \begin_inset space ~
34304 Definition\SpecialChar menuseparator
34311 <row interlinespace="2.5mm">
34312 <cell alignment="center" valignment="top" usebox="none">
34315 \begin_layout Plain Layout
34318 arg "math-macro-make-optional"
34326 <cell alignment="center" valignment="top" usebox="none">
34329 \begin_layout Plain Layout
34332 Edit\SpecialChar menuseparator
34333 Math\SpecialChar menuseparator
34335 \begin_inset space ~
34338 Definition\SpecialChar menuseparator
34339 Transform First Non-Optional to
34340 \begin_inset Newline newline
34344 \begin_inset Phantom HPhantom
34347 \begin_layout Plain Layout
34350 Edit\SpecialChar menuseparator
34351 Math\SpecialChar menuseparator
34353 \begin_inset space ~
34356 Definition\SpecialChar menuseparator
34368 <row interlinespace="2.5mm">
34369 <cell alignment="center" valignment="top" usebox="none">
34372 \begin_layout Plain Layout
34375 arg "math-macro-make-nonoptional"
34383 <cell alignment="center" valignment="top" usebox="none">
34386 \begin_layout Plain Layout
34389 Edit\SpecialChar menuseparator
34390 Math\SpecialChar menuseparator
34392 \begin_inset space ~
34395 Definition\SpecialChar menuseparator
34396 Transform Last Optional to
34397 \begin_inset Newline newline
34401 \begin_inset Phantom HPhantom
34404 \begin_layout Plain Layout
34407 Edit\SpecialChar menuseparator
34408 Math\SpecialChar menuseparator
34410 \begin_inset space ~
34413 Definition\SpecialChar menuseparator
34419 Non-Optional Argument
34425 <row interlinespace="2.5mm">
34426 <cell alignment="center" valignment="top" usebox="none">
34429 \begin_layout Plain Layout
34432 arg "math-macro-remove-optional-param"
34440 <cell alignment="center" valignment="top" usebox="none">
34443 \begin_layout Plain Layout
34446 Edit\SpecialChar menuseparator
34447 Math\SpecialChar menuseparator
34449 \begin_inset space ~
34452 Definition\SpecialChar menuseparator
34453 Remove Optional Argument
34459 <row interlinespace="2.5mm">
34460 <cell alignment="center" valignment="top" usebox="none">
34463 \begin_layout Plain Layout
34466 arg "math-macro-add-optional-param"
34474 <cell alignment="center" valignment="top" usebox="none">
34477 \begin_layout Plain Layout
34480 Edit\SpecialChar menuseparator
34481 Math\SpecialChar menuseparator
34483 \begin_inset space ~
34486 Definition\SpecialChar menuseparator
34487 Insert Optional Argument
34493 <row interlinespace="2.5mm">
34494 <cell alignment="center" valignment="top" usebox="none">
34497 \begin_layout Plain Layout
34500 arg "math-macro-remove-greedy-param"
34508 <cell alignment="center" valignment="top" usebox="none">
34511 \begin_layout Plain Layout
34514 Edit\SpecialChar menuseparator
34515 Math\SpecialChar menuseparator
34517 \begin_inset space ~
34520 Definition\SpecialChar menuseparator
34521 Remove Last Argument
34522 \begin_inset Newline newline
34526 \begin_inset Phantom HPhantom
34529 \begin_layout Plain Layout
34532 Edit\SpecialChar menuseparator
34533 Math\SpecialChar menuseparator
34535 \begin_inset space ~
34538 Definition\SpecialChar menuseparator
34544 Spitting Out To The Right
34550 <row interlinespace="2.5mm">
34551 <cell alignment="center" valignment="top" usebox="none">
34554 \begin_layout Plain Layout
34557 arg "math-macro-append-greedy-param"
34565 <cell alignment="center" valignment="top" usebox="none">
34568 \begin_layout Plain Layout
34571 Edit\SpecialChar menuseparator
34572 Math\SpecialChar menuseparator
34574 \begin_inset space ~
34577 Definition\SpecialChar menuseparator
34579 \begin_inset Newline newline
34583 \begin_inset Phantom HPhantom
34586 \begin_layout Plain Layout
34589 Edit\SpecialChar menuseparator
34590 Math\SpecialChar menuseparator
34592 \begin_inset space ~
34595 Definition\SpecialChar menuseparator
34601 Eating From The Right
34607 <row interlinespace="2.5mm">
34608 <cell alignment="center" valignment="top" usebox="none">
34611 \begin_layout Plain Layout
34614 arg "math-macro-add-greedy-optional-param"
34622 <cell alignment="center" valignment="top" usebox="none">
34625 \begin_layout Plain Layout
34628 Edit\SpecialChar menuseparator
34629 Math\SpecialChar menuseparator
34631 \begin_inset space ~
34634 Definition\SpecialChar menuseparator
34635 Append Optional Argument
34636 \begin_inset Newline newline
34640 \begin_inset Phantom HPhantom
34643 \begin_layout Plain Layout
34646 Edit\SpecialChar menuseparator
34647 Math\SpecialChar menuseparator
34649 \begin_inset space ~
34652 Definition\SpecialChar menuseparator
34658 Eating From The Right
34671 \begin_layout Section
34672 Computer Algebra Systems
34675 \begin_layout Standard
34677 offers the exchange between mathematical expressions written in \SpecialChar LyX
34679 editor and external applications or user defined scripts.
34680 Currently supported applications are
34697 Note that the set of supported mathematical constructs is limited only
34698 to very simple cases.
34701 \begin_layout Subsection
34705 \begin_layout Standard
34706 Write some expression in a formula, go to the
34708 Edit\SpecialChar menuseparator
34709 Math\SpecialChar menuseparator
34710 Use Computer Algebra System
34712 menu and choose the application you have installed on the computer.
34713 After that the result of computation should show on the right side of the
34714 expression together with the
34715 \begin_inset Quotes eld
34719 \begin_inset Quotes erd
34725 \begin_layout Standard
34726 Here are few simple examples (with results from
34730 ) to show what kind of computations can be performed:
34733 \begin_layout Itemize
34734 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34740 \begin_layout Itemize
34741 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34747 \begin_layout Itemize
34748 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34754 \begin_layout Itemize
34755 \begin_inset Formula $\det\left[\begin{array}{ccc}
34759 \end{array}\right]=-56$
34765 \begin_layout Itemize
34766 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34772 \begin_layout Subsection
34776 \begin_layout Standard
34777 Currently there is no keyboard shortcut for calling the algebra applications.
34778 One can easily bind a shortcut to the
34792 \begin_inset space \thinspace{}
34796 \begin_inset space \space{}
34803 key inside the math editor.
34808 one would use this shortcut definition command:
34811 \begin_layout Standard
34814 command-alternatives paragraph-break;math-extern maxima
34817 \begin_layout Section
34819 \begin_inset Index idx
34822 \begin_layout Plain Layout
34831 \begin_layout Subsection
34833 \begin_inset Index idx
34836 \begin_layout Plain Layout
34845 \begin_layout Standard
34846 Negative numbers often look ugly in formulas because the minus sign before
34847 the number is set with the same length as the minus operator sign.
34848 When writing the negative number in normal text, the minus sign appears
34852 \begin_layout Standard
34853 Thus, the problem disappears when converting the minus sign to mathematical
34857 \begin_layout Standard
34858 An example to visualize the problem:
34859 \begin_inset Separator parbreak
34865 \begin_layout Standard
34867 \begin_inset Tabular
34868 <lyxtabular version="3" rows="3" columns="2">
34869 <features tabularvalignment="middle">
34870 <column alignment="right" valignment="top">
34871 <column alignment="left" valignment="top">
34873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34876 \begin_layout Plain Layout
34882 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34885 \begin_layout Plain Layout
34893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34896 \begin_layout Plain Layout
34902 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34905 \begin_layout Plain Layout
34906 \begin_inset Formula $x=-2$
34916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34919 \begin_layout Plain Layout
34925 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34928 \begin_layout Plain Layout
34929 \begin_inset Formula $x=\textrm{-}2$
34945 \begin_layout Subsection
34946 Comma as decimal Separator
34947 \begin_inset Index idx
34950 \begin_layout Plain Layout
34959 \begin_layout Standard
34960 In \SpecialChar LaTeX
34961 a comma inside a formula is used, according to the English convention,
34962 as number group separator.
34963 So there will be space added behind all commas in formulas.
34966 \begin_layout Standard
34967 To avoid this, the comma is highlighted and changed to mathematical text
34977 \begin_layout Standard
34978 To use all formula commas in the document as decimal separator, the file
34987 \begin_layout Plain Layout
34992 is part of the \SpecialChar LaTeX
34998 \begin_inset Index idx
35001 \begin_layout Plain Layout
35006 \begin_layout Plain Layout
35026 \begin_inset Index idx
35029 \begin_layout Plain Layout
35035 is loaded with the \SpecialChar LaTeX
35039 \begin_layout Standard
35047 \begin_layout Subsection
35049 \begin_inset CommandInset label
35051 name "subsec:Physical-Vectors"
35056 \begin_inset Index idx
35059 \begin_layout Plain Layout
35068 \begin_layout Standard
35069 Predefined vectors are offered by the \SpecialChar LaTeX
35075 \begin_inset Index idx
35078 \begin_layout Plain Layout
35084 that is loaded with the \SpecialChar LaTeX
35088 \begin_layout Standard
35096 \begin_layout Standard
35100 \begin_layout Plain Layout
35110 \begin_inset Note Note
35113 \begin_layout Plain Layout
35114 The following table will only be displayed when the \SpecialChar LaTeX
35127 \begin_layout Standard
35128 The following commands are defined:
35129 \begin_inset Separator parbreak
35135 \begin_layout Standard
35137 \begin_inset Tabular
35138 <lyxtabular version="3" rows="4" columns="2">
35139 <features tabularvalignment="middle">
35140 <column alignment="center" valignment="top">
35141 <column alignment="center" valignment="top">
35143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35146 \begin_layout Plain Layout
35152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35155 \begin_layout Plain Layout
35163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35166 \begin_layout Plain Layout
35176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35179 \begin_layout Plain Layout
35180 \begin_inset Formula $\Bra{\psi}$
35190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35193 \begin_layout Plain Layout
35203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35206 \begin_layout Plain Layout
35207 \begin_inset Formula $\Ket{\psi}$
35217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35220 \begin_layout Plain Layout
35232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35235 \begin_layout Plain Layout
35236 \begin_inset Formula $\Braket{\psi|\phi}$
35252 \begin_layout Standard
35259 assures that all vertical bars are set in the size of the surrounding brackets:
35260 \begin_inset Formula
35262 \Braket{\phi|J=\frac{3}{2}\,,\,M_{J}}
35271 \begin_layout Plain Layout
35281 \begin_inset Note Note
35284 \begin_layout Plain Layout
35285 The following will be displayed when the \SpecialChar LaTeX
35298 \begin_layout Standard
35299 You need to install the \SpecialChar LaTeX
35304 to see the rest of this subsection in the output.
35307 \begin_layout Standard
35311 \begin_layout Plain Layout
35323 \begin_layout Standard
35330 can also be achieved using the command
35336 , that is described in
35337 \begin_inset CommandInset ref
35339 reference "subsec:Automatic-Bracket-Size"
35346 \begin_layout Subsection
35347 Self-defined Fractions
35348 \begin_inset CommandInset label
35350 name "subsec:Self-defined-Fractions"
35355 \begin_inset Index idx
35358 \begin_layout Plain Layout
35359 Fractions ! self-defined
35367 \begin_layout Standard
35368 To define custom commands for fractions, the command
35375 \begin_inset Index idx
35378 \begin_layout Plain Layout
35385 \begin_layout Plain Layout
35399 is used in the following scheme:
35402 \begin_layout Standard
35415 bracket}{fraction bar thickness}{style}
35416 \begin_inset Newline newline
35420 \begin_inset Phantom HPhantom
35423 \begin_layout Plain Layout
35433 {numerator}{denominator}
35436 \begin_layout Standard
35437 The style is a number in the range of 0
35438 \begin_inset space \thinspace{}
35442 \begin_inset space \thinspace{}
35446 \begin_inset Separator parbreak
35452 \begin_layout Standard
35454 \begin_inset Tabular
35455 <lyxtabular version="3" rows="5" columns="2">
35456 <features tabularvalignment="middle">
35457 <column alignment="center" valignment="top">
35458 <column alignment="center" valignment="top">
35460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35463 \begin_layout Plain Layout
35469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35472 \begin_layout Plain Layout
35480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35483 \begin_layout Plain Layout
35489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35492 \begin_layout Plain Layout
35493 display style formula
35500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35503 \begin_layout Plain Layout
35509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35512 \begin_layout Plain Layout
35520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35523 \begin_layout Plain Layout
35529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35532 \begin_layout Plain Layout
35540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35543 \begin_layout Plain Layout
35549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35552 \begin_layout Plain Layout
35566 \begin_layout Standard
35567 When no style is given, the size is adjusted to the surrounding environment
35568 like for the command
35577 \begin_layout Standard
35578 When no fraction bar thickness is given, the predefined value of 0.4
35579 \begin_inset space \thinspace{}
35585 \begin_layout Standard
35586 \begin_inset VSpace medskip
35589 For example, the commands
35602 \begin_inset CommandInset ref
35604 reference "subsec:Fractions"
35608 are defined with the commands
35611 \begin_layout Standard
35620 genfrac{}{}{}{0}{#1}{#2}}
35623 \begin_layout Standard
35627 \begin_layout Standard
35636 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35639 \begin_layout Standard
35640 \begin_inset VSpace medskip
35643 To define a fraction where the fraction bar thickness can be given as optional
35644 argument, the following line is inserted to the \SpecialChar LaTeX
35648 \begin_layout Standard
35657 genfrac{}{}{#1}{}{#2}{#3}}
35660 \begin_layout Standard
35662 \begin_inset Formula
35664 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35665 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35670 As one can see, the distance of the numerator and the denominator to the
35671 fraction bar is round about three times the bar thickness.
35674 \begin_layout Subsection
35676 \begin_inset Index idx
35679 \begin_layout Plain Layout
35688 \begin_layout Standard
35689 There are four ways to cancel formulas or parts of formulas:
35692 \begin_layout Standard
35696 \begin_layout Plain Layout
35706 \begin_inset Note Note
35709 \begin_layout Plain Layout
35710 The following table will only be displayed when the \SpecialChar LaTeX
35721 \begin_inset Separator parbreak
35727 \begin_layout Standard
35729 \begin_inset Tabular
35730 <lyxtabular version="3" rows="5" columns="2">
35731 <features tabularvalignment="middle">
35732 <column alignment="center" valignment="top">
35733 <column alignment="center" valignment="top">
35735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35738 \begin_layout Plain Layout
35744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35747 \begin_layout Plain Layout
35749 \begin_inset Note Note
35752 \begin_layout Plain Layout
35759 are used here as spacer.
35771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35774 \begin_layout Plain Layout
35778 \begin_inset space \textvisiblespace{}
35784 \begin_inset space \textvisiblespace{}
35792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35795 \begin_layout Plain Layout
35796 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35809 \begin_layout Plain Layout
35813 \begin_inset space \textvisiblespace{}
35819 \begin_inset space \textvisiblespace{}
35827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35830 \begin_layout Plain Layout
35831 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35844 \begin_layout Plain Layout
35848 \begin_inset space \textvisiblespace{}
35854 \begin_inset space \textvisiblespace{}
35862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35865 \begin_layout Plain Layout
35866 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35879 \begin_layout Plain Layout
35883 \begin_inset space \textvisiblespace{}
35889 \begin_inset space \textvisiblespace{}
35893 \begin_inset Formula $\to$
35901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35904 \begin_layout Plain Layout
35905 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35921 \begin_layout Standard
35928 is especially suitable to visualize the reduction of fractions within formulas:
35929 \begin_inset Formula
35931 \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}}}
35939 \begin_layout Standard
35940 To change the size of
35947 \begin_inset Quotes eld
35951 \begin_inset Quotes erd
35954 value one can add the \SpecialChar LaTeX
35958 \begin_layout Standard
35963 PassOptionsToPackage{option}{cancel}
35966 \begin_layout Standard
35975 which leads to the same size as for the canceled value, or
35979 which makes is it a bit smaller than normal.
35982 \begin_layout Standard
35983 To color the cancellation bar one adds this command as \SpecialChar TeX
35987 \begin_layout Standard
35999 \begin_layout Standard
36004 can be replaced by a color of your choice.
36007 \begin_layout Standard
36011 \begin_layout Plain Layout
36027 \begin_layout Standard
36028 \begin_inset Formula
36030 \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}}}
36038 \begin_layout Standard
36042 \begin_layout Plain Layout
36056 \begin_inset Note Note
36059 \begin_layout Plain Layout
36068 \begin_layout Standard
36069 For further customizations, see the documentation of the package
36074 \begin_inset CommandInset citation
36081 \begin_inset Index idx
36084 \begin_layout Plain Layout
36093 \begin_layout Standard
36097 \begin_layout Plain Layout
36107 \begin_inset Note Note
36110 \begin_layout Plain Layout
36111 The following will be displayed when the \SpecialChar LaTeX
36124 \begin_layout Standard
36125 You need to install the \SpecialChar LaTeX
36130 to see the rest of this subsection in the output.
36133 \begin_layout Standard
36137 \begin_layout Plain Layout
36149 \begin_layout Subsection
36150 Formulas in Section Headings
36151 \begin_inset CommandInset label
36153 name "subsec:Formulas-in-Section"
36158 \begin_inset Index idx
36161 \begin_layout Plain Layout
36162 Formula ! in section headings
36170 \begin_layout Standard
36171 When formulas are used in section headings, the following has to be taken
36175 \begin_layout Standard
36176 \begin_inset Note Greyedout
36179 \begin_layout Plain Layout
36185 \begin_inset Index idx
36188 \begin_layout Plain Layout
36189 Packages ! hyperref
36194 support is enabled in the document settings dialog under
36197 \begin_inset space ~
36202 , PDF-bookmarks are created for every section heading in the table of contents.
36203 If a section heading contains formulas, they are incorrectly displayed
36204 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36213 \begin_layout Standard
36214 Both problems can be solved by inserting at the end of the section heading
36215 a short title with the menu
36217 Insert\SpecialChar menuseparator
36219 \begin_inset space ~
36225 Short titles are used as alternative for multiline section headings to
36226 keep the table of contents clearly arranged.
36227 Only the short title appears in the table of contents and therefore also
36228 in the PDF-bookmark.
36231 \begin_layout Standard
36232 When formulas should be used in the table of contents but
36236 is used, one can use the following command in \SpecialChar TeX
36240 \begin_layout Standard
36245 texorpdfstring{part}{alternative}
36246 \begin_inset Index idx
36249 \begin_layout Plain Layout
36260 \begin_layout Standard
36261 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36262 This can be characters, formulas, footnotes, but also cross-references.
36263 The alternative is used instead of the part for the bookmark.
36266 \begin_layout Standard
36267 Here are two example headings:
36268 \begin_inset VSpace -3mm
36275 \begin_layout Plain Layout
36287 \begin_layout Subsubsection
36288 Heading without formula in table of contents
36289 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36293 \begin_inset Argument 1
36296 \begin_layout Plain Layout
36297 Heading without formula in table of contents
36305 \begin_layout Subsubsection
36306 Heading with formula in table of contents
36310 \begin_layout Plain Layout
36320 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36327 \begin_layout Plain Layout
36337 \begin_layout Standard
36341 \begin_layout Plain Layout
36350 In the first heading a short title was used, in the second one
36359 \begin_layout Standard
36360 To get the same formatting as for the other headings, the complete heading
36369 \begin_layout Plain Layout
36371 \begin_inset CommandInset ref
36373 reference "subsec:Bold-Formulas"
36385 \begin_layout Subsection
36386 Formulas in multi-column Text
36387 \begin_inset Index idx
36390 \begin_layout Plain Layout
36391 Formula ! in multi-column text
36399 \begin_layout Standard
36400 Formulas in multi-column text are often too wide to fit into a column and
36401 thus need to be set over the whole page width.
36402 This is done by using the \SpecialChar LaTeX
36411 \begin_layout Plain Layout
36416 is part of every \SpecialChar LaTeX
36417 standard installation.
36423 \begin_inset Index idx
36426 \begin_layout Plain Layout
36427 Packages ! multicol
36432 , that is loaded with the \SpecialChar LaTeX
36436 \begin_layout Standard
36441 usepackage{multicol}
36444 \begin_layout Standard
36445 \begin_inset Note Greyedout
36448 \begin_layout Plain Layout
36449 Note that in this case the setting
36452 \begin_inset space ~
36459 Document\SpecialChar menuseparator
36465 \begin_inset space ~
36485 \begin_layout Standard
36486 Before the multi-column text the command
36489 \begin_layout Standard
36494 begin{multicols}{column number}
36497 \begin_layout Standard
36498 is written in \SpecialChar TeX
36500 The column number is a number in the range of 2
36501 \begin_inset space \thinspace{}
36505 \begin_inset space \thinspace{}
36509 Before the formula the multi-column text is ended by inserting the command
36512 \begin_layout Standard
36520 \begin_layout Standard
36521 in \SpecialChar TeX
36525 \begin_layout Standard
36526 Due to the command some space is automatically added before the formula.
36528 \begin_inset space \thinspace{}
36531 mm vertical space is inserted before the formula.
36532 When the formula style
36538 \begin_layout Plain Layout
36540 \begin_inset CommandInset ref
36542 reference "sec:Formula-Styles"
36554 \begin_inset space \thinspace{}
36557 mm space is inserted instead.
36560 \begin_layout Standard
36561 As example a multi-column text with a displayed formula:
36564 \begin_layout Standard
36570 \begin_layout Plain Layout
36574 begin{multicols}{2}
36579 Das Spektrum wird fouriertransformiert.
36580 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36581 , Lösungsmittel) zu trennen.
36582 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36583 nun das Aussehen des Ausgangssignals.
36584 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36585 über alle Phasen integrieren muss.
36587 \begin_inset Formula $S$
36590 unser normiertes Ausgangssignal und
36591 \begin_inset Formula $P$
36594 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36598 \begin_layout Plain Layout
36608 \begin_inset VSpace -6mm
36612 \begin_inset Formula
36614 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36623 \begin_layout Plain Layout
36627 begin{multicols}{2}
36633 \begin_inset Formula $S_{0}$
36636 das Signal ohne Gradient ist und die Normierungsbedingung
36637 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36641 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36643 \begin_inset Formula $\nicefrac{\pi}{2}$
36647 \begin_inset space \thinspace{}
36650 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36651 das Signal zusätzlich abschwächt.
36652 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36654 \begin_inset Formula $T_{2}$
36660 \begin_layout Standard
36666 \begin_layout Plain Layout
36678 \begin_layout Subsection
36679 Formulas with Description of Variables
36680 \begin_inset Index idx
36683 \begin_layout Plain Layout
36684 Formula ! with description of variables
36692 \begin_layout Standard
36693 To describe variables within a formula, like in formula
36694 \begin_inset CommandInset ref
36696 reference "eq:within"
36705 \begin_inset Formula $n$
36709 \begin_inset space ~
36712 matrix is used with left aligned columns for the
36713 \begin_inset Formula $n$
36720 \begin_layout Plain Layout
36722 \begin_inset CommandInset ref
36724 reference "sec:Matrices"
36733 To set the description in a smaller size, before the matrix e.
36734 \begin_inset space \thinspace{}
36738 \begin_inset space \space{}
36751 \begin_layout Plain Layout
36753 \begin_inset CommandInset ref
36755 reference "subsec:Font-Sizes"
36767 \begin_layout Standard
36768 When the formula style
36774 \begin_layout Plain Layout
36776 \begin_inset CommandInset ref
36778 reference "sec:Formula-Styles"
36799 \begin_layout Plain Layout
36806 only works in formulas with the style
36811 \begin_inset CommandInset ref
36813 reference "subsec:Variable-Space"
36822 is inserted before and after the matrix to have the same separation of
36823 the matrix from the equation and the side margin.
36826 \begin_layout Standard
36827 When the formula style
36831 is used, the method described in
36832 \begin_inset CommandInset ref
36834 reference "subsec:Flalign-Environment"
36838 is used to indent formulas.
36840 \begin_inset CommandInset ref
36842 reference "eq:within"
36846 consists of five columns where in the first two columns contain the equation,
36847 the third the matrix and the last one an empty \SpecialChar TeX
36849 \begin_inset Formula
36851 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36852 \rho & \textrm{density}\\
36853 V & \textrm{volume}\\
36854 g & \textrm{gravitational acceleration}
36855 \end{array} & & {}\label{eq:within}
36863 \begin_layout Subsection
36864 Upright small Greek Letters
36865 \begin_inset CommandInset label
36867 name "subsec:Upright-small-Greek"
36872 \begin_inset Index idx
36875 \begin_layout Plain Layout
36876 Greek letters ! upright
36884 \begin_layout Standard
36885 Most of the math fonts only provide italic small Greek letters.
36886 But for symbols of elementary particles like pions and neutrinos, upright
36887 Greek letters are needed.
36896 \begin_layout Plain Layout
36901 is part of the \SpecialChar LaTeX
36907 \begin_inset Index idx
36910 \begin_layout Plain Layout
36915 \begin_layout Plain Layout
36935 \begin_inset Index idx
36938 \begin_layout Plain Layout
36944 that is loaded with the \SpecialChar LaTeX
36948 \begin_layout Standard
36953 usepackage{upgreek}
36956 \begin_layout Standard
36962 \begin_layout Plain Layout
36972 \begin_inset Note Note
36975 \begin_layout Plain Layout
36976 The following table will only be displayed when the \SpecialChar LaTeX
36986 They are created when the command for a small Greek letter is started with
36992 For example the command
36999 \begin_inset Formula $\uptau$
37005 \begin_layout Standard
37006 With these commands reactions of elementary particles can be typeset:
37007 \begin_inset Formula
37009 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37017 \begin_layout Standard
37018 The upright letters are more bold and wider than the italic ones.
37019 They should therefore not be used for units like
37020 \begin_inset Quotes eld
37024 \begin_inset Quotes erd
37030 \begin_layout Standard
37034 \begin_layout Plain Layout
37044 \begin_inset Note Note
37047 \begin_layout Plain Layout
37048 The following will be displayed when the \SpecialChar LaTeX
37061 \begin_layout Standard
37062 You need to install the \SpecialChar LaTeX
37067 to see the rest of this subsection in the output.
37070 \begin_layout Standard
37074 \begin_layout Plain Layout
37086 \begin_layout Subsection
37087 Text Characters in Formulas
37088 \begin_inset Index idx
37091 \begin_layout Plain Layout
37100 \begin_layout Standard
37101 In some cases you might want to insert text characters directly into formulas.
37102 When for example the centered dot · is often used in formulas like
37103 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37106 , one would have to insert the command
37116 \begin_layout Plain Layout
37118 \begin_inset CommandInset ref
37120 reference "subsec:Binary-Operators"
37129 all the time, because this character is defined in all encodings as text
37131 But the encoding can be changed by this \SpecialChar LaTeX
37135 \begin_layout Standard
37140 Declare Inputtext{183}{
37150 f\SpecialChar ligaturebreak
37154 \begin_layout Standard
37155 The character encoding (menu
37157 Document\SpecialChar menuseparator
37158 Settings\SpecialChar menuseparator
37161 ) specifies what character appears when a keyboard key is pressed.
37162 When the key for the character '·' is pressed, internally the command
37169 But this command is not available in a formula so that you would get \SpecialChar LaTeX
37171 With the changed encoding the right command is chosen automatically, depending
37172 on if the character was inserted into a formula or not.
37175 \begin_layout Standard
37176 The encoding of several characters is saved in definition files.
37177 For example the encoding
37181 is defined in the file
37185 which is in the installation folder of \SpecialChar LaTeX
37187 Encodings should only be changed via the \SpecialChar LaTeX
37188 -preamble and not in the definition
37190 Otherwise documents could not be edited by other \SpecialChar LyX
37191 users working on other
37195 \begin_layout Standard
37196 \begin_inset VSpace medskip
37199 Besides the centered dot, in this document the degree sign ° is defined
37200 with the following \SpecialChar LaTeX
37201 -preamble line so that it can be directly inserted into
37205 \begin_layout Standard
37210 DeclareInputtext{176}{
37220 f\SpecialChar ligaturebreak
37224 \begin_layout Subsection
37226 -comments in formulas
37227 \begin_inset Index idx
37230 \begin_layout Plain Layout
37240 \begin_layout Standard
37241 In text you can insert a comment that will only be visible in the \SpecialChar LaTeX
37243 code of your file with the menu
37245 Insert\SpecialChar menuseparator
37246 Note\SpecialChar menuseparator
37250 This is not possible in a formula but you can insert \SpecialChar LaTeX
37255 \begin_layout Standard
37263 \begin_layout Standard
37264 This creates a box in which you can write your comment.
37265 Due to a bug in \SpecialChar LyX
37270 \begin_layout Plain Layout
37271 \begin_inset CommandInset href
37273 name "LyX-bug #9002"
37274 target "http://www.lyx.org/trac/ticket/9002"
37283 you cannot write normal text inside the comment, even when you use mathematical
37284 text, you will see its \SpecialChar LaTeX
37285 -commands in the \SpecialChar LaTeX
37287 \begin_inset Newline newline
37290 This a formula with a \SpecialChar LaTeX
37292 \begin_inset Formula
37294 A=B%\text{This is the comment}
37302 \begin_layout Standard
37303 \begin_inset Newpage newpage
37309 \begin_layout Section
37312 \begin_inset Index idx
37315 \begin_layout Plain Layout
37324 \begin_layout Standard
37325 This section is a summary of the most important typographic rules, listed
37330 \begin_layout Plain Layout
37331 This collection was partly taken from the German semi-official dictionary
37333 \begin_inset Quotes eld
37337 \begin_inset Quotes erd
37341 \begin_inset CommandInset citation
37347 that lists some of the ISO rules.
37348 More rules are listed in
37349 \begin_inset CommandInset citation
37363 \begin_layout Itemize
37372 \begin_layout Plain Layout
37373 done with font styles, see
37374 \begin_inset CommandInset ref
37376 reference "subsec:Font-Styles"
37385 , no matter if they appear in italic text: 30
37386 \begin_inset space \thinspace{}
37390 \begin_inset Newline newline
37393 Between the value and the unit is the smallest space, see
37394 \begin_inset CommandInset ref
37396 reference "subsec:Predefined-Space"
37401 \begin_inset Newline newline
37404 This convention is automatically fulfilled when the command
37411 When it is entered to a formula, two boxes appear.
37412 In the first one the value is inserted, in the second one the unit, and
37414 \begin_inset Formula $\unit[30]{km/h}$
37418 \begin_inset space \thinspace{}
37428 is not a real \SpecialChar LaTeX
37429 command but the command
37435 , therefore you cannot use it in \SpecialChar TeX
37439 \begin_layout Itemize
37440 Percent and perthousand signs are set like physical units:
37441 \begin_inset Newline newline
37445 \begin_inset space \thinspace{}
37451 \begin_layout Itemize
37452 The degree sign follows directly on the value: 15°, but not when it is used
37454 \begin_inset space \thinspace{}
37460 \begin_layout Itemize
37461 In numbers with more than four digits the smallest space is inserted before
37462 every third digit to group them:
37472 \begin_inset space \thinspace{}
37476 \begin_inset space \thinspace{}
37482 \begin_layout Itemize
37483 For dimensions like 120×90×40
37484 \begin_inset space \thinspace{}
37487 cm the multiplication sign
37488 \begin_inset Quotes eld
37492 \begin_inset Quotes erd
37496 It is available either via the command
37504 Insert\SpecialChar menuseparator
37505 Special Character\SpecialChar menuseparator
37511 \begin_layout Itemize
37512 Functions with names consisting of several letters are set upright to avoid
37514 \begin_inset CommandInset ref
37516 reference "subsec:Predefined-Functions"
37523 \begin_layout Itemize
37524 Indices consisting of several letters, are set upright:
37525 \begin_inset Formula $E_{\mathrm{kin}}$
37529 \begin_inset Newline newline
37532 Components of matrices are set italic:
37533 \begin_inset Formula $\hat{H}_{kl}$
37539 \begin_layout Itemize
37540 The differentiation/integration operator 'd', the Euler's number 'e' and
37541 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37545 \begin_layout Itemize
37546 The character that denotes a
37550 transformation is inserted either by the command
37555 \begin_inset space \textvisiblespace{}
37562 Insert\SpecialChar menuseparator
37563 Special Character\SpecialChar menuseparator
37564 Symbols\SpecialChar menuseparator
37566 \begin_inset space ~
37572 \begin_inset Formula $\mathscr{F}$
37578 \begin_layout Standard
37579 \begin_inset Newpage newpage
37585 \begin_layout Section
37587 \begin_inset Index idx
37590 \begin_layout Plain Layout
37599 \begin_layout Standard
37600 Some characters and symbols can be created with several commands.
37601 Here is a list of the synonym commands:
37604 \begin_layout Standard
37605 \begin_inset VSpace bigskip
37609 \begin_inset space \hfill{}
37613 \begin_inset Tabular
37614 <lyxtabular version="3" rows="12" columns="2">
37615 <features tabularvalignment="middle">
37616 <column alignment="center" valignment="top" width="0pt">
37617 <column alignment="center" valignment="top" width="0pt">
37619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37622 \begin_layout Plain Layout
37628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37631 \begin_layout Plain Layout
37633 \begin_inset Note Note
37636 \begin_layout Plain Layout
37643 is only used as spacer.
37655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37658 \begin_layout Plain Layout
37666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37669 \begin_layout Plain Layout
37673 \begin_layout Plain Layout
37686 \begin_layout Plain Layout
37700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37703 \begin_layout Plain Layout
37711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37714 \begin_layout Plain Layout
37724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37727 \begin_layout Plain Layout
37735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37738 \begin_layout Plain Layout
37748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37751 \begin_layout Plain Layout
37759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37762 \begin_layout Plain Layout
37770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37773 \begin_layout Plain Layout
37781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37784 \begin_layout Plain Layout
37792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37795 \begin_layout Plain Layout
37803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37806 \begin_layout Plain Layout
37816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37819 \begin_layout Plain Layout
37827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37830 \begin_layout Plain Layout
37840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37843 \begin_layout Plain Layout
37851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37854 \begin_layout Plain Layout
37864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37867 \begin_layout Plain Layout
37875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37878 \begin_layout Plain Layout
37888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37891 \begin_layout Plain Layout
37899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37902 \begin_layout Plain Layout
37910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37913 \begin_layout Plain Layout
37921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37924 \begin_layout Plain Layout
37936 \begin_inset space \hfill{}
37940 \begin_inset Tabular
37941 <lyxtabular version="3" rows="12" columns="2">
37942 <features tabularvalignment="middle">
37943 <column alignment="center" valignment="top" width="0pt">
37944 <column alignment="center" valignment="top" width="0pt">
37946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37949 \begin_layout Plain Layout
37955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37958 \begin_layout Plain Layout
37966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37969 \begin_layout Plain Layout
37977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37980 \begin_layout Plain Layout
37992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37995 \begin_layout Plain Layout
38003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38006 \begin_layout Plain Layout
38016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38019 \begin_layout Plain Layout
38027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38030 \begin_layout Plain Layout
38040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38043 \begin_layout Plain Layout
38051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38054 \begin_layout Plain Layout
38062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38065 \begin_layout Plain Layout
38073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38076 \begin_layout Plain Layout
38084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38087 \begin_layout Plain Layout
38095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38098 \begin_layout Plain Layout
38108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38111 \begin_layout Plain Layout
38119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38122 \begin_layout Plain Layout
38132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38135 \begin_layout Plain Layout
38143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38146 \begin_layout Plain Layout
38156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38159 \begin_layout Plain Layout
38167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38170 \begin_layout Plain Layout
38180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38183 \begin_layout Plain Layout
38191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38194 \begin_layout Plain Layout
38204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
38207 \begin_layout Plain Layout
38215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
38218 \begin_layout Plain Layout
38232 \begin_inset space \hfill{}
38238 \begin_layout Standard
38239 \begin_inset Newpage newpage
38245 \begin_layout Bibliography
38246 \begin_inset CommandInset bibitem
38247 LatexCommand bibitem
38259 The \SpecialChar LaTeX
38263 Addison Wesley, 2004
38266 \begin_layout Bibliography
38267 \begin_inset CommandInset bibitem
38268 LatexCommand bibitem
38274 \begin_inset CommandInset href
38277 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38281 of \SpecialChar LaTeX
38285 \begin_layout Bibliography
38286 \begin_inset CommandInset bibitem
38287 LatexCommand bibitem
38293 \begin_inset CommandInset href
38296 target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf"
38304 \begin_layout Plain Layout
38313 -\SpecialChar LaTeX
38317 \begin_layout Bibliography
38318 \begin_inset CommandInset bibitem
38319 LatexCommand bibitem
38325 \begin_inset CommandInset href
38328 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38332 of all symbols available with \SpecialChar LaTeX
38336 \begin_layout Bibliography
38337 \begin_inset CommandInset bibitem
38338 LatexCommand bibitem
38344 \begin_inset CommandInset href
38346 name "Documentation"
38347 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38351 of the \SpecialChar LaTeX
38357 \begin_inset Index idx
38360 \begin_layout Plain Layout
38369 \begin_layout Bibliography
38370 \begin_inset CommandInset bibitem
38371 LatexCommand bibitem
38377 \begin_inset CommandInset href
38379 name "Documentation"
38380 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38384 of the \SpecialChar LaTeX
38390 \begin_inset Index idx
38393 \begin_layout Plain Layout
38394 Packages ! hyperref
38402 \begin_layout Bibliography
38403 \begin_inset CommandInset bibitem
38404 LatexCommand bibitem
38410 \begin_inset CommandInset href
38412 name "Documentation"
38413 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38417 of the \SpecialChar LaTeX
38423 \begin_inset Index idx
38426 \begin_layout Plain Layout
38435 \begin_layout Bibliography
38436 \begin_inset CommandInset bibitem
38437 LatexCommand bibitem
38448 Auflage, Duden 2001
38451 \begin_layout Bibliography
38452 \begin_inset CommandInset bibitem
38453 LatexCommand bibitem
38459 \begin_inset CommandInset href
38462 target "http://physics.nist.gov/Document/checklist.pdf"
38466 for reviewing manuscripts
38469 \begin_layout Standard
38470 \begin_inset CommandInset index_print
38471 LatexCommand printindex