1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
52 % don't load packages twice
53 % see first footnote in sec. 9.3
54 \@ifundefined{textcolor}{\usepackage{color}}{}
56 % the pages of the TOC are numbered roman
57 % and a PDF-bookmark for the TOC is added
59 \let\myTOC\tableofcontents
60 \renewcommand{\tableofcontents}{%
62 \pdfbookmark[1]{\contentsname}{}
65 \pagenumbering{arabic}}
67 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
75 \usepackage[samesize]{cancel}
77 % enables calculation of values
80 % for multiple columns used in sec. 23.7
86 % for the Fourier transformation symbol
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
114 % ------------------------------------
115 % used to check for needed LaTeX packages
118 % check for package eurosym
119 % used for the Euro symbol
121 \IfFileExists{eurosym.sty}
122 {\usepackage[gennarrow]{eurosym}
123 \setboolean{eurosym}{true}}
124 {\setboolean{eurosym}{false}}
126 % check for package braket
127 % used for physical vectors
129 \IfFileExists{braket.sty}
131 \setboolean{braket}{true}}
132 {\setboolean{braket}{false}}
134 % check for package cancel
136 \IfFileExists{cancel.sty}
138 \setboolean{cancel}{true}}
139 {\setboolean{cancel}{false}}
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
149 \use_default_options false
150 \maintain_unincluded_children false
156 \font_typewriter default
157 \font_default_family default
158 \use_non_tex_fonts false
165 \default_output_format default
167 \bibtex_command default
168 \index_command default
172 \pdf_title "LyX's Math Manual"
173 \pdf_author "LyX Team, Uwe Stöhr"
174 \pdf_subject "LyX-documentation about math"
175 \pdf_keywords "LyX, Mathed"
177 \pdf_bookmarksnumbered true
178 \pdf_bookmarksopen true
179 \pdf_bookmarksopenlevel 1
180 \pdf_breaklinks false
184 \pdf_pdfusetitle false
185 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
195 \paperorientation portrait
198 \notefontcolor #0000ff
205 \paragraph_separation skip
207 \quotes_language english
210 \paperpagestyle plain
214 \tracking_changes false
215 \output_changes false
217 \html_be_strict false
223 LyX's detailed Math manual
231 \begin_layout Plain Layout
233 If you have comments or error corrections, please send them to the LyX Documenta
237 \begin_inset CommandInset href
239 name "lyx-docs@lists.lyx.org"
240 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
251 \begin_inset Note Note
254 \begin_layout Plain Layout
261 \begin_inset Newline newline
265 \begin_inset Newline newline
273 \begin_layout Standard
274 \begin_inset CommandInset toc
275 LatexCommand tableofcontents
282 \begin_layout Standard
283 \begin_inset Note Note
286 \begin_layout Plain Layout
287 To export this document to PDF, PS or DVI the LaTeX-packages
289 braket, cancel, eurosym,
300 If they are not installed the document can be export anyway but the sections
301 where the packages are required will not appear in the output.
306 ; if it is not installed, this file cannot be exported.
309 \begin_layout Plain Layout
310 The latest PDF-version of this document can be found here:
311 \begin_inset Newline newline
316 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
324 \begin_layout Standard
325 \begin_inset Newpage newpage
331 \begin_layout Section
335 \begin_layout Standard
336 This document explains LyX's math features and is furthermore a collection
337 of LaTeX-commands used for mathematical characters and constructs.
338 The explanations are designed for the usage of commands.
339 It is therefore required that you have read the section
350 \begin_layout Standard
351 Most of the characters and many constructs explained in this manual are
352 also accessible via the menu
356 \SpecialChar \menuseparator
372 But everybody who has to write lots of formulas will notice that it is
373 much faster to use commands instead of the math toolbar.
374 Therefore this manual is focused on commands but also mentions the correspondin
375 g toolbar buttons when available.
378 \begin_layout Standard
379 If not specially mentioned the commands are only available within formulas.
380 To be able to use all commands explained in this document, the option
384 must be used in the document settings (menu
386 Document\SpecialChar \menuseparator
387 Settings\SpecialChar \menuseparator
398 \begin_layout Plain Layout
401 Use AMS math package automatically
407 \begin_layout Plain Layout
416 -math when math constructs are found that are supported by LyX.
424 \begin_layout Standard
425 This document doesn't list all
429 \begin_layout Plain Layout
442 \begin_layout Plain Layout
447 \begin_layout Plain Layout
456 -math commands is in the file
459 \begin_inset CommandInset href
462 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
468 , which is part of every LaTeX standard installation.
473 for lucidity reasons.
476 \begin_layout Section
480 \begin_layout Standard
481 To create an inline formula
482 \begin_inset Index idx
485 \begin_layout Plain Layout
491 that is embedded into a text line, use one of the shortcuts
497 or the toolbar button
498 \begin_inset Graphics
499 filename ../images/math-mode.png
505 \begin_inset Newline newline
508 To create a display style formula
509 \begin_inset Index idx
512 \begin_layout Plain Layout
513 Formula ! display style
518 that will appear bigger and in an own paragraph, use one of these shortcuts:
528 \begin_layout Standard
529 To change a display style formula to an inline formula, set the cursor into
530 the formula and use one of the shortcuts
538 Edit\SpecialChar \menuseparator
539 Math\SpecialChar \menuseparator
543 The same way is used to change an inline formula to a display style formula.
546 \begin_layout Standard
547 To display parts of an inline formula in the size of a display style formula,
555 \begin_inset Index idx
558 \begin_layout Plain Layout
567 Then a new blue box appears in which the desired formula part is inserted.
570 \begin_layout Standard
571 Only inline formulas are allowed inside tables.
574 \begin_layout Standard
579 can be turned on in the menu
581 View\SpecialChar \menuseparator
585 When you click there on
586 \begin_inset Quotes eld
590 \begin_inset Quotes erd
593 the toolbar will be shown permanently at the bottom; this state is visualized
598 menu with a checkmark.
599 When you click in this state again on
600 \begin_inset Quotes eld
604 \begin_inset Quotes erd
615 is only shown when the cursor is within a formula; this state is visualized
616 by the renaming of the menu entry from
617 \begin_inset Quotes eld
621 \begin_inset Quotes erd
625 \begin_inset Quotes eld
633 \begin_inset Quotes erd
639 \begin_layout Standard
641 \begin_inset Index idx
644 \begin_layout Plain Layout
650 is invoked by pressing the toolbar button
651 \begin_inset Graphics
652 filename ../images/ert-insert.png
659 Insert\SpecialChar \menuseparator
664 \begin_layout Plain Layout
680 \begin_inset Note Note
683 \begin_layout Plain Layout
684 In LyX there are three
685 \begin_inset Quotes eld
689 \begin_inset Quotes erd
692 that appear in the output with sub- and superscript letters: TeX, LaTeX
696 \begin_layout Plain Layout
697 To avoid that these names are recognized as proper names, a TeX-brace pair
706 \begin_layout Standard
707 To change the LaTeX-preamble
708 \begin_inset Index idx
711 \begin_layout Plain Layout
719 Document\SpecialChar \menuseparator
720 Settings\SpecialChar \menuseparator
725 \begin_layout Plain Layout
741 \begin_layout Standard
742 To edit matrices, case differentiations and multiline formulas subsequently,
745 Edit\SpecialChar \menuseparator
750 Edit\SpecialChar \menuseparator
752 \begin_inset space \thinspace{}
756 \begin_inset space \thinspace{}
766 When lines and columns are swapped via the menu, the column or line where
767 the cursor is in is exchanged with the column to the right or the line
769 Is the cursor in the last column or row, the exchange is done with the
770 column to the left or the line above.
773 \begin_layout Standard
774 To write text in formulas
778 \begin_layout Plain Layout
779 For multiline formulas the command
786 \begin_inset CommandInset ref
788 reference "sub:Text-in-multiline"
802 \begin_inset Index idx
805 \begin_layout Plain Layout
812 \begin_inset Index idx
815 \begin_layout Plain Layout
822 This mode is invoked with the shortcut
828 or by the insertion of the command
835 \begin_inset Index idx
838 \begin_layout Plain Layout
847 The text appears black in LyX and can therefore be distinguished from the
848 other formula parts that appear blue.
849 In the output mathematical text is set upright, in contrary to other formula
853 \begin_layout Subsection*
857 \begin_layout Standard
858 Most of the LaTeX-commands for math constructs have the following scheme:
861 \begin_layout Standard
877 \begin_layout Standard
878 A command starts always with a backslash
879 \begin_inset Quotes gld
889 \begin_inset Quotes grd
893 To omit optional arguments, also omit the associated brackets.
894 The braces around the required arguments are named in this document as
896 \begin_inset Index idx
899 \begin_layout Plain Layout
906 If you add in a formula a left brace to a command name, LyX creates automatical
908 In all other cases TeX-braces are created in formulas with the command
916 TeX-braces appear red in LyX, in contrary to normal braces that appear
918 In TeX-mode no command is needed to get TeX-braces.
919 TeX-braces don't appear in the output.
922 \begin_layout Standard
923 When commands without arguments, like commands for symbols are entered in
924 TeX-mode, a space character must
928 be behind the command to end it.
929 This space doesn't appear in the output.
930 When the space should appear in the output, the space must be followed
931 by a protected space in normal text.
934 \begin_layout Standard
935 A protected space is inserted with
938 arg "space-insert protected"
944 \begin_layout Subsection*
945 \begin_inset Newpage newpage
951 \begin_layout Itemize
956 \begin_layout Plain Layout
957 This visible space character can be created with the command
964 \begin_inset Index idx
967 \begin_layout Plain Layout
975 , inserted in TeX-mode.
984 \begin_layout Plain Layout
997 denotes a space character to be input.
1000 \begin_layout Itemize
1002 \begin_inset Formula $\to$
1005 denotes the usage of the corresponding arrow key on the keyboard.
1008 \begin_layout Subsection*
1012 \begin_layout Standard
1014 \begin_inset Float table
1020 \begin_layout Plain Layout
1022 \begin_inset Caption
1024 \begin_layout Plain Layout
1025 \begin_inset CommandInset label
1027 name "tab:Available-units"
1039 \begin_layout Plain Layout
1041 \begin_inset Tabular
1042 <lyxtabular version="3" rows="13" columns="2">
1043 <features tabularvalignment="middle">
1044 <column alignment="center" valignment="top" width="0">
1045 <column alignment="center" valignment="top" width="0">
1047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1050 \begin_layout Plain Layout
1056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1059 \begin_layout Plain Layout
1067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1070 \begin_layout Plain Layout
1076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1079 \begin_layout Plain Layout
1087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1090 \begin_layout Plain Layout
1096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1099 \begin_layout Plain Layout
1107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1110 \begin_layout Plain Layout
1116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1119 \begin_layout Plain Layout
1121 \begin_inset space \thinspace{}
1125 \begin_inset space \thinspace{}
1135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1138 \begin_layout Plain Layout
1144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1147 \begin_layout Plain Layout
1149 \begin_inset space \thinspace{}
1153 \begin_inset space \thinspace{}
1163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1166 \begin_layout Plain Layout
1172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1175 \begin_layout Plain Layout
1177 \begin_inset space \thinspace{}
1181 \begin_inset space \thinspace{}
1191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1194 \begin_layout Plain Layout
1200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1203 \begin_layout Plain Layout
1205 \begin_inset space \thinspace{}
1209 \begin_inset space \thinspace{}
1219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1222 \begin_layout Plain Layout
1228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1231 \begin_layout Plain Layout
1233 \begin_inset space \thinspace{}
1237 \begin_inset space \thinspace{}
1247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1250 \begin_layout Plain Layout
1256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1259 \begin_layout Plain Layout
1261 \begin_inset space \thinspace{}
1265 \begin_inset Formula $\approx$
1269 \begin_inset space \thinspace{}
1279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1282 \begin_layout Plain Layout
1288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1291 \begin_layout Plain Layout
1293 \begin_inset space \thinspace{}
1297 \begin_inset space \thinspace{}
1307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1310 \begin_layout Plain Layout
1316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1319 \begin_layout Plain Layout
1323 \begin_inset Quotes eld
1329 \begin_inset Quotes erd
1339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1342 \begin_layout Plain Layout
1348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1351 \begin_layout Plain Layout
1353 \begin_inset Quotes eld
1361 \begin_inset Quotes erd
1371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1374 \begin_layout Plain Layout
1380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1383 \begin_layout Plain Layout
1385 \begin_inset space \thinspace{}
1389 \begin_inset Formula $\nicefrac{1}{18}$
1393 \begin_inset space \thinspace{}
1414 \begin_layout Standard
1415 \begin_inset Newpage newpage
1421 \begin_layout Section
1425 \begin_layout Subsection
1427 \begin_inset Index idx
1430 \begin_layout Plain Layout
1437 \begin_inset Index idx
1440 \begin_layout Plain Layout
1447 \begin_inset Index idx
1450 \begin_layout Plain Layout
1455 \begin_layout Plain Layout
1466 \begin_layout Plain Layout
1479 \begin_inset Index idx
1482 \begin_layout Plain Layout
1487 \begin_layout Plain Layout
1498 \begin_layout Plain Layout
1513 \begin_layout Standard
1514 Indices are created with an underscore
1515 \begin_inset Quotes eld
1519 \begin_inset Quotes erd
1522 or via the math toolbar button
1523 \begin_inset Graphics
1524 filename ../images/math-subscript.png
1529 , exponents with a caret
1530 \begin_inset Quotes eld
1534 \begin_inset Quotes erd
1537 or via the math toolbar button
1538 \begin_inset Graphics
1539 filename ../images/math-superscript.png
1547 \begin_layout Standard
1549 \begin_inset Tabular
1550 <lyxtabular version="3" rows="4" columns="2">
1551 <features tabularvalignment="middle">
1552 <column alignment="center" valignment="top" width="0pt">
1553 <column alignment="center" valignment="top" width="0pt">
1555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1558 \begin_layout Plain Layout
1564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1567 \begin_layout Plain Layout
1569 \begin_inset Note Note
1572 \begin_layout Plain Layout
1579 is only used as spacer.
1591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1594 \begin_layout Plain Layout
1600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1603 \begin_layout Plain Layout
1604 \begin_inset Formula $B_{V}$
1614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1617 \begin_layout Plain Layout
1623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1626 \begin_layout Plain Layout
1627 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1640 \begin_layout Plain Layout
1645 \begin_layout Plain Layout
1659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1662 \begin_layout Plain Layout
1663 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1679 \begin_layout Standard
1680 As the caret is in some languages an accent, vowels will be accentuated
1681 in this case and not set as exponents
1685 \begin_layout Plain Layout
1686 Depending on the used keyboard settings this can also happen for other character
1693 To get in this case exponents, press
1697 after the caret as in the last example.
1700 \begin_layout Subsection
1702 \begin_inset CommandInset label
1704 name "sub:Fractions"
1709 \begin_inset Index idx
1712 \begin_layout Plain Layout
1721 \begin_layout Standard
1722 Fractions are generated with the command
1729 \begin_inset Index idx
1732 \begin_layout Plain Layout
1740 or via the math toolbar button
1741 \begin_inset Graphics
1742 filename ../images/math/frac.png
1748 The font size is adjusted automatically, depending on whether the fraction
1749 is in an inline or display style formula.
1750 With the math toolbar button
1751 \begin_inset Graphics
1752 filename ../images/math/frac-square.png
1757 you can select different fraction types.
1760 \begin_layout Standard
1768 \begin_inset Index idx
1771 \begin_layout Plain Layout
1779 a fraction can be created that has in any case the size of a display style
1788 \begin_inset Index idx
1791 \begin_layout Plain Layout
1799 the fraction appears always with the size of an inline formula.
1803 \begin_layout Standard
1804 A line with the fraction
1805 \begin_inset Formula $\frac{1}{2}$
1808 that was created with the command
1817 \begin_layout Standard
1818 A line with the fraction
1819 \begin_inset Formula $\dfrac{1}{2}$
1822 that was created with the command
1831 \begin_layout Standard
1833 \begin_inset Tabular
1834 <lyxtabular version="3" rows="4" columns="2">
1835 <features tabularvalignment="middle">
1836 <column alignment="center" valignment="top" width="0pt">
1837 <column alignment="center" valignment="top" width="0pt">
1839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1842 \begin_layout Plain Layout
1848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1851 \begin_layout Plain Layout
1853 \begin_inset Note Note
1856 \begin_layout Plain Layout
1863 is only used as spacer.
1875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1878 \begin_layout Plain Layout
1885 \begin_layout Plain Layout
1895 \begin_inset Formula $\downarrow$
1903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1906 \begin_layout Plain Layout
1907 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1920 \begin_layout Plain Layout
1927 \begin_layout Plain Layout
1937 \begin_inset Formula $\downarrow$
1945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1948 \begin_layout Plain Layout
1949 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1962 \begin_layout Plain Layout
1969 \begin_layout Plain Layout
1982 \begin_layout Plain Layout
1997 \begin_layout Plain Layout
2007 \begin_inset Formula $\downarrow$
2011 \begin_inset Formula $\downarrow\downarrow$
2019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2022 \begin_layout Plain Layout
2023 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2039 \begin_layout Standard
2040 \begin_inset VSpace bigskip
2044 \begin_inset Newpage newpage
2047 For nested fractions the command
2054 \begin_inset Index idx
2057 \begin_layout Plain Layout
2067 \begin_inset VSpace -3mm
2073 \begin_layout Standard
2074 \begin_inset Formula \begin{align*}
2075 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2076 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2084 \begin_layout Standard
2085 The command for the example above is:
2088 \begin_layout Standard
2097 \begin_layout Plain Layout
2107 \begin_inset Formula $\downarrow$
2116 \begin_layout Plain Layout
2131 \begin_layout Plain Layout
2141 \begin_inset Formula $\downarrow$
2145 \begin_inset Formula $\downarrow$
2151 \begin_layout Standard
2152 \begin_inset VSpace medskip
2158 \begin_layout Standard
2165 sets the fraction always in the size of a displayed formula, also when
2166 it is part of another fraction.
2169 \begin_layout Standard
2170 It is possible to specify the alignment of the numerator.
2177 is used to left align it, the command
2190 centers the numerator.
2191 These fractions demonstrate the different alignments:
2194 \begin_layout Standard
2195 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2199 \begin_inset Formula $\cfrac{A}{B+C}$
2203 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2209 \begin_layout Standard
2210 \begin_inset Note Greyedout
2213 \begin_layout Plain Layout
2230 are no real LaTeX commands but represent the command
2234 cfrac[alignment]{numerator}{denominator}
2237 Therefore you cannot use them in TeX code.
2245 \begin_layout Standard
2246 \begin_inset VSpace medskip
2249 It is often advantageous to combine
2262 \begin_inset Formula \[
2263 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2271 \begin_layout Standard
2272 For inline fractions with a sloped fraction stroke you can use the command
2280 \begin_inset Index idx
2283 \begin_layout Plain Layout
2292 \begin_inset Formula $\nicefrac{5}{31}$
2302 \begin_inset Index idx
2305 \begin_layout Plain Layout
2314 \begin_inset Formula $\unitfrac{5}{31}$
2317 There is furthermore the command
2323 that offers to write a fraction in combination with a number:
2324 \begin_inset Formula $\unitfrac[2]{1}{3}$
2330 \begin_layout Standard
2331 \begin_inset Note Greyedout
2334 \begin_layout Plain Layout
2345 is not a real LaTeX command but the command
2346 \begin_inset Newline newline
2353 unitfrac[number]{numerator}{denominator}
2356 Therefore you cannot use it in TeX code.
2364 \begin_layout Standard
2365 How to define own fractions where the fraction stroke can be changed, is
2367 \begin_inset CommandInset ref
2369 reference "sub:Self-defined-Fractions"
2376 \begin_layout Subsection
2378 \begin_inset Index idx
2381 \begin_layout Plain Layout
2390 \begin_layout Standard
2391 Square roots are created with
2398 \begin_inset Index idx
2401 \begin_layout Plain Layout
2409 or the math toolbar button
2410 \begin_inset Graphics
2411 filename ../images/math/sqrt.png
2416 , all other roots with the command
2423 \begin_inset Index idx
2426 \begin_layout Plain Layout
2434 or with the math toolbar button
2435 \begin_inset Graphics
2436 filename ../images/math/root.png
2444 \begin_layout Standard
2446 \begin_inset Tabular
2447 <lyxtabular version="3" rows="3" columns="2">
2448 <features tabularvalignment="middle">
2449 <column alignment="center" valignment="top" width="0pt">
2450 <column alignment="center" valignment="top" width="0pt">
2452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2455 \begin_layout Plain Layout
2461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2464 \begin_layout Plain Layout
2466 \begin_inset Note Note
2469 \begin_layout Plain Layout
2476 is only used as spacer.
2488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2491 \begin_layout Plain Layout
2498 \begin_layout Plain Layout
2512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2529 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2546 \begin_inset Formula $\downarrow$
2554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2557 \begin_layout Plain Layout
2558 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2574 \begin_layout Standard
2575 A square root can also be created with
2581 when the root index field is left empty.
2584 \begin_layout Standard
2585 With certain indices the distance to the root is too small, like in this
2587 \begin_inset Formula $\sqrt[\beta]{B}$
2591 \begin_inset Newline newline
2595 \begin_inset Formula $\beta$
2599 To avoid this, the commands
2606 \begin_inset Index idx
2609 \begin_layout Plain Layout
2624 \begin_inset Index idx
2627 \begin_layout Plain Layout
2635 are used with the following scheme:
2638 \begin_layout Standard
2652 \begin_layout Standard
2653 Distance is the number of Big Points (unit bp;
2654 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2657 ), that the index should be moved to the left or top, resp..
2658 The commands are written to the index.
2659 This way the command
2660 \begin_inset Newline newline
2670 \begin_inset Formula $\to$
2676 \begin_inset Formula $\to$
2685 \begin_layout Plain Layout
2695 \begin_inset Formula $\to$
2699 \begin_inset Newline newline
2704 produces a correct typeset formula:
2705 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2711 \begin_layout Subsection
2712 Binomial Coefficients
2713 \begin_inset Index idx
2716 \begin_layout Plain Layout
2717 Binomial coefficients
2725 \begin_layout Standard
2726 Binomial coefficients are inserted with the command
2733 \begin_inset Index idx
2736 \begin_layout Plain Layout
2744 or with the submenu of the math toolbar button
2745 \begin_inset Graphics
2746 filename ../images/math/frac-square.png
2752 Analog to fractions (
2771 \begin_inset Index idx
2774 \begin_layout Plain Layout
2789 \begin_inset Index idx
2792 \begin_layout Plain Layout
2801 For other brackets around binomial coeficients there are the commands
2808 \begin_inset Index idx
2811 \begin_layout Plain Layout
2826 \begin_inset Index idx
2829 \begin_layout Plain Layout
2840 \begin_layout Standard
2842 \begin_inset Tabular
2843 <lyxtabular version="3" rows="6" columns="2">
2844 <features tabularvalignment="middle">
2845 <column alignment="center" valignment="top" width="0pt">
2846 <column alignment="center" valignment="top" width="0pt">
2848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2860 \begin_layout Plain Layout
2862 \begin_inset Note Note
2865 \begin_layout Plain Layout
2872 is only used as spacer.
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2887 \begin_layout Plain Layout
2894 \begin_layout Plain Layout
2904 \begin_inset Formula $\downarrow$
2912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2929 \begin_layout Plain Layout
2936 \begin_layout Plain Layout
2946 \begin_inset Formula $\downarrow$
2954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2957 \begin_layout Plain Layout
2958 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2971 \begin_layout Plain Layout
2978 \begin_layout Plain Layout
2988 \begin_inset Formula $\downarrow$
2996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2999 \begin_layout Plain Layout
3000 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3020 \begin_layout Plain Layout
3030 \begin_inset Formula $\downarrow$
3038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3055 \begin_layout Plain Layout
3062 \begin_layout Plain Layout
3072 \begin_inset Formula $\downarrow$
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3083 \begin_layout Plain Layout
3084 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3100 \begin_layout Subsection
3101 Case Differentiations
3102 \begin_inset Index idx
3105 \begin_layout Plain Layout
3106 Case differentiations
3114 \begin_layout Standard
3116 \begin_inset Tabular
3117 <lyxtabular version="3" rows="3" columns="2">
3118 <features tabularvalignment="middle">
3119 <column alignment="center" valignment="top" width="0pt">
3120 <column alignment="center" valignment="top" width="0pt">
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3125 \begin_layout Plain Layout
3131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3134 \begin_layout Plain Layout
3142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3145 \begin_layout Plain Layout
3152 \begin_layout Plain Layout
3162 \begin_inset Formula $\to$
3166 \begin_inset Index idx
3169 \begin_layout Plain Layout
3182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3185 \begin_layout Plain Layout
3186 \begin_inset Formula $\begin{cases}
3197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3200 \begin_layout Plain Layout
3207 \begin_layout Plain Layout
3219 arg "newline-insert newline"
3227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3230 \begin_layout Plain Layout
3231 \begin_inset Formula $\begin{cases}
3232 A & \textrm{for }x>0\\
3233 B & \textrm{for }x=0
3250 \begin_layout Standard
3257 or the usage of the math toolbar button
3258 \begin_inset Graphics
3259 filename ../images/math/cases.png
3264 you can create new lines with the shortcut
3267 arg "newline-insert newline"
3270 or the table toolbar button
3271 \begin_inset Graphics
3272 filename ../images/tabular-feature_append-row.png
3280 \begin_layout Standard
3287 is also available via the menu
3289 Insert\SpecialChar \menuseparator
3290 Math\SpecialChar \menuseparator
3296 \begin_layout Subsection
3298 \begin_inset Index idx
3301 \begin_layout Plain Layout
3310 \begin_layout Standard
3318 \begin_inset Index idx
3321 \begin_layout Plain Layout
3329 every character can be displayed canceled.
3330 The characters are quasi accentuated by a slash.
3333 \begin_layout Standard
3335 \begin_inset Tabular
3336 <lyxtabular version="3" rows="4" columns="2">
3337 <features tabularvalignment="middle">
3338 <column alignment="center" valignment="top" width="0pt">
3339 <column alignment="center" valignment="top" width="0pt">
3341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3344 \begin_layout Plain Layout
3350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3353 \begin_layout Plain Layout
3361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3364 \begin_layout Plain Layout
3372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3375 \begin_layout Plain Layout
3376 \begin_inset Formula $\not=$
3386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3389 \begin_layout Plain Layout
3399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3402 \begin_layout Plain Layout
3403 \begin_inset Formula $\not\le$
3413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3416 \begin_layout Plain Layout
3426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3429 \begin_layout Plain Layout
3430 \begin_inset Formula $\not\parallel$
3446 \begin_layout Standard
3447 The last example shows, that not all negations look good.
3448 Therefore there are for some negations special commands (see
3449 \begin_inset CommandInset ref
3451 reference "sub:Mathematical-Symbols"
3456 \begin_inset CommandInset ref
3458 reference "sec:Relations"
3465 \begin_layout Subsection
3467 \begin_inset CommandInset label
3469 name "sub:Placeholders"
3474 \begin_inset Index idx
3477 \begin_layout Plain Layout
3484 \begin_inset Index idx
3487 \begin_layout Plain Layout
3488 Chemical characters ! Isotopes
3494 \begin_inset Index idx
3497 \begin_layout Plain Layout
3502 \begin_layout Plain Layout
3513 \begin_layout Plain Layout
3528 \begin_layout Standard
3530 \begin_inset space \thinspace{}
3534 \begin_inset space \space{}
3541 \begin_layout Plain Layout
3542 Typesetting isotopes and chemical symbols is described in
3543 \begin_inset CommandInset ref
3545 reference "sub:Chemical-Symbols-and"
3554 the following problem occurs:
3557 \begin_layout Standard
3559 \begin_inset Tabular
3560 <lyxtabular version="3" rows="2" columns="2">
3561 <features tabularvalignment="middle">
3562 <column alignment="center" valignment="top" width="0pt">
3563 <column alignment="center" valignment="top" width="0pt">
3565 <cell alignment="center" valignment="top" usebox="none">
3568 \begin_layout Plain Layout
3569 Indices created with sub- and superscripts:
3574 <cell alignment="center" valignment="top" usebox="none">
3577 \begin_layout Plain Layout
3578 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3588 <cell alignment="center" valignment="top" usebox="none">
3591 \begin_layout Plain Layout
3597 <cell alignment="center" valignment="top" usebox="none">
3600 \begin_layout Plain Layout
3601 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3615 \begin_inset Note Note
3618 \begin_layout Plain Layout
3625 is only used as spacer.
3633 \begin_layout Standard
3634 The shorter index is by default placed below or above the first character
3635 of the longer index.
3636 To avoid this there is the command
3643 \begin_inset Index idx
3646 \begin_layout Plain Layout
3654 or the math toolbar button
3655 \begin_inset space \thinspace{}
3662 \begin_layout Plain Layout
3663 can be found in the submenu of the toolbar button
3664 \begin_inset Graphics
3665 filename ../images/math/space.png
3676 \begin_inset Graphics
3677 filename ../images/math/phantom.png
3682 that creates one or more phantom characters.
3689 a small blue box appears that is superposed with two red arrows.
3690 The arrows indicate that the complete width and height of the box content
3691 will be created as placeholder.
3692 Phantom characters are accordingly placeholders with the size of the characters.
3695 \begin_layout Standard
3697 \begin_inset Tabular
3698 <lyxtabular version="3" rows="4" columns="2">
3699 <features tabularvalignment="middle">
3700 <column alignment="center" valignment="top" width="0">
3701 <column alignment="center" valignment="top" width="0">
3703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3706 \begin_layout Plain Layout
3712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3715 \begin_layout Plain Layout
3717 \begin_inset Note Note
3720 \begin_layout Plain Layout
3727 is only used as spacer.
3739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3742 \begin_layout Plain Layout
3747 \begin_layout Plain Layout
3762 \begin_layout Plain Layout
3772 \begin_inset Formula $\to$
3779 \begin_layout Plain Layout
3793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3796 \begin_layout Plain Layout
3797 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3810 \begin_layout Plain Layout
3815 \begin_layout Plain Layout
3830 \begin_layout Plain Layout
3840 \begin_inset Formula $\to$
3847 \begin_layout Plain Layout
3861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3864 \begin_layout Plain Layout
3865 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3878 \begin_layout Plain Layout
3885 \begin_layout Plain Layout
3900 \begin_layout Plain Layout
3910 \begin_inset Formula $\to$
3917 \begin_layout Plain Layout
3931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3934 \begin_layout Plain Layout
3935 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3951 \begin_layout Standard
3952 Furthermore there are the commands
3959 \begin_inset Index idx
3962 \begin_layout Plain Layout
3971 \begin_inset space ~
3975 \begin_inset Graphics
3976 filename ../images/math/vphantom.png
3988 \begin_inset Index idx
3991 \begin_layout Plain Layout
4000 \begin_inset space ~
4004 \begin_inset Graphics
4005 filename ../images/math/hphantom.png
4017 creates only space for the maximal height of the characters in the box
4018 but not for its width.
4025 creates only space for the width of the box content.
4026 Therefore the boxes of both commands have only one red arrow.
4029 \begin_layout Standard
4040 \begin_layout Plain Layout
4055 space for the height of the integral sign,
4059 \begin_layout Plain Layout
4066 creates an integral sign, see
4067 \begin_inset CommandInset ref
4069 reference "sub:Big-Operators"
4078 because this is the larger character.
4079 An example application is in
4080 \begin_inset CommandInset ref
4082 reference "sub:Multiline-Brackets"
4089 \begin_layout Standard
4090 Placeholders can also be used for text when it is inserted via the menu
4093 Insert\SpecialChar \menuseparator
4094 Formatting\SpecialChar \menuseparator
4100 \begin_layout Standard
4102 \begin_inset Newline newline
4106 \begin_inset Phantom Phantom
4109 \begin_layout Plain Layout
4118 \begin_layout Subsection
4120 \begin_inset Index idx
4123 \begin_layout Plain Layout
4130 \begin_inset Index idx
4133 \begin_layout Plain Layout
4134 Formula ! underlined
4142 \begin_layout Standard
4144 \begin_inset Tabular
4145 <lyxtabular version="3" rows="4" columns="2">
4146 <features tabularvalignment="middle">
4147 <column alignment="center" valignment="top" width="0pt">
4148 <column alignment="center" valignment="top" width="0pt">
4150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4153 \begin_layout Plain Layout
4159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4162 \begin_layout Plain Layout
4164 \begin_inset Note Note
4167 \begin_layout Plain Layout
4174 is only used as spacer.
4186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4189 \begin_layout Plain Layout
4196 \begin_layout Plain Layout
4206 \begin_inset Index idx
4209 \begin_layout Plain Layout
4222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4225 \begin_layout Plain Layout
4226 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4239 \begin_layout Plain Layout
4246 \begin_layout Plain Layout
4256 \begin_inset Index idx
4259 \begin_layout Plain Layout
4272 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4275 \begin_layout Plain Layout
4276 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4289 \begin_layout Plain Layout
4296 \begin_layout Plain Layout
4311 \begin_layout Plain Layout
4325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4328 \begin_layout Plain Layout
4329 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4345 \begin_layout Standard
4346 In the last example it doesn't matter if first
4361 \begin_layout Standard
4362 To double underline e.
4363 \begin_inset space \thinspace{}
4367 \begin_inset space \space{}
4379 \begin_layout Standard
4380 It is possible to place up to 6 lines above or below characters.
4383 \begin_layout Standard
4384 \begin_inset VSpace bigskip
4387 Custom lines can be created using the command
4394 \begin_inset Index idx
4397 \begin_layout Plain Layout
4405 which has the following scheme:
4408 \begin_layout Standard
4413 rule[vertical offset]{length}{thickness}
4416 \begin_layout Standard
4417 The optional vertical offset shifts the line upwards (or downwards, when
4418 the value is negative).
4420 \begin_inset CommandInset ref
4422 reference "tab:Available-units"
4426 can be used for the values.
4427 Here are two example lines created with the commands
4428 \begin_inset Newline newline
4435 rule[-2ex]{3cm}{2pt}
4446 \begin_layout Standard
4448 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4454 \begin_layout Standard
4461 can also be used for text when a line is inserted via the menu
4463 Insert\SpecialChar \menuseparator
4464 Formatting\SpecialChar \menuseparator
4466 \begin_inset space ~
4474 \begin_layout Standard
4476 \begin_inset CommandInset line
4487 \begin_layout Subsection
4489 \begin_inset CommandInset label
4496 \begin_inset Index idx
4499 \begin_layout Plain Layout
4508 \begin_layout Standard
4509 There are different types of ellipses available.
4513 \begin_layout Plain Layout
4514 In the math toolbar in the submenu of the button
4515 \begin_inset Graphics
4516 filename ../images/math/ldots.png
4526 For listings dots at the baseline are used (
4533 \begin_inset Index idx
4536 \begin_layout Plain Layout
4544 ), while for operations dots are needed that are on the same height as the
4552 \begin_inset Index idx
4555 \begin_layout Plain Layout
4564 When using the command
4571 \begin_inset Index idx
4574 \begin_layout Plain Layout
4582 , LaTeX decides on the basis of the next character what type is used.
4585 \begin_layout Standard
4587 \begin_inset Tabular
4588 <lyxtabular version="3" rows="9" columns="2">
4589 <features tabularvalignment="middle">
4590 <column alignment="center" valignment="top" width="0pt">
4591 <column alignment="center" valignment="top" width="0pt">
4593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4596 \begin_layout Plain Layout
4602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4605 \begin_layout Plain Layout
4613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4616 \begin_layout Plain Layout
4621 \begin_layout Plain Layout
4636 \begin_layout Plain Layout
4650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4653 \begin_layout Plain Layout
4654 \begin_inset Formula $A_{1},\dots,A_{n}$
4664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4667 \begin_layout Plain Layout
4672 \begin_layout Plain Layout
4687 \begin_layout Plain Layout
4701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4704 \begin_layout Plain Layout
4705 \begin_inset Formula $A_{1}+\dots+A_{n}$
4715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4718 \begin_layout Plain Layout
4723 \begin_layout Plain Layout
4738 \begin_layout Plain Layout
4752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4755 \begin_layout Plain Layout
4756 \begin_inset Formula $A_{1},\ldots,A_{n}$
4766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4769 \begin_layout Plain Layout
4774 \begin_layout Plain Layout
4789 \begin_layout Plain Layout
4803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4806 \begin_layout Plain Layout
4807 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4820 \begin_layout Plain Layout
4828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4831 \begin_layout Plain Layout
4832 \begin_inset Formula $\vdots$
4842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4845 \begin_layout Plain Layout
4853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4856 \begin_layout Plain Layout
4857 \begin_inset Formula $\ddots$
4867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4870 \begin_layout Plain Layout
4878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4881 \begin_layout Plain Layout
4882 \begin_inset Formula $\iddots$
4892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4895 \begin_layout Plain Layout
4897 \begin_inset space \thinspace{}
4900 matrix with the different dots
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4908 \begin_layout Plain Layout
4909 \begin_inset Formula $\begin{array}{ccc}
4910 A_{11} & \cdots & A_{1m}\\
4911 \vdots & \ddots & \vdots\\
4912 A_{n1} & \cdots & A_{nm}
4929 \begin_layout Standard
4930 The ellipses available in menu
4932 Insert\SpecialChar \menuseparator
4934 \begin_inset space ~
4948 \begin_layout Standard
4949 \begin_inset VSpace medskip
4958 , one of the options
4960 Use mathdots package (automatically)
4962 must be set in the document settings under
4965 \begin_inset space ~
4971 \begin_inset Newline newline
4976 Use mathdots package
4978 will improve the appearance of all dots in the documents if their font
4979 style or size is not the default.
4982 \begin_layout Standard
4983 \begin_inset VSpace medskip
4986 Specially for matrices there are ellipses that span over several columns.
4987 They are created with the command
4994 \begin_inset Index idx
4997 \begin_layout Plain Layout
5005 , that has the following scheme:
5008 \begin_layout Standard
5013 hdotsfor[distance]{number of columns}
5016 \begin_layout Standard
5017 The number of columns specifies how many columns should be spanned.
5018 Distance is a factor for the distance between the dots.
5021 \begin_layout Standard
5022 In the following matrix the command
5028 was inserted in the first box of the second line, to get an ellipsis with
5029 a dot distance twice as long as with the command
5036 \begin_inset Formula \[
5037 \left(\begin{array}{cccc}
5046 Note that the matrix fields that should be spanned must be empty, otherwise
5047 you get LaTeX-errors.
5050 \begin_layout Standard
5051 \begin_inset VSpace bigskip
5054 Furthermore you can fill with the command
5061 \begin_inset Index idx
5064 \begin_layout Plain Layout
5072 the rest of a line with dots.
5073 The effect of these commands is the same like with
5080 \begin_inset CommandInset ref
5082 reference "sub:Variable-Space"
5089 \begin_layout Standard
5090 For example the command
5098 \begin_layout Plain Layout
5112 \begin_layout Standard
5113 \begin_inset Formula $A\dotfill B$
5119 \begin_layout Standard
5126 there is for a line the command
5133 \begin_inset Index idx
5136 \begin_layout Plain Layout
5147 \begin_layout Standard
5148 \begin_inset Formula $A\hrulefill B$
5154 \begin_layout Standard
5155 To use the commands for text, they have to be inserted in TeX-mode.
5158 \begin_layout Section
5160 \begin_inset CommandInset label
5167 \begin_inset Index idx
5170 \begin_layout Plain Layout
5179 \begin_layout Standard
5180 Matrices can be inserted via the math toolbar button
5181 \begin_inset Graphics
5182 filename ../images/dialog-show_mathmatrix.png
5189 Insert\SpecialChar \menuseparator
5190 Math\SpecialChar \menuseparator
5194 In the matrix dialog you can specify the number of columns and rows, the
5195 alignment and the decoration.
5196 The vertical alignment is hereby only of importance for matrices in inline
5200 \begin_layout Standard
5201 The first matrix is top
5202 \begin_inset Formula $\begin{array}[t]{cccc}
5210 \begin_inset Formula $\begin{array}{cccc}
5217 and the third bottom
5218 \begin_inset Formula $\begin{array}[b]{cccc}
5228 \begin_layout Standard
5229 The horizontal alignment specifies how the column entries should be aligned.
5230 It is set by entering a letter for every column.
5235 denotes left aligned,
5244 To create for example a 4
5249 \begin_inset space ~
5252 matrix where the first column is left aligned, the second and third are
5253 centered and the last one is right aligned, one enters for the horizontal
5259 Normally are in a matrix all columns centered, therefore the default is
5260 for every column is a
5267 \begin_layout Standard
5268 Horizontal alignment:
5271 \begin_layout Standard
5277 \begin_inset Formula $\begin{array}{lll}
5289 \begin_inset Formula $\begin{array}{ccc}
5301 \begin_inset Formula $\begin{array}{rrr}
5311 \begin_layout Standard
5312 To add or delete rows and columns subsequently, the math toolbar buttons
5314 \begin_inset Graphics
5315 filename ../images/tabular-feature_append-row.png
5321 \begin_inset Graphics
5322 filename ../images/tabular-feature_delete-row.png
5328 \begin_inset space \thinspace{}
5333 Edit\SpecialChar \menuseparator
5337 New rows can also be created with
5340 arg "newline-insert newline"
5346 \begin_layout Standard
5347 \begin_inset VSpace bigskip
5354 adds parentheses in the selected style around the matrix.
5355 Alternatively, parentheses can can either be created with the commands
5363 \begin_inset Index idx
5366 \begin_layout Plain Layout
5381 \begin_inset Index idx
5384 \begin_layout Plain Layout
5395 \begin_inset space ~
5401 \begin_inset CommandInset ref
5403 reference "sub:Automatic-Bracket-Size"
5407 , or by using the following commands:
5408 \begin_inset VSpace medskip
5414 \begin_layout Standard
5415 \begin_inset space \hfill{}
5419 \begin_inset Tabular
5420 <lyxtabular version="3" rows="4" columns="2">
5421 <features tabularvalignment="middle">
5422 <column alignment="center" valignment="top" width="0">
5423 <column alignment="center" valignment="top" width="0">
5425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5428 \begin_layout Plain Layout
5434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5437 \begin_layout Plain Layout
5439 \begin_inset Note Note
5442 \begin_layout Plain Layout
5449 is only used as spacer.
5461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5464 \begin_layout Plain Layout
5471 \begin_layout Plain Layout
5485 \begin_inset space \thinspace{}
5493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5496 \begin_layout Plain Layout
5497 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5498 0 & \textrm{-}\mathrm{i}\\
5500 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5513 \begin_layout Plain Layout
5520 \begin_layout Plain Layout
5534 \begin_inset space \thinspace{}
5542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5545 \begin_layout Plain Layout
5546 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5547 0 & \textrm{-}\mathrm{i}\\
5549 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5562 \begin_layout Plain Layout
5569 \begin_layout Plain Layout
5583 \begin_inset space \thinspace{}
5591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5594 \begin_layout Plain Layout
5595 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5596 0 & \textrm{-}\mathrm{i}\\
5598 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5612 \begin_inset space \hfill{}
5616 \begin_inset Tabular
5617 <lyxtabular version="3" rows="4" columns="2">
5618 <features tabularvalignment="middle">
5619 <column alignment="center" valignment="top" width="0">
5620 <column alignment="center" valignment="top" width="0">
5622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5625 \begin_layout Plain Layout
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5645 \begin_layout Plain Layout
5652 \begin_layout Plain Layout
5666 \begin_inset space \thinspace{}
5674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5677 \begin_layout Plain Layout
5678 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5679 0 & \textrm{-}\mathrm{i}\\
5681 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5694 \begin_layout Plain Layout
5701 \begin_layout Plain Layout
5715 \begin_inset space \thinspace{}
5723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5726 \begin_layout Plain Layout
5727 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5728 0 & \textrm{-}\mathrm{i}\\
5730 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5743 \begin_layout Plain Layout
5750 \begin_layout Plain Layout
5764 \begin_inset space \thinspace{}
5772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5775 \begin_layout Plain Layout
5776 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5777 0 & \textrm{-}\mathrm{i}\\
5779 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5793 \begin_inset space \hfill{}
5799 \begin_layout Standard
5800 \begin_inset VSpace medskip
5804 \begin_inset space \thinspace{}
5808 \begin_inset space \space{}
5817 is inserted, a blue box appears between two vertical lines where the matrix
5819 \begin_inset Newline newline
5822 Note that decorated matrices ignore the vertical alignment.
5825 \begin_layout Standard
5826 \begin_inset VSpace bigskip
5829 As all multiline formulas are matrices, the length
5836 \begin_inset Index idx
5839 \begin_layout Plain Layout
5847 that is described in
5848 \begin_inset CommandInset ref
5850 reference "sub:Column-Separation"
5854 can also be used to change the column separation of matrices.
5857 \begin_layout Standard
5858 To change the row separation, the command
5865 \begin_inset Index idx
5868 \begin_layout Plain Layout
5877 It is used as follows:
5880 \begin_layout Standard
5887 arraystretch}{stretch factor}
5888 \begin_inset Index idx
5891 \begin_layout Plain Layout
5902 \begin_layout Standard
5909 assigns the stretch factor to the predefined command
5917 \begin_inset space \thinspace{}
5921 \begin_inset space \space{}
5924 the row separation, use the factor 2.
5925 This is then used for all following matrices.
5926 To go back to the original separation, assign the factor 1 to
5935 \begin_layout Standard
5936 To set matrices into a text line, the command
5943 \begin_inset Index idx
5946 \begin_layout Plain Layout
5955 When it is inserted a blue box with two dashed lines appears.
5956 In this box the matrix is inserted.
5959 \begin_layout Standard
5961 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5963 \end{smallmatrix}\right)$
5969 \begin_layout Section
5970 Brackets and Delimiters
5971 \begin_inset Index idx
5974 \begin_layout Plain Layout
5981 \begin_inset Index idx
5984 \begin_layout Plain Layout
5993 \begin_layout Subsection
5994 Vertical Brackets and Delimiters
5995 \begin_inset Index idx
5998 \begin_layout Plain Layout
6007 \begin_layout Standard
6008 \begin_inset space \hfill{}
6012 \begin_inset Tabular
6013 <lyxtabular version="3" rows="9" columns="2">
6014 <features tabularvalignment="middle">
6015 <column alignment="center" valignment="top" width="0pt">
6016 <column alignment="center" valignment="top" width="0pt">
6018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6021 \begin_layout Plain Layout
6027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6030 \begin_layout Plain Layout
6038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6041 \begin_layout Plain Layout
6047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6050 \begin_layout Plain Layout
6051 \begin_inset Formula $($
6061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6064 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6073 \begin_layout Plain Layout
6074 \begin_inset Formula $\{$
6084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6087 \begin_layout Plain Layout
6093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6096 \begin_layout Plain Layout
6097 \begin_inset Formula $[$
6107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6110 \begin_layout Plain Layout
6118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6121 \begin_layout Plain Layout
6122 \begin_inset Formula $\langle$
6132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6135 \begin_layout Plain Layout
6143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6146 \begin_layout Plain Layout
6147 \begin_inset Formula $\lceil$
6157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6160 \begin_layout Plain Layout
6168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6171 \begin_layout Plain Layout
6172 \begin_inset Formula $\lfloor$
6182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6185 \begin_layout Plain Layout
6191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6194 \begin_layout Plain Layout
6195 \begin_inset Formula $/$
6205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6208 \begin_layout Plain Layout
6214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6217 \begin_layout Plain Layout
6218 \begin_inset Formula $|$
6232 \begin_inset space \hfill{}
6236 \begin_inset Tabular
6237 <lyxtabular version="3" rows="9" columns="2">
6238 <features tabularvalignment="middle">
6239 <column alignment="center" valignment="top" width="0pt">
6240 <column alignment="center" valignment="top" width="0pt">
6242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6245 \begin_layout Plain Layout
6251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6254 \begin_layout Plain Layout
6262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6265 \begin_layout Plain Layout
6271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6274 \begin_layout Plain Layout
6275 \begin_inset Formula $)$
6285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6288 \begin_layout Plain Layout
6294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6297 \begin_layout Plain Layout
6298 \begin_inset Formula $\}$
6308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6311 \begin_layout Plain Layout
6317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6320 \begin_layout Plain Layout
6321 \begin_inset Formula $]$
6331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6334 \begin_layout Plain Layout
6342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6345 \begin_layout Plain Layout
6346 \begin_inset Formula $\rangle$
6356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6359 \begin_layout Plain Layout
6367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6370 \begin_layout Plain Layout
6371 \begin_inset Formula $\rceil$
6381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6384 \begin_layout Plain Layout
6392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6395 \begin_layout Plain Layout
6396 \begin_inset Formula $\rfloor$
6406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6409 \begin_layout Plain Layout
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6422 \begin_layout Plain Layout
6423 \begin_inset Formula $\backslash$
6433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6436 \begin_layout Plain Layout
6444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6447 \begin_layout Plain Layout
6448 \begin_inset Formula $\|$
6462 \begin_inset space \hfill{}
6468 \begin_layout Standard
6471 \begin_inset Note Greyedout
6474 \begin_layout Plain Layout
6479 In TeX-mode the command
6486 \begin_inset Index idx
6489 \begin_layout Plain Layout
6497 must be used for the backslash, because the command
6505 produces there a line break.
6513 \begin_layout Standard
6514 For all characters listed above the size can be adjusted with the commands
6515 described in the following two subsections.
6516 When using these commands, the characters < and > can directly be used
6517 instead of the commands
6532 \begin_layout Subsubsection
6534 \begin_inset CommandInset label
6536 name "sub:Manual-Bracket-Size"
6541 \begin_inset Index idx
6544 \begin_layout Plain Layout
6545 Bracket size ! manual
6553 \begin_layout Standard
6554 The bracket size can be specified manually by the LaTeX-commands
6561 \begin_inset Index idx
6564 \begin_layout Plain Layout
6597 denotes the smallest and
6603 the largest bracket size.
6606 \begin_layout Standard
6607 These commands are used to emphasize levels of brackets:
6610 \begin_layout Standard
6612 \begin_inset Tabular
6613 <lyxtabular version="3" rows="2" columns="2">
6614 <features tabularvalignment="middle">
6615 <column alignment="center" valignment="top" width="0pt">
6616 <column alignment="center" valignment="top" width="0pt">
6618 <cell alignment="center" valignment="top" usebox="none">
6621 \begin_layout Plain Layout
6622 all brackets in the same size:
6627 <cell alignment="center" valignment="top" usebox="none">
6630 \begin_layout Plain Layout
6631 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6641 <cell alignment="center" valignment="top" usebox="none">
6644 \begin_layout Plain Layout
6650 <cell alignment="center" valignment="top" usebox="none">
6653 \begin_layout Plain Layout
6654 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6668 \begin_inset Note Note
6671 \begin_layout Plain Layout
6678 is only used as spacer.
6686 \begin_layout Standard
6687 For the second formula the command
6697 \begin_layout Plain Layout
6711 \begin_layout Standard
6712 Here is an overview about all bracket sizes:
6715 \begin_layout Standard
6735 \begin_layout Plain Layout
6752 \begin_layout Plain Layout
6765 \begin_layout Plain Layout
6781 \begin_layout Standard
6783 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6789 \begin_layout Standard
6796 -commands there is the variant
6803 \begin_inset Index idx
6806 \begin_layout Plain Layout
6814 that adds a bit more space between the bracket and its content, and the
6828 \begin_inset Index idx
6831 \begin_layout Plain Layout
6841 , that don't add additional space.
6846 at the end of the command
6852 is for a left bracket; for a right bracket this will be replaced by an
6858 A left or right bracket can each be an opening or closing bracket.
6861 \begin_layout Standard
6862 In the following table is a comparison of the variants:
6865 \begin_layout Standard
6867 \begin_inset Tabular
6868 <lyxtabular version="3" rows="5" columns="2">
6869 <features tabularvalignment="middle">
6870 <column alignment="center" valignment="middle" width="0">
6871 <column alignment="center" valignment="middle" width="0">
6873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6876 \begin_layout Plain Layout
6882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6885 \begin_layout Plain Layout
6887 \begin_inset Note Note
6890 \begin_layout Plain Layout
6897 is only used as spacer.
6909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6912 \begin_layout Plain Layout
6927 \begin_layout Plain Layout
6945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6948 \begin_layout Plain Layout
6949 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6962 \begin_layout Plain Layout
6977 \begin_layout Plain Layout
6995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6998 \begin_layout Plain Layout
6999 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7012 \begin_layout Plain Layout
7027 \begin_layout Plain Layout
7045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7048 \begin_layout Plain Layout
7049 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7062 \begin_layout Plain Layout
7074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7077 \begin_layout Plain Layout
7078 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7094 \begin_layout Subsubsection
7095 Automatic Bracket Size
7096 \begin_inset CommandInset label
7098 name "sub:Automatic-Bracket-Size"
7103 \begin_inset Index idx
7106 \begin_layout Plain Layout
7107 Bracket size ! automatic
7115 \begin_layout Standard
7116 Brackets with variable size can be inserted with the commands
7123 \begin_inset Index idx
7126 \begin_layout Plain Layout
7141 \begin_inset Index idx
7144 \begin_layout Plain Layout
7152 or via the math toolbar button
7153 \begin_inset Graphics
7154 filename ../images/dialog-show_mathdelimiter.png
7172 the wanted bracket must be inserted.
7173 The bracket size will then automatically be calculated for the output.
7176 \begin_layout Standard
7178 normal bracket: The command
7188 \begin_layout Plain Layout
7198 \begin_inset Formula $\downarrow$
7205 \begin_layout Plain Layout
7217 \begin_inset Formula \[
7226 \begin_layout Standard
7228 multiline bracket: The command
7240 \begin_layout Plain Layout
7250 \begin_inset Formula $\downarrow$
7257 \begin_layout Plain Layout
7271 \begin_inset Formula \[
7272 \ln\left(\frac{A}{C}\right)
7280 \begin_layout Standard
7296 \begin_inset space ~
7302 This has the advantage that you can see in LyX immediately the real bracket
7303 size and that the matching right bracket will be created too.
7304 \begin_inset Newline newline
7307 The command for the last example would then be:
7321 \begin_layout Plain Layout
7331 \begin_inset Formula $\downarrow$
7337 \begin_layout Standard
7338 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7339 For example the command
7349 \begin_layout Plain Layout
7359 \begin_inset Formula $\downarrow$
7366 \begin_layout Plain Layout
7382 \begin_inset Formula \[
7383 \left.\frac{A}{B}\right\}
7402 will be converted by LyX to brackets in the right size when the document
7403 is reloaded and an omitted bracket will appear as dashed line.
7406 \begin_layout Standard
7407 \begin_inset VSpace bigskip
7410 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7418 \begin_inset Index idx
7421 \begin_layout Plain Layout
7429 is additionally available for all brackets and limits.
7430 With this command the height of the following character is adapted to the
7431 one of the surrounding brackets, what is e.
7432 \begin_inset space \thinspace{}
7436 \begin_inset space \space{}
7439 needed for physical vectors:
7440 \begin_inset Formula \[
7441 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7446 For physical vectors there is a special LaTeX-package, described in
7447 \begin_inset CommandInset ref
7449 reference "sub:Physical-Vectors"
7456 \begin_layout Subsection
7458 \begin_inset Index idx
7461 \begin_layout Plain Layout
7462 Brackets ! horizontal
7470 \begin_layout Standard
7472 \begin_inset Tabular
7473 <lyxtabular version="3" rows="4" columns="2">
7474 <features tabularvalignment="middle">
7475 <column alignment="center" valignment="top" width="0pt">
7476 <column alignment="center" valignment="top" width="0pt">
7478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7481 \begin_layout Plain Layout
7483 \begin_inset Note Note
7486 \begin_layout Plain Layout
7493 is only used as spacer.
7503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7506 \begin_layout Plain Layout
7514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7517 \begin_layout Plain Layout
7521 \begin_layout Plain Layout
7536 \begin_layout Plain Layout
7549 \begin_layout Plain Layout
7562 \begin_layout Plain Layout
7575 \begin_layout Plain Layout
7583 \begin_inset Index idx
7586 \begin_layout Plain Layout
7599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7602 \begin_layout Plain Layout
7603 \begin_inset Formula $\overbrace{A+B}^{3}$
7613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7616 \begin_layout Plain Layout
7620 \begin_layout Plain Layout
7635 \begin_layout Plain Layout
7648 \begin_layout Plain Layout
7661 \begin_layout Plain Layout
7669 \begin_inset Index idx
7672 \begin_layout Plain Layout
7685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7688 \begin_layout Plain Layout
7689 \begin_inset Formula $\underbrace{A+B}_{5}$
7699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7702 \begin_layout Plain Layout
7709 \begin_layout Plain Layout
7724 \begin_layout Plain Layout
7737 \begin_layout Plain Layout
7750 \begin_layout Plain Layout
7763 \begin_layout Plain Layout
7776 \begin_layout Plain Layout
7789 \begin_layout Plain Layout
7803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7806 \begin_layout Plain Layout
7807 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7823 \begin_layout Standard
7824 In the last example it doesn't matter if
7836 is inserted at first.
7839 \begin_layout Standard
7840 \begin_inset VSpace bigskip
7843 When brackets are needed that overlap each other, multiline formulas, as
7845 \begin_inset CommandInset ref
7847 reference "sec:Multiline-Formulas"
7852 \begin_inset Formula \begin{eqnarray*}
7853 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7854 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7859 In the first row the formula is inserted together with the first brace.
7860 It is hereby important that the space command
7864 \begin_layout Plain Layout
7865 Space commands are explained in
7866 \begin_inset CommandInset ref
7868 reference "sub:Predefined-Space"
7883 is inserted before the first
7884 \begin_inset Formula $d$
7887 , because the brace that ends behind the
7888 \begin_inset Formula $q$
7891 prevents that the following
7892 \begin_inset Quotes eld
7896 \begin_inset Quotes erd
7899 is surrounded by space.
7903 \begin_layout Plain Layout
7904 because a bracket is not handled as character, see
7905 \begin_inset CommandInset ref
7907 reference "sub:Binary-Operators"
7916 In the second row the second brace is inserted.
7917 As it should begin before the
7918 \begin_inset Formula $b$
7933 \begin_layout Plain Layout
7941 \begin_inset CommandInset ref
7943 reference "sub:Placeholders"
7952 This space is needed because the
7953 \begin_inset Quotes eld
7957 \begin_inset Quotes erd
7960 is also surrounded by space in the formula.
7961 The brace is placed under the command
7970 \begin_layout Standard
7971 It gets more complicated when brackets overlap each other, like in the following
7976 \begin_layout Plain Layout
7988 \begin_inset Formula \begin{eqnarray*}
7989 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7990 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
7999 \begin_layout Plain Layout
8010 The first formula row is the same as the second row of the previous example,
8011 with the difference that the brace is above.
8012 The second row contains the formula together with the second brace.
8013 To avoid that there is space between the upper brace in the first row and
8014 the formula, the row spacing need to be reduced.
8015 This is not easily possible due to a bug in LyX
8019 \begin_layout Plain Layout
8020 \begin_inset CommandInset href
8022 name "LyX-bug #1505"
8023 target "http://www.lyx.org/trac/ticket/1505"
8033 As solution for the problem, the global formula row separation
8040 \begin_inset Index idx
8043 \begin_layout Plain Layout
8051 must be changed to -6
8052 \begin_inset space \thinspace{}
8055 pt before the formula with the command
8070 is set back after the formula to the standard value of 3
8071 \begin_inset space \thinspace{}
8074 pt using the same command.
8075 More about the row separation in formulas is explained in
8076 \begin_inset CommandInset ref
8078 reference "sub:Line-Separation"
8085 \begin_layout Section
8087 \begin_inset Index idx
8090 \begin_layout Plain Layout
8099 \begin_layout Standard
8100 Arrows can be inserted via the math toolbar button
8101 \begin_inset Graphics
8102 filename ../images/math/leftarrow.png
8107 or the commands listed in the following subsections.
8110 \begin_layout Standard
8111 \begin_inset Newpage newpage
8117 \begin_layout Subsection
8119 \begin_inset Index idx
8122 \begin_layout Plain Layout
8131 \begin_layout Standard
8132 \begin_inset space \hfill{}
8136 \begin_inset Tabular
8137 <lyxtabular version="3" rows="8" columns="2">
8138 <features tabularvalignment="middle">
8139 <column alignment="center" valignment="top" width="0pt">
8140 <column alignment="center" valignment="top" width="0pt">
8142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8145 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8165 \begin_layout Plain Layout
8173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8176 \begin_layout Plain Layout
8177 \begin_inset Formula $\gets$
8187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8190 \begin_layout Plain Layout
8198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8201 \begin_layout Plain Layout
8202 \begin_inset Formula $\Leftarrow$
8212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8215 \begin_layout Plain Layout
8223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8226 \begin_layout Plain Layout
8227 \begin_inset Formula $\longleftarrow$
8237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8240 \begin_layout Plain Layout
8248 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8251 \begin_layout Plain Layout
8252 \begin_inset Formula $\Longleftarrow$
8262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8265 \begin_layout Plain Layout
8273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8276 \begin_layout Plain Layout
8277 \begin_inset Formula $\leftharpoonup$
8287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8290 \begin_layout Plain Layout
8298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8301 \begin_layout Plain Layout
8302 \begin_inset Formula $\leftharpoondown$
8312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8315 \begin_layout Plain Layout
8323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8326 \begin_layout Plain Layout
8327 \begin_inset Formula $\hookleftarrow$
8341 \begin_inset space \hfill{}
8345 \begin_inset Tabular
8346 <lyxtabular version="3" rows="8" columns="2">
8347 <features tabularvalignment="middle">
8348 <column alignment="center" valignment="top" width="0pt">
8349 <column alignment="center" valignment="top" width="0pt">
8351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8354 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8374 \begin_layout Plain Layout
8382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8385 \begin_layout Plain Layout
8386 \begin_inset Formula $\to$
8396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8399 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8411 \begin_inset Formula $\Rightarrow$
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8424 \begin_layout Plain Layout
8432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8435 \begin_layout Plain Layout
8436 \begin_inset Formula $\longrightarrow$
8446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8449 \begin_layout Plain Layout
8457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8460 \begin_layout Plain Layout
8461 \begin_inset Formula $\Longrightarrow$
8471 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8474 \begin_layout Plain Layout
8482 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8485 \begin_layout Plain Layout
8486 \begin_inset Formula $\rightharpoonup$
8496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8499 \begin_layout Plain Layout
8507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8510 \begin_layout Plain Layout
8511 \begin_inset Formula $\rightharpoondown$
8521 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8524 \begin_layout Plain Layout
8532 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8535 \begin_layout Plain Layout
8536 \begin_inset Formula $\hookrightarrow$
8550 \begin_inset space \hfill{}
8556 \begin_layout Standard
8557 \begin_inset space \hfill{}
8561 \begin_inset Tabular
8562 <lyxtabular version="3" rows="6" columns="2">
8563 <features tabularvalignment="middle">
8564 <column alignment="center" valignment="top" width="0pt">
8565 <column alignment="center" valignment="top" width="0pt">
8567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8570 \begin_layout Plain Layout
8576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8579 \begin_layout Plain Layout
8587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8601 \begin_layout Plain Layout
8602 \begin_inset Formula $\leftrightarrow$
8612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8615 \begin_layout Plain Layout
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8626 \begin_layout Plain Layout
8627 \begin_inset Formula $\Leftrightarrow$
8637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8640 \begin_layout Plain Layout
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8651 \begin_layout Plain Layout
8652 \begin_inset Formula $\longleftrightarrow$
8662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8665 \begin_layout Plain Layout
8673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8676 \begin_layout Plain Layout
8677 \begin_inset Formula $\Longleftrightarrow$
8687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8690 \begin_layout Plain Layout
8698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8701 \begin_layout Plain Layout
8702 \begin_inset Formula $\rightleftharpoons$
8716 \begin_inset space \hspace{}
8721 \begin_inset space \hfill{}
8725 \begin_inset Tabular
8726 <lyxtabular version="3" rows="5" columns="2">
8727 <features tabularvalignment="middle">
8728 <column alignment="center" valignment="top" width="0pt">
8729 <column alignment="center" valignment="top" width="0pt">
8731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8734 \begin_layout Plain Layout
8740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8743 \begin_layout Plain Layout
8751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8754 \begin_layout Plain Layout
8762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8765 \begin_layout Plain Layout
8766 \begin_inset Formula $\mapsto$
8776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8779 \begin_layout Plain Layout
8787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8790 \begin_layout Plain Layout
8791 \begin_inset Formula $\longmapsto$
8801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8804 \begin_layout Plain Layout
8812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8815 \begin_layout Plain Layout
8816 \begin_inset Formula $\leadsto$
8826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8829 \begin_layout Plain Layout
8837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8840 \begin_layout Plain Layout
8841 \begin_inset Formula $\dasharrow$
8855 \begin_inset space \hfill{}
8861 \begin_layout Standard
8862 \begin_inset VSpace medskip
8865 Arrows used as accent like e.
8866 \begin_inset space \thinspace{}
8870 \begin_inset space \space{}
8873 vector arrows are listed in
8874 \begin_inset CommandInset ref
8876 reference "sec:Accents"
8883 \begin_layout Standard
8884 \begin_inset VSpace bigskip
8887 Furthermore there are the labeled arrows
8888 \begin_inset Index idx
8891 \begin_layout Plain Layout
8904 \begin_inset Index idx
8907 \begin_layout Plain Layout
8922 \begin_inset Index idx
8925 \begin_layout Plain Layout
8932 \begin_layout Plain Layout
8947 When inserting one of these commands in a formula, an arrow with two blue
8948 boxes appear where the label can be inserted.
8949 The length of the arrow adapts to the label width.
8952 \begin_layout Standard
8954 \begin_inset Tabular
8955 <lyxtabular version="3" rows="3" columns="2">
8956 <features tabularvalignment="middle">
8957 <column alignment="center" valignment="top" width="0pt">
8958 <column alignment="center" valignment="top" width="0pt">
8960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8963 \begin_layout Plain Layout
8969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8972 \begin_layout Plain Layout
8974 \begin_inset Note Note
8977 \begin_layout Plain Layout
8984 is only used as spacer.
8996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8999 \begin_layout Plain Layout
9006 \begin_layout Plain Layout
9016 \begin_inset Formula $\downarrow$
9020 \begin_inset Formula $\to$
9028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9031 \begin_layout Plain Layout
9032 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9045 \begin_layout Plain Layout
9052 \begin_layout Plain Layout
9062 \begin_inset Formula $\downarrow$
9066 \begin_inset Formula $\to$
9074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9077 \begin_layout Plain Layout
9078 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9094 \begin_layout Subsection
9095 Vertical and diagonal Arrows
9096 \begin_inset Index idx
9099 \begin_layout Plain Layout
9106 \begin_inset Index idx
9109 \begin_layout Plain Layout
9118 \begin_layout Standard
9119 \begin_inset space \hfill{}
9123 \begin_inset Tabular
9124 <lyxtabular version="3" rows="7" columns="2">
9125 <features tabularvalignment="middle">
9126 <column alignment="center" valignment="top" width="0pt">
9127 <column alignment="center" valignment="top" width="0pt">
9129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9132 \begin_layout Plain Layout
9138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9141 \begin_layout Plain Layout
9149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9152 \begin_layout Plain Layout
9160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9163 \begin_layout Plain Layout
9164 \begin_inset Formula $\uparrow$
9174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9177 \begin_layout Plain Layout
9185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9188 \begin_layout Plain Layout
9189 \begin_inset Formula $\Uparrow$
9199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9202 \begin_layout Plain Layout
9210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9213 \begin_layout Plain Layout
9214 \begin_inset Formula $\updownarrow$
9224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9227 \begin_layout Plain Layout
9235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9238 \begin_layout Plain Layout
9239 \begin_inset Formula $\Updownarrow$
9249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9252 \begin_layout Plain Layout
9260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9263 \begin_layout Plain Layout
9264 \begin_inset Formula $\Downarrow$
9274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9277 \begin_layout Plain Layout
9285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9288 \begin_layout Plain Layout
9289 \begin_inset Formula $\downarrow$
9303 \begin_inset space \hfill{}
9307 \begin_inset Tabular
9308 <lyxtabular version="3" rows="5" columns="2">
9309 <features tabularvalignment="middle">
9310 <column alignment="center" valignment="top" width="0pt">
9311 <column alignment="center" valignment="top" width="0pt">
9313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9316 \begin_layout Plain Layout
9322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9325 \begin_layout Plain Layout
9333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9336 \begin_layout Plain Layout
9344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9347 \begin_layout Plain Layout
9348 \begin_inset Formula $\nearrow$
9358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9361 \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 $\searrow$
9383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9386 \begin_layout Plain Layout
9394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9397 \begin_layout Plain Layout
9398 \begin_inset Formula $\swarrow$
9408 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9411 \begin_layout Plain Layout
9419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9422 \begin_layout Plain Layout
9423 \begin_inset Formula $\nwarrow$
9437 \begin_inset space \hfill{}
9443 \begin_layout Standard
9444 \begin_inset VSpace medskip
9447 Vertical arrows can be used also as delimiter together with the commands
9449 \begin_inset CommandInset ref
9451 reference "sub:Manual-Bracket-Size"
9456 \begin_inset CommandInset ref
9458 reference "sub:Automatic-Bracket-Size"
9465 \begin_layout Standard
9466 \begin_inset Newpage newpage
9472 \begin_layout Section
9474 \begin_inset CommandInset label
9481 \begin_inset Index idx
9484 \begin_layout Plain Layout
9493 \begin_layout Standard
9494 Accents can be inserted via the math toolbar button
9495 \begin_inset Graphics
9496 filename ../images/math/hat.png
9501 or the commands listed in the following subsections.
9504 \begin_layout Subsection
9505 Accents for one Character
9509 \begin_layout Plain Layout
9522 \begin_layout Plain Layout
9524 \begin_inset CommandInset ref
9526 reference "sub:Accents-in-Text"
9539 \begin_layout Plain Layout
9547 \begin_inset Note Note
9550 \begin_layout Plain Layout
9557 is used to avoid that the footnote appears in the PDF-bookmark.
9560 \begin_layout Plain Layout
9568 \begin_inset CommandInset ref
9570 reference "sub:Formulas-in-Section"
9580 \begin_inset CommandInset label
9582 name "sub:Accents-for-one"
9587 \begin_inset Index idx
9590 \begin_layout Plain Layout
9591 Accents ! for one character
9599 \begin_layout Standard
9600 \begin_inset space \hfill{}
9604 \begin_inset Tabular
9605 <lyxtabular version="3" rows="8" columns="2">
9606 <features tabularvalignment="middle">
9607 <column alignment="center" valignment="top" width="0pt">
9608 <column alignment="center" valignment="top" width="0pt">
9610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9613 \begin_layout Plain Layout
9619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9622 \begin_layout Plain Layout
9624 \begin_inset Note Note
9627 \begin_layout Plain Layout
9634 is only used as spacer.
9646 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9649 \begin_layout Plain Layout
9656 \begin_layout Plain Layout
9670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9673 \begin_layout Plain Layout
9674 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9684 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9687 \begin_layout Plain Layout
9694 \begin_layout Plain Layout
9708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9711 \begin_layout Plain Layout
9712 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9725 \begin_layout Plain Layout
9732 \begin_layout Plain Layout
9746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9749 \begin_layout Plain Layout
9750 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9760 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9763 \begin_layout Plain Layout
9770 \begin_layout Plain Layout
9784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9787 \begin_layout Plain Layout
9788 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9801 \begin_layout Plain Layout
9808 \begin_layout Plain Layout
9818 \begin_inset Index idx
9821 \begin_layout Plain Layout
9832 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9835 \begin_layout Plain Layout
9836 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9849 \begin_layout Plain Layout
9856 \begin_layout Plain Layout
9870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9873 \begin_layout Plain Layout
9874 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9884 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9887 \begin_layout Plain Layout
9894 \begin_layout Plain Layout
9908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9911 \begin_layout Plain Layout
9912 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9926 \begin_inset space \hfill{}
9930 \begin_inset Tabular
9931 <lyxtabular version="3" rows="7" columns="2">
9932 <features tabularvalignment="middle">
9933 <column alignment="center" valignment="top" width="0pt">
9934 <column alignment="center" valignment="top" width="0pt">
9936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9939 \begin_layout Plain Layout
9945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9948 \begin_layout Plain Layout
9956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9959 \begin_layout Plain Layout
9966 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9984 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9997 \begin_layout Plain Layout
10004 \begin_layout Plain Layout
10018 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10021 \begin_layout Plain Layout
10022 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10035 \begin_layout Plain Layout
10042 \begin_layout Plain Layout
10056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10059 \begin_layout Plain Layout
10060 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10070 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10073 \begin_layout Plain Layout
10080 \begin_layout Plain Layout
10094 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10111 \begin_layout Plain Layout
10118 \begin_layout Plain Layout
10132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10135 \begin_layout Plain Layout
10136 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10149 \begin_layout Plain Layout
10156 \begin_layout Plain Layout
10170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10173 \begin_layout Plain Layout
10174 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10188 \begin_inset space \hfill{}
10194 \begin_layout Standard
10195 \begin_inset VSpace bigskip
10201 \begin_layout Standard
10202 You can directly insert accents like é to formulas.
10203 LyX will transform them to the corresponding accent command.
10205 \begin_inset Index idx
10208 \begin_layout Plain Layout
10214 it is better to insert a quotation mark before the vowel.
10215 These two characters are then treated by LaTeX as
10219 character when the formula part with the umlaut is marked as German.
10227 \begin_inset Quotes eld
10231 \begin_inset Quotes erd
10234 umlauts are created as demonstrated in the following example:
10237 \begin_layout Standard
10238 \begin_inset VSpace -2mm
10244 \begin_layout Standard
10246 \begin_inset Tabular
10247 <lyxtabular version="3" rows="3" columns="2">
10248 <features tabularvalignment="middle">
10249 <column alignment="center" valignment="top" width="0">
10250 <column alignment="center" valignment="top" width="0">
10252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10255 \begin_layout Plain Layout
10261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10264 \begin_layout Plain Layout
10266 \begin_inset Note Note
10269 \begin_layout Plain Layout
10277 \begin_inset space \thinspace{}
10280 pt space are only used as spacer.
10292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10295 \begin_layout Plain Layout
10298 \begin_inset Quotes grd
10306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10309 \begin_layout Plain Layout
10310 \begin_inset space \hspace{}
10317 \begin_inset Formula $"i$
10327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10330 \begin_layout Plain Layout
10337 \begin_layout Plain Layout
10351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10354 \begin_layout Plain Layout
10355 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10371 \begin_layout Standard
10372 Another advantage to
10378 is that umlauts can directly be converted to mathematical text because
10379 the accent commands above are
10385 in mathematical text
10388 To convert an accented character to mathematical text, only the character
10389 under the accent may be converted.
10390 This applies also for all other conversions, e.
10391 \begin_inset space \thinspace{}
10395 \begin_inset space \space{}
10401 \begin_layout Standard
10402 In mathematical text, umlauts and other accented characters can directly
10406 \begin_layout Subsection
10407 Accents for Operators
10408 \begin_inset Index idx
10411 \begin_layout Plain Layout
10412 Accents ! for operators
10420 \begin_layout Standard
10428 \begin_inset Index idx
10431 \begin_layout Plain Layout
10446 \begin_inset Index idx
10449 \begin_layout Plain Layout
10457 characters can be placed above or below an operator, respectively, to accent
10466 \begin_inset Index idx
10469 \begin_layout Plain Layout
10477 characters can be set before and behind an operator.
10478 The command scheme is:
10481 \begin_layout Standard
10497 \begin_layout Standard
10504 must always be before the operator that should be accented.
10505 You can accent with several characters and even with other operators and
10513 for example only characters behind an operator, write nothing between the
10514 first braces but don't omit the braces.
10517 \begin_layout Standard
10518 For example the command
10523 \begin_inset Formula $\to$
10533 \begin_inset Formula $\to$
10542 \begin_layout Plain Layout
10558 \begin_inset Formula \[
10559 \sideset{}{'}\sum_{k=1}^{n}
10567 \begin_layout Standard
10576 \begin_layout Plain Layout
10591 \begin_layout Plain Layout
10603 \begin_inset Formula $\uparrow$
10611 \begin_inset Formula \[
10612 \overset{a}{\maltese}
10617 As seen in the last example, with
10629 also symbols and characters can be accented; with
10635 this is not possible.
10638 \begin_layout Subsection
10639 Accents for several Characters
10640 \begin_inset Index idx
10643 \begin_layout Plain Layout
10644 Accents ! for several characters
10652 \begin_layout Standard
10653 \begin_inset space \hfill{}
10657 \begin_inset Tabular
10658 <lyxtabular version="3" rows="5" columns="2">
10659 <features tabularvalignment="middle">
10660 <column alignment="center" valignment="top" width="0pt">
10661 <column alignment="center" valignment="top" width="0pt">
10663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10666 \begin_layout Plain Layout
10672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10675 \begin_layout Plain Layout
10677 \begin_inset Note Note
10680 \begin_layout Plain Layout
10687 is only used as spacer.
10699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10702 \begin_layout Plain Layout
10709 \begin_layout Plain Layout
10723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10726 \begin_layout Plain Layout
10727 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10740 \begin_layout Plain Layout
10747 \begin_layout Plain Layout
10761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10764 \begin_layout Plain Layout
10765 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10778 \begin_layout Plain Layout
10785 \begin_layout Plain Layout
10799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10802 \begin_layout Plain Layout
10803 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10816 \begin_layout Plain Layout
10819 underleftrightarrow
10823 \begin_layout Plain Layout
10837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10840 \begin_layout Plain Layout
10841 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10855 \begin_inset space \hfill{}
10859 \begin_inset Tabular
10860 <lyxtabular version="3" rows="5" columns="2">
10861 <features tabularvalignment="middle">
10862 <column alignment="center" valignment="top" width="0pt">
10863 <column alignment="center" valignment="top" width="0pt">
10865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10868 \begin_layout Plain Layout
10874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10877 \begin_layout Plain Layout
10885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10888 \begin_layout Plain Layout
10895 \begin_layout Plain Layout
10909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10912 \begin_layout Plain Layout
10913 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10926 \begin_layout Plain Layout
10933 \begin_layout Plain Layout
10947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10950 \begin_layout Plain Layout
10951 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10964 \begin_layout Plain Layout
10971 \begin_layout Plain Layout
10985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10988 \begin_layout Plain Layout
10989 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11002 \begin_layout Plain Layout
11009 \begin_layout Plain Layout
11023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11026 \begin_layout Plain Layout
11027 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
11041 \begin_inset space \hfill{}
11047 \begin_layout Standard
11048 \begin_inset VSpace medskip
11051 With these commands as many characters as you like can be accented.
11064 will only be set in the output with a length of three characters, as shown
11065 in the following example:
11066 \begin_inset Formula \[
11067 \widetilde{A+B=C-D}
11075 \begin_layout Standard
11083 \begin_inset Index idx
11086 \begin_layout Plain Layout
11101 \begin_inset Index idx
11104 \begin_layout Plain Layout
11112 described in the previous subsection it is also possible to accent several
11122 \begin_layout Plain Layout
11132 \begin_inset Formula $\downarrow$
11138 \begin_inset Formula \[
11139 \underset{***}{A=B}
11147 \begin_layout Section
11149 \begin_inset CommandInset label
11156 \begin_inset Index idx
11159 \begin_layout Plain Layout
11168 \begin_layout Subsection
11170 \begin_inset CommandInset label
11172 name "sub:Predefined-Space"
11177 \begin_inset Index idx
11180 \begin_layout Plain Layout
11181 Space ! horizontal ! predefined
11189 \begin_layout Standard
11190 Sometimes it is necessary to insert horizontal space to a formula.
11191 This is done by inserting a protected space (shortcut
11194 arg "space-insert protected"
11199 \begin_inset Quotes eld
11208 \begin_layout Plain Layout
11220 \begin_inset Quotes erd
11223 appears and by pressing
11227 several times one can select one of eight different space sizes.
11228 The spaces can also be inserted using the math toolbar button
11229 \begin_inset Graphics
11230 filename ../images/math/space.png
11235 or special commands.
11236 Independent from the inserted command, one can select the size again by
11244 \begin_layout Standard
11247 \begin_inset VSpace -5mm
11251 \begin_inset Tabular
11252 <lyxtabular version="3" rows="3" columns="7">
11253 <features tabularvalignment="middle">
11254 <column alignment="center" valignment="middle" width="6.8cm">
11255 <column alignment="center" valignment="top" width="0">
11256 <column alignment="center" valignment="top" width="0">
11257 <column alignment="center" valignment="top" width="0">
11258 <column alignment="center" valignment="top" width="0">
11259 <column alignment="center" valignment="top" width="0">
11260 <column alignment="center" valignment="top" width="0">
11262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11274 \begin_layout Plain Layout
11282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11285 \begin_layout Plain Layout
11293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11296 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11318 \begin_layout Plain Layout
11326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11329 \begin_layout Plain Layout
11339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11342 \begin_layout Plain Layout
11347 keystrokes after inserting the protected space
11352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11355 \begin_layout Plain Layout
11361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11373 \begin_layout Plain Layout
11379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11382 \begin_layout Plain Layout
11388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11391 \begin_layout Plain Layout
11397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11400 \begin_layout Plain Layout
11408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11411 \begin_layout Plain Layout
11417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11421 \begin_inset Formula $A\, B$
11429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11432 \begin_layout Plain Layout
11433 \begin_inset Formula $A\: B$
11441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11444 \begin_layout Plain Layout
11445 \begin_inset Formula $A\; B$
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11456 \begin_layout Plain Layout
11457 \begin_inset Formula $A\quad B$
11465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11468 \begin_layout Plain Layout
11469 \begin_inset Formula $A\qquad B$
11477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11480 \begin_layout Plain Layout
11481 \begin_inset Formula $A\! B$
11497 \begin_layout Standard
11498 The last size seem to produce no space.
11499 It is displayed red in LyX contrary to the other sizes, because it is a
11501 There are two more negative spaces:
11504 \begin_layout Standard
11506 \begin_inset Tabular
11507 <lyxtabular version="3" rows="3" columns="3">
11508 <features tabularvalignment="middle">
11509 <column alignment="center" valignment="middle" width="6.8cm">
11510 <column alignment="center" valignment="top" width="0pt">
11511 <column alignment="center" valignment="top" width="0pt">
11513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11516 \begin_layout Plain Layout
11522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11525 \begin_layout Plain Layout
11533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11536 \begin_layout Plain Layout
11546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11549 \begin_layout Plain Layout
11554 keystrokes after inserting the protected space
11559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11562 \begin_layout Plain Layout
11568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11571 \begin_layout Plain Layout
11579 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11582 \begin_layout Plain Layout
11588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11591 \begin_layout Plain Layout
11592 \begin_inset Formula $A\negmedspace B$
11600 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11603 \begin_layout Plain Layout
11604 \begin_inset Formula $A\negthickspace B$
11620 \begin_layout Standard
11621 Negative spaces can lead to characters overlapping each other.
11622 Thus they can be used to enforce ligatures, what is e.
11623 \begin_inset space \thinspace{}
11627 \begin_inset space \space{}
11630 useful for summation operators:
11633 \begin_layout Standard
11635 \begin_inset Tabular
11636 <lyxtabular version="3" rows="3" columns="2">
11637 <features tabularvalignment="middle">
11638 <column alignment="center" valignment="top" width="0">
11639 <column alignment="center" valignment="top" width="0">
11641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11644 \begin_layout Plain Layout
11650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11653 \begin_layout Plain Layout
11655 \begin_inset Note Note
11658 \begin_layout Plain Layout
11665 is only used as spacer.
11677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11680 \begin_layout Plain Layout
11689 \begin_layout Plain Layout
11703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11706 \begin_layout Plain Layout
11707 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11720 \begin_layout Plain Layout
11731 \begin_layout Plain Layout
11745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11748 \begin_layout Plain Layout
11749 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11765 \begin_layout Standard
11766 Relations like for example equal signs, are always surrounded by space.
11767 To suppress this, the equal sign is placed into a TeX-brace.
11768 The following example demonstrates this:
11771 \begin_layout Standard
11773 \begin_inset Tabular
11774 <lyxtabular version="3" rows="2" columns="2">
11775 <features tabularvalignment="middle">
11776 <column alignment="center" valignment="top" width="0pt">
11777 <column alignment="center" valignment="top" width="0pt">
11779 <cell alignment="center" valignment="top" usebox="none">
11782 \begin_layout Plain Layout
11788 <cell alignment="center" valignment="top" usebox="none">
11791 \begin_layout Plain Layout
11792 \begin_inset Formula $A=B$
11802 <cell alignment="center" valignment="top" usebox="none">
11805 \begin_layout Plain Layout
11806 \begin_inset Note Note
11809 \begin_layout Plain Layout
11816 is only used as spacer.
11822 \begin_inset Formula $\raisebox{5mm}{}$
11825 equation without space
11830 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11833 \begin_layout Plain Layout
11834 \begin_inset Formula $A{=}B$
11850 \begin_layout Standard
11852 The command for the last formula is:
11857 \begin_inset Formula $\to$
11863 \begin_layout Standard
11864 \begin_inset VSpace bigskip
11867 Spaces are needed for physical units, because the space between the value
11868 and the unit is the smallest one and not a normal space.
11869 For units in text, the smallest space is inserted via the menu
11871 Insert\SpecialChar \menuseparator
11872 Formatting\SpecialChar \menuseparator
11874 \begin_inset space ~
11882 arg "space-insert thin"
11888 \begin_layout Standard
11889 An example to visualize the difference:
11892 \begin_layout Standard
11893 \begin_inset Tabular
11894 <lyxtabular version="3" rows="2" columns="2">
11895 <features tabularvalignment="middle">
11896 <column alignment="left" valignment="top" width="0">
11897 <column alignment="left" valignment="top" width="0">
11899 <cell alignment="center" valignment="top" usebox="none">
11902 \begin_layout Plain Layout
11904 \begin_inset Formula $\cdot$
11912 <cell alignment="center" valignment="top" usebox="none">
11915 \begin_layout Plain Layout
11916 space between value and unit
11923 <cell alignment="center" valignment="top" usebox="none">
11926 \begin_layout Plain Layout
11928 \begin_inset space \thinspace{}
11932 \begin_inset Formula $\cdot$
11940 <cell alignment="center" valignment="top" usebox="none">
11943 \begin_layout Plain Layout
11944 smallest space between value and unit
11957 \begin_layout Subsection
11962 \begin_layout Plain Layout
11975 \begin_layout Plain Layout
11976 for vertical space in formulas see
11977 \begin_inset CommandInset ref
11979 reference "sub:Line-Separation"
11992 \begin_layout Plain Layout
12000 \begin_inset Note Note
12003 \begin_layout Plain Layout
12006 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
12009 \begin_layout Plain Layout
12012 texorpdfstring is in section
12013 \begin_inset CommandInset ref
12015 reference "sub:Formulas-in-Section"
12025 \begin_inset CommandInset label
12027 name "sub:Variable-Space"
12032 \begin_inset Index idx
12035 \begin_layout Plain Layout
12036 Space ! horizontal ! variable
12044 \begin_layout Standard
12045 Space with a defined length can be inserted with the command
12052 \begin_inset Index idx
12055 \begin_layout Plain Layout
12065 \begin_inset Quotes eld
12074 \begin_layout Plain Layout
12086 \begin_inset Quotes erd
12090 The length can be specified by left-clicking on the
12091 \begin_inset Quotes eld
12100 \begin_layout Plain Layout
12112 \begin_inset Quotes erd
12116 The length may also be negative.
12117 To insert so many space that the formula uses all available space, the
12125 \begin_inset Index idx
12128 \begin_layout Plain Layout
12139 \begin_layout Standard
12140 \begin_inset VSpace -1mm
12146 \begin_layout Standard
12148 \begin_inset Tabular
12149 <lyxtabular version="3" rows="4" columns="2">
12150 <features tabularvalignment="middle">
12151 <column alignment="center" valignment="top" width="0">
12152 <column alignment="center" valignment="top" width="0">
12154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12157 \begin_layout Plain Layout
12165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12168 \begin_layout Plain Layout
12176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12179 \begin_layout Plain Layout
12186 \begin_layout Plain Layout
12196 \begin_inset Formula $\to$
12202 \begin_inset space \thinspace{}
12210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12213 \begin_layout Plain Layout
12214 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12227 \begin_layout Plain Layout
12234 \begin_layout Plain Layout
12244 \begin_inset Formula $\to$
12250 \begin_inset space \thinspace{}
12258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12261 \begin_layout Plain Layout
12262 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12275 \begin_layout Plain Layout
12282 \begin_layout Plain Layout
12296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12299 \begin_layout Plain Layout
12300 \begin_inset Formula $A=A\hfill B=B$
12316 \begin_layout Standard
12317 In the last example the available space is given by the longest column entry
12319 In an inline formula the space depends on the length of the line in which
12327 Thus, when the line uses the full width, no space will be created.
12334 only has an effect on displayed formulas when the formula style
12339 (Formula styles are explained in
12340 \begin_inset CommandInset ref
12342 reference "sec:Formula-Styles"
12349 \begin_layout Standard
12356 , there are the commands
12368 that fill the space with a pattern, see
12369 \begin_inset CommandInset ref
12371 reference "sub:Ellipses"
12378 \begin_layout Standard
12379 For text, variable space can be inserted via the menu
12381 Insert\SpecialChar \menuseparator
12382 Formatting\SpecialChar \menuseparator
12384 \begin_inset space ~
12392 \begin_layout Standard
12393 This is a line with
12394 \begin_inset space \hspace{}
12399 \begin_inset space \thinspace{}
12405 \begin_layout Standard
12406 This is a line with
12407 \begin_inset space \hfill{}
12413 \begin_layout Subsection
12414 Space besides inline Formulas
12415 \begin_inset Index idx
12418 \begin_layout Plain Layout
12419 Space ! besides inline formulas
12427 \begin_layout Standard
12428 The space that surrounds inline formulas can be adjusted with the length
12436 \begin_inset Index idx
12439 \begin_layout Plain Layout
12448 The value of a length is set with the command
12455 \begin_inset Index idx
12458 \begin_layout Plain Layout
12466 that has the following scheme:
12469 \begin_layout Standard
12474 setlength{length name}{value}
12477 \begin_layout Standard
12485 \begin_inset space \thinspace{}
12491 \begin_layout Standard
12501 \begin_layout Standard
12502 is inserted in TeX-mode.
12504 \begin_inset space \thinspace{}
12507 mm space will now be set around all inline formulas:
12511 \begin_layout Plain Layout
12525 \begin_layout Standard
12526 This is a line with an inline formula
12527 \begin_inset Formula $A=B$
12531 \begin_inset space \thinspace{}
12534 mm surrounding space.
12538 \begin_layout Plain Layout
12552 \begin_layout Standard
12553 To return to the predefined value,
12559 is set to the value 0
12560 \begin_inset space \thinspace{}
12566 \begin_layout Section
12568 \begin_inset Index idx
12571 \begin_layout Plain Layout
12578 \begin_inset Index idx
12581 \begin_layout Plain Layout
12586 \begin_layout Plain Layout
12597 \begin_layout Plain Layout
12612 \begin_layout Standard
12613 Boxes for text are described in chapter
12620 \begin_inset space ~
12628 \begin_layout Subsection
12630 \begin_inset CommandInset label
12632 name "sub:Boxes-with-Frame"
12637 \begin_inset Index idx
12640 \begin_layout Plain Layout
12649 \begin_layout Standard
12650 It is possible to frame formulas or parts of it with the commands
12657 \begin_inset Index idx
12660 \begin_layout Plain Layout
12675 \begin_inset Index idx
12678 \begin_layout Plain Layout
12689 \begin_layout Standard
12690 When one of these commands is inserted to a formula, a blue box appears
12691 within a frame to enter formula parts.
12698 an additional formula has to be created by
12702 within this box, because the box content will otherwise be treated as mathemati
12710 is used, a new formula is automatically created inside the frame.
12713 \begin_layout Standard
12720 is not suitable to frame displayed formulas because the formula will always
12721 be set in the size of the text.
12728 is in contrary not suitable to frame inline formulas, because the formula
12729 will always be set in the size of a displayed formula.
12732 \begin_layout Standard
12739 there is the command
12746 \begin_inset Index idx
12749 \begin_layout Plain Layout
12757 where additionally the frame width and the alignment can be specified.
12764 is used in the following scheme:
12767 \begin_layout Standard
12772 framebox[frame width][position]{box content}
12775 \begin_layout Standard
12776 The position can either be
12793 right aligns the formula in the box.
12794 When no position is given, the formula will be centered.
12795 \begin_inset Newline newline
12798 Is no width given, also no position can be given.
12799 In this case the frame width is adjusted to the box content like for
12808 \begin_layout Standard
12815 is inserted, a box appears containing three blue boxes.
12816 The first two boxes are surrounded by brackets and denote the two optional
12818 The third box is for formula parts like for
12827 \begin_layout Standard
12829 \begin_inset Tabular
12830 <lyxtabular version="3" rows="5" columns="2">
12831 <features tabularvalignment="middle">
12832 <column alignment="center" valignment="top" width="0">
12833 <column alignment="center" valignment="top" width="0">
12835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12838 \begin_layout Plain Layout
12844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12847 \begin_layout Plain Layout
12849 \begin_inset Note Note
12852 \begin_layout Plain Layout
12859 is only used as spacer.
12871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12874 \begin_layout Plain Layout
12881 \begin_layout Plain Layout
12900 \begin_layout Plain Layout
12914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12917 \begin_layout Plain Layout
12918 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12931 \begin_layout Plain Layout
12938 \begin_layout Plain Layout
12953 \begin_layout Plain Layout
12967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12970 \begin_layout Plain Layout
12971 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12984 \begin_layout Plain Layout
12991 \begin_layout Plain Layout
13005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13008 \begin_layout Plain Layout
13009 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
13019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13022 \begin_layout Plain Layout
13029 \begin_layout Plain Layout
13039 \begin_inset Formula $\to$
13043 \begin_inset Formula $\to$
13056 \begin_layout Plain Layout
13066 \begin_inset Formula $\downarrow$
13074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13077 \begin_layout Plain Layout
13078 \begin_inset Formula $\raisebox{6mm}{}$
13082 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
13086 \begin_inset Formula $\raisebox{-4mm}{}$
13102 \begin_layout Standard
13103 The frame thickness can also be adjusted.
13104 To do this the following commands have to be inserted in TeX-mode before
13108 \begin_layout Standard
13118 \begin_inset Quotes eld
13122 \begin_inset Quotes erd
13136 \begin_inset Quotes eld
13140 \begin_inset Quotes erd
13146 \begin_layout Standard
13147 \begin_inset Quotes eld
13151 \begin_inset Quotes erd
13154 specifies the minimal distance between the frame and the first character
13156 An example for this is the following framed formula:
13160 \begin_layout Plain Layout
13172 \begin_inset Formula \[
13178 Before this formula the commands
13181 \begin_layout Standard
13203 \begin_layout Standard
13204 were inserted in TeX-mode.
13205 The given values are used for all following boxes.
13208 \begin_layout Standard
13209 To return to the standard frame size, the command
13212 \begin_layout Standard
13237 \begin_layout Plain Layout
13251 \begin_layout Standard
13252 is inserted in TeX-mode before the next formula.
13255 \begin_layout Subsection
13256 Boxes without Frame
13257 \begin_inset CommandInset label
13259 name "sub:Boxes-without-Frame"
13264 \begin_inset Index idx
13267 \begin_layout Plain Layout
13268 Boxes ! without frame
13276 \begin_layout Standard
13277 For boxes without a frame there are the following box commands:
13284 \begin_inset Index idx
13287 \begin_layout Plain Layout
13302 \begin_inset Index idx
13305 \begin_layout Plain Layout
13320 \begin_inset Index idx
13323 \begin_layout Plain Layout
13334 \begin_layout Standard
13341 a box can be super- or subscripted.
13342 But in contrary to normal super- and subscripting, the characters in the
13343 box keep their font size.
13350 is used in the following scheme:
13353 \begin_layout Standard
13358 raisebox{height}{box content}
13361 \begin_layout Standard
13362 When the box should contain a formula, an extra formula is needed like for
13373 \begin_inset Note Greyedout
13376 \begin_layout Plain Layout
13387 this extra formula is created by pressing
13391 twice instead of once because LyX doesn't yet support
13405 \begin_layout Standard
13407 \begin_inset Tabular
13408 <lyxtabular version="3" rows="4" columns="2">
13409 <features tabularvalignment="middle">
13410 <column alignment="center" valignment="top" width="0">
13411 <column alignment="center" valignment="top" width="0">
13413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13416 \begin_layout Plain Layout
13422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13425 \begin_layout Plain Layout
13433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13436 \begin_layout Plain Layout
13440 \begin_inset Formula $\to$
13446 \begin_inset Formula $\to$
13454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13457 \begin_layout Plain Layout
13458 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13471 \begin_layout Plain Layout
13475 \begin_inset Formula $\to$
13481 \begin_inset Formula $\to$
13489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13492 \begin_layout Plain Layout
13493 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13506 \begin_layout Plain Layout
13510 \begin_inset Formula $\to$
13529 \begin_layout Plain Layout
13543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13546 \begin_layout Plain Layout
13547 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13563 \begin_layout Standard
13588 , with the difference that there is no frame.
13591 \begin_layout Subsection
13593 \begin_inset CommandInset label
13595 name "sub:Colored-Boxes"
13600 \begin_inset Index idx
13603 \begin_layout Plain Layout
13612 \begin_layout Standard
13613 To be able to use all commands explained in this section, the LaTeX-package
13622 \begin_layout Plain Layout
13627 is part of every LaTeX standard installation.
13633 \begin_inset Index idx
13636 \begin_layout Plain Layout
13642 has to be loaded in the LaTeX-preamble with the line
13646 \begin_layout Plain Layout
13647 When text is colored somewhere in the document with a predefined color,
13648 LyX loads the LaTeX-package
13653 Thus it is possible that the package is loaded twice, but this doesn't
13660 \begin_inset Note Note
13663 \begin_layout Plain Layout
13664 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13673 \begin_layout Standard
13681 \begin_layout Standard
13682 \begin_inset VSpace medskip
13685 To color boxes, the command
13692 \begin_inset Index idx
13695 \begin_layout Plain Layout
13703 is used in the following scheme:
13706 \begin_layout Standard
13711 colorbox{color}{box content}
13714 \begin_layout Standard
13715 The box content can also be a box and a
13721 can also be part of another box (see the 2nd and 3rd example).
13722 When the box should contain a formula, an extra formula has to be created,
13723 the same way as for
13733 \begin_layout Plain Layout
13734 This also applies for the command
13748 \begin_layout Standard
13749 One of the following predefined colors can be chosen:
13752 \begin_layout Standard
13786 \begin_layout Standard
13788 \begin_inset Tabular
13789 <lyxtabular version="3" rows="4" columns="2">
13790 <features tabularvalignment="middle">
13791 <column alignment="center" valignment="top" width="0">
13792 <column alignment="center" valignment="top" width="0">
13794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13797 \begin_layout Plain Layout
13803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13806 \begin_layout Plain Layout
13808 \begin_inset Note Note
13811 \begin_layout Plain Layout
13818 is only used as spacer.
13830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13833 \begin_layout Plain Layout
13837 \begin_inset Formula $\to$
13847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13850 \begin_layout Plain Layout
13851 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13864 \begin_layout Plain Layout
13868 \begin_inset Formula $\to$
13879 \begin_layout Plain Layout
13893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13896 \begin_layout Plain Layout
13897 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13910 \begin_layout Plain Layout
13917 \begin_layout Plain Layout
13929 \begin_inset Formula $\to$
13948 \begin_layout Plain Layout
13962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13965 \begin_layout Plain Layout
13966 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13982 \begin_layout Standard
13989 only colors the box but not the characters in the box.
13990 To color all characters, the whole formula is highlighted and the wanted
13991 color is chosen in the
13994 \begin_inset space ~
14000 The dialog can be called with the toolbar button
14001 \begin_inset Graphics
14002 filename ../images/dialog-show_character.png
14009 Edit\SpecialChar \menuseparator
14011 \begin_inset space ~
14014 Style\SpecialChar \menuseparator
14018 The formula number has then the same color as the formula.
14019 When the formula number should get another color than the formula characters,
14020 the color must be changed within the formula.
14023 \begin_layout Standard
14027 \begin_layout Standard
14030 \begin_inset Formula \begin{equation}
14031 \int A=B\label{eq:red}
14039 \begin_inset Formula \begin{equation}
14040 \textcolor{red}{\int A=B}\label{eq:redgreen}
14048 \begin_layout Standard
14050 \begin_inset CommandInset ref
14056 is completely colored red.
14057 \begin_inset Newline newline
14061 \begin_inset CommandInset ref
14063 reference "eq:redgreen"
14067 was first completely colored green to set the color for the formula number.
14068 Subsequently the formula characters were colored red.
14071 \begin_layout Standard
14072 \begin_inset VSpace bigskip
14075 To color the frame different than the rest of the box, the command
14082 \begin_inset Index idx
14085 \begin_layout Plain Layout
14093 is used in the following scheme:
14096 \begin_layout Standard
14101 fcolorbox{frame color}{color}{box content}
14104 \begin_layout Standard
14111 is an extension of the command
14118 The frame width is set, like for
14141 \begin_layout Plain Layout
14153 \begin_inset Formula \[
14154 \fcolorbox{cyan}{magenta}{A=B}
14163 \begin_layout Plain Layout
14177 \begin_layout Standard
14178 This formula was created with the command
14179 \begin_inset Newline newline
14187 \begin_inset Formula $\to$
14193 \begin_inset Formula $\to$
14203 \begin_layout Standard
14204 \begin_inset VSpace bigskip
14207 To use other colors than the predefined ones, they have to be defined first.
14210 \begin_layout Standard
14211 One can for example define the color
14212 \begin_inset Quotes eld
14220 \begin_inset Quotes erd
14223 with the LaTeX-preamble line:
14226 \begin_layout Standard
14231 definecolor{darkgreen}{cmyk}{0.5,
14246 \begin_inset Index idx
14249 \begin_layout Plain Layout
14260 \begin_layout Standard
14265 is the color space that denotes the colors
14282 The four comma separated numbers are the portion factor for the corresponding
14283 colors of the color space.
14284 The factors can be in the range of 0
14285 \begin_inset space \thinspace{}
14289 \begin_inset space \thinspace{}
14297 also the color space
14301 can be used for definitions.
14318 , so that there are in this case three portion factors for the corresponding
14320 Furthermore there is the color space
14324 with one portion factor for the gray value.
14327 \begin_layout Standard
14328 As example a framed box with the new defined color
14332 where the characters have been colored
14337 \begin_inset Formula \begin{equation}
14338 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14346 \begin_layout Standard
14347 Self-defined colors can also be used for text with the help of the command
14355 \begin_inset Index idx
14358 \begin_layout Plain Layout
14367 \begin_layout Standard
14371 \begin_layout Plain Layout
14375 textcolor{darkgreen}{
14381 \begin_inset Quotes eld
14385 \begin_inset Quotes erd
14392 \begin_layout Plain Layout
14402 \begin_layout Standard
14410 \begin_inset Index idx
14413 \begin_layout Plain Layout
14421 is used in the scheme
14425 textcolor{color}{characters to color}
14430 \begin_layout Subsection
14432 \begin_inset CommandInset label
14434 name "sub:Paragraph-Boxes"
14439 \begin_inset Index idx
14442 \begin_layout Plain Layout
14443 Boxes ! as paragraph
14451 \begin_layout Standard
14452 A box that can contain several lines and paragraphs, a so called paragraph
14453 box (parbox), can be created with the menu
14455 Insert\SpecialChar \menuseparator
14458 or the toolbar button
14459 \begin_inset Graphics
14460 filename ../images/box-insert.png
14468 \begin_layout Standard
14469 The following example shows a framed parbox in a line:
14472 \begin_layout Standard
14473 \begin_inset VSpace medskip
14477 \begin_inset Box Boxed
14487 height_special "totalheight"
14490 \begin_layout Plain Layout
14491 This is a paragraph box.
14493 \begin_inset space \thinspace{}
14496 cm long and can also contain formulas:
14497 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14508 \begin_layout Standard
14509 \begin_inset VSpace medskip
14515 \begin_layout Standard
14516 Such a box is created by right-clicking on the gray box inset.
14517 A dialog pops up showing the box properties.
14531 \begin_inset space \thinspace{}
14536 Vertical Box Alignment
14541 \begin_layout Standard
14542 \begin_inset VSpace medskip
14545 In LaTeX a parbox is created with the command
14552 \begin_inset Index idx
14555 \begin_layout Plain Layout
14563 that has the following scheme:
14566 \begin_layout Standard
14571 parbox[position]{width}{box content}
14574 \begin_layout Standard
14588 for bottom means that the box is aligned within the surrounding text with
14594 for top this is done with the first line.
14595 When no position is given, the box will be vertically centered, see section
14603 \begin_inset space ~
14608 manual for examples.
14611 \begin_layout Standard
14612 \begin_inset VSpace bigskip
14615 To frame formulas completely, including the formula number, the formula
14616 must be set into a parbox.
14617 To do this, the command
14631 is inserted in TeX-mode before the formula.
14639 \begin_inset Index idx
14642 \begin_layout Plain Layout
14650 is hereby the line width set for the document.
14651 Because the frame is outside the parbox, 2
14652 \begin_inset space \thinspace{}
14655 times the frame separation and the frame thickness must be subtracted from
14657 As this is not automatically done by LyX due to a bug
14661 \begin_layout Plain Layout
14662 \begin_inset CommandInset href
14664 name "LyX-bug #4483"
14665 target "http://www.lyx.org/trac/ticket/4483"
14674 , TeX-mode has to be used.
14675 To be able to multiply and subtract in arguments, the LaTeX-package
14683 \begin_layout Plain Layout
14688 is part of every LaTeX standard installation.
14694 \begin_inset Index idx
14697 \begin_layout Plain Layout
14703 must be loaded in the LaTeX-preamble with the line
14706 \begin_layout Standard
14714 \begin_layout Standard
14715 Behind the formula both boxes are closed by entering
14720 Here is an example:
14724 \begin_layout Plain Layout
14738 \begin_layout Standard
14742 \begin_layout Plain Layout
14760 \begin_inset Formula \begin{equation}
14761 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14770 \begin_layout Plain Layout
14781 \begin_layout Plain Layout
14795 \begin_layout Standard
14796 \begin_inset VSpace medskip
14799 As a parbox is used as argument of
14805 , there is in this case no difference between
14820 \begin_layout Standard
14821 \begin_inset VSpace bigskip
14824 Paragraph boxes are very useful to comment formulas directly.
14831 is used in combination with the command
14845 \begin_inset CommandInset ref
14847 reference "sub:User-defined-Numbering"
14854 \begin_layout Standard
14855 An example of a formula commented with
14864 \begin_layout Standard
14868 \begin_layout Plain Layout
14881 This is a description.
14882 It is distinctly separated from the formula and multiline.
14886 \begin_layout Plain Layout
14898 \begin_layout Standard
14899 Such a formula must be inserted completely in TeX-mode because LyX does
14900 not yet support the command
14907 The formula is created with the following command sequence:
14910 \begin_layout Standard
14923 is inserted in TeX-mode.
14927 \begin_layout Plain Layout
14928 When the formula style
14940 can also be replaced by
14947 (formula styles see
14948 \begin_inset CommandInset ref
14950 reference "sec:Formula-Styles"
14959 Then the description follows as normal text and finally
14965 is inserted in TeX-mode.
14978 hereby create a displayed formula.
14981 \begin_layout Standard
14988 can be seen in this example that was
14989 \begin_inset Quotes eld
14993 \begin_inset Quotes erd
14996 using the mathematical textmode:
14997 \begin_inset Formula \[
14998 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
15006 \begin_layout Section
15008 \begin_inset Index idx
15011 \begin_layout Plain Layout
15020 \begin_layout Subsection
15022 \begin_inset CommandInset label
15024 name "sub:Big-Operators"
15029 \begin_inset Index idx
15032 \begin_layout Plain Layout
15039 \begin_inset Index idx
15042 \begin_layout Plain Layout
15049 \begin_inset Index idx
15052 \begin_layout Plain Layout
15061 \begin_layout Standard
15062 To be able to use all integral operators listed here, the option
15064 Use esint package automatically
15066 must be set in the document settings under
15069 \begin_inset space ~
15077 \begin_layout Standard
15078 \begin_inset space \hfill{}
15082 \begin_inset Tabular
15083 <lyxtabular version="3" rows="11" columns="2">
15084 <features tabularvalignment="middle">
15085 <column alignment="center" valignment="top" width="0pt">
15086 <column alignment="center" valignment="top" width="0pt">
15088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15091 \begin_layout Plain Layout
15097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15100 \begin_layout Plain Layout
15108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15111 \begin_layout Plain Layout
15115 \begin_inset Index idx
15118 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\int$
15145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\oint$
15170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15173 \begin_layout Plain Layout
15181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15184 \begin_layout Plain Layout
15185 \begin_inset Formula $\ointctrclockwise$
15195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15209 \begin_layout Plain Layout
15210 \begin_inset Formula $\ointclockwise$
15220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15223 \begin_layout Plain Layout
15231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15234 \begin_layout Plain Layout
15235 \begin_inset Formula $\sqint$
15245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15248 \begin_layout Plain Layout
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15259 \begin_layout Plain Layout
15261 \begin_inset Formula $\fint$
15271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15274 \begin_layout Plain Layout
15282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15285 \begin_layout Plain Layout
15287 \begin_inset Formula $\landupint$
15297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15300 \begin_layout Plain Layout
15308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15311 \begin_layout Plain Layout
15313 \begin_inset Formula $\landdownint$
15323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15326 \begin_layout Plain Layout
15334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15337 \begin_layout Plain Layout
15338 \begin_inset Formula $\bigcap$
15348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15351 \begin_layout Plain Layout
15359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15362 \begin_layout Plain Layout
15363 \begin_inset Formula $\bigcup$
15377 \begin_inset space \hfill{}
15381 \begin_inset Tabular
15382 <lyxtabular version="3" rows="11" columns="2">
15383 <features tabularvalignment="middle">
15384 <column alignment="center" valignment="top" width="0pt">
15385 <column alignment="center" valignment="top" width="0pt">
15387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15390 \begin_layout Plain Layout
15396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15399 \begin_layout Plain Layout
15407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15410 \begin_layout Plain Layout
15414 \begin_inset Index idx
15417 \begin_layout Plain Layout
15430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Plain Layout
15434 \begin_inset Formula $\sum$
15444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15447 \begin_layout Plain Layout
15451 \begin_inset Index idx
15454 \begin_layout Plain Layout
15467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15470 \begin_layout Plain Layout
15471 \begin_inset Formula $\prod$
15481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15484 \begin_layout Plain Layout
15492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15495 \begin_layout Plain Layout
15496 \begin_inset Formula $\coprod$
15506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15509 \begin_layout Plain Layout
15517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15520 \begin_layout Plain Layout
15521 \begin_inset Formula $\bigodot$
15531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15534 \begin_layout Plain Layout
15542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15545 \begin_layout Plain Layout
15546 \begin_inset Formula $\bigotimes$
15556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15559 \begin_layout Plain Layout
15567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15570 \begin_layout Plain Layout
15571 \begin_inset Formula $\bigoplus$
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15584 \begin_layout Plain Layout
15592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15595 \begin_layout Plain Layout
15596 \begin_inset Formula $\bigwedge$
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
15621 \begin_inset Formula $\bigvee$
15631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15634 \begin_layout Plain Layout
15642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15645 \begin_layout Plain Layout
15646 \begin_inset Formula $\bigsqcup$
15656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15659 \begin_layout Plain Layout
15667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15670 \begin_layout Plain Layout
15671 \begin_inset Formula $\biguplus$
15685 \begin_inset space \hfill{}
15691 \begin_layout Standard
15692 All big operators can also be inserted via the math toolbar button
15693 \begin_inset Graphics
15694 filename ../images/math/intop.png
15702 \begin_layout Standard
15703 The operators are called big because they are bigger than the sometimes
15704 equal looking binary operators.
15705 All big operators can have limits as described in the next subsection.
15708 \begin_layout Standard
15709 For all integral operators there is a second version available, ending on
15727 These operators are different from
15734 \begin_inset space \space{}
15737 in the style the operator limits are displayed, see
15738 \begin_inset CommandInset ref
15740 reference "sub:Operator-Limits"
15748 \begin_layout Subsubsection*
15749 Advice for Integrals
15752 \begin_layout Standard
15757 in an integral is an operator, that therefore has to be set upright.
15758 This is done by highlighting the
15762 and using the keyboard shortcut
15772 \begin_layout Plain Layout
15778 \begin_inset CommandInset ref
15780 reference "sub:Font-Styles"
15790 Finally the smallest space is inserted before the
15794 , as this is usual for operators.
15798 \begin_layout Standard
15800 \begin_inset Formula $\int A(x)dx$
15804 \begin_inset Newline newline
15808 \begin_inset Phantom HPhantom
15811 \begin_layout Plain Layout
15818 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15824 \begin_layout Standard
15825 For multiple integrals there are the following commands:
15826 \begin_inset VSpace medskip
15832 \begin_layout Standard
15833 \begin_inset space \hfill{}
15837 \begin_inset Tabular
15838 <lyxtabular version="3" rows="4" columns="2">
15839 <features tabularvalignment="middle">
15840 <column alignment="center" valignment="top" width="0">
15841 <column alignment="center" valignment="top" width="0">
15843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15846 \begin_layout Plain Layout
15852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15855 \begin_layout Plain Layout
15857 \begin_inset Note Note
15860 \begin_layout Plain Layout
15867 is only used as spacer.
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 $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
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 $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15932 \begin_layout Plain Layout
15940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15943 \begin_layout Plain Layout
15944 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15958 \begin_inset space \hfill{}
15962 \begin_inset Tabular
15963 <lyxtabular version="3" rows="4" columns="2">
15964 <features tabularvalignment="middle">
15965 <column alignment="center" valignment="top" width="0">
15966 <column alignment="center" valignment="top" width="0">
15968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15971 \begin_layout Plain Layout
15977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15980 \begin_layout Plain Layout
15988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15991 \begin_layout Plain Layout
15999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16002 \begin_layout Plain Layout
16003 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
16013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16016 \begin_layout Plain Layout
16024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16027 \begin_layout Plain Layout
16028 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
16038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16041 \begin_layout Plain Layout
16049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16052 \begin_layout Plain Layout
16053 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
16067 \begin_inset space \hfill{}
16073 \begin_layout Subsection
16075 \begin_inset CommandInset label
16077 name "sub:Operator-Limits"
16082 \begin_inset Index idx
16085 \begin_layout Plain Layout
16094 \begin_layout Standard
16095 Limits are created by super- and subscripts:
16098 \begin_layout Standard
16100 \begin_inset Tabular
16101 <lyxtabular version="3" rows="2" columns="2">
16102 <features tabularvalignment="middle">
16103 <column alignment="center" valignment="top" width="0pt">
16104 <column alignment="center" valignment="top" width="0pt">
16106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16109 \begin_layout Plain Layout
16115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16118 \begin_layout Plain Layout
16120 \begin_inset Note Note
16123 \begin_layout Plain Layout
16130 is only used as spacer.
16142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16145 \begin_layout Plain Layout
16154 \begin_layout Plain Layout
16164 \begin_inset Formula $\to$
16168 \begin_inset Formula $\to$
16176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16179 \begin_layout Plain Layout
16180 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16196 \begin_layout Standard
16197 Limits of inline formulas are set right beside the operator.
16198 Limits in displayed formulas are set above or below the operator, except
16199 for integral limits.
16202 \begin_layout Standard
16203 To force that the limits are set beside the operator, the cursor is set
16204 directly behind the operator and the limits type is changed with the menu
16207 Edit\SpecialChar \menuseparator
16208 Math\SpecialChar \menuseparator
16227 \begin_layout Standard
16228 The default limits type is this:
16229 \begin_inset Formula \[
16230 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16235 This is how it looks when the limits type was changed to
16242 \begin_inset Formula \[
16243 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16248 For integrals, except those ending with
16264 etc., the limits are by default set beside the operator.
16265 But for multiple integrals the limits are often set below the operator.
16266 In the following example the limits type was therefore set to
16270 and so set below the integrals:
16271 \begin_inset Formula \begin{equation}
16272 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16280 \begin_layout Standard
16281 \begin_inset VSpace medskip
16284 To specify conditions for limits, the commands
16291 \begin_inset Index idx
16294 \begin_layout Plain Layout
16309 \begin_inset Index idx
16312 \begin_layout Plain Layout
16321 To create for example this expression
16322 \begin_inset Formula \begin{equation}
16323 \sum_{\begin{subarray}{c}
16327 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16335 \begin_layout Standard
16336 the following has to be done:
16337 \begin_inset Newline newline
16352 \begin_layout Plain Layout
16364 One is now in a blue box under the summation operator and insert there
16373 \begin_layout Plain Layout
16385 The blue box is now within a purple box and now several lines can be written
16387 A new line is created by inserting a line break (
16390 arg "newline-insert newline"
16395 \begin_inset Newline newline
16400 0<k<1000 Ctrl+Return
16401 \begin_inset Newline newline
16406 is typed in, a new box appears below for the new line.
16409 \begin_layout Standard
16410 The alignment of the lines can be changed to left aligned with the
16420 Edit\SpecialChar \menuseparator
16424 To get right alignment,
16432 \begin_layout Plain Layout
16443 is inserted at the beginning of the line.
16446 \begin_layout Standard
16459 with the difference that the lines are always centered.
16462 \begin_layout Standard
16463 \begin_inset VSpace bigskip
16467 \begin_inset CommandInset ref
16469 reference "eq:substack"
16473 there can be too much space beside an operator, because the characters
16474 following the operator are set beside the limits.
16477 \begin_layout Standard
16478 To avoid this, the following macro can be used in the LaTeX-preamble:
16481 \begin_layout Standard
16495 \begin_inset Newline newline
16507 \begin_inset Newline newline
16514 mathclapinternal #1#2{
16518 mathsurround =0pt #1{#2}$}}
16521 \begin_layout Standard
16522 This defines the command
16529 \begin_inset Index idx
16532 \begin_layout Plain Layout
16540 that sets the width of the limit to 0
16541 \begin_inset space \thinspace{}
16545 The command scheme is
16548 \begin_layout Standard
16556 \begin_layout Standard
16557 where the limit can consist of several conditions.
16560 \begin_layout Standard
16562 \begin_inset CommandInset ref
16564 reference "eq:substack"
16568 , one uses the command
16571 \begin_layout Standard
16584 \begin_layout Plain Layout
16593 0<k<1000 Ctrl+Return
16596 \begin_layout Standard
16597 to create the lower limit.
16598 The summand is now directly behind the summation operator:
16599 \begin_inset Formula \[
16600 \sum_{\mathclap{\substack{0<k<1000\\
16612 \begin_layout Standard
16613 \begin_inset VSpace bigskip
16616 How to use one limit for several operators is described in
16617 \begin_inset CommandInset ref
16619 reference "sub:Self-defined-Operators"
16626 \begin_layout Subsection
16628 \begin_inset CommandInset label
16630 name "sub:Binary-Operators"
16635 \begin_inset Index idx
16638 \begin_layout Plain Layout
16647 \begin_layout Standard
16648 Binary operators are surrounded by space when there is a character before
16650 \begin_inset VSpace medskip
16656 \begin_layout Standard
16657 \begin_inset space \hfill{}
16661 \begin_inset Tabular
16662 <lyxtabular version="3" rows="13" columns="2">
16663 <features tabularvalignment="middle">
16664 <column alignment="center" valignment="top" width="0pt">
16665 <column alignment="center" valignment="top" width="0pt">
16667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16670 \begin_layout Plain Layout
16672 \begin_inset Note Note
16675 \begin_layout Plain Layout
16682 is only used as spacer.
16692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16695 \begin_layout Plain Layout
16703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16706 \begin_layout Plain Layout
16712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16715 \begin_layout Plain Layout
16716 \begin_inset Formula $+$
16726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16729 \begin_layout Plain Layout
16735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16738 \begin_layout Plain Layout
16739 \begin_inset Formula $-$
16749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16752 \begin_layout Plain Layout
16760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16763 \begin_layout Plain Layout
16764 \begin_inset Formula $\pm$
16774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16777 \begin_layout Plain Layout
16785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16788 \begin_layout Plain Layout
16789 \begin_inset Formula $\mp$
16799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16802 \begin_layout Plain Layout
16810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16813 \begin_layout Plain Layout
16814 \begin_inset Formula $\cdot$
16824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16827 \begin_layout Plain Layout
16835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16838 \begin_layout Plain Layout
16839 \begin_inset Formula $\times$
16849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16852 \begin_layout Plain Layout
16860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16863 \begin_layout Plain Layout
16864 \begin_inset Formula $\div$
16874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16877 \begin_layout Plain Layout
16881 \begin_layout Plain Layout
16894 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $*$
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\star$
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16959 \begin_layout Plain Layout
16960 \begin_inset Formula $\circ$
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16973 \begin_layout Plain Layout
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16984 \begin_layout Plain Layout
16985 \begin_inset Formula $\diamond$
16995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16998 \begin_layout Plain Layout
17006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\bullet$
17024 \begin_inset space \hfill{}
17028 \begin_inset Tabular
17029 <lyxtabular version="3" rows="13" columns="2">
17030 <features tabularvalignment="middle">
17031 <column alignment="center" valignment="top" width="0pt">
17032 <column alignment="center" valignment="top" width="0pt">
17034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17037 \begin_layout Plain Layout
17043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17057 \begin_layout Plain Layout
17065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17068 \begin_layout Plain Layout
17069 \begin_inset Formula $\nabla$
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17082 \begin_layout Plain Layout
17090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17093 \begin_layout Plain Layout
17094 \begin_inset Formula $\bigtriangledown$
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17107 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17119 \begin_inset Formula $\bigtriangleup$
17129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17132 \begin_layout Plain Layout
17140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17143 \begin_layout Plain Layout
17144 \begin_inset Formula $\Box$
17154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17157 \begin_layout Plain Layout
17165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17168 \begin_layout Plain Layout
17169 \begin_inset Formula $\cap$
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17182 \begin_layout Plain Layout
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\cup$
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\dagger$
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17243 \begin_layout Plain Layout
17244 \begin_inset Formula $\ddagger$
17254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17257 \begin_layout Plain Layout
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17268 \begin_layout Plain Layout
17269 \begin_inset Formula $\wr$
17279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17294 \begin_inset Formula $\bigcirc$
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17318 \begin_layout Plain Layout
17319 \begin_inset Formula $\wedge$
17329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17332 \begin_layout Plain Layout
17340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17343 \begin_layout Plain Layout
17344 \begin_inset Formula $\vee$
17358 \begin_inset space \hfill{}
17362 \begin_inset Tabular
17363 <lyxtabular version="3" rows="13" columns="2">
17364 <features tabularvalignment="middle">
17365 <column alignment="center" valignment="top" width="0pt">
17366 <column alignment="center" valignment="top" width="0pt">
17368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17371 \begin_layout Plain Layout
17377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17391 \begin_layout Plain Layout
17399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17402 \begin_layout Plain Layout
17403 \begin_inset Formula $\oplus$
17413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17416 \begin_layout Plain Layout
17424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17427 \begin_layout Plain Layout
17428 \begin_inset Formula $\ominus$
17438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17441 \begin_layout Plain Layout
17449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17452 \begin_layout Plain Layout
17453 \begin_inset Formula $\otimes$
17463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17466 \begin_layout Plain Layout
17474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17477 \begin_layout Plain Layout
17478 \begin_inset Formula $\oslash$
17488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17491 \begin_layout Plain Layout
17499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17502 \begin_layout Plain Layout
17503 \begin_inset Formula $\odot$
17513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17516 \begin_layout Plain Layout
17524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17527 \begin_layout Plain Layout
17528 \begin_inset Formula $\amalg$
17538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17541 \begin_layout Plain Layout
17549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17552 \begin_layout Plain Layout
17553 \begin_inset Formula $\uplus$
17563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17566 \begin_layout Plain Layout
17574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17577 \begin_layout Plain Layout
17578 \begin_inset Formula $\setminus$
17588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17591 \begin_layout Plain Layout
17599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17602 \begin_layout Plain Layout
17603 \begin_inset Formula $\sqcap$
17613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17616 \begin_layout Plain Layout
17624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17627 \begin_layout Plain Layout
17628 \begin_inset Formula $\sqcup$
17638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17641 \begin_layout Plain Layout
17649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17652 \begin_layout Plain Layout
17653 \begin_inset Formula $\triangleleft$
17663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17666 \begin_layout Plain Layout
17674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17677 \begin_layout Plain Layout
17678 \begin_inset Formula $\triangleright$
17692 \begin_inset space \hfill{}
17698 \begin_layout Standard
17699 All binary operators can also be inserted via the math toolbar button
17700 \begin_inset Graphics
17701 filename ../images/math/pm.png
17709 \begin_layout Standard
17710 To typeset the Laplace operator also
17727 \begin_inset Formula $\nabla^{2}$
17730 ) can be used instead of
17739 \begin_layout Standard
17746 Insert\SpecialChar \menuseparator
17758 \begin_layout Subsection
17759 Self-defined Operators
17760 \begin_inset CommandInset label
17762 name "sub:Self-defined-Operators"
17767 \begin_inset Index idx
17770 \begin_layout Plain Layout
17771 Operators ! self-defined
17779 \begin_layout Standard
17780 With the help of the command
17784 DeclareMathOperator
17787 \begin_inset Index idx
17790 \begin_layout Plain Layout
17795 DeclareMathOperator
17800 custom operators can be defined in the LaTeX-preamble.
17801 Its command scheme is:
17804 \begin_layout Standard
17809 DeclareMathOperator{new command}{display}
17812 \begin_layout Standard
17813 Display can be characters or symbols that define how the operator looks
17815 To define a big operator a * is set behind the command.
17816 All self-defined big operators can have limits as described in
17817 \begin_inset CommandInset ref
17819 reference "sub:Operator-Limits"
17826 \begin_layout Standard
17827 For example the LaTeX-preamble line
17830 \begin_layout Standard
17835 DeclareMathOperator*{
17842 \begin_layout Standard
17843 defines the command
17849 , that inserts a big operator consisting of the lozenge symbol from
17850 \begin_inset CommandInset ref
17852 reference "sub:Miscellaneous-Symbols"
17857 \begin_inset Formula \[
17858 \Lozenge_{n=1}^{\infty}
17863 The command for this formula is:
17874 \begin_inset Formula $\to$
17880 \begin_layout Standard
17881 \begin_inset VSpace bigskip
17884 When self-defined operators are not used several times in the document,
17885 they can also be defined with the commands
17892 \begin_inset Index idx
17895 \begin_layout Plain Layout
17910 \begin_inset Index idx
17913 \begin_layout Plain Layout
17921 , which have the following scheme:
17924 \begin_layout Standard
17938 \begin_layout Standard
17945 defines big operators,
17954 \begin_layout Standard
17962 \begin_inset space \thinspace{}
17966 \begin_inset space \space{}
17969 be used to use one limit for several operators:
17972 \begin_layout Standard
17973 \begin_inset Formula \[
17974 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
17982 \begin_layout Standard
17983 The command for the formula above is:
17984 \begin_inset Newline newline
18003 \begin_layout Plain Layout
18015 \begin_inset Formula $\to$
18024 \begin_layout Plain Layout
18038 \begin_layout Section
18040 \begin_inset Index idx
18043 \begin_layout Plain Layout
18052 \begin_layout Subsection
18054 \begin_inset CommandInset label
18056 name "sub:Font-Styles"
18061 \begin_inset Index idx
18064 \begin_layout Plain Layout
18073 \begin_layout Standard
18074 Latin letters in formulas can be set in one of the following font styles:
18075 \begin_inset VSpace -2mm
18081 \begin_layout Standard
18083 \begin_inset Tabular
18084 <lyxtabular version="3" rows="7" columns="3">
18085 <features tabularvalignment="middle">
18086 <column alignment="center" valignment="top" width="0">
18087 <column alignment="center" valignment="top" width="0">
18088 <column alignment="center" valignment="top" width="0">
18090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18093 \begin_layout Plain Layout
18099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18102 \begin_layout Plain Layout
18108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18111 \begin_layout Plain Layout
18119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18122 \begin_layout Plain Layout
18131 \begin_layout Plain Layout
18147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18150 \begin_layout Plain Layout
18151 \begin_inset Formula $\mathbb{ABC}$
18159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18162 \begin_layout Plain Layout
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18178 \begin_layout Plain Layout
18187 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18207 \begin_inset Formula $\mathbf{AbC}$
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18218 \begin_layout Plain Layout
18231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18234 \begin_layout Plain Layout
18243 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18263 \begin_inset Formula $\boldsymbol{AbC}$
18271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18277 arg "font-boldsymbol"
18287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18290 \begin_layout Plain Layout
18299 \begin_layout Plain Layout
18315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18318 \begin_layout Plain Layout
18319 \begin_inset Formula $\mathcal{ABC}$
18327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18330 \begin_layout Plain Layout
18343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18346 \begin_layout Plain Layout
18355 \begin_layout Plain Layout
18371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18374 \begin_layout Plain Layout
18375 \begin_inset Formula $\mathfrak{AbC}$
18383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18386 \begin_layout Plain Layout
18394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18397 \begin_layout Plain Layout
18406 \begin_layout Plain Layout
18422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18425 \begin_layout Plain Layout
18426 \begin_inset Formula $\mathscr{AbC}$
18434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18437 \begin_layout Plain Layout
18451 \begin_layout Standard
18453 \begin_inset Tabular
18454 <lyxtabular version="3" rows="5" columns="3">
18455 <features tabularvalignment="middle">
18456 <column alignment="center" valignment="top" width="0">
18457 <column alignment="center" valignment="top" width="0">
18458 <column alignment="center" valignment="top" width="0">
18460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18463 \begin_layout Plain Layout
18469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18472 \begin_layout Plain Layout
18478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18481 \begin_layout Plain Layout
18489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18492 \begin_layout Plain Layout
18501 \begin_layout Plain Layout
18517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18520 \begin_layout Plain Layout
18521 \begin_inset Formula $\mathit{AbC}$
18529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18532 \begin_layout Plain Layout
18540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18543 \begin_layout Plain Layout
18552 \begin_layout Plain Layout
18568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18571 \begin_layout Plain Layout
18572 \begin_inset Formula $\mathrm{AbC}$
18580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18583 \begin_layout Plain Layout
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18599 \begin_layout Plain Layout
18608 \begin_layout Plain Layout
18624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18627 \begin_layout Plain Layout
18628 \begin_inset Formula $\mathsf{AbC}$
18636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18639 \begin_layout Plain Layout
18652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18655 \begin_layout Plain Layout
18664 \begin_layout Plain Layout
18680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18683 \begin_layout Plain Layout
18684 \begin_inset Formula $\mathtt{AbC}$
18692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18695 \begin_layout Plain Layout
18698 arg "font-typewriter"
18714 \begin_layout Standard
18715 \begin_inset Note Greyedout
18718 \begin_layout Plain Layout
18735 can only be used for big letters.
18743 \begin_layout Standard
18744 Predefined is the style
18753 \begin_layout Standard
18754 The style commands work also for letters in mathematical constructs:
18755 \begin_inset Formula \[
18756 \mathfrak{A=\frac{b}{C}}
18764 \begin_layout Standard
18765 Characters in mathematical text don't appear in a math font style but in
18766 the text font style
18773 That their style can't be set correctly via the text style dialog is a
18778 \begin_layout Plain Layout
18779 \begin_inset CommandInset href
18781 name "LyX-bug #4629"
18782 target "http://www.lyx.org/trac/ticket/4629"
18794 \begin_layout Standard
18795 Instead of the style commands the dialog
18797 Edit\SpecialChar \menuseparator
18798 Math\SpecialChar \menuseparator
18801 or the toolbar button
18802 \begin_inset Graphics
18803 filename ../images/math/font.png
18811 \begin_layout Subsection
18813 \begin_inset CommandInset label
18815 name "sub:Bold-Formulas"
18820 \begin_inset Index idx
18823 \begin_layout Plain Layout
18832 \begin_layout Standard
18833 To make a complete formula bold, the command
18839 from the previous subsection cannot be used, because it doesn't work for
18840 small Greek letters.
18841 Furthermore it prints Latin letters always upright, like in the following
18845 \begin_layout Standard
18846 \begin_inset Formula \[
18847 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18855 \begin_layout Standard
18856 To display the formula correctly, the command
18863 \begin_inset Formula \[
18864 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18869 It is also possible to set the formula in a
18871 boldmath environment
18874 This environment is created by inserting the command
18881 \begin_inset Index idx
18884 \begin_layout Plain Layout
18893 To end the environment, the command
18900 \begin_inset Index idx
18903 \begin_layout Plain Layout
18911 is inserted in TeX-mode.
18915 \begin_layout Plain Layout
18925 \begin_inset Formula \[
18926 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
18935 \begin_layout Plain Layout
18947 \begin_layout Subsection
18949 \begin_inset Index idx
18952 \begin_layout Plain Layout
18961 \begin_layout Standard
18962 Formulas can be colored like normal text: Highlight a formula or a formula
18968 Here is a formula in magenta:
18969 \begin_inset Formula \[
18970 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
18978 \begin_layout Standard
18979 You can also define your own colors as described in
18980 \begin_inset CommandInset ref
18982 reference "sub:Colored-Boxes"
18987 They can be used with the TeX code command
18994 \begin_inset Index idx
18997 \begin_layout Plain Layout
19008 \begin_layout Standard
19013 textcolor{color}{characters or formula}
19016 \begin_layout Standard
19017 The following example was colored completely dark green and partly red:
19020 \begin_layout Standard
19024 \begin_layout Plain Layout
19028 textcolor{darkgreen}{
19034 \begin_inset Formula \[
19035 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19044 \begin_layout Plain Layout
19054 \begin_layout Standard
19055 Due to a bug in LyX only complete formulas can be colored with self-defined
19060 \begin_layout Plain Layout
19061 \begin_inset CommandInset href
19063 name "LyX-bug #5269"
19064 target "http://www.lyx.org/trac/ticket/5269"
19076 \begin_layout Subsection
19078 \begin_inset CommandInset label
19080 name "sub:Font-Sizes"
19085 \begin_inset Index idx
19088 \begin_layout Plain Layout
19097 \begin_layout Standard
19098 For characters in formulas there are, analog to characters in text, the
19099 following size commands:
19102 \begin_layout Standard
19146 \begin_inset Newline newline
19168 \begin_layout Standard
19169 The size produced by the commands depends on the document font size, that
19170 corresponds with the command
19177 The other commands produce smaller or larger sizes than
19184 The font size can however not exceed a certain value.
19185 Is for example the document font size 12
19186 \begin_inset space \thinspace{}
19195 switches to the same size as
19205 \begin_layout Standard
19206 A size command is inserted in TeX-mode before the formula and sets the size
19207 for all following formula and text characters.
19208 To switch back to the initial size, the command
19214 is inserted behind the formula in TeX-mode.
19217 \begin_layout Standard
19218 \begin_inset Newpage newpage
19224 \begin_layout Standard
19225 Within a formula the size can be changed using the following size commands:
19228 \begin_layout Standard
19231 \begin_inset Tabular
19232 <lyxtabular version="3" rows="5" columns="2">
19233 <features tabularvalignment="middle">
19234 <column alignment="center" valignment="top" width="0">
19235 <column alignment="center" valignment="top" width="0">
19237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19240 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19251 \begin_inset Note Note
19254 \begin_layout Plain Layout
19261 is only used as spacer.
19273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19276 \begin_layout Plain Layout
19280 \begin_inset Index idx
19283 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19338 \begin_layout Plain Layout
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19349 \begin_layout Plain Layout
19350 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19363 \begin_layout Plain Layout
19371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19374 \begin_layout Plain Layout
19375 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19391 \begin_layout Standard
19392 After entering these commands, a blue box appears in which the formula parts
19396 \begin_layout Standard
19397 There is a further method to change the font size, that though only works
19398 for symbols or letters in mathematical text.
19399 To use it, one of the above text size commands is inserted in mathematical
19401 All following characters until the end of the mathematical text or until
19402 another size command will have the selected size.
19404 \begin_inset VSpace -2mm
19410 \begin_layout Standard
19414 \begin_layout Plain Layout
19424 \begin_inset Formula \[
19425 A=\frac{B}{c}\cdot\maltese
19431 \begin_inset Formula \[
19432 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19441 \begin_layout Plain Layout
19453 \begin_layout Standard
19454 \begin_inset VSpace medskip
19457 Before both formulas the command
19464 The command for the second formula is:
19465 \begin_inset Newline newline
19476 \begin_layout Plain Layout
19491 \begin_layout Plain Layout
19506 \begin_layout Plain Layout
19521 \begin_layout Plain Layout
19531 \begin_inset Formula $\to$
19535 \begin_inset Formula $\to$
19539 \begin_inset Newline newline
19543 \begin_inset space \hspace*{}
19557 \begin_layout Plain Layout
19572 \begin_layout Plain Layout
19587 \begin_layout Plain Layout
19599 \begin_layout Standard
19600 If a symbol cannot be displayed in different sizes, it will always be displayed
19601 in the default size.
19604 \begin_layout Standard
19605 \begin_inset Newpage newpage
19611 \begin_layout Section
19613 \begin_inset Index idx
19616 \begin_layout Plain Layout
19625 \begin_layout Standard
19626 Greek letters can also be inserted via the toolbar button
19627 \begin_inset Graphics
19628 filename ../images/math/alpha.png
19634 All international typesetting norms purport that Greek letters in math
19635 have to be typeset italic/slanted.
19636 In some languages, like French or Russian, they are nevertheless sometimes
19640 \begin_layout Subsection
19642 \begin_inset Index idx
19645 \begin_layout Plain Layout
19646 Greek letters ! small
19654 \begin_layout Standard
19655 \begin_inset space \hfill{}
19659 \begin_inset Tabular
19660 <lyxtabular version="3" rows="11" columns="2">
19661 <features tabularvalignment="middle">
19662 <column alignment="center" valignment="top" width="0pt">
19663 <column alignment="center" valignment="top" width="0pt">
19665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19668 \begin_layout Plain Layout
19674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19677 \begin_layout Plain Layout
19685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19688 \begin_layout Plain Layout
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19699 \begin_layout Plain Layout
19700 \begin_inset Formula $\alpha$
19710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19713 \begin_layout Plain Layout
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19724 \begin_layout Plain Layout
19725 \begin_inset Formula $\beta$
19735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19738 \begin_layout Plain Layout
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19749 \begin_layout Plain Layout
19750 \begin_inset Formula $\gamma$
19760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19763 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19775 \begin_inset Formula $\delta$
19785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19788 \begin_layout Plain Layout
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19799 \begin_layout Plain Layout
19800 \begin_inset Formula $\epsilon$
19810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19813 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19824 \begin_layout Plain Layout
19825 \begin_inset Formula $\varepsilon$
19835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19838 \begin_layout Plain Layout
19846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19849 \begin_layout Plain Layout
19850 \begin_inset Formula $\zeta$
19860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19863 \begin_layout Plain Layout
19871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19874 \begin_layout Plain Layout
19875 \begin_inset Formula $\eta$
19885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19888 \begin_layout Plain Layout
19896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19899 \begin_layout Plain Layout
19900 \begin_inset Formula $\theta$
19910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19913 \begin_layout Plain Layout
19921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19924 \begin_layout Plain Layout
19925 \begin_inset Formula $\vartheta$
19939 \begin_inset space \hfill{}
19943 \begin_inset Tabular
19944 <lyxtabular version="3" rows="12" columns="2">
19945 <features tabularvalignment="middle">
19946 <column alignment="center" valignment="top" width="0pt">
19947 <column alignment="center" valignment="top" width="0pt">
19949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19952 \begin_layout Plain Layout
19958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\iota$
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\kappa$
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\varkappa$
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\lambda$
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20072 \begin_layout Plain Layout
20080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20083 \begin_layout Plain Layout
20084 \begin_inset Formula $\mu$
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20097 \begin_layout Plain Layout
20105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20108 \begin_layout Plain Layout
20109 \begin_inset Formula $\nu$
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20122 \begin_layout Plain Layout
20130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20133 \begin_layout Plain Layout
20134 \begin_inset Formula $\xi$
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20147 \begin_layout Plain Layout
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Plain Layout
20157 \begin_inset Formula $o$
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20170 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20182 \begin_inset Formula $\pi$
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20195 \begin_layout Plain Layout
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Plain Layout
20207 \begin_inset Formula $\varpi$
20217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20220 \begin_layout Plain Layout
20228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20231 \begin_layout Plain Layout
20232 \begin_inset Formula $\rho$
20246 \begin_inset space \hfill{}
20250 \begin_inset Tabular
20251 <lyxtabular version="3" rows="11" columns="2">
20252 <features tabularvalignment="middle">
20253 <column alignment="center" valignment="top" width="0pt">
20254 <column alignment="center" valignment="top" width="0pt">
20256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20259 \begin_layout Plain Layout
20265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20268 \begin_layout Plain Layout
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20279 \begin_layout Plain Layout
20287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20290 \begin_layout Plain Layout
20291 \begin_inset Formula $\varrho$
20301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20304 \begin_layout Plain Layout
20312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20315 \begin_layout Plain Layout
20316 \begin_inset Formula $\sigma$
20326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20329 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20341 \begin_inset Formula $\varsigma$
20351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20354 \begin_layout Plain Layout
20362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20365 \begin_layout Plain Layout
20366 \begin_inset Formula $\tau$
20376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20379 \begin_layout Plain Layout
20387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20390 \begin_layout Plain Layout
20391 \begin_inset Formula $\upsilon$
20401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20404 \begin_layout Plain Layout
20412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20415 \begin_layout Plain Layout
20416 \begin_inset Formula $\phi$
20426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20429 \begin_layout Plain Layout
20437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20440 \begin_layout Plain Layout
20441 \begin_inset Formula $\varphi$
20451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20454 \begin_layout Plain Layout
20462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20465 \begin_layout Plain Layout
20466 \begin_inset Formula $\chi$
20476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20479 \begin_layout Plain Layout
20487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20490 \begin_layout Plain Layout
20491 \begin_inset Formula $\psi$
20501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20504 \begin_layout Plain Layout
20512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20515 \begin_layout Plain Layout
20516 \begin_inset Formula $\omega$
20530 \begin_inset space \hfill{}
20536 \begin_layout Standard
20537 \begin_inset VSpace medskip
20543 \begin_layout Standard
20544 How to create special upright Greek letters is explained in
20545 \begin_inset CommandInset ref
20547 reference "sub:Upright-small-Greek"
20554 \begin_layout Subsection
20556 \begin_inset Index idx
20559 \begin_layout Plain Layout
20560 Greek letters ! big
20568 \begin_layout Standard
20569 \begin_inset space \hfill{}
20573 \begin_inset Tabular
20574 <lyxtabular version="3" rows="7" columns="2">
20575 <features tabularvalignment="middle">
20576 <column alignment="center" valignment="top" width="0pt">
20577 <column alignment="center" valignment="top" width="0pt">
20579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20582 \begin_layout Plain Layout
20588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Plain Layout
20599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20602 \begin_layout Plain Layout
20610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20613 \begin_layout Plain Layout
20614 \begin_inset Formula $\Gamma$
20624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20627 \begin_layout Plain Layout
20635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20638 \begin_layout Plain Layout
20639 \begin_inset Formula $\Delta$
20649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20652 \begin_layout Plain Layout
20660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20663 \begin_layout Plain Layout
20664 \begin_inset Formula $\Theta$
20674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20677 \begin_layout Plain Layout
20685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20688 \begin_layout Plain Layout
20689 \begin_inset Formula $\Lambda$
20699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20702 \begin_layout Plain Layout
20710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20713 \begin_layout Plain Layout
20714 \begin_inset Formula $\Xi$
20724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20727 \begin_layout Plain Layout
20735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20738 \begin_layout Plain Layout
20739 \begin_inset Formula $\Pi$
20753 \begin_inset space \hfill{}
20757 \begin_inset Tabular
20758 <lyxtabular version="3" rows="6" columns="2">
20759 <features tabularvalignment="middle">
20760 <column alignment="center" valignment="top" width="0pt">
20761 <column alignment="center" valignment="top" width="0pt">
20763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20766 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20786 \begin_layout Plain Layout
20794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20797 \begin_layout Plain Layout
20798 \begin_inset Formula $\Sigma$
20808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20811 \begin_layout Plain Layout
20819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20822 \begin_layout Plain Layout
20823 \begin_inset Formula $\Upsilon$
20833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20836 \begin_layout Plain Layout
20844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20847 \begin_layout Plain Layout
20848 \begin_inset Formula $\Phi$
20858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20861 \begin_layout Plain Layout
20869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20872 \begin_layout Plain Layout
20873 \begin_inset Formula $\Psi$
20883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20886 \begin_layout Plain Layout
20894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20897 \begin_layout Plain Layout
20898 \begin_inset Formula $\Omega$
20912 \begin_inset space \hfill{}
20918 \begin_layout Standard
20919 \begin_inset VSpace medskip
20922 That the big Greek letters appear upright is caused by a design bug when
20924 To get correct italic big letters, begin every command with
20929 For example the command
20936 \begin_inset Formula $\varGamma$
20940 Another way is to load the package
20948 \begin_layout Plain Layout
20953 is part of the LaTeX-package
20958 \begin_inset Index idx
20961 \begin_layout Plain Layout
20966 \begin_layout Plain Layout
20986 \begin_inset Index idx
20989 \begin_layout Plain Layout
20995 with the LaTeX-preamble line
20998 \begin_layout Standard
21003 usepackage{fixmath}
21006 \begin_layout Standard
21007 Then all big Greek letters in a document will automatically be typeset italic.
21010 \begin_layout Subsection
21012 \begin_inset Index idx
21015 \begin_layout Plain Layout
21016 Greek letters ! bold
21024 \begin_layout Standard
21025 Greek letters cannot be set with different font styles like Latin letters.
21026 They can only be made bold with the command
21033 \begin_inset Index idx
21036 \begin_layout Plain Layout
21047 \begin_layout Standard
21049 \begin_inset Tabular
21050 <lyxtabular version="3" rows="3" columns="2">
21051 <features tabularvalignment="middle">
21052 <column alignment="center" valignment="top" width="0">
21053 <column alignment="center" valignment="top" width="0">
21055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21058 \begin_layout Plain Layout
21064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21067 \begin_layout Plain Layout
21075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21078 \begin_layout Plain Layout
21090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21093 \begin_layout Plain Layout
21094 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21107 \begin_layout Plain Layout
21119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21122 \begin_layout Plain Layout
21123 \begin_inset Formula $\theta\boldsymbol{\theta}$
21139 \begin_layout Section
21144 \begin_layout Plain Layout
21157 \begin_layout Plain Layout
21158 A list with all symbols of most of the LaTeX-packages can be found in
21159 \begin_inset CommandInset citation
21174 \begin_layout Plain Layout
21182 \begin_inset Note Note
21185 \begin_layout Plain Layout
21188 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21191 \begin_layout Plain Layout
21194 texorpdfstring is in section
21195 \begin_inset CommandInset ref
21197 reference "sub:Formulas-in-Section"
21207 \begin_inset Index idx
21210 \begin_layout Plain Layout
21219 \begin_layout Standard
21220 Many of the symbols listed in this section can also be inserted via the
21222 \begin_inset Graphics
21223 filename ../images/math/nabla.png
21229 \begin_inset Graphics
21230 filename ../images/math/digamma.png
21238 \begin_layout Subsection
21239 Mathematical Symbols
21240 \begin_inset CommandInset label
21242 name "sub:Mathematical-Symbols"
21247 \begin_inset Index idx
21250 \begin_layout Plain Layout
21251 Symbols ! mathematical
21259 \begin_layout Standard
21260 \begin_inset space \hfill{}
21264 \begin_inset Tabular
21265 <lyxtabular version="3" rows="10" columns="2">
21266 <features tabularvalignment="middle">
21267 <column alignment="center" valignment="top" width="0pt">
21268 <column alignment="center" valignment="top" width="0pt">
21270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21273 \begin_layout Plain Layout
21279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21282 \begin_layout Plain Layout
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21293 \begin_layout Plain Layout
21301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21304 \begin_layout Plain Layout
21305 \begin_inset Formula $\neg$
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21318 \begin_layout Plain Layout
21326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21329 \begin_layout Plain Layout
21330 \begin_inset Formula $\Im$
21340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21343 \begin_layout Plain Layout
21351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21354 \begin_layout Plain Layout
21355 \begin_inset Formula $\Re$
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21368 \begin_layout Plain Layout
21376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21379 \begin_layout Plain Layout
21380 \begin_inset Formula $\aleph$
21390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21393 \begin_layout Plain Layout
21401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21404 \begin_layout Plain Layout
21405 \begin_inset Formula $\partial$
21415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21418 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21430 \begin_inset Formula $\infty$
21440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21443 \begin_layout Plain Layout
21451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21454 \begin_layout Plain Layout
21455 \begin_inset Formula $\wp$
21465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21468 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\imath$
21490 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21504 \begin_layout Plain Layout
21505 \begin_inset Formula $\jmath$
21519 \begin_inset space \hfill{}
21523 \begin_inset Tabular
21524 <lyxtabular version="3" rows="10" columns="2">
21525 <features tabularvalignment="middle">
21526 <column alignment="center" valignment="top" width="0pt">
21527 <column alignment="center" valignment="top" width="0pt">
21529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21541 \begin_layout Plain Layout
21543 \begin_inset Note Note
21546 \begin_layout Plain Layout
21553 is only used as spacer.
21565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21568 \begin_layout Plain Layout
21576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21579 \begin_layout Plain Layout
21580 \begin_inset Formula $\forall$
21590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21593 \begin_layout Plain Layout
21601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21604 \begin_layout Plain Layout
21605 \begin_inset Formula $\exists$
21615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21618 \begin_layout Plain Layout
21626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21629 \begin_layout Plain Layout
21630 \begin_inset Formula $\nexists$
21640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21643 \begin_layout Plain Layout
21651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21654 \begin_layout Plain Layout
21655 \begin_inset Formula $\emptyset$
21665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21668 \begin_layout Plain Layout
21676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21679 \begin_layout Plain Layout
21680 \begin_inset Formula $\varnothing$
21690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21693 \begin_layout Plain Layout
21701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21704 \begin_layout Plain Layout
21705 \begin_inset Formula $\dag$
21715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21718 \begin_layout Plain Layout
21726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21729 \begin_layout Plain Layout
21730 \begin_inset Formula $\ddag$
21740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21743 \begin_layout Plain Layout
21751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21754 \begin_layout Plain Layout
21758 \begin_layout Plain Layout
21768 \begin_inset Formula $\complement$
21775 \begin_layout Plain Layout
21789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21792 \begin_layout Plain Layout
21800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21803 \begin_layout Plain Layout
21804 \begin_inset Formula $\Bbbk$
21818 \begin_inset space \hfill{}
21822 \begin_inset Tabular
21823 <lyxtabular version="3" rows="10" columns="2">
21824 <features tabularvalignment="middle">
21825 <column alignment="center" valignment="top" width="0pt">
21826 <column alignment="center" valignment="top" width="0pt">
21828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21831 \begin_layout Plain Layout
21837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21851 \begin_layout Plain Layout
21859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21862 \begin_layout Plain Layout
21863 \begin_inset Formula $\prime$
21873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21876 \begin_layout Plain Layout
21884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21887 \begin_layout Plain Layout
21888 \begin_inset Formula $\backprime$
21898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21901 \begin_layout Plain Layout
21909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21912 \begin_layout Plain Layout
21913 \begin_inset Formula $\mho$
21923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21926 \begin_layout Plain Layout
21934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21937 \begin_layout Plain Layout
21938 \begin_inset Formula $\triangle$
21948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21951 \begin_layout Plain Layout
21959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21962 \begin_layout Plain Layout
21963 \begin_inset Formula $\angle$
21973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21976 \begin_layout Plain Layout
21984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21987 \begin_layout Plain Layout
21988 \begin_inset Formula $\measuredangle$
21998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22001 \begin_layout Plain Layout
22009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22012 \begin_layout Plain Layout
22013 \begin_inset Formula $\sphericalangle$
22023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22026 \begin_layout Plain Layout
22034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22037 \begin_layout Plain Layout
22038 \begin_inset Formula $\top$
22048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22062 \begin_layout Plain Layout
22063 \begin_inset Formula $\bot$
22077 \begin_inset space \hfill{}
22083 \begin_layout Subsection
22084 Miscellaneous Symbols
22085 \begin_inset CommandInset label
22087 name "sub:Miscellaneous-Symbols"
22092 \begin_inset Index idx
22095 \begin_layout Plain Layout
22096 Symbols ! miscellaneous
22104 \begin_layout Standard
22107 \begin_inset Tabular
22108 <lyxtabular version="3" rows="10" columns="2">
22109 <features tabularvalignment="middle">
22110 <column alignment="center" valignment="top" width="0pt">
22111 <column alignment="center" valignment="top" width="0pt">
22113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22116 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22125 \begin_layout Plain Layout
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22136 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22148 \begin_inset Formula $\flat$
22158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22161 \begin_layout Plain Layout
22169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22173 \begin_inset Formula $\natural$
22183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22186 \begin_layout Plain Layout
22194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22198 \begin_inset Formula $\sharp$
22208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22211 \begin_layout Plain Layout
22219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22222 \begin_layout Plain Layout
22223 \begin_inset Formula $\surd$
22233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22236 \begin_layout Plain Layout
22244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22247 \begin_layout Plain Layout
22248 \begin_inset Formula $\checkmark$
22258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\yen$
22283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22298 \begin_inset Formula $\pounds$
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22320 \begin_layout Plain Layout
22321 \begin_inset Formula $\$$
22331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22344 \begin_inset Formula $§$
22358 \begin_inset Tabular
22359 <lyxtabular version="3" rows="10" columns="2">
22360 <features tabularvalignment="middle">
22361 <column alignment="center" valignment="top" width="0">
22362 <column alignment="center" valignment="top" width="0">
22364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22376 \begin_layout Plain Layout
22384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22387 \begin_layout Plain Layout
22395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22398 \begin_layout Plain Layout
22399 \begin_inset Formula $\hbar$
22409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22412 \begin_layout Plain Layout
22420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22423 \begin_layout Plain Layout
22424 \begin_inset Formula $\hslash$
22434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22437 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22448 \begin_layout Plain Layout
22449 \begin_inset Formula $\clubsuit$
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22473 \begin_layout Plain Layout
22474 \begin_inset Formula $\spadesuit$
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22487 \begin_layout Plain Layout
22495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22498 \begin_layout Plain Layout
22499 \begin_inset Formula $\bigstar$
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 $\blacklozenge$
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 $\blacktriangle$
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 $\blacktriangledown$
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 $\bullet$
22613 \begin_inset Tabular
22614 <lyxtabular version="3" rows="10" columns="2">
22615 <features tabularvalignment="middle">
22616 <column alignment="center" valignment="top" width="0pt">
22617 <column alignment="center" valignment="top" width="0pt">
22619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22622 \begin_layout Plain Layout
22628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22631 \begin_layout Plain Layout
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22654 \begin_inset Formula $\diamondsuit$
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22678 \begin_layout Plain Layout
22679 \begin_inset Formula $\Diamond$
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22703 \begin_layout Plain Layout
22704 \begin_inset Formula $\heartsuit$
22714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\P$
22739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\copyright$
22764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\circledR$
22789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\maltese$
22814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\diagup$
22839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\diagdown$
22870 \begin_layout Standard
22871 \begin_inset VSpace medskip
22874 More symbols are listed in
22875 \begin_inset CommandInset ref
22877 reference "sub:Miscellaneous-special-Characters"
22884 \begin_layout Standard
22885 Some symbols can be displayed in different sizes, see
22886 \begin_inset CommandInset ref
22888 reference "sub:Font-Sizes"
22895 \begin_layout Subsection
22897 \begin_inset Index idx
22900 \begin_layout Plain Layout
22901 Symbols ! Euro-symbol
22907 \begin_inset Index idx
22910 \begin_layout Plain Layout
22917 \begin_layout Plain Layout
22934 \begin_layout Standard
22935 To use the Euro symbol in formulas, the LaTeX-package
22940 \begin_inset Index idx
22943 \begin_layout Plain Layout
22949 must be installed and loaded with the LaTeX-preamble line
22952 \begin_layout Standard
22957 usepackage[gennarrow]{eurosym}
22960 \begin_layout Standard
22961 The Euro symbol can now be inserted with the command
22968 \begin_inset Index idx
22971 \begin_layout Plain Layout
22982 \begin_layout Standard
22983 The Euro symbol can directly be inserted with the € key in mathematical
22984 text, without having
22999 can also be inserted in TeX-mode.
23000 The official currency symbol can then be inserted with the command
23007 \begin_inset Index idx
23010 \begin_layout Plain Layout
23018 , that is only available in TeX-mode.
23021 \begin_layout Standard
23025 \begin_layout Plain Layout
23035 \begin_inset Note Note
23038 \begin_layout Plain Layout
23039 The following table will only be displayed when the LaTeX-package
23051 \begin_layout Standard
23052 An overview about the different Euro symbols:
23055 \begin_layout Standard
23057 \begin_inset Tabular
23058 <lyxtabular version="3" rows="4" columns="3">
23059 <features tabularvalignment="middle">
23060 <column alignment="center" valignment="top" width="0pt">
23061 <column alignment="center" valignment="top" width="0pt">
23062 <column alignment="center" valignment="top" width="0pt">
23064 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23067 \begin_layout Plain Layout
23073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23076 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23096 \begin_layout Plain Layout
23102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23105 \begin_layout Plain Layout
23113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23116 \begin_layout Plain Layout
23117 \begin_inset Formula $\euro$
23127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23130 \begin_layout Plain Layout
23136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23139 \begin_layout Plain Layout
23145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23148 \begin_layout Plain Layout
23149 \begin_inset Formula $\mbox{€}$
23159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23162 \begin_layout Plain Layout
23168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23171 \begin_layout Plain Layout
23179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23182 \begin_layout Plain Layout
23186 \begin_layout Plain Layout
23208 \begin_layout Standard
23212 \begin_layout Plain Layout
23222 \begin_inset Note Note
23225 \begin_layout Plain Layout
23226 The following will be displayed when the LaTeX-package
23238 \begin_layout Standard
23239 You need to install the LaTeX-package
23243 to see the rest of this subsection in the output.
23246 \begin_layout Standard
23250 \begin_layout Plain Layout
23262 \begin_layout Section
23264 \begin_inset CommandInset label
23266 name "sec:Relations"
23271 \begin_inset Index idx
23274 \begin_layout Plain Layout
23281 \begin_inset Index idx
23284 \begin_layout Plain Layout
23289 \begin_layout Plain Layout
23300 \begin_layout Plain Layout
23315 \begin_layout Standard
23316 All relations can also be inserted via the toolbar button
23317 \begin_inset Graphics
23318 filename ../images/math/leq.png
23326 \begin_layout Standard
23327 \begin_inset space \hfill{}
23331 \begin_inset Tabular
23332 <lyxtabular version="3" rows="17" columns="2">
23333 <features tabularvalignment="middle">
23334 <column alignment="center" valignment="top" width="0pt">
23335 <column alignment="center" valignment="top" width="0pt">
23337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23340 \begin_layout Plain Layout
23346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23349 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23360 \begin_layout Plain Layout
23366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23369 \begin_layout Plain Layout
23370 \begin_inset Formula $<$
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23383 \begin_layout Plain Layout
23391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23394 \begin_layout Plain Layout
23395 \begin_inset Formula $\le$
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23408 \begin_layout Plain Layout
23416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23419 \begin_layout Plain Layout
23420 \begin_inset Formula $\ll$
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23433 \begin_layout Plain Layout
23441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23444 \begin_layout Plain Layout
23445 \begin_inset Formula $\prec$
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23458 \begin_layout Plain Layout
23466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23469 \begin_layout Plain Layout
23470 \begin_inset Formula $\preceq$
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 $\subset$
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23508 \begin_layout Plain Layout
23516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23519 \begin_layout Plain Layout
23520 \begin_inset Formula $\subseteq$
23530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23533 \begin_layout Plain Layout
23541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23544 \begin_layout Plain Layout
23545 \begin_inset Formula $\sqsubseteq$
23555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23558 \begin_layout Plain Layout
23566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23569 \begin_layout Plain Layout
23570 \begin_inset Formula $\in$
23580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23583 \begin_layout Plain Layout
23591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23594 \begin_layout Plain Layout
23595 \begin_inset Formula $\vdash$
23605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23608 \begin_layout Plain Layout
23616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23619 \begin_layout Plain Layout
23620 \begin_inset Formula $\smile$
23630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23633 \begin_layout Plain Layout
23641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23644 \begin_layout Plain Layout
23645 \begin_inset Formula $\lhd$
23655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23658 \begin_layout Plain Layout
23666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23669 \begin_layout Plain Layout
23670 \begin_inset Formula $\unlhd$
23680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23683 \begin_layout Plain Layout
23691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23694 \begin_layout Plain Layout
23695 \begin_inset Formula $\gtrless$
23705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23708 \begin_layout Plain Layout
23716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23719 \begin_layout Plain Layout
23720 \begin_inset Formula $\mid$
23730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23733 \begin_layout Plain Layout
23741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23744 \begin_layout Plain Layout
23745 \begin_inset Formula $\nmid$
23759 \begin_inset space \hfill{}
23763 \begin_inset Tabular
23764 <lyxtabular version="3" rows="17" columns="2">
23765 <features tabularvalignment="middle">
23766 <column alignment="center" valignment="top" width="0pt">
23767 <column alignment="center" valignment="top" width="0pt">
23769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23772 \begin_layout Plain Layout
23778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23781 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23792 \begin_layout Plain Layout
23798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23801 \begin_layout Plain Layout
23802 \begin_inset Formula $=$
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23826 \begin_layout Plain Layout
23827 \begin_inset Formula $\not=$
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23840 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23851 \begin_layout Plain Layout
23852 \begin_inset Formula $\equiv$
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23865 \begin_layout Plain Layout
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23876 \begin_layout Plain Layout
23877 \begin_inset Formula $\sim$
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23890 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23901 \begin_layout Plain Layout
23902 \begin_inset Formula $\simeq$
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23915 \begin_layout Plain Layout
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23926 \begin_layout Plain Layout
23927 \begin_inset Formula $\approx$
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23940 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23951 \begin_layout Plain Layout
23952 \begin_inset Formula $\cong$
23962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23965 \begin_layout Plain Layout
23973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23976 \begin_layout Plain Layout
23977 \begin_inset Formula $\bowtie$
23987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23990 \begin_layout Plain Layout
23998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24001 \begin_layout Plain Layout
24002 \begin_inset Formula $\notin$
24012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24015 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24026 \begin_layout Plain Layout
24027 \begin_inset Formula $\perp$
24037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24040 \begin_layout Plain Layout
24048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24051 \begin_layout Plain Layout
24052 \begin_inset Formula $\propto$
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24076 \begin_layout Plain Layout
24077 \begin_inset Formula $\asymp$
24087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24090 \begin_layout Plain Layout
24098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24101 \begin_layout Plain Layout
24102 \begin_inset Formula $\doteq$
24112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24115 \begin_layout Plain Layout
24123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24126 \begin_layout Plain Layout
24127 \begin_inset Formula $\circeq$
24137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24140 \begin_layout Plain Layout
24148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24151 \begin_layout Plain Layout
24152 \begin_inset Formula $\models$
24162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24165 \begin_layout Plain Layout
24173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24176 \begin_layout Plain Layout
24177 \begin_inset Formula $\widehat{=}$
24191 \begin_inset space \hfill{}
24195 \begin_inset Tabular
24196 <lyxtabular version="3" rows="17" columns="2">
24197 <features tabularvalignment="middle">
24198 <column alignment="center" valignment="top" width="0pt">
24199 <column alignment="center" valignment="top" width="0pt">
24201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24204 \begin_layout Plain Layout
24210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24213 \begin_layout Plain Layout
24221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24224 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24233 \begin_layout Plain Layout
24234 \begin_inset Formula $>$
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24247 \begin_layout Plain Layout
24255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24258 \begin_layout Plain Layout
24259 \begin_inset Formula $\ge$
24269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24272 \begin_layout Plain Layout
24280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24283 \begin_layout Plain Layout
24284 \begin_inset Formula $\gg$
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24297 \begin_layout Plain Layout
24305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24308 \begin_layout Plain Layout
24309 \begin_inset Formula $\succ$
24319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24322 \begin_layout Plain Layout
24330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24333 \begin_layout Plain Layout
24334 \begin_inset Formula $\succeq$
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24359 \begin_inset Formula $\supset$
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24384 \begin_inset Formula $\supseteq$
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24397 \begin_layout Plain Layout
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24408 \begin_layout Plain Layout
24409 \begin_inset Formula $\sqsupseteq$
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24433 \begin_layout Plain Layout
24434 \begin_inset Formula $\ni$
24444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24447 \begin_layout Plain Layout
24455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24458 \begin_layout Plain Layout
24459 \begin_inset Formula $\dashv$
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24472 \begin_layout Plain Layout
24480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24483 \begin_layout Plain Layout
24484 \begin_inset Formula $\frown$
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24497 \begin_layout Plain Layout
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24508 \begin_layout Plain Layout
24509 \begin_inset Formula $\rhd$
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24522 \begin_layout Plain Layout
24530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24533 \begin_layout Plain Layout
24534 \begin_inset Formula $\unrhd$
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24547 \begin_layout Plain Layout
24555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24558 \begin_layout Plain Layout
24559 \begin_inset Formula $\lessgtr$
24569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24572 \begin_layout Plain Layout
24580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24583 \begin_layout Plain Layout
24584 \begin_inset Formula $\parallel$
24594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24608 \begin_layout Plain Layout
24609 \begin_inset Formula $\nparallel$
24623 \begin_inset space \hfill{}
24629 \begin_layout Standard
24630 \begin_inset VSpace medskip
24645 are bigger than the equal looking operators
24660 \begin_layout Standard
24661 Relations are, in contrary to symbols, always surrounded by space.
24664 \begin_layout Standard
24665 Relations with labels can be created with the command
24672 \begin_inset Index idx
24675 \begin_layout Plain Layout
24686 \begin_layout Standard
24688 \begin_inset Tabular
24689 <lyxtabular version="3" rows="2" columns="2">
24690 <features tabularvalignment="middle">
24691 <column alignment="center" valignment="top" width="0">
24692 <column alignment="center" valignment="top" width="0">
24694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24697 \begin_layout Plain Layout
24703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24706 \begin_layout Plain Layout
24708 \begin_inset Note Note
24711 \begin_layout Plain Layout
24718 is only used as spacer.
24730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24740 \begin_layout Plain Layout
24757 \begin_layout Plain Layout
24767 \begin_inset Formula $\downarrow$
24776 \begin_layout Plain Layout
24789 \begin_layout Plain Layout
24803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24806 \begin_layout Plain Layout
24807 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24823 \begin_layout Section
24827 \begin_layout Subsection
24828 Predefined Functions
24829 \begin_inset CommandInset label
24831 name "sub:Predefined-Functions"
24836 \begin_inset Index idx
24839 \begin_layout Plain Layout
24840 Functions ! predefined
24848 \begin_layout Standard
24849 In general, variables are set
24853 in mathematical expressions, but not function names, because
24854 \begin_inset Formula $sin$
24857 could be misunderstood as
24858 \begin_inset Formula $s\cdot i\cdot n$
24862 Therefore there are predefined functions, that are additionally a bit separated
24864 They are inserted as commands starting with a backslash before their name.
24867 \begin_layout Standard
24869 \begin_inset Tabular
24870 <lyxtabular version="3" rows="2" columns="4">
24871 <features tabularvalignment="middle">
24872 <column alignment="center" valignment="top" width="0pt">
24873 <column alignment="center" valignment="top" width="0pt">
24874 <column alignment="center" valignment="top" width="0pt">
24875 <column alignment="center" valignment="top" width="0pt">
24877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24880 \begin_layout Plain Layout
24886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24889 \begin_layout Plain Layout
24895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24898 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24907 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24918 \begin_layout Plain Layout
24924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24927 \begin_layout Plain Layout
24928 \begin_inset Formula $Asin(x)+B$
24936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24939 \begin_layout Plain Layout
24947 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24950 \begin_layout Plain Layout
24951 \begin_inset Formula $A\sin(x)+B$
24967 \begin_layout Standard
24968 The following functions are predefined:
24971 \begin_layout Standard
24972 \begin_inset VSpace -2mm
24978 \begin_layout Standard
24980 \begin_inset Tabular
24981 <lyxtabular version="3" rows="9" columns="4">
24982 <features tabularvalignment="middle">
24983 <column alignment="center" valignment="top" width="0pt">
24984 <column alignment="center" valignment="top" width="0pt">
24985 <column alignment="center" valignment="top" width="0pt">
24986 <column alignment="center" valignment="top" width="0pt">
24988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25000 \begin_layout Plain Layout
25006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25009 \begin_layout Plain Layout
25015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25018 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25029 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25051 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25062 \begin_layout Plain Layout
25072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25075 \begin_layout Plain Layout
25083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25097 \begin_layout Plain Layout
25105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25108 \begin_layout Plain Layout
25118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25121 \begin_layout Plain Layout
25129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25132 \begin_layout Plain Layout
25140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25154 \begin_layout Plain Layout
25164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25167 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25189 \begin_layout Plain Layout
25197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25200 \begin_layout Plain Layout
25210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25213 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25224 \begin_layout Plain Layout
25232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25235 \begin_layout Plain Layout
25243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25246 \begin_layout Plain Layout
25256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25259 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25270 \begin_layout Plain Layout
25278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25281 \begin_layout Plain Layout
25289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25292 \begin_layout Plain Layout
25302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25305 \begin_layout Plain Layout
25313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25316 \begin_layout Plain Layout
25324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25327 \begin_layout Plain Layout
25335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25338 \begin_layout Plain Layout
25348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25351 \begin_layout Plain Layout
25359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25362 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25373 \begin_layout Plain Layout
25381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25384 \begin_layout Plain Layout
25400 \begin_layout Standard
25401 They can also be inserted with the math toolbar button
25402 \begin_inset Graphics
25403 filename ../images/math/functions.png
25411 \begin_layout Subsection
25412 Self-defined Functions
25413 \begin_inset Index idx
25416 \begin_layout Plain Layout
25417 Functions ! self-defined
25425 \begin_layout Standard
25426 To use a function that is not predefined, like for example the sign function
25427 sgn(x), there are two possibilities:
25430 \begin_layout Itemize
25431 Define the function by inserting the following line to the LaTeX-preamble
25435 \begin_layout Plain Layout
25440 DeclareMathOperator
25443 \begin_inset CommandInset ref
25445 reference "sub:Self-defined-Operators"
25455 \begin_inset Newline newline
25459 \begin_inset VSpace -3mm
25463 \begin_inset Newline newline
25470 DeclareMathOperator{
25475 \begin_inset Index idx
25478 \begin_layout Plain Layout
25483 DeclareMathOperator
25489 \begin_inset Newline newline
25493 \begin_inset VSpace -2mm
25497 \begin_inset Newline newline
25500 Now the new defined function can be called with the command
25509 \begin_layout Itemize
25510 Write the formula as usual, mark the formula name, in our example the letters
25515 , and change it to mathematical text.
25516 At last a space is inserted between prefactor and function.
25519 \begin_layout Standard
25520 The result is the same with both methods as with a predefined function
25524 \begin_layout Plain Layout
25525 In LyX self-defined functions are displayed red, predefined ones black.
25533 \begin_layout Standard
25535 \begin_inset Tabular
25536 <lyxtabular version="3" rows="3" columns="2">
25537 <features tabularvalignment="middle">
25538 <column alignment="center" valignment="top" width="0pt">
25539 <column alignment="center" valignment="top" width="0pt">
25541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25544 \begin_layout Plain Layout
25550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25553 \begin_layout Plain Layout
25561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25564 \begin_layout Plain Layout
25572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25575 \begin_layout Plain Layout
25576 \begin_inset Formula $A\sgn(x)+B$
25586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25593 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25604 \begin_layout Plain Layout
25605 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25621 \begin_layout Standard
25622 The first method is more suitable when the self-defined function should
25623 be used several times.
25626 \begin_layout Subsection
25628 \begin_inset Index idx
25631 \begin_layout Plain Layout
25640 \begin_layout Standard
25641 For limits there are defined besides
25648 \begin_inset Index idx
25651 \begin_layout Plain Layout
25671 furthermore the following functions:
25674 \begin_layout Standard
25676 \begin_inset Tabular
25677 <lyxtabular version="3" rows="5" columns="2">
25678 <features tabularvalignment="middle">
25679 <column alignment="center" valignment="top" width="0">
25680 <column alignment="center" valignment="top" width="0">
25682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25685 \begin_layout Plain Layout
25691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25694 \begin_layout Plain Layout
25696 \begin_inset Note Note
25699 \begin_layout Plain Layout
25706 is only used as spacer.
25718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25721 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25732 \begin_layout Plain Layout
25733 \begin_inset Formula $\varliminf$
25743 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25746 \begin_layout Plain Layout
25754 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25757 \begin_layout Plain Layout
25758 \begin_inset Formula $\varlimsup$
25768 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25771 \begin_layout Plain Layout
25779 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25782 \begin_layout Plain Layout
25783 \begin_inset Formula $\varprojlim$
25793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25796 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25808 \begin_inset Formula $\varinjlim$
25812 \begin_inset Formula $\raisebox{-2.5mm}{}$
25828 \begin_layout Standard
25829 \begin_inset VSpace medskip
25832 The limit is created by inserting a subscript.
25833 It is set right beside the function in an inline formula:
25836 \begin_layout Standard
25838 \begin_inset Tabular
25839 <lyxtabular version="3" rows="2" columns="2">
25840 <features tabularvalignment="middle">
25841 <column alignment="center" valignment="top" width="0pt">
25842 <column alignment="center" valignment="top" width="0pt">
25844 <cell alignment="center" valignment="top" usebox="none">
25847 \begin_layout Plain Layout
25853 <cell alignment="center" valignment="top" usebox="none">
25856 \begin_layout Plain Layout
25857 \begin_inset space \hspace{}
25862 \begin_inset Note Note
25865 \begin_layout Plain Layout
25872 are used here as spacer.
25884 <cell alignment="center" valignment="top" usebox="none">
25887 \begin_layout Plain Layout
25896 \begin_layout Plain Layout
25909 \begin_layout Plain Layout
25923 <cell alignment="center" valignment="top" usebox="none">
25926 \begin_layout Plain Layout
25927 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25943 \begin_layout Standard
25944 In a displayed formula the limit is set below the formula, as usual:
25945 \begin_inset Formula \[
25954 \begin_layout Subsection
25956 \begin_inset Index idx
25959 \begin_layout Plain Layout
25960 Functions ! modulo-
25968 \begin_layout Standard
25969 The modulo-function is special, because it exists in four variants.
25972 \begin_layout Standard
25973 The variants in a displayed formula:
25974 \begin_inset Formula \begin{align*}
25975 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25976 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25977 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25978 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25979 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
25987 \begin_layout Standard
25988 In an inline formula less space is set before the function names for all
25992 \begin_layout Section
25994 \begin_inset Index idx
25997 \begin_layout Plain Layout
26006 \begin_layout Subsection
26007 Special Characters in Mathematical Text
26010 \begin_layout Standard
26011 The following commands can only be used in mathematical text or in TeX-mode:
26014 \begin_layout Standard
26015 \begin_inset space \hfill{}
26019 \begin_inset Tabular
26020 <lyxtabular version="3" rows="8" columns="2">
26021 <features tabularvalignment="middle">
26022 <column alignment="block" valignment="top" width="0">
26023 <column alignment="block" valignment="top" width="0">
26025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26028 \begin_layout Plain Layout
26034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26037 \begin_layout Plain Layout
26045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26048 \begin_layout Plain Layout
26056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26059 \begin_layout Plain Layout
26060 \begin_inset Formula $\textrm{œ}$
26070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26073 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26084 \begin_layout Plain Layout
26085 \begin_inset Formula $\textrm{Œ}$
26095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26098 \begin_layout Plain Layout
26106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26109 \begin_layout Plain Layout
26110 \begin_inset Formula $\textrm{æ}$
26120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26123 \begin_layout Plain Layout
26131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26134 \begin_layout Plain Layout
26135 \begin_inset Formula $\textrm{Æ}$
26145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26148 \begin_layout Plain Layout
26156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26159 \begin_layout Plain Layout
26160 \begin_inset Formula $\textrm{\aa}$
26170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26173 \begin_layout Plain Layout
26177 \begin_inset Index idx
26180 \begin_layout Plain Layout
26187 \begin_layout Plain Layout
26208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26211 \begin_layout Plain Layout
26212 \begin_inset Formula $\textrm{Å}$
26222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26225 \begin_layout Plain Layout
26233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26236 \begin_layout Plain Layout
26237 \begin_inset Formula $\textrm{ı}$
26251 \begin_inset space \hfill{}
26255 \begin_inset Tabular
26256 <lyxtabular version="3" rows="8" columns="2">
26257 <features tabularvalignment="middle">
26258 <column alignment="block" valignment="top" width="0">
26259 <column alignment="center" valignment="top" width="0">
26261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26264 \begin_layout Plain Layout
26266 \begin_inset Note Note
26269 \begin_layout Plain Layout
26271 \begin_inset space \thinspace{}
26274 mm is used for separation, because otherwise the output will be ¡ and ¿
26285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26288 \begin_layout Plain Layout
26296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26299 \begin_layout Plain Layout
26307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26310 \begin_layout Plain Layout
26311 \begin_inset Formula $\textrm{ø}$
26321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26324 \begin_layout Plain Layout
26332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26335 \begin_layout Plain Layout
26336 \begin_inset Formula $\textrm{Ø}$
26346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26349 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26361 \begin_inset Formula $\textrm{ł}$
26371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26374 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26385 \begin_layout Plain Layout
26386 \begin_inset Formula $\textrm{Ł}$
26396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26399 \begin_layout Plain Layout
26401 \begin_inset space \hspace{}
26409 \begin_layout Plain Layout
26423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26426 \begin_layout Plain Layout
26427 \begin_inset Formula $\textrm{!`}$
26437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26440 \begin_layout Plain Layout
26442 \begin_inset space \hspace{}
26450 \begin_layout Plain Layout
26464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26467 \begin_layout Plain Layout
26468 \begin_inset Formula $\textrm{?`}$
26478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26481 \begin_layout Plain Layout
26489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26492 \begin_layout Plain Layout
26493 \begin_inset Formula $\textrm{ȷ}$
26507 \begin_inset space \hfill{}
26513 \begin_layout Standard
26515 \begin_inset Formula $\textrm{\textrm{Å}}$
26519 \begin_inset Formula $\textrm{\textrm{Ø}}$
26522 can also be inserted via the math toolbar button
26523 \begin_inset Graphics
26524 filename ../images/math/digamma.png
26532 \begin_layout Standard
26533 An exception are the commands
26536 \begin_inset space \hspace{}
26545 \begin_inset space \hspace{}
26551 , because they can be inserted in LyX directly to text.
26554 \begin_layout Subsection
26556 \begin_inset CommandInset label
26558 name "sub:Accents-in-Text"
26563 \begin_inset Index idx
26566 \begin_layout Plain Layout
26575 \begin_layout Standard
26576 With the following commands all letters can be accented.
26577 The commands must be inserted in TeX-mode.
26580 \begin_layout Standard
26581 \begin_inset space \hfill{}
26585 \begin_inset Tabular
26586 <lyxtabular version="3" rows="8" columns="2">
26587 <features tabularvalignment="middle">
26588 <column alignment="block" valignment="top" width="0">
26589 <column alignment="block" valignment="top" width="0">
26591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26594 \begin_layout Plain Layout
26600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26603 \begin_layout Plain Layout
26611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26614 \begin_layout Plain Layout
26618 \begin_inset Quotes grd
26626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26629 \begin_layout Plain Layout
26633 \begin_layout Plain Layout
26649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26652 \begin_layout Plain Layout
26660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26663 \begin_layout Plain Layout
26667 \begin_layout Plain Layout
26683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26686 \begin_layout Plain Layout
26693 \begin_layout Plain Layout
26707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26710 \begin_layout Plain Layout
26714 \begin_layout Plain Layout
26730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26733 \begin_layout Plain Layout
26741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26744 \begin_layout Plain Layout
26748 \begin_layout Plain Layout
26764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26767 \begin_layout Plain Layout
26774 \begin_layout Plain Layout
26788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26791 \begin_layout Plain Layout
26795 \begin_layout Plain Layout
26811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26814 \begin_layout Plain Layout
26821 \begin_layout Plain Layout
26835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26838 \begin_layout Plain Layout
26842 \begin_layout Plain Layout
26858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26861 \begin_layout Plain Layout
26868 \begin_layout Plain Layout
26882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26885 \begin_layout Plain Layout
26889 \begin_layout Plain Layout
26909 \begin_inset space \hfill{}
26913 \begin_inset Tabular
26914 <lyxtabular version="3" rows="8" columns="2">
26915 <features tabularvalignment="middle">
26916 <column alignment="block" valignment="top" width="0">
26917 <column alignment="center" valignment="top" width="0">
26919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26922 \begin_layout Plain Layout
26928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26931 \begin_layout Plain Layout
26939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26942 \begin_layout Plain Layout
26949 \begin_layout Plain Layout
26963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26966 \begin_layout Plain Layout
26970 \begin_layout Plain Layout
26986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26989 \begin_layout Plain Layout
26997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27000 \begin_layout Plain Layout
27004 \begin_layout Plain Layout
27020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27023 \begin_layout Plain Layout
27027 \begin_inset Index idx
27030 \begin_layout Plain Layout
27041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27044 \begin_layout Plain Layout
27048 \begin_layout Plain Layout
27064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27067 \begin_layout Plain Layout
27075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27078 \begin_layout Plain Layout
27082 \begin_layout Plain Layout
27098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27101 \begin_layout Plain Layout
27108 \begin_layout Plain Layout
27122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27125 \begin_layout Plain Layout
27129 \begin_layout Plain Layout
27145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27148 \begin_layout Plain Layout
27155 \begin_layout Plain Layout
27169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27172 \begin_layout Plain Layout
27176 \begin_layout Plain Layout
27192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27195 \begin_layout Plain Layout
27202 \begin_layout Plain Layout
27216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27219 \begin_layout Plain Layout
27223 \begin_layout Plain Layout
27243 \begin_inset space \hfill{}
27249 \begin_layout Standard
27250 \begin_inset VSpace medskip
27259 also two different characters can be accented.
27268 \begin_layout Plain Layout
27283 \begin_layout Plain Layout
27295 \begin_layout Standard
27308 can in combination with vowels directly be inserted with the keyboard without
27310 The same applies for the tilde
27314 \begin_layout Plain Layout
27315 This only applies for keyboards where the tilde is defined as accent.
27324 in combination with
27339 \begin_layout Standard
27382 and accents that are inserted directly with the keyboard are also available
27383 in mathematical text.
27384 For the other accents there are special math commands to be used in formulas,
27386 \begin_inset CommandInset ref
27388 reference "sub:Accents-for-one"
27395 \begin_layout Standard
27396 \begin_inset VSpace bigskip
27399 Furthermore, with the command
27406 \begin_inset Index idx
27409 \begin_layout Plain Layout
27417 all numbers and letters can be set into a circle, quasi accented with a
27418 circle, similar to the copyright symbol.
27421 \begin_layout Standard
27423 \begin_inset Tabular
27424 <lyxtabular version="3" rows="3" columns="2">
27425 <features tabularvalignment="middle">
27426 <column alignment="center" valignment="top" width="0">
27427 <column alignment="center" valignment="top" width="0">
27429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27432 \begin_layout Plain Layout
27438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27441 \begin_layout Plain Layout
27443 \begin_inset Note Note
27446 \begin_layout Plain Layout
27453 is only used as spacer.
27465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27468 \begin_layout Plain Layout
27476 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27479 \begin_layout Plain Layout
27483 \begin_layout Plain Layout
27499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27502 \begin_layout Plain Layout
27513 raisebox{-1.5pt}{W}}
27518 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27521 \begin_layout Plain Layout
27522 \begin_inset Formula $\raisebox{4.5mm}{}$
27529 \begin_layout Plain Layout
27547 \begin_inset Formula $\raisebox{-2mm}{}$
27563 \begin_layout Standard
27564 One has to take care that the character fits in the circle.
27575 \begin_layout Plain Layout
27577 \begin_inset CommandInset ref
27579 reference "sub:Font-Sizes"
27588 specifies thereby the size of the circle.
27599 \begin_layout Plain Layout
27601 \begin_inset CommandInset ref
27603 reference "sub:Boxes-without-Frame"
27612 the character can be centered.
27615 \begin_layout Subsection
27617 \begin_inset Index idx
27620 \begin_layout Plain Layout
27629 \begin_layout Standard
27630 Minuscule numbers are created with the command
27637 \begin_inset Index idx
27640 \begin_layout Plain Layout
27649 The command can be used in formulas and in TeX-mode.
27650 The command scheme is:
27653 \begin_layout Standard
27658 oldstylenums{number}
27661 \begin_layout Standard
27666 oldstylenums{0123456789
27669 \begin_inset Formula $\oldstylenums{0123456789}$
27675 \begin_layout Subsection
27676 Miscellaneous special Characters
27677 \begin_inset CommandInset label
27679 name "sub:Miscellaneous-special-Characters"
27684 \begin_inset Index idx
27687 \begin_layout Plain Layout
27688 Special characters ! miscellaneous
27696 \begin_layout Standard
27697 The following characters can only be inserted to formulas by using commands:
27700 \begin_layout Standard
27702 \begin_inset Tabular
27703 <lyxtabular version="3" rows="4" columns="2">
27704 <features tabularvalignment="middle">
27705 <column alignment="center" valignment="top" width="0">
27706 <column alignment="center" valignment="top" width="0">
27708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27711 \begin_layout Plain Layout
27717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27720 \begin_layout Plain Layout
27728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27731 \begin_layout Plain Layout
27738 \begin_layout Plain Layout
27752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27755 \begin_layout Plain Layout
27756 \begin_inset Formula $\mathcircumflex$
27766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27769 \begin_layout Plain Layout
27777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27780 \begin_layout Plain Layout
27781 \begin_inset Formula $\_$
27791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27794 \begin_layout Plain Layout
27799 \begin_layout Plain Layout
27811 \begin_inset Index idx
27814 \begin_layout Plain Layout
27827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27830 \begin_layout Plain Layout
27831 \begin_inset Formula $^{\circ}$
27847 \begin_layout Standard
27848 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27849 contains the following line
27853 \begin_layout Plain Layout
27854 More about this is described in
27855 \begin_inset CommandInset ref
27857 reference "sub:Text-Characters-in"
27869 \begin_layout Standard
27874 DeclareInputtext{176}{
27887 \begin_layout Section
27889 \begin_inset CommandInset label
27891 name "sec:Formula-Styles"
27896 \begin_inset Index idx
27899 \begin_layout Plain Layout
27908 \begin_layout Itemize
27909 There are two different alignment styles:
27913 \begin_layout Description
27914 Centered is the predefined standard
27917 \begin_layout Description
27918 Indented for this the option
27922 must be inserted in the menu
27924 Document\SpecialChar \menuseparator
27930 \begin_inset space ~
27936 \begin_layout Standard
27941 is used, the indentation can be adjusted with the length
27948 \begin_inset Index idx
27951 \begin_layout Plain Layout
27960 Should the distance be 15
27961 \begin_inset space \thinspace{}
27964 mm, the following command line is inserted in the LaTeX-preamble
27967 \begin_layout Standard
27977 \begin_layout Standard
27978 When no length is specified, the predefined value of 30
27979 \begin_inset space \thinspace{}
27986 \begin_layout Itemize
27987 And two different numbering styles:
27991 \begin_layout Description
27992 Right is the predefined standard
27995 \begin_layout Description
27996 Left for this the option
28000 must be inserted in the menu
28002 Document\SpecialChar \menuseparator
28008 \begin_inset space ~
28015 \begin_layout Standard
28024 can also be used together.
28025 In this case both options are inserted, separated by a comma.
28028 \begin_layout Standard
28029 The chosen styles are used for all displayed formulas of the document.
28030 When both, centered and indented formulas should be created in a document,
28036 The indented formulas are then set in a flalign environment, see
28037 \begin_inset CommandInset ref
28039 reference "sub:Flalign-Environment"
28046 \begin_layout Section
28048 \begin_inset CommandInset label
28050 name "sec:Multiline-Formulas"
28055 \begin_inset Index idx
28058 \begin_layout Plain Layout
28059 Formula ! multiline
28067 \begin_layout Subsection
28071 \begin_layout Standard
28072 In LyX multiline formulas are created by pressing
28077 arg "newline-insert newline"
28083 This creates either an
28085 eqnarray environment
28087 that is described in
28088 \begin_inset CommandInset ref
28090 reference "sub:Eqnarray-Environment"
28094 or, when the option
28096 Use AMS math package
28098 in the document settings is selected, an
28102 that is described in
28103 \begin_inset CommandInset ref
28105 reference "sub:Standard-align-Environment"
28112 \begin_layout Standard
28113 There are other multiline formula environments that can be created via the
28116 Insert\SpecialChar \menuseparator
28120 These environments are described in the following sections.
28123 \begin_layout Standard
28124 In all multiline formula environments a new line is created by pressing
28128 arg "newline-insert newline"
28132 To add or delete lines, the math toolbar buttons
28133 \begin_inset Graphics
28134 filename ../images/tabular-feature_append-row.png
28140 \begin_inset Graphics
28141 filename ../images/tabular-feature_delete-row.png
28146 , respectively, or the menu
28148 Edit\SpecialChar \menuseparator
28154 \begin_layout Subsubsection
28156 \begin_inset CommandInset label
28158 name "sub:Line-Separation"
28163 \begin_inset Index idx
28166 \begin_layout Plain Layout
28167 Formula ! multiline ! Line separation
28175 \begin_layout Standard
28176 There is sometimes not enough space in multiline formulas between the lines:
28177 \begin_inset Formula \begin{eqnarray*}
28178 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}\\
28179 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
28187 \begin_layout Standard
28188 In LaTeX additional line space is specified as optional argument of the
28190 This is not yet possible in LyX
28194 \begin_layout Plain Layout
28196 \begin_inset CommandInset href
28198 name "LyX-bug #1505"
28199 target "http://www.lyx.org/trac/ticket/1505"
28208 , therefore the whole formula must be inserted in TeX-mode.
28209 To add in our example space, the command
28217 is inserted at the end of the first line.
28222 \begin_layout Plain Layout
28229 \begin_layout Plain Layout
28231 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28234 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28241 \begin_layout Plain Layout
28245 left(B^{2}+x_{0}^{2}
28253 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28258 \begin_layout Plain Layout
28270 \begin_layout Standard
28271 \begin_inset VSpace bigskip
28274 To set the line separation for all lines in a formula, the length
28281 \begin_inset Index idx
28284 \begin_layout Plain Layout
28294 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28305 \begin_inset space \thinspace{}
28310 \begin_inset space \thinspace{}
28313 mm additional line separation as in the previous example, the command
28316 \begin_layout Standard
28326 \begin_layout Standard
28327 is inserted in TeX-mode before the formula.
28328 This requires that the LaTeX-package
28336 \begin_layout Plain Layout
28341 is part of every LaTeX standard installation.
28347 \begin_inset Index idx
28350 \begin_layout Plain Layout
28356 was loaded in LaTeX-preamble with the line
28359 \begin_layout Standard
28367 \begin_layout Standard
28372 \begin_layout Plain Layout
28384 \begin_inset Formula \begin{eqnarray*}
28385 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}\\
28386 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
28394 \begin_layout Standard
28398 \begin_layout Plain Layout
28409 To get back to the predefined distance,
28415 is set to the value 3
28416 \begin_inset space \thinspace{}
28422 \begin_layout Subsubsection
28424 \begin_inset CommandInset label
28426 name "sub:Column-Separation"
28431 \begin_inset Index idx
28434 \begin_layout Plain Layout
28435 Formula ! multiline ! Column separation
28443 \begin_layout Standard
28444 Multiline formulas form a matrix.
28445 A formula in the eqnarray environment is for example a matrix with three
28447 By changing the column separation in this environment, the space beside
28448 the relation sign can be changed.
28451 \begin_layout Standard
28452 The column separation is specified with the length
28459 \begin_inset Index idx
28462 \begin_layout Plain Layout
28471 \begin_inset Newline newline
28474 column separation = 2
28475 \begin_inset space \thinspace{}
28485 \begin_inset Newline newline
28491 \begin_layout Standard
28501 \begin_layout Standard
28502 inserted in TeX-mode, sets for all following formulas a column separation
28504 \begin_inset space \thinspace{}
28508 To get back to the predefined distance,
28515 \begin_inset space \thinspace{}
28521 \begin_layout Standard
28523 \begin_inset space \thinspace{}
28526 cm column separation:
28530 \begin_layout Plain Layout
28542 \begin_inset Formula \begin{eqnarray*}
28549 A formula with the predefined column separation for matrices of 10
28550 \begin_inset space \thinspace{}
28557 \begin_layout Plain Layout
28569 \begin_inset Formula \begin{eqnarray*}
28579 \begin_layout Subsubsection
28581 \begin_inset Index idx
28584 \begin_layout Plain Layout
28593 \begin_layout Standard
28594 Long formulas can be typeset using these methods:
28597 \begin_layout Itemize
28598 When one side of the equation is much shorther than the line width, this
28599 one is chosen for the left side and the right side is typeset over two
28601 \begin_inset Formula \begin{eqnarray}
28602 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 \\
28603 & & -\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}
28608 The minus sign at the beginning of the second line does normally not appear
28609 as operator because it is the first character of the line.
28610 Thus it would not be surrounded by space and could not be distinguished
28611 from the fraction bar.
28613 \begin_inset space \thinspace{}
28616 pt space was inserted behind the minus sign with the command
28626 \begin_layout Plain Layout
28634 \begin_inset CommandInset ref
28636 reference "sub:Variable-Space"
28646 \begin_inset Index idx
28649 \begin_layout Plain Layout
28660 \begin_layout Itemize
28661 When both sides of the equation are too long, the command
28668 \begin_inset Index idx
28671 \begin_layout Plain Layout
28680 It is inserted to the first column of the first line and effects that all
28681 further insertions overwrite the following columns:
28682 \begin_inset Formula \begin{eqnarray}
28683 \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 \\
28684 & & -\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 \\
28685 & & =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}
28690 After the insertion of
28696 , the cursor is in a purple box that is a bit shifted to the left from the
28698 In this the formula is inserted.
28699 \begin_inset Newline newline
28702 The content of the further lines is inserted to the second or another formula
28704 The greater the column number where it was inserted, the larger the indentation.
28705 \begin_inset VSpace medskip
28709 \begin_inset Newline newline
28713 \begin_inset Note Greyedout
28716 \begin_layout Plain Layout
28717 Note the following when using
28726 \begin_layout Itemize
28727 The formula doesn't use the full page width.
28729 \begin_inset space \thinspace{}
28733 \begin_inset space \space{}
28737 \begin_inset Formula $-B^{2}$
28740 is added to the first line in the above example, it would have been outside
28742 To better use the width, negative space can be inserted at the beginning
28746 \begin_layout Itemize
28747 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28752 \begin_layout Plain Layout
28753 \begin_inset CommandInset href
28755 name "LyX-bug #1429"
28756 target "http://www.lyx.org/trac/ticket/1429"
28765 One can only set the cursor at the beginning of the line and move it with
28774 \begin_layout Itemize
28775 Other methods to set long formulas are offered by the environments described
28777 \begin_inset CommandInset ref
28779 reference "sub:Multline-Environment"
28784 \begin_inset CommandInset ref
28786 reference "sub:Multiline-Formula-Parts"
28793 \begin_layout Subsubsection
28795 \begin_inset CommandInset label
28797 name "sub:Multiline-Brackets"
28802 \begin_inset Index idx
28805 \begin_layout Plain Layout
28806 Brackets ! for multiline expressions
28814 \begin_layout Standard
28815 For brackets spanning multiple lines the following problem occurs:
28816 \begin_inset Formula \begin{eqnarray*}
28817 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28818 & & \left.\cdots+B-D\right]
28826 \begin_layout Standard
28827 The closing bracket is smaller than the opening bracket because brackets
28828 with variable size may not span multiple lines.
28831 \begin_layout Standard
28832 To set the bracket size for the second line correctly, the first line is
28840 \begin_inset Index idx
28843 \begin_layout Plain Layout
28851 and the second line with
28859 \begin_layout Plain Layout
28873 \begin_inset CommandInset ref
28875 reference "sub:Automatic-Bracket-Size"
28887 \begin_inset Index idx
28890 \begin_layout Plain Layout
28916 \begin_layout Plain Layout
28935 \begin_layout Plain Layout
28954 \begin_layout Plain Layout
28966 \begin_inset Formula $\downarrow$
28972 \begin_inset Index idx
28975 \begin_layout Plain Layout
28983 is inserted, because the multiplication operator with its limits is the
28984 largest symbol in the first line and this should be the size for the bracket
28985 in the second line.
28988 \begin_layout Standard
28989 The result is this:
28990 \begin_inset Formula \begin{eqnarray*}
28991 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28992 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29000 \begin_layout Subsection
29004 \begin_layout Standard
29005 Align environments can be used for every kind of multiline formulas.
29006 They are specially useful to set several formulas side by side.
29009 \begin_layout Standard
29010 Align environments consist of columns.
29011 The odd columns are right aligned, the even ones left aligned.
29012 Every line in an Align environment can be numbered.
29015 \begin_layout Standard
29016 Align environments are created via the menu
29018 Insert\SpecialChar \menuseparator
29024 Edit\SpecialChar \menuseparator
29025 Math\SpecialChar \menuseparator
29026 Change Formula Type
29028 already existing formulas can be converted to Align environments.
29031 \begin_layout Standard
29032 To add or delete columns, the math toolbar buttons
29033 \begin_inset Graphics
29034 filename ../images/tabular-feature_append-column.png
29040 \begin_inset Graphics
29041 filename ../images/tabular-feature_delete-column.png
29046 , respectively, or the menu
29048 Edit\SpecialChar \menuseparator
29054 \begin_layout Subsubsection
29055 Standard align Environment
29056 \begin_inset CommandInset label
29058 name "sub:Standard-align-Environment"
29063 \begin_inset Index idx
29066 \begin_layout Plain Layout
29067 Formula ! multiline ! align environment
29075 \begin_layout Standard
29076 This Align environment is created by presssing
29079 arg "newline-insert newline"
29082 in a formula or by the menu
29084 Insert\SpecialChar \menuseparator
29085 Math\SpecialChar \menuseparator
29086 AMS align Environment
29091 \begin_layout Standard
29092 An example for two formulas set side by side, that are created with a four
29093 column align environment:
29094 \begin_inset Formula \begin{align*}
29095 A & =\sin(B) & C & =D\\
29096 C & \ne A & B & \ne D
29101 As it can be seen, the formulas in this environment are placed so as if
29110 \begin_layout Plain Layout
29118 \begin_inset CommandInset ref
29120 reference "sub:Variable-Space"
29131 before the first and after every even column.
29132 When the formula style
29138 \begin_layout Plain Layout
29140 \begin_inset CommandInset ref
29142 reference "sec:Formula-Styles"
29153 is used, the formula is set without the
29159 before the first column.
29162 \begin_layout Subsubsection
29163 Alignat Environment
29164 \begin_inset Index idx
29167 \begin_layout Plain Layout
29168 Formula ! multiline ! alignat environment
29176 \begin_layout Standard
29177 The alignat environment has no predefined column separation.
29178 It can be inserted manually with the spaces that are described
29179 \begin_inset CommandInset ref
29181 reference "sub:Space"
29188 \begin_layout Standard
29189 The above example in the alignat environment where 1
29190 \begin_inset space \thinspace{}
29193 cm space was inserted at the beginning of the second formula:
29194 \begin_inset Formula \begin{alignat*}{2}
29195 A & =\sin(B) & \hspace{1cm}C & =D\\
29196 C & \ne A & B & \ne D
29201 Because the column separation can be set separately for every column, this
29202 environment is especially suitable to set three and more formulas side
29206 \begin_layout Subsubsection
29207 Flalign Environment
29208 \begin_inset CommandInset label
29210 name "sub:Flalign-Environment"
29215 \begin_inset Index idx
29218 \begin_layout Plain Layout
29219 Formula ! multiline ! flalign environment
29227 \begin_layout Standard
29228 In this environment the first two columns are always set as much as possible
29229 to the left and the last two ones to the right.
29231 \begin_inset Formula \begin{flalign*}
29232 A & =1 & B & =2 & C & =3\\
29233 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29241 \begin_layout Standard
29242 By creating a flalign environment with an odd number of columns where an
29243 empty TeX-brace is inserted to the last column, several formulas in a document
29244 can be set to the left, although the formula style
29249 As example the indented formula
29250 \begin_inset CommandInset ref
29252 reference "eq:VolInt"
29257 \begin_inset Formula \begin{flalign}
29258 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29263 The first two columns contain the formula.
29264 To indent it as with the formula style
29269 \begin_inset space \thinspace{}
29272 pt space was inserted at the beginning of the first column.
29275 \begin_layout Subsection
29276 Eqnarray Environment
29277 \begin_inset CommandInset label
29279 name "sub:Eqnarray-Environment"
29284 \begin_inset Index idx
29287 \begin_layout Plain Layout
29288 Formula ! multiline ! eqnarray environment
29296 \begin_layout Standard
29297 When this environment has been created, three blue boxes appear.
29298 The content of the first box is right aligned, the content of the last
29300 The content of the middle box appears centered and a bit smaller, because
29301 it is designed to insert there only relation characters.
29302 \begin_inset Formula \begin{eqnarray*}
29303 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29313 \begin_layout Subsection
29315 \begin_inset Index idx
29318 \begin_layout Plain Layout
29319 Formula ! multiline ! gather environment
29327 \begin_layout Standard
29328 This environment consists of only one centered column.
29329 Every line can be numbered.
29330 \begin_inset Formula \begin{gather}
29340 \begin_layout Subsection
29341 Multline Environment
29342 \begin_inset CommandInset label
29344 name "sub:Multline-Environment"
29349 \begin_inset Index idx
29352 \begin_layout Plain Layout
29353 Formula ! multiline ! multline environment
29361 \begin_layout Standard
29362 The multline environment consists, like the gather environment, of only
29364 But the first line is left aligned, the last one right aligned.
29365 All other lines are centered.
29366 Therefore this environment is suitable for long formulas.
29368 \begin_inset CommandInset ref
29370 reference "eq:lefteqn"
29374 in the multline environment:
29375 \begin_inset Formula \begin{multline}
29376 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}\\
29377 -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}\\
29378 =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}}
29386 \begin_layout Standard
29387 In the output only the last (first) line of a multline environment appears
29388 numbered when the document numbering is right (left).
29392 \begin_layout Plain Layout
29393 numbering styles see
29394 \begin_inset CommandInset ref
29396 reference "sec:Formula-Styles"
29408 \begin_layout Standard
29416 \begin_inset Index idx
29419 \begin_layout Plain Layout
29434 \begin_inset Index idx
29437 \begin_layout Plain Layout
29445 a centered line can be right or left aligned, respectively.
29446 The commands are used as follows:
29449 \begin_layout Standard
29454 shoveright{line content}
29460 shoveleft{line content}
29463 \begin_layout Standard
29464 \begin_inset VSpace medskip
29474 \begin_inset Index idx
29477 \begin_layout Plain Layout
29485 specifies the distance of the first line from the left page margin.
29486 Predefined is the length 0
29487 \begin_inset space \thinspace{}
29493 \begin_layout Standard
29494 As example the above formula where the command
29497 \begin_layout Standard
29507 \begin_layout Standard
29508 was inserted in TeX-mode before:
29512 \begin_layout Plain Layout
29524 \begin_inset Formula \begin{multline}
29525 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}\\
29526 \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}}\\
29527 =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}}
29536 \begin_layout Plain Layout
29547 The second line was left aligned using
29556 \begin_layout Subsection
29557 Multiline Formula Parts
29558 \begin_inset CommandInset label
29560 name "sub:Multiline-Formula-Parts"
29565 \begin_inset Index idx
29568 \begin_layout Plain Layout
29569 Formula ! multiline ! formula parts
29577 \begin_layout Standard
29578 To display only parts of a formula with multiple lines, one of the following
29579 environments are used:
29596 They can be inserted via the menu
29598 Insert\SpecialChar \menuseparator
29601 or by using the commands described in this section.
29604 \begin_layout Standard
29605 The first three have the same properties as the corresponding multiline
29606 formula environments, but it is possible to set further formula parts beside
29609 \begin_inset Formula \[
29610 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29611 \Delta E\Delta t & \ge\frac{\hbar}{2}
29613 \right\} \textrm{Uncertainty relations}
29621 \begin_layout Standard
29622 To get this formula, a displayed formula is created where the command
29629 \begin_inset Index idx
29632 \begin_layout Plain Layout
29641 A purple box appears around the blue formula box where now columns and
29642 lines can be added.
29643 Outside the multiline environment other formula parts can be set, like
29647 \begin_layout Standard
29648 The aligned environment is also suitable for long formulas whose lines are
29649 horizontally aligned.
29650 Using aligned in a displayed formula has the advantage that the formula
29651 number is vertically centered behind the lines.
29653 \begin_inset CommandInset ref
29655 reference "eq:shortlong"
29659 in the aligned environment:
29660 \begin_inset Formula \begin{equation}
29661 \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}|}\\
29662 & -\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}|}
29671 \begin_layout Standard
29672 To use the environments
29691 \begin_inset Index idx
29694 \begin_layout Plain Layout
29709 \begin_inset Index idx
29712 \begin_layout Plain Layout
29727 \begin_inset Index idx
29730 \begin_layout Plain Layout
29738 are inserted, respectively.
29739 The split environment has the same properties as the aligned environment
29740 but it can only have two columns.
29743 \begin_layout Subsection
29744 Text in multiline Formulas
29745 \begin_inset CommandInset label
29747 name "sub:Text-in-multiline"
29752 \begin_inset Index idx
29755 \begin_layout Plain Layout
29762 \begin_inset Index idx
29765 \begin_layout Plain Layout
29766 Formula ! multiline ! text
29774 \begin_layout Standard
29775 In the Align environments, and the multline and gather environment, text
29776 can be inserted that will appear in a separate line and doesn't affect
29777 the column alignment.
29778 To do this, the command
29785 \begin_inset Index idx
29788 \begin_layout Plain Layout
29796 is used in the following scheme:
29799 \begin_layout Standard
29807 \begin_layout Standard
29808 The text should not be longer than a line because it cannot be hyphenated.
29809 As LyX doesn't yet support
29815 directly, the text is written as mathematical text.
29822 must hereby be at the beginning of a line and appears in the output above
29824 An example where the text was inserted at the beginning of the second line:
29825 \begin_inset Formula \begin{align}
29826 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29827 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29835 \begin_layout Section
29837 \begin_inset Index idx
29840 \begin_layout Plain Layout
29847 \begin_inset Index idx
29850 \begin_layout Plain Layout
29851 Formula ! numbering|see
29855 \begin_layout Plain Layout
29866 \begin_layout Plain Layout
29881 \begin_layout Subsection
29885 \begin_layout Standard
29886 Numbered formulas can be created with the menu
29888 Insert\SpecialChar \menuseparator
29889 Math\SpecialChar \menuseparator
29891 \begin_inset space ~
29899 \begin_inset space ~
29905 Existing formulas can be numbered with the menu
29907 Edit\SpecialChar \menuseparator
29908 Math\SpecialChar \menuseparator
29910 \begin_inset space ~
29918 arg "math-number-toggle"
29922 The formula number is displayed in LyX behind the formula as number sign
29924 The number sign is replaced in the output by the formula number.
29927 \begin_layout Standard
29928 When numbering is turned on in multiline formulas, all lines will be numbered.
29929 But the numbering can be controlled with the menu
29931 Edit\SpecialChar \menuseparator
29932 Math\SpecialChar \menuseparator
29934 \begin_inset space ~
29938 \begin_inset space ~
29942 \begin_inset space ~
29950 arg "math-number-line-toggle"
29956 \begin_layout Standard
29957 Except for inline formulas, all formulas can be numbered with two different
29959 \begin_inset CommandInset ref
29961 reference "sec:Formula-Styles"
29968 \begin_layout Subsection
29970 \begin_inset Index idx
29973 \begin_layout Plain Layout
29974 Cross-references ! to formulas
29982 \begin_layout Standard
29983 All labeled formulas can be cross-referenced.
29984 A label is added by the menu
29986 Insert\SpecialChar \menuseparator
29989 or the toolbar button
29990 \begin_inset Graphics
29991 filename ../images/label-insert.png
29997 The cursor must hereby be inside a displayed formula.
29998 A dialog pops up displaying the prefix
30003 The label is inserted there behind the prefix.
30004 The predefined prefix means
30005 \begin_inset Quotes eld
30009 \begin_inset Quotes erd
30012 and makes it easier to find labels in large documents because it marks
30013 it as formula label to divide it from e.
30014 \begin_inset space \thinspace{}
30018 \begin_inset space \space{}
30022 To change a label, the menu
30024 Insert\SpecialChar \menuseparator
30030 \begin_layout Standard
30031 The name of the label is displayed in LyX within two parentheses behind
30033 A formula with a label is always numbered.
30036 \begin_layout Standard
30037 Cross-references are inserted via the menu
30039 Insert\SpecialChar \menuseparator
30042 or with the toolbar button
30043 \begin_inset Graphics
30044 filename ../images/dialog-show-new-inset_ref.png
30050 A formula cross-reference appears in the output as formula number.
30051 When in the cross-reference dialog window the format
30055 is chosen, the cross-reference appears in the output as formula number
30057 \begin_inset Newline newline
30060 By right-clicking on a cross-reference in LyX, one jumps to the formula
30061 that is referenced.
30064 \begin_layout Standard
30065 Here are as examples cross-references to formulas of the following subsections:
30066 \begin_inset Note Note
30069 \begin_layout Plain Layout
30070 Note the different cross-reference types.
30078 \begin_layout Standard
30080 \begin_inset CommandInset ref
30087 \begin_inset CommandInset ref
30095 \begin_inset CommandInset ref
30101 ) big Latin letters are used for the numbering in contrary to (
30102 \begin_inset CommandInset ref
30111 \begin_layout Standard
30112 \begin_inset VSpace medskip
30115 When the argument of
30123 \begin_layout Plain Layout
30131 \begin_inset CommandInset ref
30133 reference "sub:User-defined-Numbering"
30144 contains a box like in
30145 \begin_inset CommandInset ref
30147 reference "sub:Paragraph-Boxes"
30151 , the formula cannot be referenced.
30154 \begin_layout Subsection
30156 \begin_inset Index idx
30159 \begin_layout Plain Layout
30160 Formula numbering ! subnumbering
30168 \begin_layout Standard
30169 With the help of the commands
30173 begin{subequations}
30181 formulas can be subnumbered.
30182 Both commands are inserted in TeX-mode.
30185 \begin_layout Standard
30187 \begin_inset Formula \begin{equation}
30197 \begin_layout Plain Layout
30201 addtocounter{equation}{-1}
30210 \begin_layout Plain Layout
30214 begin{subequations}
30220 \begin_inset VSpace -5mm
30224 \begin_inset Formula \begin{equation}
30231 \begin_inset Formula \begin{equation}
30240 \begin_layout Standard
30244 \begin_layout Plain Layout
30256 \begin_layout Standard
30257 To create the example, the following is done:
30260 \begin_layout Enumerate
30261 first formula is inserted
30264 \begin_layout Enumerate
30269 addtocounter{equation}{-1}
30271 begin{subequations}
30272 \begin_inset Index idx
30275 \begin_layout Plain Layout
30284 \begin_inset Newline newline
30289 is inserted after the first formula
30292 \begin_layout Enumerate
30293 second formula is inserted
30296 \begin_layout Enumerate
30297 third formula is inserted
30300 \begin_layout Enumerate
30307 is inserted after the third formula
30310 \begin_layout Standard
30311 Every formula between the commands
30323 is subnumbered as a, b,
30324 \begin_inset Newline linebreak
30327 c, \SpecialChar \ldots{}
30328 For multiline formulas every line will be subnumbered.
30329 All subnumbered formulas are treated as
30334 But as every numbered formula increases the counter
30338 by one, the command
30344 is needed to decrease it.
30345 Otherwise the formulas
30346 \begin_inset CommandInset ref
30353 \begin_inset CommandInset ref
30360 \begin_inset CommandInset ref
30366 would be numbered as
30367 \begin_inset CommandInset ref
30374 \begin_inset CommandInset ref
30381 \begin_inset CommandInset ref
30390 \begin_layout Standard
30391 By inserting the commands in TeX-mode, a space is created between the first
30394 \begin_inset space \thinspace{}
30397 mm vertical space is inserted after the command
30401 begin{subequations}
30404 When the formula style
30410 \begin_layout Plain Layout
30412 \begin_inset CommandInset ref
30414 reference "sec:Formula-Styles"
30426 \begin_inset space \thinspace{}
30429 mm space is inserted instead.
30432 \begin_layout Standard
30433 Here is an example for a multiline formula where the numbering was turned
30434 off for the second line:
30438 \begin_layout Plain Layout
30442 begin{subequations}
30448 \begin_inset Formula \begin{eqnarray}
30449 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30450 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30451 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30460 \begin_layout Plain Layout
30472 \begin_layout Subsection
30473 User-defined Numbering
30474 \begin_inset CommandInset label
30476 name "sub:User-defined-Numbering"
30481 \begin_inset Index idx
30484 \begin_layout Plain Layout
30485 Formula numbering ! user-defined
30493 \begin_layout Standard
30494 \begin_inset Index idx
30497 \begin_layout Plain Layout
30498 Formula numbering ! self-defined delimiters
30503 With the standard numbering parentheses are set around the formula number.
30504 To replace the parentheses for example by vertical bars, the following
30505 line is added to the LaTeX-preamble:
30508 \begin_layout Standard
30520 \begin_inset Note Note
30523 \begin_layout Plain Layout
30524 This macro is already declared in the LaTeX-preamble for testing.
30525 To activate it, remove the percent sign at the beginning.
30533 \begin_layout Standard
30534 To use other characters, the vertical bars besides the
30538 are replaced by one ore more characters.
30539 To get only the formula number the vertical bars are omitted.
30542 \begin_layout Standard
30543 \begin_inset VSpace bigskip
30546 When there should be an expression of your choice instead of the consecutive
30547 formula number in parentheses behind the formula, the command
30554 \begin_inset Index idx
30557 \begin_layout Plain Layout
30566 \begin_inset Formula \begin{equation}
30567 A+B=C\tag{something}\label{eq:tag}
30572 In this example the command
30580 \begin_layout Plain Layout
30591 was inserted to the formula.
30594 \begin_layout Standard
30603 \begin_layout Plain Layout
30614 is inserted instead, the star prevents the parentheses around the expression:
30615 \begin_inset Formula \[
30616 A+B=C\tag*{something}
30624 \begin_layout Standard
30625 \begin_inset VSpace bigskip
30628 To restart the formula numbering with new document parts or sections, the
30629 following command is used:
30632 \begin_layout Standard
30637 @addtoreset{equation}{part}
30640 \begin_inset Index idx
30643 \begin_layout Plain Layout
30648 \begin_layout Plain Layout
30659 \begin_layout Plain Layout
30672 \begin_layout Plain Layout
30683 \begin_layout Plain Layout
30696 \begin_inset Newline newline
30700 \begin_inset Newline newline
30707 @addtoreset{equation}{section}
30710 \begin_layout Standard
30711 To be able to use these commands in TeX-mode, the
30712 \begin_inset Quotes eld
30716 \begin_inset Quotes erd
30719 character has to be made
30720 \begin_inset Quotes eld
30724 \begin_inset Quotes erd
30727 for LaTeX using the command
30741 So the command sequence in TeX-mode is:
30744 \begin_layout Standard
30750 \begin_inset Newline newline
30755 @addtoreset{equation}{section}
30756 \begin_inset Newline newline
30764 \begin_layout Standard
30765 In the LaTeX-preamble
30777 can be omitted as they are automatically internally inserted by LyX.
30780 \begin_layout Standard
30795 \begin_layout Plain Layout
30800 is part of the LaTeX-package
30805 \begin_inset Index idx
30808 \begin_layout Plain Layout
30809 Packages ! carlisle
30814 that is part of every LaTeX standard installation.
30820 \begin_inset Index idx
30823 \begin_layout Plain Layout
30824 Packages ! remreset
30829 has to be loaded in the LaTeX-preamble with the line
30832 \begin_layout Standard
30837 usepackage{remreset}
30840 \begin_layout Standard
30848 \begin_inset Index idx
30851 \begin_layout Plain Layout
30856 \begin_layout Plain Layout
30867 \begin_layout Plain Layout
30880 \begin_layout Plain Layout
30891 \begin_layout Plain Layout
30903 can be used with the same scheme as
30912 \begin_layout Standard
30913 \begin_inset VSpace bigskip
30916 Sometimes formulas should be numbered in the following form:
30919 \begin_layout Standard
30922 (section number.formula number)
30925 \begin_layout Standard
30926 The formula number should start with every section with
30927 \begin_inset Quotes eld
30931 \begin_inset Quotes erd
30937 \begin_layout Standard
30938 For this case there is the command
30945 \begin_inset Index idx
30948 \begin_layout Plain Layout
30956 , which is used with the following scheme:
30959 \begin_layout Standard
30964 numberwithin{counter}{sectioning}
30967 \begin_layout Standard
30968 Counter denotes what kind of numbering is affected, sectioning denotes what
30969 number is before the dot.
30972 \begin_layout Standard
30973 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30976 \begin_layout Standard
30981 numberwithin{equation}{section}
30984 \begin_layout Standard
30985 This is the result:
30989 \begin_layout Plain Layout
30993 numberwithin{equation}{section}
30999 \begin_inset Formula \begin{equation}
31008 \begin_layout Standard
31010 \begin_inset space \thinspace{}
31014 \begin_inset space \space{}
31017 tables so that the number of the part is the sectioning,
31018 \begin_inset Newline newline
31025 numberwithin{table}{part}
31030 \begin_layout Standard
31031 To go back to the standard numbering or to prevent this kind of numbering
31032 when it is defined by the document class, the following command is inserted
31033 as TeX-Code or to the LaTeX-preamble:
31036 \begin_layout Standard
31046 \begin_inset Index idx
31049 \begin_layout Plain Layout
31063 \begin_layout Plain Layout
31079 \begin_inset Newline newline
31087 \begin_inset Newline newline
31099 \begin_layout Standard
31106 uses internally the command
31112 , described above, that also needs to be reverted.
31116 \begin_layout Plain Layout
31123 \begin_layout Plain Layout
31127 @removefromreset{equation}{section}
31130 \begin_layout Plain Layout
31142 \begin_layout Subsection
31143 Numbering with Roman Numbers and Letters
31144 \begin_inset Index idx
31147 \begin_layout Plain Layout
31148 Formula numbering ! with letters
31154 \begin_inset Index idx
31157 \begin_layout Plain Layout
31158 Formula numbering ! with Roman numbers
31166 \begin_layout Standard
31167 Formulas can also be numbered with Roman numbers and Latin letters.
31168 To number for example with small Roman numbers, the command
31171 \begin_layout Standard
31183 \begin_layout Standard
31184 is inserted before the formula in TeX-mode.
31192 \begin_inset Index idx
31195 \begin_layout Plain Layout
31203 redefines the predefined command
31219 \begin_layout Plain Layout
31226 has the same scheme like the command
31232 that is described in
31233 \begin_inset CommandInset ref
31235 reference "sub:The-Command-newcommand"
31248 is the formula counter.
31255 is used as prefix for a counter, the value of the counter is output as
31257 When a formula is numbered, LaTeX sets internally the command
31263 behind the formula.
31269 \begin_inset Index idx
31272 \begin_layout Plain Layout
31282 outputs the counter as small Roman number.
31285 \begin_layout Standard
31286 All formulas behind the command
31296 are now numbered Roman.
31297 To switch to numbering with big Roman numbers, the command is inserted
31311 \begin_inset Index idx
31314 \begin_layout Plain Layout
31326 \begin_inset Quotes eld
31330 \begin_inset Quotes erd
31333 with small Latin letters there is the command
31340 \begin_inset Index idx
31343 \begin_layout Plain Layout
31351 , for big ones there is the command
31358 \begin_inset Index idx
31361 \begin_layout Plain Layout
31374 \begin_layout Standard
31375 \begin_inset Note Greyedout
31378 \begin_layout Plain Layout
31383 Only maximal 26 formulas can be numbered with Latin letters in one document.
31391 \begin_layout Standard
31395 \begin_layout Plain Layout
31411 \begin_layout Standard
31412 \begin_inset Formula \begin{equation}
31413 A=\textrm{small roman}
31422 \begin_layout Plain Layout
31436 \begin_inset Formula \begin{equation}
31437 B=\textrm{big Roman}\label{eq:Rom}
31446 \begin_layout Plain Layout
31460 \begin_inset Formula \begin{equation}
31461 C=\textrm{small Latin}
31470 \begin_layout Plain Layout
31484 \begin_inset Formula \begin{equation}
31485 D=\textrm{big Latin}\label{eq:Lat}
31493 \begin_layout Standard
31494 To switch back to the default numbering, insert the command:
31497 \begin_layout Standard
31507 \begin_inset Index idx
31510 \begin_layout Plain Layout
31521 \begin_layout Standard
31525 \begin_layout Plain Layout
31539 \begin_inset Formula \begin{equation}
31548 \begin_layout Standard
31549 \begin_inset VSpace medskip
31552 As you see, formulas are numbered serially independent from the numbering
31554 When then numbering should start with
31555 \begin_inset Quotes eld
31559 \begin_inset Quotes erd
31562 when the style is changed, new equation counters have to be defined.
31563 A description about this can be found in the file
31564 \begin_inset CommandInset href
31566 name "Formula-numbering.lyx"
31567 target "run:Formula-numbering.lyx"
31574 \begin_layout Section
31575 Chemical Symbols and Equations
31576 \begin_inset CommandInset label
31578 name "sub:Chemical-Symbols-and"
31583 \begin_inset Index idx
31586 \begin_layout Plain Layout
31587 Chemical characters ! Symbols
31593 \begin_inset Index idx
31596 \begin_layout Plain Layout
31603 \begin_inset Index idx
31606 \begin_layout Plain Layout
31615 \begin_layout Standard
31616 An example text from chemistry:
31619 \begin_layout Quote
31621 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31624 -ion reacts with two
31625 \begin_inset Formula $\mathrm{Na^{+}}$
31628 -ions to sodium sulfate
31629 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31633 The chemical equation for this is:
31634 \begin_inset Formula \begin{equation}
31635 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31643 \begin_layout Standard
31644 This chemical equation can directly be created as formula.
31645 To avoid that the symbols appear italic, everything is highlighted and
31646 changed by the shortcut
31652 to the upright font style.
31656 \begin_layout Plain Layout
31662 \begin_inset CommandInset ref
31664 reference "sub:Font-Styles"
31676 \begin_layout Standard
31677 A more convenient way to typeset chemical formulas is to use the command
31685 \begin_inset Index idx
31688 \begin_layout Plain Layout
31696 that is available when the LaTeX-package
31701 \begin_inset Index idx
31704 \begin_layout Plain Layout
31717 to a formula a new blue box appears where chemical formulas can be inserted
31718 in an intuitive way.
31721 \begin_layout Standard
31723 \begin_inset Tabular
31724 <lyxtabular version="3" rows="9" columns="2">
31725 <features tabularvalignment="middle">
31726 <column alignment="center" valignment="top" width="0">
31727 <column alignment="center" valignment="top" width="0">
31729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31732 \begin_layout Plain Layout
31738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31741 \begin_layout Plain Layout
31743 \begin_inset Note Note
31746 \begin_layout Plain Layout
31753 is only used as spacer.
31765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31768 \begin_layout Plain Layout
31775 \begin_layout Plain Layout
31789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31792 \begin_layout Plain Layout
31793 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31806 \begin_layout Plain Layout
31813 \begin_layout Plain Layout
31827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31830 \begin_layout Plain Layout
31831 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31844 \begin_layout Plain Layout
31851 \begin_layout Plain Layout
31865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31868 \begin_layout Plain Layout
31869 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31882 \begin_layout Plain Layout
31889 \begin_layout Plain Layout
31903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31906 \begin_layout Plain Layout
31907 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31920 \begin_layout Plain Layout
31927 \begin_layout Plain Layout
31942 \begin_layout Plain Layout
31957 \begin_layout Plain Layout
31971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31974 \begin_layout Plain Layout
31975 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31988 \begin_layout Plain Layout
31995 \begin_layout Plain Layout
32005 \begin_inset Formula $\downarrow$
32009 \begin_inset Formula $\to$
32017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32020 \begin_layout Plain Layout
32021 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32034 \begin_layout Plain Layout
32041 \begin_layout Plain Layout
32054 \begin_layout Plain Layout
32067 \begin_layout Plain Layout
32080 \begin_layout Plain Layout
32093 \begin_layout Plain Layout
32107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32110 \begin_layout Plain Layout
32111 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32124 \begin_layout Plain Layout
32131 \begin_layout Plain Layout
32144 \begin_layout Plain Layout
32157 \begin_layout Plain Layout
32170 \begin_layout Plain Layout
32187 \begin_layout Plain Layout
32201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32204 \begin_layout Plain Layout
32205 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32221 \begin_layout Standard
32222 \begin_inset Note Greyedout
32225 \begin_layout Plain Layout
32230 Inserting a formula to a
32236 box will lead to LaTeX errors.
32237 In this case TeX code has to be used like for
32251 \begin_layout Plain Layout
32272 \begin_layout Standard
32279 the command for equation
32280 \begin_inset space ~
32284 \begin_inset CommandInset ref
32286 reference "eq:chem-reaction"
32291 \begin_inset Newline newline
32302 \begin_layout Plain Layout
32315 \begin_layout Plain Layout
32328 \begin_layout Plain Layout
32341 \begin_layout Plain Layout
32354 \begin_layout Plain Layout
32367 \begin_layout Plain Layout
32379 \begin_layout Standard
32380 To create multiline chemical equations first a multiline formula is created
32382 \begin_inset CommandInset ref
32384 reference "sec:Multiline-Formulas"
32389 Afterwards the command
32395 is used in every small blue box of the formula.
32397 \begin_inset CommandInset ref
32399 reference "eq:TEOS-reaction-1"
32404 \begin_inset CommandInset ref
32406 reference "eq:TEOS-reaction-2"
32410 are an example of a multi-stage chemical reaction where every equation
32411 has its own number.
32412 \begin_inset Formula \begin{eqnarray}
32413 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32414 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32422 \begin_layout Standard
32433 package provides the command
32440 \begin_inset Index idx
32443 \begin_layout Plain Layout
32451 that has to be used for special cases.
32452 For more information about
32458 and more examples have a look at the documentation of
32463 \begin_inset CommandInset citation
32472 \begin_layout Standard
32473 \begin_inset Newpage newpage
32479 \begin_layout Section
32483 \begin_layout Standard
32484 LyX supports two types of commutative diagrams:
32492 that are explained in the following.
32495 \begin_layout Subsection
32497 \begin_inset Index idx
32500 \begin_layout Plain Layout
32509 \begin_layout Standard
32510 Diagrams of this type visualize relations by vertical and horizontal lines
32512 \begin_inset Formula \[
32513 \begin{CD}A@>>>B@>>>C\\
32524 \begin_layout Standard
32525 To get them, the command
32530 \begin_inset Index idx
32533 \begin_layout Plain Layout
32543 is inserted to a formula.
32544 A blue box appears with two dashed lines where further commands can be
32549 arg "newline-insert newline"
32552 a new line is created.
32553 Horizontal relations are inserted in odd, vertical in even formula lines.
32556 \begin_layout Standard
32557 To create the relations there are the following commands:
32560 \begin_layout Itemize
32565 creates a left arrow,
32576 \begin_layout Itemize
32581 creates an up arrow,
32589 a vertical equal sign
32592 \begin_layout Itemize
32598 is a placeholder for non-existent relations
32601 \begin_layout Standard
32602 All arrows can be labeled as follows:
32605 \begin_layout Itemize
32606 Is text inserted between the first and second < or >, resp., it is placed
32608 When it is inserted between the second and third one, it appears under
32612 \begin_layout Itemize
32613 When text for vertical arrows is inserted between the first and second A
32614 or V, resp., it is placed left beside the arrow.
32615 When it is inserted between the second and third one, it appears right
32617 If the text contains an A or V, these letters must be set into a TeX-brace.
32620 \begin_layout Standard
32621 As example a diagram with all possible relations:
32624 \begin_layout Standard
32625 \begin_inset Formula \[
32626 \begin{CD}A@>j>>B@>>k>C@=F\\
32637 \begin_layout Standard
32638 The command for this is:
32639 \begin_inset Newline newline
32650 \begin_layout Plain Layout
32659 A@>j>>B@>>k>C@=F Ctrl+Return
32660 \begin_inset Newline newline
32664 \begin_inset Phantom HPhantom
32667 \begin_layout Plain Layout
32676 \begin_layout Plain Layout
32695 \begin_inset Formula $\to$
32701 \begin_inset Newline newline
32705 \begin_inset Phantom HPhantom
32708 \begin_layout Plain Layout
32717 \begin_layout Plain Layout
32734 \begin_layout Subsection
32736 \begin_inset Index idx
32739 \begin_layout Plain Layout
32740 Diagrams ! xymatrix
32748 \begin_layout Standard
32749 To be able to use xymatrices, the LaTeX-package
32754 A xymatrix is created by inserting the command
32761 Then you are able to add new matrix columns and rows like for normal matrices,
32763 \begin_inset CommandInset ref
32765 reference "sec:Matrices"
32772 \begin_layout Standard
32773 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32775 All possibilities to create commutative diagrams and decorations are explained
32780 that you find in the menu
32782 Help\SpecialChar \menuseparator
32784 \begin_inset space ~
32792 \begin_layout Subsection
32798 \begin_inset Index idx
32801 \begin_layout Plain Layout
32810 \begin_layout Standard
32815 -diagrams, the LaTeX-package
32824 -diagram is created by inserting the command
32831 Then you are able to add new matrix columns and rows like for normal matrices,
32833 \begin_inset CommandInset ref
32835 reference "sec:Matrices"
32842 \begin_layout Standard
32843 Examples how to create
32847 diagrams in LyX is given in the
32849 Feynman-diagram manual
32851 that you find in the menu
32853 Help\SpecialChar \menuseparator
32855 \begin_inset space ~
32863 \begin_layout Section
32864 User-defined Commands
32865 \begin_inset Index idx
32868 \begin_layout Plain Layout
32869 User-defined commands
32877 \begin_layout Standard
32878 \begin_inset Note Greyedout
32881 \begin_layout Plain Layout
32886 The names of user-defined commands and macros may only consist of Latin
32895 \begin_layout Subsection
32899 \begin_inset CommandInset label
32901 name "sub:The-Command-newcommand"
32906 \begin_inset Index idx
32909 \begin_layout Plain Layout
32910 User-defined commands !
32918 \begin_inset Index idx
32921 \begin_layout Plain Layout
32932 \begin_layout Standard
32933 Many LaTeX-commands are too long to be used frequently.
32934 But it is possible to define with the command
32940 new shorter commands.
32943 \begin_layout Standard
32944 The command scheme of
32953 \begin_layout Standard
32958 newcommand{new command name}[number of arguments][optional
32963 \begin_inset Newline newline
32967 \begin_inset Phantom HPhantom
32970 \begin_layout Plain Layout
32980 {command definition}
32983 \begin_layout Standard
32984 \begin_inset Note Greyedout
32987 \begin_layout Plain Layout
32992 Assure that the name of the new command is not already used in your document
32993 or by LaTeX-packages that you use.
32994 When you for example define the command
33006 , you get an error message because
33012 is already defined as command for
33013 \begin_inset Quotes eld
33017 \begin_inset Formula $\le$
33021 \begin_inset Quotes erd
33032 \begin_layout Standard
33033 The number of arguments is an integer in the range 0
33034 \begin_inset space \thinspace{}
33038 \begin_inset space \thinspace{}
33041 9 and specifies how many arguments the new command should have.
33042 With the optional value a value for an optional argument can be predefined.
33043 When this is done, the
33051 rgument of the new command is automatically an optional one.
33054 \begin_layout Standard
33055 Here are some examples:
33058 \begin_layout Itemize
33059 To define the command
33071 , the LaTeX-preamble line is:
33072 \begin_inset VSpace medskip
33076 \begin_inset Newline newline
33090 \begin_layout Itemize
33091 To define the command
33103 , the argument (that should be underlined) must be taken into account.
33104 For this the preamble line is:
33105 \begin_inset VSpace medskip
33109 \begin_inset Newline newline
33123 \begin_inset VSpace medskip
33127 \begin_inset Newline newline
33134 acts as argument placeholder, the
33138 behind it denotes that it is the placeholder for the first argument.
33141 \begin_layout Itemize
33149 \begin_inset space \thinspace{}
33153 \begin_inset space \space{}
33163 \begin_inset VSpace medskip
33167 \begin_inset Newline newline
33178 framebox#1#2{$#3$}}
33181 \begin_inset VSpace medskip
33185 \begin_inset Newline newline
33188 The two Dollar signs creates the extra formula needed for
33195 \begin_inset CommandInset ref
33197 reference "sub:Boxes-with-Frame"
33204 \begin_layout Itemize
33205 To create a new command for
33211 where the color for the box needn't to be specified, the argument for the
33212 color is defined optional:
33213 \begin_inset VSpace medskip
33217 \begin_inset Newline newline
33228 fcolorbox{#2}{#1}{$#3$}}
33231 \begin_inset VSpace medskip
33235 \begin_inset Newline newline
33238 When the color is not specified when using
33244 , the predefined color
33251 \begin_layout Standard
33252 A test of the new defined commands:
33255 \begin_layout Standard
33257 \begin_inset Tabular
33258 <lyxtabular version="3" rows="6" columns="2">
33259 <features tabularvalignment="middle">
33260 <column alignment="center" valignment="top" width="0">
33261 <column alignment="center" valignment="top" width="0">
33263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33266 \begin_layout Plain Layout
33272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33275 \begin_layout Plain Layout
33277 \begin_inset Note Note
33280 \begin_layout Plain Layout
33287 is only used as spacer.
33299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33302 \begin_layout Plain Layout
33309 \begin_layout Plain Layout
33323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33326 \begin_layout Plain Layout
33327 \begin_inset Formula $A\gr B$
33337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33340 \begin_layout Plain Layout
33348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33351 \begin_layout Plain Layout
33352 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33365 \begin_layout Plain Layout
33369 \begin_inset Formula $\to$
33375 \begin_inset Formula $\to$
33386 \begin_layout Plain Layout
33400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33403 \begin_layout Plain Layout
33404 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33417 \begin_layout Plain Layout
33421 \begin_inset Formula $\to$
33432 \begin_layout Plain Layout
33446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33449 \begin_layout Plain Layout
33450 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33463 \begin_layout Plain Layout
33469 \begin_inset Formula $\to$
33480 \begin_layout Plain Layout
33494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33497 \begin_layout Plain Layout
33498 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33514 \begin_layout Subsection
33516 \begin_inset Index idx
33519 \begin_layout Plain Layout
33520 User-defined commands! Math macros
33526 \begin_inset Index idx
33529 \begin_layout Plain Layout
33538 \begin_layout Standard
33539 User-defined commands are especially convenient for complex expressions.
33540 When you are for example dealing in a document with quadratic equations,
33541 the same solution type occurs several times.
33542 The general form of a quadratic equation is
33543 \begin_inset Formula \[
33544 0=\lambda^{2}+p\lambda+q
33549 The general form of the solution is
33550 \begin_inset Formula \[
33551 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33559 \begin_layout Standard
33560 To define a command for the solution formula where only the three parameters
33562 \begin_inset Formula $\lambda$
33566 \begin_inset Formula $p$
33570 \begin_inset Formula $q$
33573 need to be specified and the index of
33574 \begin_inset Formula $\lambda$
33577 can be given optionally, the LaTeX-preamble line is
33578 \begin_inset Newline newline
33594 \begin_inset Newline newline
33598 \begin_inset Phantom HPhantom
33601 \begin_layout Plain Layout
33615 frac{#3^{2}}{4}-#4}}
33618 \begin_layout Standard
33619 To create with this the solution formula, the command
33620 \begin_inset Newline newline
33630 \begin_inset Formula $\to$
33636 \begin_inset Formula $\to$
33643 is inserted to a formula
33648 \begin_layout Standard
33649 The definition of the new command is unintuitive because one has to know
33650 the schemes of all used LaTeX commands, e.
33651 \begin_inset space \thinspace{}
33655 \begin_inset space \space{}
33658 that a fraction is inserted in LaTeX as
33662 frac{numerator}{denominator}
33665 Furthermore one can easily forget a brace in the definition and cannot
33666 see in LyX what the new command is doing.
33667 To avoid these problems LyX offers the possibility to use math macros instead
33677 \begin_layout Standard
33678 A math macro is created by using the menu
33680 Insert\SpecialChar \menuseparator
33681 Math\SpecialChar \menuseparator
33684 or the toolbar button
33685 \begin_inset Graphics
33686 filename ../images/math-macro_newmacroname_newcommand.png
33692 The math macro toolbar appears together with the following box where the
33694 \begin_inset Newline newline
33698 \begin_inset space \hspace*{\fill}
33702 \begin_inset Graphics
33703 filename clipart/macrobox.png
33708 \begin_inset space \hspace*{\fill}
33712 \begin_inset Newline newline
33716 \begin_inset FormulaMacro
33717 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33722 newmacroname is the default name of the macro that should be changed to
33723 something sensible.
33724 The wanted formula is inserted in the first blue box.
33725 An argument placeholder is inserted with the command
33732 \begin_inset space \thinspace{}
33736 \begin_inset space \space{}
33745 or by using the macro toolbar button
33746 \begin_inset Graphics
33747 filename ../images/math-macro-add-param.png
33753 Argument placeholders are displayed red.
33754 Maximum 9 arguments are possible.
33755 Optional arguments are created with the toolbar button
33756 \begin_inset Graphics
33757 filename ../images/math-macro-add-optional-param.png
33763 The first non-optional argument can be transformed to an optional one with
33765 \begin_inset Graphics
33766 filename ../images/math-macro-make-optional.png
33772 In the second blue box the appearance of the macro in LyX can be defined.
33773 Normally you want to see it as it is defined, so the box is kept empty.
33774 But when you have created a macro that needs lot of space on the screen,
33775 you can insert in the box for example
33776 \begin_inset Newline newline
33806 \begin_inset Newline newline
33811 For the macro only the arguments with the macro name in front of them will
33812 then be displayed in LyX, leading to a better overview.
33813 The formula appears in the output as defined in the first box.
33814 \begin_inset Newline newline
33817 The appearance of macros in formulas can furthermore be changed for single
33818 macros by setting the cursor in the macro and using the menu
33820 View\SpecialChar \menuseparator
33822 \begin_inset space ~
33826 \begin_inset space ~
33834 \begin_layout Standard
33835 To use a macro, the macro name is inserted as command to a formula, in our
33843 Our macro looks in LyX like this:
33844 \begin_inset Newline newline
33848 \begin_inset space \hspace*{\fill}
33852 \begin_inset Graphics
33853 filename clipart/macrouse.png
33858 \begin_inset space \hspace*{\fill}
33862 \begin_inset Newline newline
33865 Here is our macro example with the arguments
33866 \begin_inset Formula $x$
33870 \begin_inset Formula $\ln(x)$
33874 \begin_inset Formula $B$
33880 \begin_layout Standard
33881 \begin_inset Formula \[
33890 \begin_layout Standard
33891 LyX offers in the menu
33893 Tools\SpecialChar \menuseparator
33894 Preferences\SpecialChar \menuseparator
33895 Editing\SpecialChar \menuseparator
33898 different styles to edit macros.
33899 To find the style that suits you the most, choose a style and set the cursor
33900 in a macro formula to see the difference.
33903 \begin_layout Standard
33904 A math macro is transformed internally to a
33910 command when exporting the document.
33917 command is not placed in the LaTeX-preamble, therefore macros can only
33918 be used in formulas that are in the document below the macro definition
33922 \begin_layout Standard
33923 Math macros can also be directly be created from a
33930 When writing for example the command
33933 \begin_inset Newline newline
33942 xleftarrow[#2]{#1}}
33943 \begin_inset Newline newline
33948 in LyX as normal text, highlighting it completely and using then the shortcut
33953 , the command will be transformed to a math macro.
33954 Using this method you need to be careful that the
33960 command is typed correctly, otherwise you get a faulty macro leading to
33964 \begin_layout Standard
33965 Math macros currently yet have the problem that further formulas in macro
33966 definitions are handled wrongly.
33967 Therefore the example
33974 \begin_inset CommandInset ref
33976 reference "sub:The-Command-newcommand"
33980 cannot be created as macro.
33983 \begin_layout Standard
33984 When the cursor is in a macro definition box, you will see the macro toolbar
33988 \begin_layout Standard
33989 \begin_inset VSpace defskip
33995 \begin_layout Standard
33996 \begin_inset Graphics
33997 filename clipart/MacroToolbar.png
34002 \begin_inset Index idx
34005 \begin_layout Plain Layout
34014 \begin_layout Standard
34015 \begin_inset VSpace defskip
34021 \begin_layout Standard
34022 The macro toolbar contains from left to right the following buttons:
34025 \begin_layout Standard
34026 \begin_inset VSpace defskip
34032 \begin_layout Standard
34033 \begin_inset Tabular
34034 <lyxtabular version="3" rows="9" columns="2">
34035 <features islongtable="true" longtabularalignment="center">
34036 <column alignment="left" valignment="top" width="0">
34037 <column alignment="left" valignment="top" width="85col%">
34038 <row interlinespace="2.5mm">
34039 <cell alignment="center" valignment="top" usebox="none">
34042 \begin_layout Plain Layout
34043 \begin_inset Graphics
34044 filename ../images/math-macro-remove-param.png
34045 rotateOrigin center
34054 <cell alignment="center" valignment="top" usebox="none">
34057 \begin_layout Plain Layout
34060 Edit\SpecialChar \menuseparator
34061 Math\SpecialChar \menuseparator
34063 \begin_inset space ~
34066 Definition\SpecialChar \menuseparator
34067 Remove Last Argument
34073 <row interlinespace="2.5mm">
34074 <cell alignment="center" valignment="top" usebox="none">
34077 \begin_layout Plain Layout
34078 \begin_inset Graphics
34079 filename ../images/math-macro-add-param.png
34080 rotateOrigin center
34089 <cell alignment="center" valignment="top" usebox="none">
34092 \begin_layout Plain Layout
34095 Edit\SpecialChar \menuseparator
34096 Math\SpecialChar \menuseparator
34098 \begin_inset space ~
34101 Definition\SpecialChar \menuseparator
34108 <row interlinespace="2.5mm">
34109 <cell alignment="center" valignment="top" usebox="none">
34112 \begin_layout Plain Layout
34113 \begin_inset Graphics
34114 filename ../images/math-macro-make-optional.png
34115 rotateOrigin center
34124 <cell alignment="center" valignment="top" usebox="none">
34127 \begin_layout Plain Layout
34130 Edit\SpecialChar \menuseparator
34131 Math\SpecialChar \menuseparator
34133 \begin_inset space ~
34136 Definition\SpecialChar \menuseparator
34137 Make First Non-Optional into
34138 \begin_inset Newline newline
34142 \begin_inset Phantom HPhantom
34145 \begin_layout Plain Layout
34148 Edit\SpecialChar \menuseparator
34149 Math\SpecialChar \menuseparator
34151 \begin_inset space ~
34154 Definition\SpecialChar \menuseparator
34166 <row interlinespace="2.5mm">
34167 <cell alignment="center" valignment="top" usebox="none">
34170 \begin_layout Plain Layout
34171 \begin_inset Graphics
34172 filename ../images/math-macro-make-nonoptional.png
34173 rotateOrigin center
34182 <cell alignment="center" valignment="top" usebox="none">
34185 \begin_layout Plain Layout
34188 Edit\SpecialChar \menuseparator
34189 Math\SpecialChar \menuseparator
34191 \begin_inset space ~
34194 Definition\SpecialChar \menuseparator
34195 Make Last Optional into
34196 \begin_inset Newline newline
34200 \begin_inset Phantom HPhantom
34203 \begin_layout Plain Layout
34206 Edit\SpecialChar \menuseparator
34207 Math\SpecialChar \menuseparator
34209 \begin_inset space ~
34212 Definition\SpecialChar \menuseparator
34218 Non-Optional Argument
34224 <row interlinespace="2.5mm">
34225 <cell alignment="center" valignment="top" usebox="none">
34228 \begin_layout Plain Layout
34229 \begin_inset Graphics
34230 filename ../images/math-macro-remove-optional-param.png
34231 rotateOrigin center
34240 <cell alignment="center" valignment="top" usebox="none">
34243 \begin_layout Plain Layout
34246 Edit\SpecialChar \menuseparator
34247 Math\SpecialChar \menuseparator
34249 \begin_inset space ~
34252 Definition\SpecialChar \menuseparator
34253 Remove Optional Argument
34259 <row interlinespace="2.5mm">
34260 <cell alignment="center" valignment="top" usebox="none">
34263 \begin_layout Plain Layout
34264 \begin_inset Graphics
34265 filename ../images/math-macro-add-optional-param.png
34266 rotateOrigin center
34275 <cell alignment="center" valignment="top" usebox="none">
34278 \begin_layout Plain Layout
34281 Edit\SpecialChar \menuseparator
34282 Math\SpecialChar \menuseparator
34284 \begin_inset space ~
34287 Definition\SpecialChar \menuseparator
34288 Insert Optional Argument
34294 <row interlinespace="2.5mm">
34295 <cell alignment="center" valignment="top" usebox="none">
34298 \begin_layout Plain Layout
34299 \begin_inset Graphics
34300 filename ../images/math-macro-remove-greedy-param.png
34301 rotateOrigin center
34310 <cell alignment="center" valignment="top" usebox="none">
34313 \begin_layout Plain Layout
34316 Edit\SpecialChar \menuseparator
34317 Math\SpecialChar \menuseparator
34319 \begin_inset space ~
34322 Definition\SpecialChar \menuseparator
34323 Remove Last Argument
34324 \begin_inset Newline newline
34328 \begin_inset Phantom HPhantom
34331 \begin_layout Plain Layout
34334 Edit\SpecialChar \menuseparator
34335 Math\SpecialChar \menuseparator
34337 \begin_inset space ~
34340 Definition\SpecialChar \menuseparator
34346 Spitting Out To The Right
34352 <row interlinespace="2.5mm">
34353 <cell alignment="center" valignment="top" usebox="none">
34356 \begin_layout Plain Layout
34357 \begin_inset Graphics
34358 filename ../images/math-macro-append-greedy-param.png
34359 rotateOrigin center
34368 <cell alignment="center" valignment="top" usebox="none">
34371 \begin_layout Plain Layout
34374 Edit\SpecialChar \menuseparator
34375 Math\SpecialChar \menuseparator
34377 \begin_inset space ~
34380 Definition\SpecialChar \menuseparator
34382 \begin_inset Newline newline
34386 \begin_inset Phantom HPhantom
34389 \begin_layout Plain Layout
34392 Edit\SpecialChar \menuseparator
34393 Math\SpecialChar \menuseparator
34395 \begin_inset space ~
34398 Definition\SpecialChar \menuseparator
34404 Eating From The Right
34410 <row interlinespace="2.5mm">
34411 <cell alignment="center" valignment="top" usebox="none">
34414 \begin_layout Plain Layout
34415 \begin_inset Graphics
34416 filename ../images/math-macro-add-greedy-optional-param.png
34417 rotateOrigin center
34426 <cell alignment="center" valignment="top" usebox="none">
34429 \begin_layout Plain Layout
34432 Edit\SpecialChar \menuseparator
34433 Math\SpecialChar \menuseparator
34435 \begin_inset space ~
34438 Definition\SpecialChar \menuseparator
34439 Append Optional Argument
34440 \begin_inset Newline newline
34444 \begin_inset Phantom HPhantom
34447 \begin_layout Plain Layout
34450 Edit\SpecialChar \menuseparator
34451 Math\SpecialChar \menuseparator
34453 \begin_inset space ~
34456 Definition\SpecialChar \menuseparator
34462 Eating From The Right
34475 \begin_layout Section
34476 Computer Algebra Systems
34479 \begin_layout Standard
34480 LyX offers the exchange between mathematical expressions written in LyX's
34481 math editor and external applications or user defined scripts.
34482 Currently supported applications are
34499 Note that the set of supported mathematical constructs is limited only
34500 to very simple cases.
34503 \begin_layout Subsection
34507 \begin_layout Standard
34508 Write some expression in a formula, go to the
34510 Edit\SpecialChar \menuseparator
34511 Math\SpecialChar \menuseparator
34512 Use Computer Algebra System
34514 menu and choose the application you have installed on the computer.
34515 After that the result of computation should show on the right side of the
34516 expression together with the
34517 \begin_inset Quotes eld
34521 \begin_inset Quotes erd
34527 \begin_layout Standard
34528 Here are few simple examples (with results from
34532 ) to show what kind of computations can be performed:
34535 \begin_layout Itemize
34536 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34542 \begin_layout Itemize
34543 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34549 \begin_layout Itemize
34550 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34556 \begin_layout Itemize
34557 \begin_inset Formula $\det\left[\begin{array}{ccc}
34561 \end{array}\right]=-56$
34567 \begin_layout Itemize
34568 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34574 \begin_layout Subsection
34578 \begin_layout Standard
34579 Currently there is no keyboard shortcut for calling the algebra applications.
34580 One can easily bind a shortcut to the
34584 LyX function (see the
34592 \begin_inset space \thinspace{}
34596 \begin_inset space ~
34603 key inside the math editor.
34608 one would use this shortcut definition command:
34611 \begin_layout Standard
34614 command-alternatives break-paragraph;math-extern maxima
34617 \begin_layout Standard
34618 \begin_inset Newpage newpage
34624 \begin_layout Section
34626 \begin_inset Index idx
34629 \begin_layout Plain Layout
34638 \begin_layout Subsection
34640 \begin_inset Index idx
34643 \begin_layout Plain Layout
34652 \begin_layout Standard
34653 Negative numbers often look ugly in formulas because the minus sign before
34654 the number is set with the same length as the minus operator sign.
34655 When writing the negative number in normal text, the minus sign appears
34659 \begin_layout Standard
34660 Thus, the problem disappears when converting the minus sign to mathematical
34664 \begin_layout Standard
34665 An example to visualize the problem:
34668 \begin_layout Standard
34670 \begin_inset Tabular
34671 <lyxtabular version="3" rows="3" columns="2">
34672 <features tabularvalignment="middle">
34673 <column alignment="right" valignment="top" width="0">
34674 <column alignment="left" valignment="top" width="0">
34676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34679 \begin_layout Plain Layout
34685 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34688 \begin_layout Plain Layout
34696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34699 \begin_layout Plain Layout
34705 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34708 \begin_layout Plain Layout
34709 \begin_inset Formula $x=-2$
34719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34722 \begin_layout Plain Layout
34728 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34731 \begin_layout Plain Layout
34732 \begin_inset Formula $x=\textrm{-}2$
34748 \begin_layout Subsection
34749 Comma as decimal Separator
34750 \begin_inset Index idx
34753 \begin_layout Plain Layout
34762 \begin_layout Standard
34763 In LaTeX a comma inside a formula is used, according to the English convention,
34764 as number group separator.
34765 So there will be space added behind all commas in formulas.
34768 \begin_layout Standard
34769 To avoid this, the comma is highlighted and changed to mathematical text
34779 \begin_layout Standard
34780 To use all formula commas in the document as decimal separator, the file
34789 \begin_layout Plain Layout
34794 is part of the LaTeX-package
34799 \begin_inset Index idx
34802 \begin_layout Plain Layout
34807 \begin_layout Plain Layout
34827 \begin_inset Index idx
34830 \begin_layout Plain Layout
34836 is loaded with the LaTeX-preamble line
34839 \begin_layout Standard
34847 \begin_layout Subsection
34849 \begin_inset CommandInset label
34851 name "sub:Physical-Vectors"
34856 \begin_inset Index idx
34859 \begin_layout Plain Layout
34868 \begin_layout Standard
34869 Predefined vectors are offered by the LaTeX-package
34874 \begin_inset Index idx
34877 \begin_layout Plain Layout
34883 that is loaded with the LaTeX-preamble line
34886 \begin_layout Standard
34894 \begin_layout Standard
34898 \begin_layout Plain Layout
34908 \begin_inset Note Note
34911 \begin_layout Plain Layout
34912 The following table will only be displayed when the LaTeX-package
34924 \begin_layout Standard
34925 The following commands are defined:
34928 \begin_layout Standard
34930 \begin_inset Tabular
34931 <lyxtabular version="3" rows="4" columns="2">
34932 <features tabularvalignment="middle">
34933 <column alignment="center" valignment="top" width="0">
34934 <column alignment="center" valignment="top" width="0">
34936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34939 \begin_layout Plain Layout
34945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34948 \begin_layout Plain Layout
34956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34959 \begin_layout Plain Layout
34969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34972 \begin_layout Plain Layout
34973 \begin_inset Formula $\Bra{\psi}$
34983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34986 \begin_layout Plain Layout
34996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34999 \begin_layout Plain Layout
35000 \begin_inset Formula $\Ket{\psi}$
35010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35013 \begin_layout Plain Layout
35025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35028 \begin_layout Plain Layout
35029 \begin_inset Formula $\Braket{\psi|\phi}$
35045 \begin_layout Standard
35052 assures that all vertical bars are set in the size of the surrounding brackets:
35053 \begin_inset Formula \[
35054 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35063 \begin_layout Plain Layout
35073 \begin_inset Note Note
35076 \begin_layout Plain Layout
35077 The following will be displayed when the LaTeX-package
35089 \begin_layout Standard
35090 You need to install the LaTeX-package
35094 to see the rest of this subsection in the output.
35097 \begin_layout Standard
35101 \begin_layout Plain Layout
35113 \begin_layout Standard
35120 can also be achieved using the command
35126 , that is described in
35127 \begin_inset CommandInset ref
35129 reference "sub:Automatic-Bracket-Size"
35136 \begin_layout Subsection
35137 Self-defined Fractions
35138 \begin_inset CommandInset label
35140 name "sub:Self-defined-Fractions"
35145 \begin_inset Index idx
35148 \begin_layout Plain Layout
35149 Fractions ! self-defined
35157 \begin_layout Standard
35158 To define custom commands for fractions, the command
35165 \begin_inset Index idx
35168 \begin_layout Plain Layout
35176 is used in the following scheme:
35179 \begin_layout Standard
35192 bracket}{fraction bar thickness}{style}
35193 \begin_inset Newline newline
35197 \begin_inset Phantom HPhantom
35200 \begin_layout Plain Layout
35210 {numerator}{denominator}
35213 \begin_layout Standard
35214 The style is a number in the range of 0
35215 \begin_inset space \thinspace{}
35219 \begin_inset space \thinspace{}
35225 \begin_layout Standard
35227 \begin_inset Tabular
35228 <lyxtabular version="3" rows="5" columns="2">
35229 <features tabularvalignment="middle">
35230 <column alignment="center" valignment="top" width="0">
35231 <column alignment="center" valignment="top" width="0">
35233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35236 \begin_layout Plain Layout
35242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35245 \begin_layout Plain Layout
35253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35256 \begin_layout Plain Layout
35262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35265 \begin_layout Plain Layout
35266 display style formula
35273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35276 \begin_layout Plain Layout
35282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35285 \begin_layout Plain Layout
35293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35296 \begin_layout Plain Layout
35302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35305 \begin_layout Plain Layout
35313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35316 \begin_layout Plain Layout
35322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35325 \begin_layout Plain Layout
35339 \begin_layout Standard
35340 When no style is given, the size is adjusted to the surrounding environment
35341 like for the command
35350 \begin_layout Standard
35351 When no fraction bar thickness is given, the predefined value of 0.4
35352 \begin_inset space \thinspace{}
35358 \begin_layout Standard
35359 \begin_inset VSpace medskip
35362 For example, the commands
35375 \begin_inset CommandInset ref
35377 reference "sub:Fractions"
35381 are defined with the commands
35384 \begin_layout Standard
35393 genfrac{}{}{}{0}{#1}{#2}}
35396 \begin_layout Standard
35400 \begin_layout Standard
35409 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35412 \begin_layout Standard
35413 \begin_inset VSpace medskip
35416 To define a fraction where the fraction bar thickness can be given as optional
35417 argument, the following line is inserted to the LaTeX-preamble:
35420 \begin_layout Standard
35429 genfrac{}{}{#1}{}{#2}{#3}}
35432 \begin_layout Standard
35434 \begin_inset Formula \begin{align*}
35435 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35436 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35441 As one can see, the distance of the numerator and the denominator to the
35442 fraction bar is round about three times the bar thickness.
35445 \begin_layout Subsection
35447 \begin_inset Index idx
35450 \begin_layout Plain Layout
35459 \begin_layout Standard
35460 To cancel formulas or formula parts, the LaTeX-package
35465 \begin_inset Index idx
35468 \begin_layout Plain Layout
35474 has to be loaded with the LaTeX-preamble line
35477 \begin_layout Standard
35482 usepackage[samesize]{cancel}
35485 \begin_layout Standard
35489 \begin_layout Plain Layout
35499 \begin_inset Note Note
35502 \begin_layout Plain Layout
35503 The following table will only be displayed when the LaTeX-package
35515 \begin_layout Standard
35516 There are four ways to cancel formulas:
35519 \begin_layout Standard
35521 \begin_inset Tabular
35522 <lyxtabular version="3" rows="5" columns="2">
35523 <features tabularvalignment="middle">
35524 <column alignment="center" valignment="top" width="0">
35525 <column alignment="center" valignment="top" width="0">
35527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35530 \begin_layout Plain Layout
35536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35539 \begin_layout Plain Layout
35541 \begin_inset Note Note
35544 \begin_layout Plain Layout
35551 are used here as spacer.
35563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35566 \begin_layout Plain Layout
35575 \begin_layout Plain Layout
35589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35592 \begin_layout Plain Layout
35593 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35606 \begin_layout Plain Layout
35615 \begin_layout Plain Layout
35629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35632 \begin_layout Plain Layout
35633 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35646 \begin_layout Plain Layout
35655 \begin_layout Plain Layout
35669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35672 \begin_layout Plain Layout
35673 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35686 \begin_layout Plain Layout
35690 \begin_inset Formula $\to$
35701 \begin_layout Plain Layout
35715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35718 \begin_layout Plain Layout
35719 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35735 \begin_layout Standard
35742 is especially suitable to visualize the reduction of fractions within formulas:
35743 \begin_inset Formula \[
35744 \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}}}
35752 \begin_layout Standard
35756 \begin_layout Plain Layout
35766 \begin_inset Note Note
35769 \begin_layout Plain Layout
35770 The following will be displayed when the LaTeX-package
35782 \begin_layout Standard
35783 You need to install the LaTeX-package
35787 to see the rest of this subsection in the output.
35790 \begin_layout Standard
35794 \begin_layout Plain Layout
35806 \begin_layout Subsection
35807 Formulas in Section Headings
35808 \begin_inset CommandInset label
35810 name "sub:Formulas-in-Section"
35815 \begin_inset Index idx
35818 \begin_layout Plain Layout
35819 Formula ! in section headings
35827 \begin_layout Standard
35828 When formulas are used in section headings, the following has to be taken
35832 \begin_layout Standard
35833 \begin_inset Note Greyedout
35836 \begin_layout Plain Layout
35842 \begin_inset Index idx
35845 \begin_layout Plain Layout
35846 Packages ! hyperref
35851 support is enabled in the document settings dialog under
35854 \begin_inset space ~
35859 , PDF-bookmarks are created for every section heading in the table of contents.
35860 If a section heading contains formulas, they are incorrectly displayed
35861 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35870 \begin_layout Standard
35871 Both problems can be solved by inserting at the end of the section heading
35872 a short title with the menu
35874 Insert\SpecialChar \menuseparator
35876 \begin_inset space ~
35882 Short titles are used as alternative for multiline section headings to
35883 keep the table of contents clearly arranged.
35884 Only the short title appears in the table of contents and therefore also
35885 in the PDF-bookmark.
35888 \begin_layout Standard
35889 When formulas should be used in the table of contents but
35893 is used, one can use the following command in TeX-mode:
35896 \begin_layout Standard
35901 texorpdfstring{part}{alternative}
35902 \begin_inset Index idx
35905 \begin_layout Plain Layout
35916 \begin_layout Standard
35917 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35918 This can be characters, formulas, footnotes, but also cross-references.
35919 The alternative is used instead of the part for the bookmark.
35922 \begin_layout Standard
35923 Here are two example headings:
35924 \begin_inset VSpace -3mm
35931 \begin_layout Plain Layout
35943 \begin_layout Subsubsection
35944 Heading without formula in table of contents
35945 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35949 \begin_inset Argument
35952 \begin_layout Plain Layout
35953 Heading without formula in table of contents
35961 \begin_layout Subsubsection
35962 Heading with formula in table of contents
35966 \begin_layout Plain Layout
35976 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35983 \begin_layout Plain Layout
35993 \begin_layout Standard
35997 \begin_layout Plain Layout
36006 In the first heading a short title was used, in the second one
36015 \begin_layout Standard
36016 To get the same formatting as for the other headings, the complete heading
36025 \begin_layout Plain Layout
36027 \begin_inset CommandInset ref
36029 reference "sub:Bold-Formulas"
36041 \begin_layout Subsection
36042 Formulas in multi-column Text
36043 \begin_inset Index idx
36046 \begin_layout Plain Layout
36047 Formula ! in multi-column text
36055 \begin_layout Standard
36056 Formulas in multi-column text are often too wide to fit into a column and
36057 thus need to be set over the whole page width.
36058 This is done by using the LaTeX-package
36066 \begin_layout Plain Layout
36071 is part of every LaTeX standard installation.
36077 \begin_inset Index idx
36080 \begin_layout Plain Layout
36081 Packages ! multicol
36086 , that is loaded with the LaTeX-preamble line
36089 \begin_layout Standard
36094 usepackage{multicol}
36097 \begin_layout Standard
36098 \begin_inset Note Greyedout
36101 \begin_layout Plain Layout
36102 Note herby that the setting
36105 \begin_inset space ~
36112 Document\SpecialChar \menuseparator
36118 \begin_inset space ~
36138 \begin_layout Standard
36139 Before the multi-column text the command
36142 \begin_layout Standard
36147 begin{multicols}{column number}
36150 \begin_layout Standard
36151 is written in TeX-mode.
36152 The column number is a number in the range of 2
36153 \begin_inset space \thinspace{}
36157 \begin_inset space \thinspace{}
36161 Before the formula the multi-column text is ended by inserting the command
36164 \begin_layout Standard
36172 \begin_layout Standard
36176 \begin_layout Standard
36177 Due to the command some space is automatically added before the formula.
36179 \begin_inset space \thinspace{}
36182 mm vertical space is inserted before the formula.
36183 When the formula style
36189 \begin_layout Plain Layout
36191 \begin_inset CommandInset ref
36193 reference "sec:Formula-Styles"
36205 \begin_inset space \thinspace{}
36208 mm space is inserted instead.
36211 \begin_layout Standard
36212 As example a multi-column text with a displayed formula:
36215 \begin_layout Standard
36221 \begin_layout Plain Layout
36225 begin{multicols}{2}
36230 Das Spektrum wird fouriertransformiert.
36231 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36232 , Lösungsmittel) zu trennen.
36233 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36234 nun das Aussehen des Ausgangssignals.
36235 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36236 über alle Phasen integrieren muss.
36238 \begin_inset Formula $S$
36241 unser normiertes Ausgangssignal und
36242 \begin_inset Formula $P$
36245 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36249 \begin_layout Plain Layout
36259 \begin_inset VSpace -6mm
36263 \begin_inset Formula \begin{equation}
36264 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36273 \begin_layout Plain Layout
36277 begin{multicols}{2}
36283 \begin_inset Formula $S_{0}$
36286 das Signal ohne Gradient ist und die Normierungsbedingung
36287 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36291 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36293 \begin_inset Formula $\nicefrac{\pi}{2}$
36297 \begin_inset space \thinspace{}
36300 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36301 das Signal zusätzlich abschwächt.
36302 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36304 \begin_inset Formula $T_{2}$
36310 \begin_layout Standard
36316 \begin_layout Plain Layout
36328 \begin_layout Subsection
36329 Formulas with Description of Variables
36330 \begin_inset Index idx
36333 \begin_layout Plain Layout
36334 Formula ! with description of variables
36342 \begin_layout Standard
36343 To describe variables within a formula, like in formula
36344 \begin_inset CommandInset ref
36346 reference "eq:within"
36355 \begin_inset Formula $n$
36359 \begin_inset space ~
36362 matrix is used with left aligned columns for the
36363 \begin_inset Formula $n$
36370 \begin_layout Plain Layout
36372 \begin_inset CommandInset ref
36374 reference "sec:Matrices"
36383 To set the description in a smaller size, before the matrix e.
36384 \begin_inset space \thinspace{}
36388 \begin_inset space \space{}
36401 \begin_layout Plain Layout
36403 \begin_inset CommandInset ref
36405 reference "sub:Font-Sizes"
36417 \begin_layout Standard
36418 When the formula style
36424 \begin_layout Plain Layout
36426 \begin_inset CommandInset ref
36428 reference "sec:Formula-Styles"
36449 \begin_layout Plain Layout
36456 only works in formulas with the style
36461 \begin_inset CommandInset ref
36463 reference "sub:Variable-Space"
36472 is inserted before and after the matrix to have the same separation of
36473 the matrix from the equation and the side margin.
36476 \begin_layout Standard
36477 When the formula style
36481 is used, the method described in
36482 \begin_inset CommandInset ref
36484 reference "sub:Flalign-Environment"
36488 is used to indent formulas.
36490 \begin_inset CommandInset ref
36492 reference "eq:within"
36496 consists of five columns whereas in the first two columns contain the equation,
36497 the third the matrix and the last one an empty TeX-brace.
36498 \begin_inset Formula \begin{flalign}
36499 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36500 \rho & \textrm{density}\\
36501 V & \textrm{volume}\\
36502 g & \textrm{gravitational acceleration}
36503 \end{array} & & {}\label{eq:within}
36511 \begin_layout Subsection
36512 Upright small Greek Letters
36513 \begin_inset CommandInset label
36515 name "sub:Upright-small-Greek"
36520 \begin_inset Index idx
36523 \begin_layout Plain Layout
36524 Greek letters ! upright
36532 \begin_layout Standard
36533 Most of the math fonts only provide italic small Greek letters.
36534 But for symbols of elementary particles like pions and neutrinos, upright
36535 Greek letters are needed.
36544 \begin_layout Plain Layout
36549 is part of the LaTeX-package
36554 \begin_inset Index idx
36557 \begin_layout Plain Layout
36562 \begin_layout Plain Layout
36582 \begin_inset Index idx
36585 \begin_layout Plain Layout
36591 that is loaded with the LaTeX-preamble line
36594 \begin_layout Standard
36599 usepackage{upgreek}
36602 \begin_layout Standard
36608 \begin_layout Plain Layout
36618 \begin_inset Note Note
36621 \begin_layout Plain Layout
36622 The following table will only be displayed when the LaTeX-package
36631 They are created when the command for a small Greek letters is started
36637 For example the command
36644 \begin_inset Formula $\uptau$
36650 \begin_layout Standard
36651 With these commands reactions of elementary particles can be typeset:
36652 \begin_inset Formula \[
36653 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
36661 \begin_layout Standard
36662 The upright letters are more bold and wider than the italic ones.
36663 They should therefore not be used for units like
36664 \begin_inset Quotes eld
36668 \begin_inset Quotes erd
36674 \begin_layout Standard
36678 \begin_layout Plain Layout
36688 \begin_inset Note Note
36691 \begin_layout Plain Layout
36692 The following will be displayed when the LaTeX-package
36704 \begin_layout Standard
36705 You need to install the LaTeX-package
36709 to see the rest of this subsection in the output.
36712 \begin_layout Standard
36716 \begin_layout Plain Layout
36728 \begin_layout Subsection
36729 Text Characters in Formulas
36730 \begin_inset CommandInset label
36732 name "sub:Text-Characters-in"
36737 \begin_inset Index idx
36740 \begin_layout Plain Layout
36749 \begin_layout Standard
36750 In some cases you might want to insert text characters directly into formulas.
36751 When for example the centered dot · is often used in formulas like
36752 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36755 , one would have to insert the command
36765 \begin_layout Plain Layout
36767 \begin_inset CommandInset ref
36769 reference "sub:Binary-Operators"
36778 all the time, because this character is defined in all encodings as text
36780 But the encoding can be changed by this LaTeX-preamble line:
36783 \begin_layout Standard
36788 Declare Inputtext{183}{
36798 f\SpecialChar \textcompwordmark{}
36802 \begin_layout Standard
36803 The character encoding (menu
36805 Document\SpecialChar \menuseparator
36806 Settings\SpecialChar \menuseparator
36809 ) specifies what character appears when a keyboard key is pressed.
36810 When the key for the character '·' is pressed, internally the command
36817 But this command is not available in a formula so that you would get LaTeX-erro
36819 With the changed encoding the right command is chosen automatically, depending
36820 on if the character was inserted into a formula or not.
36823 \begin_layout Standard
36824 The encoding of several characters is saved in definition files.
36825 Fore example the encoding
36829 is defined in the file
36833 that is in the installation folder of LaTeX.
36834 Encodings should only be changed via the LaTeX-preamble and not in the
36836 Otherwise own documents could not be edited by other LyX users working
36837 on other computers.
36840 \begin_layout Standard
36841 \begin_inset VSpace medskip
36844 Besides the centered dot, in this document the degree sign ° is defined
36845 with the following LaTeX-preamble line so that it can directly be inserted
36849 \begin_layout Standard
36854 DeclareInputtext{176}{
36864 f\SpecialChar \textcompwordmark{}
36868 \begin_layout Standard
36869 \begin_inset Newpage newpage
36875 \begin_layout Section
36878 \begin_inset Index idx
36881 \begin_layout Plain Layout
36890 \begin_layout Standard
36891 This section is a summary of the most important typographic rules, listed
36896 \begin_layout Plain Layout
36897 This collection was partly taken from the German semi-official dictionary
36899 \begin_inset Quotes eld
36903 \begin_inset Quotes erd
36907 \begin_inset CommandInset citation
36913 that lists some of the ISO rules.
36914 More rules are listed in
36915 \begin_inset CommandInset citation
36929 \begin_layout Itemize
36938 \begin_layout Plain Layout
36939 done with font styles, see
36940 \begin_inset CommandInset ref
36942 reference "sub:Font-Styles"
36951 , no matter if they appear in italic text: 30
36952 \begin_inset space \thinspace{}
36956 \begin_inset Newline newline
36959 Between the value and the unit is the smallest space, see
36960 \begin_inset CommandInset ref
36962 reference "sub:Predefined-Space"
36967 \begin_inset Newline newline
36970 This convention is automatically fulfilled when the command
36977 When it is entered to a formula, two boxes appear.
36978 In the first one the value is inserted, in the second one the unit, and
36980 \begin_inset Formula $\unit[30]{km/h}$
36984 \begin_inset space \thinspace{}
36994 is not a real LaTeX command but the command
37000 , therefore you cannot use it in TeX code.
37003 \begin_layout Itemize
37004 Percent and perthousand signs are set like physical units:
37005 \begin_inset Newline newline
37009 \begin_inset space \thinspace{}
37015 \begin_layout Itemize
37016 The degree sign follows directly on the value: 15°, but not when it is used
37018 \begin_inset space \thinspace{}
37024 \begin_layout Itemize
37025 In numbers with more than four digits the smallest space is inserted before
37026 every third digit to group them:
37036 \begin_inset space \thinspace{}
37040 \begin_inset space \thinspace{}
37046 \begin_layout Itemize
37047 For dimensions like 120×90×40
37048 \begin_inset space \thinspace{}
37051 cm the multiplication sign
37052 \begin_inset Quotes eld
37056 \begin_inset Quotes erd
37060 It is available either via the command
37068 Insert\SpecialChar \menuseparator
37069 Special Character\SpecialChar \menuseparator
37075 \begin_layout Itemize
37076 Functions with names consisting of several letters are set upright to avoid
37078 \begin_inset CommandInset ref
37080 reference "sub:Predefined-Functions"
37087 \begin_layout Itemize
37088 Indices consisting of several letters, are set upright:
37089 \begin_inset Formula $E_{\mathrm{kin}}$
37093 \begin_inset Newline newline
37096 Components of matrices are set italic:
37097 \begin_inset Formula $\hat{H}_{kl}$
37103 \begin_layout Itemize
37104 The differentiation/integration operator 'd', the Euler's number 'e' and
37105 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37109 \begin_layout Itemize
37110 The character that denotes a
37114 transformation is inserted either by the command
37122 \begin_layout Plain Layout
37135 Insert\SpecialChar \menuseparator
37136 Special Character\SpecialChar \menuseparator
37137 Symbols\SpecialChar \menuseparator
37139 \begin_inset space ~
37145 \begin_inset Formula $\mathscr{F}$
37151 \begin_layout Standard
37152 \begin_inset Newpage newpage
37158 \begin_layout Section
37160 \begin_inset Index idx
37163 \begin_layout Plain Layout
37172 \begin_layout Standard
37173 Some characters and symbols can be created with several commands.
37174 Here is a list of the synonym commands:
37177 \begin_layout Standard
37178 \begin_inset VSpace bigskip
37182 \begin_inset space \hfill{}
37186 \begin_inset Tabular
37187 <lyxtabular version="3" rows="12" columns="2">
37188 <features tabularvalignment="middle">
37189 <column alignment="center" valignment="top" width="0pt">
37190 <column alignment="center" valignment="top" width="0pt">
37192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37195 \begin_layout Plain Layout
37201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37204 \begin_layout Plain Layout
37206 \begin_inset Note Note
37209 \begin_layout Plain Layout
37216 is only used as spacer.
37228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37231 \begin_layout Plain Layout
37239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37242 \begin_layout Plain Layout
37246 \begin_layout Plain Layout
37259 \begin_layout Plain Layout
37273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37276 \begin_layout Plain Layout
37284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37287 \begin_layout Plain Layout
37297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37300 \begin_layout Plain Layout
37308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37311 \begin_layout Plain Layout
37321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37324 \begin_layout Plain Layout
37332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37335 \begin_layout Plain Layout
37343 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37346 \begin_layout Plain Layout
37354 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37357 \begin_layout Plain Layout
37365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37368 \begin_layout Plain Layout
37376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37379 \begin_layout Plain Layout
37389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37392 \begin_layout Plain Layout
37400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37403 \begin_layout Plain Layout
37413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37416 \begin_layout Plain Layout
37424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37427 \begin_layout Plain Layout
37437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37440 \begin_layout Plain Layout
37448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37451 \begin_layout Plain Layout
37461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37464 \begin_layout Plain Layout
37472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37475 \begin_layout Plain Layout
37483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37486 \begin_layout Plain Layout
37494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37497 \begin_layout Plain Layout
37509 \begin_inset space \hfill{}
37513 \begin_inset Tabular
37514 <lyxtabular version="3" rows="12" columns="2">
37515 <features tabularvalignment="middle">
37516 <column alignment="center" valignment="top" width="0pt">
37517 <column alignment="center" valignment="top" width="0pt">
37519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37522 \begin_layout Plain Layout
37528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37531 \begin_layout Plain Layout
37539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37542 \begin_layout Plain Layout
37550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37553 \begin_layout Plain Layout
37565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37568 \begin_layout Plain Layout
37576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37579 \begin_layout Plain Layout
37589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37592 \begin_layout Plain Layout
37600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37603 \begin_layout Plain Layout
37613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37616 \begin_layout Plain Layout
37624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37627 \begin_layout Plain Layout
37635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37638 \begin_layout Plain Layout
37646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37649 \begin_layout Plain Layout
37657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37660 \begin_layout Plain Layout
37668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37671 \begin_layout Plain Layout
37681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37684 \begin_layout Plain Layout
37692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37695 \begin_layout Plain Layout
37705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37708 \begin_layout Plain Layout
37716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37719 \begin_layout Plain Layout
37729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37732 \begin_layout Plain Layout
37740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37743 \begin_layout Plain Layout
37753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37756 \begin_layout Plain Layout
37764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37767 \begin_layout Plain Layout
37777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37780 \begin_layout Plain Layout
37788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37791 \begin_layout Plain Layout
37805 \begin_inset space \hfill{}
37811 \begin_layout Standard
37812 \begin_inset Newpage newpage
37818 \begin_layout Bibliography
37819 \labelwidthstring References
37820 \begin_inset CommandInset bibitem
37821 LatexCommand bibitem
37833 The LaTeX Companion
37836 Addison Wesley, 2004
37839 \begin_layout Bibliography
37840 \labelwidthstring References
37841 \begin_inset CommandInset bibitem
37842 LatexCommand bibitem
37848 \begin_inset CommandInset href
37851 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37855 of LaTeX's math abilities
37858 \begin_layout Bibliography
37859 \labelwidthstring References
37860 \begin_inset CommandInset bibitem
37861 LatexCommand bibitem
37867 \begin_inset CommandInset href
37870 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37878 \begin_layout Plain Layout
37890 \begin_layout Bibliography
37891 \labelwidthstring References
37892 \begin_inset CommandInset bibitem
37893 LatexCommand bibitem
37899 \begin_inset CommandInset href
37902 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37906 of all symbols available with LaTeX-packages
37909 \begin_layout Bibliography
37910 \labelwidthstring References
37911 \begin_inset CommandInset bibitem
37912 LatexCommand bibitem
37918 \begin_inset CommandInset href
37920 name "Documentation"
37921 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37925 of the LaTeX-package
37930 \begin_inset Index idx
37933 \begin_layout Plain Layout
37934 Packages ! hyperref
37942 \begin_layout Bibliography
37943 \labelwidthstring References
37944 \begin_inset CommandInset bibitem
37945 LatexCommand bibitem
37951 \begin_inset CommandInset href
37953 name "Documentation"
37954 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37958 of the LaTeX-package
37963 \begin_inset Index idx
37966 \begin_layout Plain Layout
37975 \begin_layout Bibliography
37976 \labelwidthstring References
37977 \begin_inset CommandInset bibitem
37978 LatexCommand bibitem
37984 \begin_inset CommandInset href
37987 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37998 \begin_inset CommandInset ref
38000 reference "sub:Operator-Limits"
38005 \begin_inset Index idx
38008 \begin_layout Plain Layout
38019 \begin_layout Bibliography
38020 \labelwidthstring References
38021 \begin_inset CommandInset bibitem
38022 LatexCommand bibitem
38033 Auflage, Duden 2001
38036 \begin_layout Bibliography
38037 \labelwidthstring References
38038 \begin_inset CommandInset bibitem
38039 LatexCommand bibitem
38045 \begin_inset CommandInset href
38048 target "http://physics.nist.gov/Document/checklist.pdf"
38052 for reviewing manuscripts
38055 \begin_layout Standard
38056 \begin_inset CommandInset index_print
38057 LatexCommand printindex