1 #LyX 1.6.5svn 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}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package upgreek
141 \IfFileExists{upgreek.sty}
142 {\usepackage{upgreek}
143 \setboolean{upgreek}{true}}
144 {\setboolean{upgreek}{false}}
146 % check for package mhchem
147 % used for chemical equations
149 \IfFileExists{mhchem.sty}
151 \setboolean{mhchem}{true}}
152 {\setboolean{mhchem}{false}}
154 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
155 \use_default_options false
160 \font_typewriter default
161 \font_default_family default
171 \pdf_title "LyX's Math Manual"
172 \pdf_author "LyX Team, Uwe Stöhr"
173 \pdf_subject "LyX-documentation about math"
174 \pdf_keywords "LyX, Mathed"
176 \pdf_bookmarksnumbered true
177 \pdf_bookmarksopen true
178 \pdf_bookmarksopenlevel 1
179 \pdf_breaklinks false
183 \pdf_pdfusetitle false
184 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
191 \paperorientation portrait
194 \paragraph_separation skip
196 \quotes_language english
199 \paperpagestyle plain
203 \tracking_changes false
204 \output_changes false
212 LyX's detailed Math manual
220 \begin_layout Plain Layout
222 If you have comments or error corrections, please send them to the LyX Documenta
226 \begin_inset CommandInset href
228 name "lyx-docs@lists.lyx.org"
229 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
240 \begin_inset Note Note
243 \begin_layout Plain Layout
250 \begin_inset Newline newline
254 \begin_inset Newline newline
262 \begin_layout Standard
263 \begin_inset CommandInset toc
264 LatexCommand tableofcontents
271 \begin_layout Standard
272 \begin_inset Note Note
275 \begin_layout Plain Layout
276 To export this document to PDF, PS, or DVI the LaTeX-packages
289 If they are not installed you can export the document anyway but the sections
290 where the packages are required won't appear in the output.
293 \begin_layout Plain Layout
294 The latest PDF-version of this document can be found here:
295 \begin_inset Newline newline
300 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
308 \begin_layout Standard
309 \begin_inset Newpage newpage
315 \begin_layout Section
319 \begin_layout Standard
320 This document explains LyX's math features and is furthermore a collection
321 of LaTeX-commands used for mathematical characters and constructs.
322 The explanations are designed for the usage of commands.
323 It is therefore required that you have read the section
334 \begin_layout Standard
335 Most of the characters and many constructs explained in this manual are
336 also accessible via the menu
340 \SpecialChar \menuseparator
356 But everybody who has to write lots of formulas will notice that it is
357 much faster to use commands instead of the math toolbar.
358 Therefore this manual is focused on commands but also mentions the correspondin
359 g toolbar buttons when available.
362 \begin_layout Standard
363 If not specially mentioned the commands are only available within formulas.
364 To be able to use all commands explained in this document, the option
368 must be used in the document settings (menu
370 Document\SpecialChar \menuseparator
371 Settings\SpecialChar \menuseparator
382 \begin_layout Plain Layout
385 Use AMS math package automatically
391 \begin_layout Plain Layout
400 -math when math constructs are found that are supported by LyX.
408 \begin_layout Standard
409 This document doesn't list all
413 \begin_layout Plain Layout
426 \begin_layout Plain Layout
431 \begin_layout Plain Layout
440 -math commands is in the file
443 \begin_inset CommandInset href
446 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
452 , which is part of every LaTeX standard installation.
457 for lucidity reasons.
460 \begin_layout Section
464 \begin_layout Standard
465 To create an inline formula
469 \begin_layout Plain Layout
475 that is embedded into a text line, use one of the shortcuts
481 or the toolbar button
482 \begin_inset Graphics
483 filename ../images/math-mode.png
489 \begin_inset Newline newline
492 To create a display style formula
496 \begin_layout Plain Layout
497 Formula ! display style
502 that will appear bigger and in an own paragraph, use one of these shortcuts:
512 \begin_layout Standard
513 To change a display style formula to an inline formula, set the cursor into
514 the formula and use one of the shortcuts
522 Edit\SpecialChar \menuseparator
523 Math\SpecialChar \menuseparator
527 The same way is used to change an inline formula to a display style formula.
530 \begin_layout Standard
531 To display parts of an inline formula in the size of a display style formula,
540 \begin_layout Plain Layout
551 Then a new blue box appears in which the desired formula part is inserted.
554 \begin_layout Standard
555 Only inline formulas are allowed inside tables.
558 \begin_layout Standard
563 can be turned on in the menu
565 View\SpecialChar \menuseparator
569 When you click there on
570 \begin_inset Quotes eld
574 \begin_inset Quotes erd
577 the toolbar will be shown permanently at the bottom; this state is visualized
582 menu with a checkmark.
583 When you click in this state again on
584 \begin_inset Quotes eld
588 \begin_inset Quotes erd
599 is only shown when the cursor is within a formula; this state is visualized
600 by the renaming of the menu entry from
601 \begin_inset Quotes eld
605 \begin_inset Quotes erd
609 \begin_inset Quotes eld
617 \begin_inset Quotes erd
623 \begin_layout Standard
628 \begin_layout Plain Layout
634 is invoked by pressing the toolbar button
635 \begin_inset Graphics
636 filename ../images/ert-insert.png
643 Insert\SpecialChar \menuseparator
648 \begin_layout Plain Layout
664 \begin_inset Note Note
667 \begin_layout Plain Layout
668 In LyX there are three
669 \begin_inset Quotes eld
673 \begin_inset Quotes erd
676 that appear in the output with sub- and superscript letters: TeX, LaTeX,
680 \begin_layout Plain Layout
681 To avoid that these names are recognized as proper names, a TeX-brace pair
690 \begin_layout Standard
691 To change the LaTeX-preamble
695 \begin_layout Plain Layout
703 Document\SpecialChar \menuseparator
704 Settings\SpecialChar \menuseparator
709 \begin_layout Plain Layout
725 \begin_layout Standard
726 To edit matrices, case differentiations, and multiline formulas subsequently,
729 Edit\SpecialChar \menuseparator
734 Edit\SpecialChar \menuseparator
736 \begin_inset space \thinspace{}
740 \begin_inset space \thinspace{}
750 When lines and columns are swapped via the menu, the column or line where
751 the cursor is in is exchanged with the column to the right or the line
753 Is the cursor in the last column or row, the exchange is done with the
754 column to the left or the line above.
757 \begin_layout Standard
758 To write text in formulas
762 \begin_layout Plain Layout
763 For multiline formulas the command
770 \begin_inset CommandInset ref
772 reference "sub:Text-in-multiline"
789 \begin_layout Plain Layout
799 \begin_layout Plain Layout
806 This mode is invoked with the the shortcut
812 or by the insertion of the command
820 \begin_layout Plain Layout
831 The text appears black in LyX and can therefore be distinguished from the
832 other formula parts that appear blue.
833 In the output mathematical text is set upright, in contrary to other formula
837 \begin_layout Subsection*
841 \begin_layout Standard
842 Most of the LaTeX-commands for math constructs have the following scheme:
845 \begin_layout Standard
861 \begin_layout Standard
862 A command starts always with a backslash
863 \begin_inset Quotes gld
873 \begin_inset Quotes grd
877 To omit optional arguments, also omit the associated brackets.
878 The braces around the required arguments are named in this document as
883 \begin_layout Plain Layout
890 If you add in a formula a left brace to a command name, LyX creates automatical
892 In all other cases TeX-braces are created in formulas with the command
900 TeX-braces appear red in LyX, in contrary to normal braces that appear
902 In TeX-mode no command is needed to get TeX-braces.
903 TeX-braces don't appear in the output.
906 \begin_layout Standard
907 When commands without arguments, like commands for symbols are entered in
908 TeX-mode, a space character must
912 be behind the command to end it.
913 This space doesn't appear in the output.
914 When the space should appear in the output, the space must be followed
915 by a protected space in normal text.
918 \begin_layout Standard
919 A protected space is inserted with
922 arg "space-insert protected"
928 \begin_layout Subsection*
929 \begin_inset Newpage newpage
935 \begin_layout Itemize
940 \begin_layout Plain Layout
941 This visible space character can be created with the command
951 \begin_layout Plain Layout
959 , inserted in TeX-mode.
968 \begin_layout Plain Layout
981 denotes a space character to be input.
984 \begin_layout Itemize
986 \begin_inset Formula $\to$
989 denotes the usage of the corresponding arrow key on the keyboard.
992 \begin_layout Subsection*
996 \begin_layout Standard
998 \begin_inset Float table
1004 \begin_layout Plain Layout
1006 \begin_inset Caption
1008 \begin_layout Plain Layout
1009 \begin_inset CommandInset label
1011 name "tab:Available-units"
1023 \begin_layout Plain Layout
1025 \begin_inset Tabular
1026 <lyxtabular version="3" rows="13" columns="2">
1028 <column alignment="center" valignment="top" width="0">
1029 <column alignment="center" valignment="top" width="0">
1031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1034 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1043 \begin_layout Plain Layout
1051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1054 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1063 \begin_layout Plain Layout
1071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1074 \begin_layout Plain Layout
1080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1083 \begin_layout Plain Layout
1091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1094 \begin_layout Plain Layout
1100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1103 \begin_layout Plain Layout
1105 \begin_inset space \thinspace{}
1109 \begin_inset space \thinspace{}
1119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1122 \begin_layout Plain Layout
1128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1131 \begin_layout Plain Layout
1133 \begin_inset space \thinspace{}
1137 \begin_inset space \thinspace{}
1147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1150 \begin_layout Plain Layout
1156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1159 \begin_layout Plain Layout
1161 \begin_inset space \thinspace{}
1165 \begin_inset space \thinspace{}
1175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1178 \begin_layout Plain Layout
1184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1187 \begin_layout Plain Layout
1189 \begin_inset space \thinspace{}
1193 \begin_inset space \thinspace{}
1203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1206 \begin_layout Plain Layout
1212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1215 \begin_layout Plain Layout
1217 \begin_inset space \thinspace{}
1221 \begin_inset space \thinspace{}
1231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1234 \begin_layout Plain Layout
1240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1243 \begin_layout Plain Layout
1245 \begin_inset space \thinspace{}
1249 \begin_inset Formula $\approx$
1253 \begin_inset space \thinspace{}
1263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1266 \begin_layout Plain Layout
1272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1275 \begin_layout Plain Layout
1277 \begin_inset space \thinspace{}
1281 \begin_inset space \thinspace{}
1291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1294 \begin_layout Plain Layout
1300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1303 \begin_layout Plain Layout
1307 \begin_inset Quotes eld
1313 \begin_inset Quotes erd
1323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1326 \begin_layout Plain Layout
1332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1335 \begin_layout Plain Layout
1337 \begin_inset Quotes eld
1345 \begin_inset Quotes erd
1355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1358 \begin_layout Plain Layout
1364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1367 \begin_layout Plain Layout
1369 \begin_inset space \thinspace{}
1373 \begin_inset Formula $\nicefrac{1}{18}$
1377 \begin_inset space \thinspace{}
1398 \begin_layout Standard
1399 \begin_inset Newpage newpage
1405 \begin_layout Section
1409 \begin_layout Subsection
1414 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1434 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1450 \begin_layout Plain Layout
1466 \begin_layout Plain Layout
1471 \begin_layout Plain Layout
1482 \begin_layout Plain Layout
1497 \begin_layout Standard
1498 Indices are created with an underscore
1499 \begin_inset Quotes eld
1503 \begin_inset Quotes erd
1506 or via the math toolbar button
1507 \begin_inset Graphics
1508 filename ../images/math-subscript.png
1513 , exponents with a caret
1514 \begin_inset Quotes eld
1518 \begin_inset Quotes erd
1521 or via the math toolbar button
1522 \begin_inset Graphics
1523 filename ../images/math-superscript.png
1531 \begin_layout Standard
1533 \begin_inset Tabular
1534 <lyxtabular version="3" rows="4" columns="2">
1536 <column alignment="center" valignment="top" width="0pt">
1537 <column alignment="center" valignment="top" width="0pt">
1539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1542 \begin_layout Plain Layout
1548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1551 \begin_layout Plain Layout
1553 \begin_inset Note Note
1556 \begin_layout Plain Layout
1563 is only used as spacer.
1575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1578 \begin_layout Plain Layout
1584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1587 \begin_layout Plain Layout
1588 \begin_inset Formula $B_{V}$
1598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1601 \begin_layout Plain Layout
1607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1610 \begin_layout Plain Layout
1611 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1624 \begin_layout Plain Layout
1629 \begin_layout Plain Layout
1643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1646 \begin_layout Plain Layout
1647 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1663 \begin_layout Standard
1664 As the caret is in some languages an accent, vowels will be accentuated
1665 in this case and not set as exponents
1669 \begin_layout Plain Layout
1670 Depending on the used keyboard settings this can also happen for other character
1677 To get in this case exponents, press
1681 after the caret as in the last example.
1684 \begin_layout Subsection
1686 \begin_inset CommandInset label
1688 name "sub:Fractions"
1696 \begin_layout Plain Layout
1705 \begin_layout Standard
1706 Fractions are generated with the command
1716 \begin_layout Plain Layout
1724 or via the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac.png
1732 The font size is adjusted automatically, depending on whether the fraction
1733 is in an inline or display style formula.
1734 With the math toolbar button
1735 \begin_inset Graphics
1736 filename ../images/math/frac-square.png
1741 you can select different fraction types.
1744 \begin_layout Standard
1753 \begin_layout Plain Layout
1763 a fraction can be created that has in any case the size of a display style
1773 \begin_layout Plain Layout
1783 the fraction appears always with the size of an inline formula.
1787 \begin_layout Standard
1788 A line with the fraction
1789 \begin_inset Formula $\frac{1}{2}$
1792 that was created with the command
1801 \begin_layout Standard
1802 A line with the fraction
1803 \begin_inset Formula $\dfrac{1}{2}$
1806 that was created with the command
1815 \begin_layout Standard
1817 \begin_inset Tabular
1818 <lyxtabular version="3" rows="4" columns="2">
1820 <column alignment="center" valignment="top" width="0pt">
1821 <column alignment="center" valignment="top" width="0pt">
1823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1826 \begin_layout Plain Layout
1832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1835 \begin_layout Plain Layout
1837 \begin_inset Note Note
1840 \begin_layout Plain Layout
1847 is only used as spacer.
1859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1862 \begin_layout Plain Layout
1869 \begin_layout Plain Layout
1879 \begin_inset Formula $\downarrow$
1887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1890 \begin_layout Plain Layout
1891 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1904 \begin_layout Plain Layout
1911 \begin_layout Plain Layout
1921 \begin_inset Formula $\downarrow$
1929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1932 \begin_layout Plain Layout
1933 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1946 \begin_layout Plain Layout
1953 \begin_layout Plain Layout
1966 \begin_layout Plain Layout
1981 \begin_layout Plain Layout
1991 \begin_inset Formula $\downarrow$
1995 \begin_inset Formula $\downarrow\downarrow$
2003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2006 \begin_layout Plain Layout
2007 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2023 \begin_layout Standard
2024 \begin_inset VSpace bigskip
2028 \begin_inset Newpage newpage
2031 For nested fractions the command
2041 \begin_layout Plain Layout
2051 \begin_inset VSpace -3mm
2057 \begin_layout Standard
2058 \begin_inset Formula \begin{align*}
2059 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2060 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2067 \begin_layout Standard
2068 The command for the example above is:
2071 \begin_layout Standard
2080 \begin_layout Plain Layout
2090 \begin_inset Formula $\downarrow$
2099 \begin_layout Plain Layout
2114 \begin_layout Plain Layout
2124 \begin_inset Formula $\downarrow$
2128 \begin_inset Formula $\downarrow$
2134 \begin_layout Standard
2135 \begin_inset VSpace medskip
2141 \begin_layout Standard
2148 sets the fraction always in the size of a displayed formula, also when
2149 it is part of another fraction.
2152 \begin_layout Standard
2153 It is possible to specify the alignment of the numerator.
2160 is used to left align it, the command
2173 centers the numerator.
2174 These fractions demonstrate the different alignments:
2177 \begin_layout Standard
2178 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2182 \begin_inset Formula $\cfrac{A}{B+C}$
2186 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2192 \begin_layout Standard
2193 \begin_inset Note Greyedout
2196 \begin_layout Plain Layout
2213 are no real LaTeX commands but represent the command
2217 cfrac[alignment]{numerator}{denominator}
2220 Therefore you cannot use them in TeX code.
2228 \begin_layout Standard
2229 \begin_inset VSpace medskip
2232 It is often advantageous to combine
2245 \begin_inset Formula \[
2246 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2253 \begin_layout Standard
2254 For inline fractions with a sloped fraction stroke you can use the command
2265 \begin_layout Plain Layout
2274 \begin_inset Formula $\nicefrac{5}{31}$
2287 \begin_layout Plain Layout
2296 \begin_inset Formula $\unitfrac{5}{31}$
2299 There is furthermore the command
2305 that offers to write a fraction in combination with a number:
2306 \begin_inset Formula $\unitfrac[2]{1}{3}$
2312 \begin_layout Standard
2313 \begin_inset Note Greyedout
2316 \begin_layout Plain Layout
2327 is not a real LaTeX command but the command
2328 \begin_inset Newline newline
2335 unitfrac[number]{numerator}{denominator}
2338 Therefore you cannot use it in TeX code.
2346 \begin_layout Standard
2347 How to define own fractions where the fraction stroke can be changed, is
2349 \begin_inset CommandInset ref
2351 reference "sub:Self-defined-Fractions"
2358 \begin_layout Subsection
2363 \begin_layout Plain Layout
2372 \begin_layout Standard
2373 Square roots are created with
2383 \begin_layout Plain Layout
2391 or the math toolbar button
2392 \begin_inset Graphics
2393 filename ../images/math/sqrt.png
2398 , all other roots with the command
2408 \begin_layout Plain Layout
2416 or with the math toolbar button
2417 \begin_inset Graphics
2418 filename ../images/math/root.png
2426 \begin_layout Standard
2428 \begin_inset Tabular
2429 <lyxtabular version="3" rows="3" columns="2">
2431 <column alignment="center" valignment="top" width="0pt">
2432 <column alignment="center" valignment="top" width="0pt">
2434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2437 \begin_layout Plain Layout
2443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2446 \begin_layout Plain Layout
2448 \begin_inset Note Note
2451 \begin_layout Plain Layout
2458 is only used as spacer.
2470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2473 \begin_layout Plain Layout
2480 \begin_layout Plain Layout
2494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2497 \begin_layout Plain Layout
2498 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2508 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2511 \begin_layout Plain Layout
2518 \begin_layout Plain Layout
2528 \begin_inset Formula $\downarrow$
2536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2539 \begin_layout Plain Layout
2540 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2556 \begin_layout Standard
2557 A square root can also be created with
2563 when the root index field is left empty.
2566 \begin_layout Standard
2567 With certain indices the distance to the root is too small, like in this
2569 \begin_inset Formula $\sqrt[\beta]{B}$
2573 \begin_inset Newline newline
2577 \begin_inset Formula $\beta$
2581 To avoid this, the commands
2591 \begin_layout Plain Layout
2609 \begin_layout Plain Layout
2617 are used with the following scheme:
2620 \begin_layout Standard
2634 \begin_layout Standard
2635 Distance is the number of Big Points (unit bp;
2636 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2639 ), that the index should be moved to the left or top, resp..
2640 The commands are written to the index.
2641 This way the command
2642 \begin_inset Newline newline
2652 \begin_inset Formula $\to$
2658 \begin_inset Formula $\to$
2667 \begin_layout Plain Layout
2677 \begin_inset Formula $\to$
2681 \begin_inset Newline newline
2686 produces a correct typeset formula:
2687 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2693 \begin_layout Subsection
2694 Binomial Coefficients
2698 \begin_layout Plain Layout
2699 Binomial coefficients
2707 \begin_layout Standard
2708 Binomial coefficients are inserted with the command
2718 \begin_layout Plain Layout
2726 or with the submenu of the math toolbar button
2727 \begin_inset Graphics
2728 filename ../images/math/frac-square.png
2734 Analog to fractions (
2754 \begin_layout Plain Layout
2774 \begin_layout Plain Layout
2783 For other brackets around binomial coeficients there are the commands
2793 \begin_layout Plain Layout
2811 \begin_layout Plain Layout
2822 \begin_layout Standard
2824 \begin_inset Tabular
2825 <lyxtabular version="3" rows="6" columns="2">
2827 <column alignment="center" valignment="top" width="0pt">
2828 <column alignment="center" valignment="top" width="0pt">
2830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2833 \begin_layout Plain Layout
2839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2842 \begin_layout Plain Layout
2844 \begin_inset Note Note
2847 \begin_layout Plain Layout
2854 is only used as spacer.
2866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2869 \begin_layout Plain Layout
2876 \begin_layout Plain Layout
2886 \begin_inset Formula $\downarrow$
2894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2897 \begin_layout Plain Layout
2898 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2911 \begin_layout Plain Layout
2918 \begin_layout Plain Layout
2928 \begin_inset Formula $\downarrow$
2936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2939 \begin_layout Plain Layout
2940 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2953 \begin_layout Plain Layout
2960 \begin_layout Plain Layout
2970 \begin_inset Formula $\downarrow$
2978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2981 \begin_layout Plain Layout
2982 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2995 \begin_layout Plain Layout
3002 \begin_layout Plain Layout
3012 \begin_inset Formula $\downarrow$
3020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3023 \begin_layout Plain Layout
3024 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3037 \begin_layout Plain Layout
3044 \begin_layout Plain Layout
3054 \begin_inset Formula $\downarrow$
3062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3065 \begin_layout Plain Layout
3066 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3082 \begin_layout Subsection
3083 Case Differentiations
3087 \begin_layout Plain Layout
3088 Case differentiations
3096 \begin_layout Standard
3098 \begin_inset Tabular
3099 <lyxtabular version="3" rows="3" columns="2">
3101 <column alignment="center" valignment="top" width="0pt">
3102 <column alignment="center" valignment="top" width="0pt">
3104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3107 \begin_layout Plain Layout
3113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3116 \begin_layout Plain Layout
3124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3127 \begin_layout Plain Layout
3134 \begin_layout Plain Layout
3144 \begin_inset Formula $\to$
3151 \begin_layout Plain Layout
3164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3167 \begin_layout Plain Layout
3168 \begin_inset Formula $\begin{cases}
3179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3182 \begin_layout Plain Layout
3189 \begin_layout Plain Layout
3201 arg "newline-insert newline"
3209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3212 \begin_layout Plain Layout
3213 \begin_inset Formula $\begin{cases}
3214 A & \textrm{for }x>0\\
3215 B & \textrm{for }x=0\end{cases}$
3231 \begin_layout Standard
3238 or the usage of the math toolbar button
3239 \begin_inset Graphics
3240 filename ../images/math/cases.png
3245 you can create new lines with the shortcut
3248 arg "newline-insert newline"
3251 or the table toolbar button
3252 \begin_inset Graphics
3253 filename ../images/tabular-feature_append-row.png
3261 \begin_layout Standard
3268 is also available via the menu
3270 Insert\SpecialChar \menuseparator
3271 Math\SpecialChar \menuseparator
3277 \begin_layout Subsection
3282 \begin_layout Plain Layout
3291 \begin_layout Standard
3302 \begin_layout Plain Layout
3310 every character can be displayed canceled.
3311 The characters are quasi accentuated by a slash.
3314 \begin_layout Standard
3316 \begin_inset Tabular
3317 <lyxtabular version="3" rows="4" columns="2">
3319 <column alignment="center" valignment="top" width="0pt">
3320 <column alignment="center" valignment="top" width="0pt">
3322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3325 \begin_layout Plain Layout
3331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3334 \begin_layout Plain Layout
3342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3345 \begin_layout Plain Layout
3353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3356 \begin_layout Plain Layout
3357 \begin_inset Formula $\not=$
3367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3370 \begin_layout Plain Layout
3380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3383 \begin_layout Plain Layout
3384 \begin_inset Formula $\not\le$
3394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3397 \begin_layout Plain Layout
3407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3410 \begin_layout Plain Layout
3411 \begin_inset Formula $\not\parallel$
3427 \begin_layout Standard
3428 The last example shows, that not all negations look good.
3429 Therefore there are for some negations special commands (see
3430 \begin_inset CommandInset ref
3432 reference "sub:Mathematical-Symbols"
3437 \begin_inset CommandInset ref
3439 reference "sec:Relations"
3446 \begin_layout Subsection
3448 \begin_inset CommandInset label
3450 name "sub:Placeholders"
3458 \begin_layout Plain Layout
3468 \begin_layout Plain Layout
3469 Chemical characters ! Isotopes
3478 \begin_layout Plain Layout
3483 \begin_layout Plain Layout
3494 \begin_layout Plain Layout
3509 \begin_layout Standard
3511 \begin_inset space \thinspace{}
3515 \begin_inset space \space{}
3522 \begin_layout Plain Layout
3523 Typesetting isotopes and chemical symbols is described in
3524 \begin_inset CommandInset ref
3526 reference "sub:Chemical-Symbols-and"
3535 the following problem occurs:
3538 \begin_layout Standard
3540 \begin_inset Tabular
3541 <lyxtabular version="3" rows="2" columns="2">
3543 <column alignment="center" valignment="top" width="0pt">
3544 <column alignment="center" valignment="top" width="0pt">
3546 <cell alignment="center" valignment="top" usebox="none">
3549 \begin_layout Plain Layout
3550 Indices created with sub- and superscripts:
3555 <cell alignment="center" valignment="top" usebox="none">
3558 \begin_layout Plain Layout
3559 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3569 <cell alignment="center" valignment="top" usebox="none">
3572 \begin_layout Plain Layout
3578 <cell alignment="center" valignment="top" usebox="none">
3581 \begin_layout Plain Layout
3582 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3596 \begin_inset Note Note
3599 \begin_layout Plain Layout
3606 is only used as spacer.
3614 \begin_layout Standard
3615 The shorter index is by default placed below or above the first character
3616 of the longer index.
3617 To avoid this there is the command
3627 \begin_layout Plain Layout
3635 or the math toolbar button
3636 \begin_inset space \thinspace{}
3643 \begin_layout Plain Layout
3644 can be found in the submenu of the toolbar button
3645 \begin_inset Graphics
3646 filename ../images/math/space.png
3657 \begin_inset Graphics
3658 filename ../images/math/phantom.png
3663 that creates one or more phantom characters.
3670 a small blue box appears that is superposed with two red arrows.
3671 The arrows indicate that the complete width and height of the box content
3672 will be created as placeholder.
3673 Phantom characters are accordingly placeholders with the size of the characters.
3676 \begin_layout Standard
3678 \begin_inset Tabular
3679 <lyxtabular version="3" rows="4" columns="2">
3681 <column alignment="center" valignment="top" width="0">
3682 <column alignment="center" valignment="top" width="0">
3684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3687 \begin_layout Plain Layout
3693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3696 \begin_layout Plain Layout
3698 \begin_inset Note Note
3701 \begin_layout Plain Layout
3708 is only used as spacer.
3720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3723 \begin_layout Plain Layout
3728 \begin_layout Plain Layout
3743 \begin_layout Plain Layout
3753 \begin_inset Formula $\to$
3760 \begin_layout Plain Layout
3774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3777 \begin_layout Plain Layout
3778 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3791 \begin_layout Plain Layout
3796 \begin_layout Plain Layout
3811 \begin_layout Plain Layout
3821 \begin_inset Formula $\to$
3828 \begin_layout Plain Layout
3842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3845 \begin_layout Plain Layout
3846 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3859 \begin_layout Plain Layout
3866 \begin_layout Plain Layout
3881 \begin_layout Plain Layout
3891 \begin_inset Formula $\to$
3898 \begin_layout Plain Layout
3912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3915 \begin_layout Plain Layout
3916 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3932 \begin_layout Standard
3933 Furthermore there are the commands
3943 \begin_layout Plain Layout
3952 \begin_inset space ~
3956 \begin_inset Graphics
3957 filename ../images/math/vphantom.png
3972 \begin_layout Plain Layout
3981 \begin_inset space ~
3985 \begin_inset Graphics
3986 filename ../images/math/hphantom.png
3998 creates only space for the maximal height of the characters in the box
3999 but not for its width.
4006 creates only space for the width of the box content.
4007 Therefore the boxes of both commands have only one red arrow.
4010 \begin_layout Standard
4021 \begin_layout Plain Layout
4036 space for the height of the integral sign,
4040 \begin_layout Plain Layout
4047 creates an integral sign, see
4048 \begin_inset CommandInset ref
4050 reference "sub:Big-Operators"
4059 because this is the larger character.
4060 An example application is in
4061 \begin_inset CommandInset ref
4063 reference "sub:Multiline-Brackets"
4070 \begin_layout Subsection
4075 \begin_layout Plain Layout
4085 \begin_layout Plain Layout
4086 Formula ! underlined
4094 \begin_layout Standard
4096 \begin_inset Tabular
4097 <lyxtabular version="3" rows="4" columns="2">
4099 <column alignment="center" valignment="top" width="0pt">
4100 <column alignment="center" valignment="top" width="0pt">
4102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4105 \begin_layout Plain Layout
4111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4114 \begin_layout Plain Layout
4116 \begin_inset Note Note
4119 \begin_layout Plain Layout
4126 is only used as spacer.
4138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4141 \begin_layout Plain Layout
4148 \begin_layout Plain Layout
4161 \begin_layout Plain Layout
4174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4177 \begin_layout Plain Layout
4178 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4191 \begin_layout Plain Layout
4198 \begin_layout Plain Layout
4211 \begin_layout Plain Layout
4224 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4227 \begin_layout Plain Layout
4228 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4241 \begin_layout Plain Layout
4248 \begin_layout Plain Layout
4263 \begin_layout Plain Layout
4277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4280 \begin_layout Plain Layout
4281 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4297 \begin_layout Standard
4298 In the last example it doesn't matter if first
4313 \begin_layout Standard
4314 To double underline e.
4315 \begin_inset space \thinspace{}
4319 \begin_inset space \space{}
4331 \begin_layout Standard
4332 It is possible to place up to 6 lines above or below characters.
4335 \begin_layout Standard
4336 \begin_inset VSpace bigskip
4339 Custom lines can be created using the command
4349 \begin_layout Plain Layout
4357 which has the following scheme:
4360 \begin_layout Standard
4365 rule[vertical offset]{length}{thickness}
4368 \begin_layout Standard
4369 The optional vertical offset shifts the line upwards (or downwards, when
4370 the value is negative).
4372 \begin_inset CommandInset ref
4374 reference "tab:Available-units"
4378 can be used for the values.
4379 Here are two example lines created with the commands
4380 \begin_inset Newline newline
4387 rule[-2ex]{3cm}{2pt}
4398 \begin_layout Standard
4400 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4406 \begin_layout Standard
4413 can also be used for text when it is inserted in TeX-mode.
4416 \begin_layout Subsection
4418 \begin_inset CommandInset label
4428 \begin_layout Plain Layout
4437 \begin_layout Standard
4438 There are different types of ellipses available.
4442 \begin_layout Plain Layout
4443 In the math toolbar in the submenu of the button
4444 \begin_inset Graphics
4445 filename ../images/math/ldots.png
4455 For listings dots at the baseline are used (
4465 \begin_layout Plain Layout
4473 ), while for operations dots are needed that are on the same height as the
4484 \begin_layout Plain Layout
4493 When using the command
4503 \begin_layout Plain Layout
4511 , LaTeX decides on the basis of the next character what type is used.
4514 \begin_layout Standard
4516 \begin_inset Tabular
4517 <lyxtabular version="3" rows="8" columns="2">
4519 <column alignment="center" valignment="top" width="0pt">
4520 <column alignment="center" valignment="top" width="0pt">
4522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4525 \begin_layout Plain Layout
4531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4534 \begin_layout Plain Layout
4542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4545 \begin_layout Plain Layout
4550 \begin_layout Plain Layout
4565 \begin_layout Plain Layout
4579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4582 \begin_layout Plain Layout
4583 \begin_inset Formula $A_{1},\dots,A_{n}$
4593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4596 \begin_layout Plain Layout
4601 \begin_layout Plain Layout
4616 \begin_layout Plain Layout
4630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4633 \begin_layout Plain Layout
4634 \begin_inset Formula $A_{1}+\dots+A_{n}$
4644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4647 \begin_layout Plain Layout
4652 \begin_layout Plain Layout
4667 \begin_layout Plain Layout
4681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4684 \begin_layout Plain Layout
4685 \begin_inset Formula $A_{1},\ldots,A_{n}$
4695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4698 \begin_layout Plain Layout
4703 \begin_layout Plain Layout
4718 \begin_layout Plain Layout
4732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4735 \begin_layout Plain Layout
4736 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4749 \begin_layout Plain Layout
4757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4760 \begin_layout Plain Layout
4761 \begin_inset Formula $\vdots$
4771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4774 \begin_layout Plain Layout
4782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4785 \begin_layout Plain Layout
4786 \begin_inset Formula $\ddots$
4796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4799 \begin_layout Plain Layout
4801 \begin_inset space \thinspace{}
4804 matrix with the different dots
4809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4812 \begin_layout Plain Layout
4813 \begin_inset Formula $\begin{array}{ccc}
4814 A_{11} & \cdots & A_{1m}\\
4815 \vdots & \ddots & \vdots\\
4816 A_{n1} & \cdots & A_{nm}\end{array}$
4832 \begin_layout Standard
4833 The ellipses available in menu
4835 Insert\SpecialChar \menuseparator
4837 \begin_inset space ~
4851 \begin_layout Standard
4852 \begin_inset VSpace medskip
4855 Specially for matrices there are ellipses that span over several columns.
4856 They are created with the command
4866 \begin_layout Plain Layout
4874 , that has the following scheme:
4877 \begin_layout Standard
4882 hdotsfor[distance]{number of columns}
4885 \begin_layout Standard
4886 The number of columns specifies how many columns should be spanned.
4887 Distance is a factor for the distance between the dots.
4890 \begin_layout Standard
4891 In the following matrix the command
4897 was inserted in the first box of the second line, to get an ellipsis with
4898 a dot distance twice as long as with the command
4905 \begin_inset Formula \[
4906 \left(\begin{array}{cccc}
4909 q & w & e & r\end{array}\right)\]
4913 Note that the matrix fields that should be spanned must be empty, otherwise
4914 you get LaTeX-errors.
4917 \begin_layout Standard
4918 \begin_inset VSpace bigskip
4921 Furthermore you can fill with the command
4931 \begin_layout Plain Layout
4939 the rest of a line with dots.
4940 The effect of these commands is the same like with
4947 \begin_inset CommandInset ref
4949 reference "sub:Variable-Space"
4956 \begin_layout Standard
4957 For example the command
4965 \begin_layout Plain Layout
4979 \begin_layout Standard
4980 \begin_inset Formula $A\dotfill B$
4986 \begin_layout Standard
4993 there is for a line the command
5003 \begin_layout Plain Layout
5014 \begin_layout Standard
5015 \begin_inset Formula $A\hrulefill B$
5021 \begin_layout Standard
5022 To use the commands for text, they have to be inserted in TeX-mode.
5025 \begin_layout Section
5027 \begin_inset CommandInset label
5037 \begin_layout Plain Layout
5046 \begin_layout Standard
5047 Matrices can be inserted via the math toolbar button
5048 \begin_inset Graphics
5049 filename ../images/dialog-show_mathmatrix.png
5056 Insert\SpecialChar \menuseparator
5057 Math\SpecialChar \menuseparator
5061 You will be asked for the number of matrix columns and rows, and the alignment.
5062 The vertical alignment is hereby only of importance for matrices in inline
5066 \begin_layout Standard
5067 The first matrix is top
5068 \begin_inset Formula $\begin{array}[t]{cccc}
5071 C & F & I & L\end{array}$
5075 \begin_inset Formula $\begin{array}{cccc}
5078 C & F & I & L\end{array}$
5081 , and the third bottom
5082 \begin_inset Formula $\begin{array}[b]{cccc}
5085 C & F & I & L\end{array}$
5091 \begin_layout Standard
5092 The horizontal alignment specifies how the column entries should be aligned.
5093 It is set by entering a letter for every column.
5098 denotes left aligned,
5107 To create for example a 4
5112 \begin_inset space ~
5115 matrix where the first column is left aligned, the second and third are
5116 centered, and the last one is right aligned, one enters for the horizontal
5122 Normally are in a matrix all columns centered, therefore the default is
5123 for every column is a
5130 \begin_layout Standard
5131 Horizontal alignment:
5134 \begin_layout Standard
5140 \begin_inset Formula $\begin{array}{lll}
5143 C & F & 10000\end{array}$
5151 \begin_inset Formula $\begin{array}{ccc}
5154 C & F & 10000\end{array}$
5162 \begin_inset Formula $\begin{array}{rrr}
5165 C & F & 10000\end{array}$
5171 \begin_layout Standard
5172 To add or delete rows and columns subsequently, the math toolbar buttons
5174 \begin_inset Graphics
5175 filename ../images/tabular-feature_append-row.png
5181 \begin_inset Graphics
5182 filename ../images/tabular-feature_delete-row.png
5188 \begin_inset space \thinspace{}
5193 Edit\SpecialChar \menuseparator
5197 New rows can also be created with
5200 arg "newline-insert newline"
5206 \begin_layout Standard
5207 \begin_inset VSpace bigskip
5210 Parentheses around a matrix can can either be created with the commands
5221 \begin_layout Plain Layout
5239 \begin_layout Plain Layout
5250 \begin_inset space ~
5256 \begin_inset CommandInset ref
5258 reference "sub:Automatic-Bracket-Size"
5262 , or by using the following commands:
5263 \begin_inset VSpace medskip
5269 \begin_layout Standard
5270 \begin_inset space \hfill{}
5274 \begin_inset Tabular
5275 <lyxtabular version="3" rows="4" columns="2">
5277 <column alignment="center" valignment="top" width="0">
5278 <column alignment="center" valignment="top" width="0">
5280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5283 \begin_layout Plain Layout
5289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5292 \begin_layout Plain Layout
5294 \begin_inset Note Note
5297 \begin_layout Plain Layout
5304 is only used as spacer.
5316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5319 \begin_layout Plain Layout
5326 \begin_layout Plain Layout
5340 \begin_inset space \thinspace{}
5348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5351 \begin_layout Plain Layout
5352 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5353 0 & \textrm{-}\mathrm{i}\\
5354 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5367 \begin_layout Plain Layout
5374 \begin_layout Plain Layout
5388 \begin_inset space \thinspace{}
5396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5399 \begin_layout Plain Layout
5400 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5401 0 & \textrm{-}\mathrm{i}\\
5402 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5415 \begin_layout Plain Layout
5422 \begin_layout Plain Layout
5436 \begin_inset space \thinspace{}
5444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5447 \begin_layout Plain Layout
5448 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5449 0 & \textrm{-}\mathrm{i}\\
5450 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5464 \begin_inset space \hfill{}
5468 \begin_inset Tabular
5469 <lyxtabular version="3" rows="4" columns="2">
5471 <column alignment="center" valignment="top" width="0">
5472 <column alignment="center" valignment="top" width="0">
5474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5477 \begin_layout Plain Layout
5483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5486 \begin_layout Plain Layout
5494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5497 \begin_layout Plain Layout
5504 \begin_layout Plain Layout
5518 \begin_inset space \thinspace{}
5526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5529 \begin_layout Plain Layout
5530 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5531 0 & \textrm{-}\mathrm{i}\\
5532 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5545 \begin_layout Plain Layout
5552 \begin_layout Plain Layout
5566 \begin_inset space \thinspace{}
5574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5577 \begin_layout Plain Layout
5578 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5579 0 & \textrm{-}\mathrm{i}\\
5580 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5593 \begin_layout Plain Layout
5600 \begin_layout Plain Layout
5614 \begin_inset space \thinspace{}
5622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5625 \begin_layout Plain Layout
5626 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5627 0 & \textrm{-}\mathrm{i}\\
5628 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5642 \begin_inset space \hfill{}
5648 \begin_layout Standard
5649 \begin_inset VSpace medskip
5653 \begin_inset space \thinspace{}
5657 \begin_inset space \space{}
5666 is inserted, a blue box appears between two vertical lines where the matrix
5670 \begin_layout Standard
5671 \begin_inset VSpace bigskip
5674 As all multiline formulas are matrices, the length
5684 \begin_layout Plain Layout
5692 that is described in
5693 \begin_inset CommandInset ref
5695 reference "sub:Column-Separation"
5699 can also be used to change the column separation of matrices.
5702 \begin_layout Standard
5703 To change the row separation, the command
5713 \begin_layout Plain Layout
5722 It is used as follows:
5725 \begin_layout Standard
5732 arraystretch}{stretch factor}
5736 \begin_layout Plain Layout
5747 \begin_layout Standard
5754 assigns the stretch factor to the predefined command
5762 \begin_inset space \thinspace{}
5766 \begin_inset space \space{}
5769 the row separation, use the factor 2.
5770 This is then used for all following matrices.
5771 To go back to the original separation, assign the factor 1 to
5780 \begin_layout Standard
5781 To set matrices into a text line, the command
5791 \begin_layout Plain Layout
5800 When it is inserted a blue box with two dashed lines appears.
5801 In this box the matrix is inserted.
5804 \begin_layout Standard
5806 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5807 C & D\end{smallmatrix}\right)$
5813 \begin_layout Section
5814 Brackets and Delimiters
5818 \begin_layout Plain Layout
5828 \begin_layout Plain Layout
5837 \begin_layout Subsection
5838 Vertical Brackets and Delimiters
5842 \begin_layout Plain Layout
5851 \begin_layout Standard
5852 \begin_inset space \hfill{}
5856 \begin_inset Tabular
5857 <lyxtabular version="3" rows="9" columns="2">
5859 <column alignment="center" valignment="top" width="0pt">
5860 <column alignment="center" valignment="top" width="0pt">
5862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5865 \begin_layout Plain Layout
5871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5874 \begin_layout Plain Layout
5882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5885 \begin_layout Plain Layout
5891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5894 \begin_layout Plain Layout
5895 \begin_inset Formula $($
5905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5908 \begin_layout Plain Layout
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5917 \begin_layout Plain Layout
5918 \begin_inset Formula $\{$
5928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5931 \begin_layout Plain Layout
5937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5940 \begin_layout Plain Layout
5941 \begin_inset Formula $[$
5951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5954 \begin_layout Plain Layout
5962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5965 \begin_layout Plain Layout
5966 \begin_inset Formula $\langle$
5976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5979 \begin_layout Plain Layout
5987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5990 \begin_layout Plain Layout
5991 \begin_inset Formula $\lceil$
6001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6004 \begin_layout Plain Layout
6012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6015 \begin_layout Plain Layout
6016 \begin_inset Formula $\lfloor$
6026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6029 \begin_layout Plain Layout
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6038 \begin_layout Plain Layout
6039 \begin_inset Formula $/$
6049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6052 \begin_layout Plain Layout
6058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6061 \begin_layout Plain Layout
6062 \begin_inset Formula $|$
6076 \begin_inset space \hfill{}
6080 \begin_inset Tabular
6081 <lyxtabular version="3" rows="9" columns="2">
6083 <column alignment="center" valignment="top" width="0pt">
6084 <column alignment="center" valignment="top" width="0pt">
6086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6089 \begin_layout Plain Layout
6095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6098 \begin_layout Plain Layout
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6109 \begin_layout Plain Layout
6115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6118 \begin_layout Plain Layout
6119 \begin_inset Formula $)$
6129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6132 \begin_layout Plain Layout
6138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6141 \begin_layout Plain Layout
6142 \begin_inset Formula $\}$
6152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6155 \begin_layout Plain Layout
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6164 \begin_layout Plain Layout
6165 \begin_inset Formula $]$
6175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6178 \begin_layout Plain Layout
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6189 \begin_layout Plain Layout
6190 \begin_inset Formula $\rangle$
6200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6203 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $\rceil$
6225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6228 \begin_layout Plain Layout
6236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6239 \begin_layout Plain Layout
6240 \begin_inset Formula $\rfloor$
6250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6253 \begin_layout Plain Layout
6263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6266 \begin_layout Plain Layout
6267 \begin_inset Formula $\backslash$
6277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6280 \begin_layout Plain Layout
6288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6291 \begin_layout Plain Layout
6292 \begin_inset Formula $\|$
6306 \begin_inset space \hfill{}
6312 \begin_layout Standard
6315 \begin_inset Note Greyedout
6318 \begin_layout Plain Layout
6323 In TeX-mode the command
6333 \begin_layout Plain Layout
6341 must be used for the backslash, because the command
6349 produces there a line break.
6357 \begin_layout Standard
6358 For all characters listed above the size can be adjusted with the commands
6359 described in the following two subsections.
6360 When using these commands, the characters < and > can directly be used
6361 instead of the commands
6376 \begin_layout Subsubsection
6378 \begin_inset CommandInset label
6380 name "sub:Manual-Bracket-Size"
6388 \begin_layout Plain Layout
6389 Bracket size ! manual
6397 \begin_layout Standard
6398 The bracket size can be specified manually by the LaTeX-commands
6408 \begin_layout Plain Layout
6441 denotes the smallest and
6447 the largest bracket size.
6450 \begin_layout Standard
6451 These commands are used to emphasize levels of brackets:
6454 \begin_layout Standard
6456 \begin_inset Tabular
6457 <lyxtabular version="3" rows="2" columns="2">
6459 <column alignment="center" valignment="top" width="0pt">
6460 <column alignment="center" valignment="top" width="0pt">
6462 <cell alignment="center" valignment="top" usebox="none">
6465 \begin_layout Plain Layout
6466 all brackets in the same size:
6471 <cell alignment="center" valignment="top" usebox="none">
6474 \begin_layout Plain Layout
6475 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6485 <cell alignment="center" valignment="top" usebox="none">
6488 \begin_layout Plain Layout
6494 <cell alignment="center" valignment="top" usebox="none">
6497 \begin_layout Plain Layout
6498 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6512 \begin_inset Note Note
6515 \begin_layout Plain Layout
6522 is only used as spacer.
6530 \begin_layout Standard
6531 For the second formula the command
6541 \begin_layout Plain Layout
6555 \begin_layout Standard
6556 Here is an overview about all bracket sizes:
6559 \begin_layout Standard
6579 \begin_layout Plain Layout
6596 \begin_layout Plain Layout
6609 \begin_layout Plain Layout
6625 \begin_layout Standard
6627 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6633 \begin_layout Standard
6640 -commands there is the variant
6650 \begin_layout Plain Layout
6658 that adds a bit more space between the bracket and its content, and the
6675 \begin_layout Plain Layout
6685 , that don't add additional space.
6690 at the end of the command
6696 is for a left bracket; for a right bracket this will be replaced by an
6702 A left or right bracket can each be an opening or closing bracket.
6705 \begin_layout Standard
6706 In the following table is a comparison of the variants:
6709 \begin_layout Standard
6711 \begin_inset Tabular
6712 <lyxtabular version="3" rows="5" columns="2">
6714 <column alignment="center" valignment="middle" width="0">
6715 <column alignment="center" valignment="middle" width="0">
6717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6720 \begin_layout Plain Layout
6726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6729 \begin_layout Plain Layout
6731 \begin_inset Note Note
6734 \begin_layout Plain Layout
6741 is only used as spacer.
6753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6756 \begin_layout Plain Layout
6771 \begin_layout Plain Layout
6789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6792 \begin_layout Plain Layout
6793 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6806 \begin_layout Plain Layout
6821 \begin_layout Plain Layout
6839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6842 \begin_layout Plain Layout
6843 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6856 \begin_layout Plain Layout
6871 \begin_layout Plain Layout
6889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6892 \begin_layout Plain Layout
6893 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6906 \begin_layout Plain Layout
6918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6921 \begin_layout Plain Layout
6922 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6938 \begin_layout Subsubsection
6939 Automatic Bracket Size
6940 \begin_inset CommandInset label
6942 name "sub:Automatic-Bracket-Size"
6950 \begin_layout Plain Layout
6951 Bracket size ! automatic
6959 \begin_layout Standard
6960 Brackets with variable size can be inserted with the commands
6970 \begin_layout Plain Layout
6988 \begin_layout Plain Layout
6996 or via the math toolbar button
6997 \begin_inset Graphics
6998 filename ../images/dialog-show_mathdelimiter.png
7016 the wanted bracket must be inserted.
7017 The bracket size will then automatically be calculated for the output.
7020 \begin_layout Standard
7022 normal bracket: The command
7032 \begin_layout Plain Layout
7042 \begin_inset Formula $\downarrow$
7049 \begin_layout Plain Layout
7061 \begin_inset Formula \[
7069 \begin_layout Standard
7071 multiline bracket: The command
7083 \begin_layout Plain Layout
7093 \begin_inset Formula $\downarrow$
7100 \begin_layout Plain Layout
7114 \begin_inset Formula \[
7115 \ln\left(\frac{A}{C}\right)\]
7122 \begin_layout Standard
7138 \begin_inset space ~
7144 This has the advantage that you can see in LyX immediately the real bracket
7145 size and that the matching right bracket will be created too.
7146 \begin_inset Newline newline
7149 The command for the last example would then be:
7163 \begin_layout Plain Layout
7173 \begin_inset Formula $\downarrow$
7179 \begin_layout Standard
7180 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7181 For example the command
7191 \begin_layout Plain Layout
7201 \begin_inset Formula $\downarrow$
7208 \begin_layout Plain Layout
7224 \begin_inset Formula \[
7225 \left.\frac{A}{B}\right\} \]
7243 will be converted by LyX to brackets in the right size when the document
7244 is reloaded and an omitted bracket will appear as dashed line.
7247 \begin_layout Standard
7248 \begin_inset VSpace bigskip
7251 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7262 \begin_layout Plain Layout
7270 is additionally available for all brackets and limits.
7271 With this command the height of the following character is adapted to the
7272 one of the surrounding brackets, what is e.
7273 \begin_inset space \thinspace{}
7277 \begin_inset space \space{}
7280 needed for physical vectors:
7281 \begin_inset Formula \[
7282 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7286 For physical vectors there is a special LaTeX-package, described in
7287 \begin_inset CommandInset ref
7289 reference "sub:Physical-Vectors"
7296 \begin_layout Subsection
7301 \begin_layout Plain Layout
7302 Brackets ! horizontal
7310 \begin_layout Standard
7312 \begin_inset Tabular
7313 <lyxtabular version="3" rows="4" columns="2">
7315 <column alignment="center" valignment="top" width="0pt">
7316 <column alignment="center" valignment="top" width="0pt">
7318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7321 \begin_layout Plain Layout
7323 \begin_inset Note Note
7326 \begin_layout Plain Layout
7333 is only used as spacer.
7343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7346 \begin_layout Plain Layout
7354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7357 \begin_layout Plain Layout
7361 \begin_layout Plain Layout
7376 \begin_layout Plain Layout
7389 \begin_layout Plain Layout
7402 \begin_layout Plain Layout
7415 \begin_layout Plain Layout
7426 \begin_layout Plain Layout
7439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7442 \begin_layout Plain Layout
7443 \begin_inset Formula $\overbrace{A+B}^{3}$
7453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7456 \begin_layout Plain Layout
7460 \begin_layout Plain Layout
7475 \begin_layout Plain Layout
7488 \begin_layout Plain Layout
7501 \begin_layout Plain Layout
7512 \begin_layout Plain Layout
7525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7528 \begin_layout Plain Layout
7529 \begin_inset Formula $\underbrace{A+B}_{5}$
7539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7542 \begin_layout Plain Layout
7549 \begin_layout Plain Layout
7564 \begin_layout Plain Layout
7577 \begin_layout Plain Layout
7590 \begin_layout Plain Layout
7603 \begin_layout Plain Layout
7616 \begin_layout Plain Layout
7629 \begin_layout Plain Layout
7643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7646 \begin_layout Plain Layout
7647 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7663 \begin_layout Standard
7664 In the last example it doesn't matter if
7676 is inserted at first.
7679 \begin_layout Standard
7680 \begin_inset VSpace bigskip
7683 When brackets are needed that overlap each other, multiline formulas, as
7685 \begin_inset CommandInset ref
7687 reference "sec:Multiline-Formulas"
7692 \begin_inset Formula \begin{eqnarray*}
7693 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7694 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7698 In the first row the formula is inserted together with the first brace.
7699 It is hereby important that the space command
7703 \begin_layout Plain Layout
7704 Space commands are explained in
7705 \begin_inset CommandInset ref
7707 reference "sub:Predefined-Space"
7722 is inserted before the first
7723 \begin_inset Formula $d$
7726 , because the brace that ends behind the
7727 \begin_inset Formula $q$
7730 prevents that the following
7731 \begin_inset Quotes eld
7735 \begin_inset Quotes erd
7738 is surrounded by space.
7742 \begin_layout Plain Layout
7743 because a bracket is not handled as character, see
7744 \begin_inset CommandInset ref
7746 reference "sub:Binary-Operators"
7755 In the second row the second brace is inserted.
7756 As it should begin before the
7757 \begin_inset Formula $b$
7772 \begin_layout Plain Layout
7780 \begin_inset CommandInset ref
7782 reference "sub:Placeholders"
7791 This space is needed because the
7792 \begin_inset Quotes eld
7796 \begin_inset Quotes erd
7799 is also surrounded by space in the formula.
7800 The brace is placed under the command
7809 \begin_layout Standard
7810 It gets more complicated when brackets overlap each other, like in the following
7815 \begin_layout Plain Layout
7827 \begin_inset Formula \begin{eqnarray*}
7828 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7829 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7837 \begin_layout Plain Layout
7848 The first formula row is the same as the second row of the previous example,
7849 with the difference that the brace is above.
7850 The second row contains the formula together with the second brace.
7851 To avoid that there is space between the upper brace in the first row and
7852 the formula, the row spacing need to be reduced.
7853 This is not easily possible due to a bug in LyX
7857 \begin_layout Plain Layout
7858 \begin_inset CommandInset href
7860 name "LyX-bug #1505"
7861 target "http://www.lyx.org/trac/ticket/1505"
7871 As solution for the problem, the global formula row separation
7881 \begin_layout Plain Layout
7889 must be changed to -6
7890 \begin_inset space \thinspace{}
7893 pt before the formula with the command
7908 is set back after the formula to the standard value of 3
7909 \begin_inset space \thinspace{}
7912 pt using the same command.
7913 More about the row separation in formulas is explained in
7914 \begin_inset CommandInset ref
7916 reference "sub:Line-Separation"
7923 \begin_layout Section
7928 \begin_layout Plain Layout
7937 \begin_layout Standard
7938 Arrows can be inserted via the math toolbar button
7939 \begin_inset Graphics
7940 filename ../images/math/leftarrow.png
7945 or the commands listed in the following subsections.
7948 \begin_layout Standard
7949 \begin_inset Newpage newpage
7955 \begin_layout Subsection
7960 \begin_layout Plain Layout
7969 \begin_layout Standard
7970 \begin_inset space \hfill{}
7974 \begin_inset Tabular
7975 <lyxtabular version="3" rows="8" columns="2">
7977 <column alignment="center" valignment="top" width="0pt">
7978 <column alignment="center" valignment="top" width="0pt">
7980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7983 \begin_layout Plain Layout
7989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7992 \begin_layout Plain Layout
8000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8003 \begin_layout Plain Layout
8011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8014 \begin_layout Plain Layout
8015 \begin_inset Formula $\gets$
8025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8028 \begin_layout Plain Layout
8036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8039 \begin_layout Plain Layout
8040 \begin_inset Formula $\Leftarrow$
8050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8053 \begin_layout Plain Layout
8061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8064 \begin_layout Plain Layout
8065 \begin_inset Formula $\longleftarrow$
8075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8078 \begin_layout Plain Layout
8086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8089 \begin_layout Plain Layout
8090 \begin_inset Formula $\Longleftarrow$
8100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8103 \begin_layout Plain Layout
8111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8114 \begin_layout Plain Layout
8115 \begin_inset Formula $\leftharpoonup$
8125 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8139 \begin_layout Plain Layout
8140 \begin_inset Formula $\leftharpoondown$
8150 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8153 \begin_layout Plain Layout
8161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8164 \begin_layout Plain Layout
8165 \begin_inset Formula $\hookleftarrow$
8179 \begin_inset space \hfill{}
8183 \begin_inset Tabular
8184 <lyxtabular version="3" rows="8" columns="2">
8186 <column alignment="center" valignment="top" width="0pt">
8187 <column alignment="center" valignment="top" width="0pt">
8189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8192 \begin_layout Plain Layout
8198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8201 \begin_layout Plain Layout
8209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8212 \begin_layout Plain Layout
8220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8223 \begin_layout Plain Layout
8224 \begin_inset Formula $\to$
8234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8237 \begin_layout Plain Layout
8245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8248 \begin_layout Plain Layout
8249 \begin_inset Formula $\Rightarrow$
8259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8262 \begin_layout Plain Layout
8270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8273 \begin_layout Plain Layout
8274 \begin_inset Formula $\longrightarrow$
8284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8287 \begin_layout Plain Layout
8295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8298 \begin_layout Plain Layout
8299 \begin_inset Formula $\Longrightarrow$
8309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8312 \begin_layout Plain Layout
8320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8323 \begin_layout Plain Layout
8324 \begin_inset Formula $\rightharpoonup$
8334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8337 \begin_layout Plain Layout
8345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8348 \begin_layout Plain Layout
8349 \begin_inset Formula $\rightharpoondown$
8359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8362 \begin_layout Plain Layout
8370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8373 \begin_layout Plain Layout
8374 \begin_inset Formula $\hookrightarrow$
8388 \begin_inset space \hfill{}
8394 \begin_layout Standard
8395 \begin_inset space \hfill{}
8399 \begin_inset Tabular
8400 <lyxtabular version="3" rows="6" columns="2">
8402 <column alignment="center" valignment="top" width="0pt">
8403 <column alignment="center" valignment="top" width="0pt">
8405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8408 \begin_layout Plain Layout
8414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8417 \begin_layout Plain Layout
8425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8428 \begin_layout Plain Layout
8436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8439 \begin_layout Plain Layout
8440 \begin_inset Formula $\leftrightarrow$
8450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8453 \begin_layout Plain Layout
8461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8464 \begin_layout Plain Layout
8465 \begin_inset Formula $\Leftrightarrow$
8475 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8486 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8489 \begin_layout Plain Layout
8490 \begin_inset Formula $\longleftrightarrow$
8500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8503 \begin_layout Plain Layout
8511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8514 \begin_layout Plain Layout
8515 \begin_inset Formula $\Longleftrightarrow$
8525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8528 \begin_layout Plain Layout
8536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8539 \begin_layout Plain Layout
8540 \begin_inset Formula $\rightleftharpoons$
8554 \begin_inset space \hspace{}
8559 \begin_inset space \hfill{}
8563 \begin_inset Tabular
8564 <lyxtabular version="3" rows="5" columns="2">
8566 <column alignment="center" valignment="top" width="0pt">
8567 <column alignment="center" valignment="top" width="0pt">
8569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8572 \begin_layout Plain Layout
8578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8581 \begin_layout Plain Layout
8589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8592 \begin_layout Plain Layout
8600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8603 \begin_layout Plain Layout
8604 \begin_inset Formula $\mapsto$
8614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8617 \begin_layout Plain Layout
8625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8628 \begin_layout Plain Layout
8629 \begin_inset Formula $\longmapsto$
8639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8642 \begin_layout Plain Layout
8650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8653 \begin_layout Plain Layout
8654 \begin_inset Formula $\leadsto$
8664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8667 \begin_layout Plain Layout
8675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8678 \begin_layout Plain Layout
8679 \begin_inset Formula $\dasharrow$
8693 \begin_inset space \hfill{}
8699 \begin_layout Standard
8700 \begin_inset VSpace medskip
8703 Arrows used as accent like e.
8704 \begin_inset space \thinspace{}
8708 \begin_inset space \space{}
8711 vector arrows are listed in
8712 \begin_inset CommandInset ref
8714 reference "sec:Accents"
8721 \begin_layout Standard
8722 \begin_inset VSpace bigskip
8725 Furthermore there are the labeled arrows
8729 \begin_layout Plain Layout
8745 \begin_layout Plain Layout
8763 \begin_layout Plain Layout
8770 \begin_layout Plain Layout
8785 When inserting one of these commands in a formula, an arrow with two blue
8786 boxes appear where the label can be inserted.
8787 The length of the arrow adapts to the label width.
8790 \begin_layout Standard
8792 \begin_inset Tabular
8793 <lyxtabular version="3" rows="3" columns="2">
8795 <column alignment="center" valignment="top" width="0pt">
8796 <column alignment="center" valignment="top" width="0pt">
8798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8801 \begin_layout Plain Layout
8807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8810 \begin_layout Plain Layout
8812 \begin_inset Note Note
8815 \begin_layout Plain Layout
8822 is only used as spacer.
8834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8837 \begin_layout Plain Layout
8844 \begin_layout Plain Layout
8854 \begin_inset Formula $\downarrow$
8858 \begin_inset Formula $\to$
8866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8869 \begin_layout Plain Layout
8870 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8883 \begin_layout Plain Layout
8890 \begin_layout Plain Layout
8900 \begin_inset Formula $\downarrow$
8904 \begin_inset Formula $\to$
8912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8932 \begin_layout Subsection
8933 Vertical and diagonal Arrows
8937 \begin_layout Plain Layout
8947 \begin_layout Plain Layout
8956 \begin_layout Standard
8957 \begin_inset space \hfill{}
8961 \begin_inset Tabular
8962 <lyxtabular version="3" rows="7" columns="2">
8964 <column alignment="center" valignment="top" width="0pt">
8965 <column alignment="center" valignment="top" width="0pt">
8967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8970 \begin_layout Plain Layout
8976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8979 \begin_layout Plain Layout
8987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8990 \begin_layout Plain Layout
8998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9001 \begin_layout Plain Layout
9002 \begin_inset Formula $\uparrow$
9012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9015 \begin_layout Plain Layout
9023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9026 \begin_layout Plain Layout
9027 \begin_inset Formula $\Uparrow$
9037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9040 \begin_layout Plain Layout
9048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9051 \begin_layout Plain Layout
9052 \begin_inset Formula $\updownarrow$
9062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9065 \begin_layout Plain Layout
9073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9076 \begin_layout Plain Layout
9077 \begin_inset Formula $\Updownarrow$
9087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9090 \begin_layout Plain Layout
9098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9101 \begin_layout Plain Layout
9102 \begin_inset Formula $\Downarrow$
9112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9115 \begin_layout Plain Layout
9123 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9126 \begin_layout Plain Layout
9127 \begin_inset Formula $\downarrow$
9141 \begin_inset space \hfill{}
9145 \begin_inset Tabular
9146 <lyxtabular version="3" rows="5" columns="2">
9148 <column alignment="center" valignment="top" width="0pt">
9149 <column alignment="center" valignment="top" width="0pt">
9151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9154 \begin_layout Plain Layout
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9163 \begin_layout Plain Layout
9171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9174 \begin_layout Plain Layout
9182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9185 \begin_layout Plain Layout
9186 \begin_inset Formula $\nearrow$
9196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9199 \begin_layout Plain Layout
9207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9210 \begin_layout Plain Layout
9211 \begin_inset Formula $\searrow$
9221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9224 \begin_layout Plain Layout
9232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9235 \begin_layout Plain Layout
9236 \begin_inset Formula $\swarrow$
9246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9249 \begin_layout Plain Layout
9257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9260 \begin_layout Plain Layout
9261 \begin_inset Formula $\nwarrow$
9275 \begin_inset space \hfill{}
9281 \begin_layout Standard
9282 \begin_inset VSpace medskip
9285 Vertical arrows can be used also as delimiter together with the commands
9287 \begin_inset CommandInset ref
9289 reference "sub:Manual-Bracket-Size"
9294 \begin_inset CommandInset ref
9296 reference "sub:Automatic-Bracket-Size"
9303 \begin_layout Standard
9304 \begin_inset Newpage newpage
9310 \begin_layout Section
9312 \begin_inset CommandInset label
9322 \begin_layout Plain Layout
9331 \begin_layout Standard
9332 Accents can be inserted via the math toolbar button
9333 \begin_inset Graphics
9334 filename ../images/math/hat.png
9339 or the commands listed in the following subsections.
9342 \begin_layout Subsection
9343 Accents for one Character
9347 \begin_layout Plain Layout
9360 \begin_layout Plain Layout
9362 \begin_inset CommandInset ref
9364 reference "sub:Accents-in-Text"
9377 \begin_layout Plain Layout
9385 \begin_inset Note Note
9388 \begin_layout Plain Layout
9391 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9394 \begin_layout Plain Layout
9397 texorpdfstring is in section
9398 \begin_inset CommandInset ref
9400 reference "sub:Formulas-in-Section"
9410 \begin_inset CommandInset label
9412 name "sub:Accents-for-one"
9420 \begin_layout Plain Layout
9421 Accents ! for one character
9429 \begin_layout Standard
9430 \begin_inset space \hfill{}
9434 \begin_inset Tabular
9435 <lyxtabular version="3" rows="8" columns="2">
9437 <column alignment="center" valignment="top" width="0pt">
9438 <column alignment="center" valignment="top" width="0pt">
9440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9443 \begin_layout Plain Layout
9449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9452 \begin_layout Plain Layout
9454 \begin_inset Note Note
9457 \begin_layout Plain Layout
9464 is only used as spacer.
9476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9479 \begin_layout Plain Layout
9486 \begin_layout Plain Layout
9500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9503 \begin_layout Plain Layout
9504 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9517 \begin_layout Plain Layout
9524 \begin_layout Plain Layout
9538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9541 \begin_layout Plain Layout
9542 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9555 \begin_layout Plain Layout
9562 \begin_layout Plain Layout
9576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9579 \begin_layout Plain Layout
9580 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9593 \begin_layout Plain Layout
9601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9604 \begin_layout Plain Layout
9605 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9618 \begin_layout Plain Layout
9625 \begin_layout Plain Layout
9638 \begin_layout Plain Layout
9649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9652 \begin_layout Plain Layout
9653 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9666 \begin_layout Plain Layout
9673 \begin_layout Plain Layout
9687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9690 \begin_layout Plain Layout
9691 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9704 \begin_layout Plain Layout
9711 \begin_layout Plain Layout
9725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9728 \begin_layout Plain Layout
9729 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9743 \begin_inset space \hfill{}
9747 \begin_inset Tabular
9748 <lyxtabular version="3" rows="7" columns="2">
9750 <column alignment="center" valignment="top" width="0pt">
9751 <column alignment="center" valignment="top" width="0pt">
9753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9756 \begin_layout Plain Layout
9762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9765 \begin_layout Plain Layout
9773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9776 \begin_layout Plain Layout
9783 \begin_layout Plain Layout
9797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9800 \begin_layout Plain Layout
9801 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9814 \begin_layout Plain Layout
9821 \begin_layout Plain Layout
9835 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9838 \begin_layout Plain Layout
9839 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9852 \begin_layout Plain Layout
9859 \begin_layout Plain Layout
9873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9876 \begin_layout Plain Layout
9877 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9890 \begin_layout Plain Layout
9897 \begin_layout Plain Layout
9911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9914 \begin_layout Plain Layout
9915 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9928 \begin_layout Plain Layout
9935 \begin_layout Plain Layout
9949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9952 \begin_layout Plain Layout
9953 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9966 \begin_layout Plain Layout
9973 \begin_layout Plain Layout
9987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9990 \begin_layout Plain Layout
9991 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10005 \begin_inset space \hfill{}
10011 \begin_layout Standard
10012 \begin_inset VSpace bigskip
10018 \begin_layout Standard
10019 You can directly insert accents like é to formulas.
10020 LyX will transform them to the corresponding accent command.
10025 \begin_layout Plain Layout
10031 it is better to insert a quotation mark before the vowel.
10032 These two characters are then treated by LaTeX as
10036 character when the formula part with the umlaut is marked as German.
10044 \begin_inset Quotes eld
10048 \begin_inset Quotes erd
10051 umlauts are created as demonstrated in the following example:
10054 \begin_layout Standard
10055 \begin_inset VSpace -2mm
10061 \begin_layout Standard
10063 \begin_inset Tabular
10064 <lyxtabular version="3" rows="3" columns="2">
10066 <column alignment="center" valignment="top" width="0">
10067 <column alignment="center" valignment="top" width="0">
10069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10072 \begin_layout Plain Layout
10078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10081 \begin_layout Plain Layout
10083 \begin_inset Note Note
10086 \begin_layout Plain Layout
10094 \begin_inset space \thinspace{}
10097 pt space are only used as spacer.
10109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10112 \begin_layout Plain Layout
10115 \begin_inset Quotes grd
10123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10126 \begin_layout Plain Layout
10127 \begin_inset space \hspace{}
10134 \begin_inset Formula $"i$
10144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10147 \begin_layout Plain Layout
10154 \begin_layout Plain Layout
10168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10171 \begin_layout Plain Layout
10172 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10188 \begin_layout Standard
10189 Another advantage to
10195 is that umlauts can directly be converted to mathematical text because
10196 the accent commands above are
10202 in mathematical text
10205 To convert an accented character to mathematical text, only the character
10206 under the accent may be converted.
10207 This applies also for all other conversions, e.
10208 \begin_inset space \thinspace{}
10212 \begin_inset space \space{}
10218 \begin_layout Standard
10219 In mathematical text, umlauts and other accented characters can directly
10223 \begin_layout Subsection
10224 Accents for Operators
10228 \begin_layout Plain Layout
10229 Accents ! for operators
10237 \begin_layout Standard
10248 \begin_layout Plain Layout
10266 \begin_layout Plain Layout
10274 characters can be placed above or below an operator, respectively, to accent
10286 \begin_layout Plain Layout
10294 characters can be set before and behind an operator.
10295 The command scheme is:
10298 \begin_layout Standard
10314 \begin_layout Standard
10321 must always be before the operator that should be accented.
10322 You can accent with several characters and even with other operators and
10330 for example only characters behind an operator, write nothing between the
10331 first braces but don't omit the braces.
10334 \begin_layout Standard
10335 For example the command
10340 \begin_inset Formula $\to$
10350 \begin_inset Formula $\to$
10359 \begin_layout Plain Layout
10375 \begin_inset Formula \[
10376 \sideset{}{'}\sum_{k=1}^{n}\]
10383 \begin_layout Standard
10392 \begin_layout Plain Layout
10407 \begin_layout Plain Layout
10419 \begin_inset Formula $\uparrow$
10427 \begin_inset Formula \[
10428 \overset{a}{\maltese}\]
10432 As seen in the last example, with
10444 also symbols and characters can be accented; with
10450 this is not possible.
10453 \begin_layout Subsection
10454 Accents for several Characters
10458 \begin_layout Plain Layout
10459 Accents ! for several characters
10467 \begin_layout Standard
10468 \begin_inset space \hfill{}
10472 \begin_inset Tabular
10473 <lyxtabular version="3" rows="5" columns="2">
10475 <column alignment="center" valignment="top" width="0pt">
10476 <column alignment="center" valignment="top" width="0pt">
10478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10481 \begin_layout Plain Layout
10487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10490 \begin_layout Plain Layout
10492 \begin_inset Note Note
10495 \begin_layout Plain Layout
10502 is only used as spacer.
10514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10517 \begin_layout Plain Layout
10524 \begin_layout Plain Layout
10538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10541 \begin_layout Plain Layout
10542 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10552 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10555 \begin_layout Plain Layout
10562 \begin_layout Plain Layout
10576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10579 \begin_layout Plain Layout
10580 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10593 \begin_layout Plain Layout
10600 \begin_layout Plain Layout
10614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10617 \begin_layout Plain Layout
10618 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10631 \begin_layout Plain Layout
10634 underleftrightarrow
10638 \begin_layout Plain Layout
10652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10655 \begin_layout Plain Layout
10656 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10670 \begin_inset space \hfill{}
10674 \begin_inset Tabular
10675 <lyxtabular version="3" rows="5" columns="2">
10677 <column alignment="center" valignment="top" width="0pt">
10678 <column alignment="center" valignment="top" width="0pt">
10680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10683 \begin_layout Plain Layout
10689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10692 \begin_layout Plain Layout
10700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10703 \begin_layout Plain Layout
10710 \begin_layout Plain Layout
10724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10727 \begin_layout Plain Layout
10728 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10741 \begin_layout Plain Layout
10748 \begin_layout Plain Layout
10762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10765 \begin_layout Plain Layout
10766 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10779 \begin_layout Plain Layout
10786 \begin_layout Plain Layout
10800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10803 \begin_layout Plain Layout
10804 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10817 \begin_layout Plain Layout
10824 \begin_layout Plain Layout
10838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10841 \begin_layout Plain Layout
10842 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10856 \begin_inset space \hfill{}
10862 \begin_layout Standard
10863 \begin_inset VSpace medskip
10866 With these commands as many characters as you like can be accented.
10879 will only be set in the output with a length of three characters, as shown
10880 in the following example:
10881 \begin_inset Formula \[
10882 \widetilde{A+B=C-D}\]
10889 \begin_layout Standard
10900 \begin_layout Plain Layout
10918 \begin_layout Plain Layout
10926 described in the previous subsection it is also possible to accent several
10936 \begin_layout Plain Layout
10946 \begin_inset Formula $\downarrow$
10952 \begin_inset Formula \[
10953 \underset{***}{A=B}\]
10960 \begin_layout Section
10962 \begin_inset CommandInset label
10972 \begin_layout Plain Layout
10981 \begin_layout Subsection
10983 \begin_inset CommandInset label
10985 name "sub:Predefined-Space"
10993 \begin_layout Plain Layout
10994 Space ! horizontal ! predefined
11002 \begin_layout Standard
11003 Sometimes it is necessary to insert horizontal space to a formula.
11004 This is done by inserting a protected space (shortcut
11007 arg "space-insert protected"
11012 \begin_inset Quotes eld
11021 \begin_layout Plain Layout
11033 \begin_inset Quotes erd
11036 appears and by pressing
11040 several times one can select one of eight different space sizes.
11041 The spaces can also be inserted using the math toolbar button
11042 \begin_inset Graphics
11043 filename ../images/math/space.png
11048 or special commands.
11049 Independent from the inserted command, one can select the size again by
11057 \begin_layout Standard
11060 \begin_inset VSpace -5mm
11064 \begin_inset Tabular
11065 <lyxtabular version="3" rows="3" columns="7">
11067 <column alignment="center" valignment="middle" width="6.8cm">
11068 <column alignment="center" valignment="top" width="0">
11069 <column alignment="center" valignment="top" width="0">
11070 <column alignment="center" valignment="top" width="0">
11071 <column alignment="center" valignment="top" width="0">
11072 <column alignment="center" valignment="top" width="0">
11073 <column alignment="center" valignment="top" width="0">
11075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11078 \begin_layout Plain Layout
11084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11087 \begin_layout Plain Layout
11095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11098 \begin_layout Plain Layout
11106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11109 \begin_layout Plain Layout
11117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11120 \begin_layout Plain Layout
11128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11142 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11155 \begin_layout Plain Layout
11160 keystrokes after inserting the protected space
11165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11177 \begin_layout Plain Layout
11183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11186 \begin_layout Plain Layout
11192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11195 \begin_layout Plain Layout
11201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11213 \begin_layout Plain Layout
11221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11224 \begin_layout Plain Layout
11230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11233 \begin_layout Plain Layout
11234 \begin_inset Formula $A\, B$
11242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11245 \begin_layout Plain Layout
11246 \begin_inset Formula $A\: B$
11254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11257 \begin_layout Plain Layout
11258 \begin_inset Formula $A\; B$
11266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11269 \begin_layout Plain Layout
11270 \begin_inset Formula $A\quad B$
11278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11281 \begin_layout Plain Layout
11282 \begin_inset Formula $A\qquad B$
11290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11293 \begin_layout Plain Layout
11294 \begin_inset Formula $A\! B$
11310 \begin_layout Standard
11311 The last size seem to produce no space.
11312 It is displayed red in LyX contrary to the other sizes, because it is a
11314 There are two more negative spaces:
11317 \begin_layout Standard
11319 \begin_inset Tabular
11320 <lyxtabular version="3" rows="3" columns="3">
11322 <column alignment="center" valignment="middle" width="6.8cm">
11323 <column alignment="center" valignment="top" width="0pt">
11324 <column alignment="center" valignment="top" width="0pt">
11326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11329 \begin_layout Plain Layout
11335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11338 \begin_layout Plain Layout
11346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11349 \begin_layout Plain Layout
11359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11362 \begin_layout Plain Layout
11367 keystrokes after inserting the protected space
11372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11375 \begin_layout Plain Layout
11381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11384 \begin_layout Plain Layout
11392 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11395 \begin_layout Plain Layout
11401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11404 \begin_layout Plain Layout
11405 \begin_inset Formula $A\negmedspace B$
11413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11416 \begin_layout Plain Layout
11417 \begin_inset Formula $A\negthickspace B$
11433 \begin_layout Standard
11434 Negative spaces can lead to characters overlapping each other.
11435 Thus they can be used to enforce ligatures, what is e.
11436 \begin_inset space \thinspace{}
11440 \begin_inset space \space{}
11443 useful for summation operators:
11446 \begin_layout Standard
11448 \begin_inset Tabular
11449 <lyxtabular version="3" rows="3" columns="2">
11451 <column alignment="center" valignment="top" width="0">
11452 <column alignment="center" valignment="top" width="0">
11454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11457 \begin_layout Plain Layout
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11466 \begin_layout Plain Layout
11468 \begin_inset Note Note
11471 \begin_layout Plain Layout
11478 is only used as spacer.
11490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11493 \begin_layout Plain Layout
11502 \begin_layout Plain Layout
11516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11519 \begin_layout Plain Layout
11520 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11533 \begin_layout Plain Layout
11544 \begin_layout Plain Layout
11558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11561 \begin_layout Plain Layout
11562 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11578 \begin_layout Standard
11579 Relations like for example equal signs, are always surrounded by space.
11580 To suppress this, the equal sign is placed into a TeX-brace.
11581 The following example demonstrates this:
11584 \begin_layout Standard
11586 \begin_inset Tabular
11587 <lyxtabular version="3" rows="2" columns="2">
11589 <column alignment="center" valignment="top" width="0pt">
11590 <column alignment="center" valignment="top" width="0pt">
11592 <cell alignment="center" valignment="top" usebox="none">
11595 \begin_layout Plain Layout
11601 <cell alignment="center" valignment="top" usebox="none">
11604 \begin_layout Plain Layout
11605 \begin_inset Formula $A=B$
11615 <cell alignment="center" valignment="top" usebox="none">
11618 \begin_layout Plain Layout
11619 \begin_inset Note Note
11622 \begin_layout Plain Layout
11629 is only used as spacer.
11635 \begin_inset Formula $\raisebox{5mm}{}$
11638 equation without space
11643 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11646 \begin_layout Plain Layout
11647 \begin_inset Formula $A{=}B$
11663 \begin_layout Standard
11665 The command for the last formula is:
11670 \begin_inset Formula $\to$
11676 \begin_layout Standard
11677 \begin_inset VSpace bigskip
11680 Spaces are needed for physical units, because the space between the value
11681 and the unit is the smallest one and not a normal space.
11682 For units in text, the smallest space is inserted via the menu
11684 Insert\SpecialChar \menuseparator
11685 Formatting\SpecialChar \menuseparator
11687 \begin_inset space ~
11695 arg "space-insert thin"
11701 \begin_layout Standard
11702 An example to visualize the difference:
11705 \begin_layout Standard
11706 \begin_inset Tabular
11707 <lyxtabular version="3" rows="2" columns="2">
11709 <column alignment="left" valignment="top" width="0">
11710 <column alignment="left" valignment="top" width="0">
11712 <cell alignment="center" valignment="top" usebox="none">
11715 \begin_layout Plain Layout
11717 \begin_inset Formula $\cdot$
11725 <cell alignment="center" valignment="top" usebox="none">
11728 \begin_layout Plain Layout
11729 space between value and unit
11736 <cell alignment="center" valignment="top" usebox="none">
11739 \begin_layout Plain Layout
11741 \begin_inset space \thinspace{}
11745 \begin_inset Formula $\cdot$
11753 <cell alignment="center" valignment="top" usebox="none">
11756 \begin_layout Plain Layout
11757 smallest space between value and unit
11770 \begin_layout Subsection
11775 \begin_layout Plain Layout
11788 \begin_layout Plain Layout
11789 for vertical space in formulas see
11790 \begin_inset CommandInset ref
11792 reference "sub:Line-Separation"
11805 \begin_layout Plain Layout
11813 \begin_inset Note Note
11816 \begin_layout Plain Layout
11819 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11822 \begin_layout Plain Layout
11825 texorpdfstring is in section
11826 \begin_inset CommandInset ref
11828 reference "sub:Formulas-in-Section"
11838 \begin_inset CommandInset label
11840 name "sub:Variable-Space"
11848 \begin_layout Plain Layout
11849 Space ! horizontal ! variable
11857 \begin_layout Standard
11858 Space with a defined length can be inserted with the command
11868 \begin_layout Plain Layout
11878 \begin_inset Quotes eld
11887 \begin_layout Plain Layout
11899 \begin_inset Quotes erd
11903 The length can be specified by left-clicking on the
11904 \begin_inset Quotes eld
11913 \begin_layout Plain Layout
11925 \begin_inset Quotes erd
11929 The length may also be negative.
11930 To insert so many space that the formula uses all available space, the
11941 \begin_layout Plain Layout
11952 \begin_layout Standard
11953 \begin_inset VSpace -1mm
11959 \begin_layout Standard
11961 \begin_inset Tabular
11962 <lyxtabular version="3" rows="4" columns="2">
11964 <column alignment="center" valignment="top" width="0">
11965 <column alignment="center" valignment="top" width="0">
11967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11970 \begin_layout Plain Layout
11978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11981 \begin_layout Plain Layout
11989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11992 \begin_layout Plain Layout
11999 \begin_layout Plain Layout
12009 \begin_inset Formula $\to$
12015 \begin_inset space \thinspace{}
12023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12026 \begin_layout Plain Layout
12027 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12040 \begin_layout Plain Layout
12047 \begin_layout Plain Layout
12057 \begin_inset Formula $\to$
12063 \begin_inset space \thinspace{}
12071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12074 \begin_layout Plain Layout
12075 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12088 \begin_layout Plain Layout
12095 \begin_layout Plain Layout
12109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12112 \begin_layout Plain Layout
12113 \begin_inset Formula $A=A\hfill B=B$
12129 \begin_layout Standard
12130 In the last example the available space is given by the longest column entry
12132 In an inline formula the space depends on the length of the line in which
12140 Thus, when the line uses the full width, no space will be created.
12147 only has an effect on displayed formulas when the formula style
12152 (Formula styles are explained in
12153 \begin_inset CommandInset ref
12155 reference "sec:Formula-Styles"
12162 \begin_layout Standard
12169 , there are the commands
12181 that fill the space with a pattern, see
12182 \begin_inset CommandInset ref
12184 reference "sub:Ellipses"
12191 \begin_layout Standard
12192 For text, variable space can be inserted via the menu
12194 Insert\SpecialChar \menuseparator
12195 Formatting\SpecialChar \menuseparator
12197 \begin_inset space ~
12205 \begin_layout Standard
12206 This is a line with
12207 \begin_inset space \hspace{}
12212 \begin_inset space \thinspace{}
12218 \begin_layout Standard
12219 This is a line with
12220 \begin_inset space \hfill{}
12226 \begin_layout Subsection
12227 Space besides inline Formulas
12231 \begin_layout Plain Layout
12232 Space ! besides inline formulas
12240 \begin_layout Standard
12241 The space that surrounds inline formulas can be adjusted with the length
12250 \begin_layout Plain Layout
12261 The value of a length is set with the command
12269 \begin_layout Plain Layout
12279 that has the following scheme:
12282 \begin_layout Standard
12287 setlength{length name}{value}
12290 \begin_layout Standard
12298 \begin_inset space \thinspace{}
12304 \begin_layout Standard
12314 \begin_layout Standard
12315 is inserted in TeX-mode.
12317 \begin_inset space \thinspace{}
12320 mm space will now be set around all inline formulas:
12324 \begin_layout Plain Layout
12338 \begin_layout Standard
12339 This is a line with an inline formula
12340 \begin_inset Formula $A=B$
12344 \begin_inset space \thinspace{}
12347 mm surrounding space.
12351 \begin_layout Plain Layout
12365 \begin_layout Standard
12366 To return to the predefined value,
12372 is set to the value 0
12373 \begin_inset space \thinspace{}
12379 \begin_layout Section
12384 \begin_layout Plain Layout
12394 \begin_layout Plain Layout
12399 \begin_layout Plain Layout
12410 \begin_layout Plain Layout
12425 \begin_layout Standard
12426 Boxes for text are described in chapter
12433 \begin_inset space ~
12441 \begin_layout Subsection
12443 \begin_inset CommandInset label
12445 name "sub:Boxes-with-Frame"
12453 \begin_layout Plain Layout
12462 \begin_layout Standard
12463 It is possible to frame formulas or parts of it with the commands
12473 \begin_layout Plain Layout
12491 \begin_layout Plain Layout
12502 \begin_layout Standard
12503 When one of these commands is inserted to a formula, a blue box appears
12504 within a frame to enter formula parts.
12511 an additional formula has to be created by
12515 within this box, because the box content will otherwise be treated as mathemati
12523 is used, a new formula is automatically created inside the frame.
12526 \begin_layout Standard
12533 is not suitable to frame displayed formulas because the formula will always
12534 be set in the size of the text.
12541 is in contrary not suitable to frame inline formulas, because the formula
12542 will always be set in the size of a displayed formula.
12545 \begin_layout Standard
12552 there is the command
12562 \begin_layout Plain Layout
12570 where additionally the frame width and the alignment can be specified.
12577 is used in the following scheme:
12580 \begin_layout Standard
12585 framebox[frame width][position]{box content}
12588 \begin_layout Standard
12589 The position can either be
12606 right aligns the formula in the box.
12607 When no position is given, the formula will be centered.
12608 \begin_inset Newline newline
12611 Is no width given, also no position can be given.
12612 In this case the frame width is adjusted to the box content like for
12621 \begin_layout Standard
12628 is inserted, a box appears containing three blue boxes.
12629 The first two boxes are surrounded by brackets and denote the two optional
12631 The third box is for formula parts like for
12640 \begin_layout Standard
12642 \begin_inset Tabular
12643 <lyxtabular version="3" rows="5" columns="2">
12645 <column alignment="center" valignment="top" width="0">
12646 <column alignment="center" valignment="top" width="0">
12648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12651 \begin_layout Plain Layout
12657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12660 \begin_layout Plain Layout
12662 \begin_inset Note Note
12665 \begin_layout Plain Layout
12672 is only used as spacer.
12684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12687 \begin_layout Plain Layout
12694 \begin_layout Plain Layout
12713 \begin_layout Plain Layout
12727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12730 \begin_layout Plain Layout
12731 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12744 \begin_layout Plain Layout
12751 \begin_layout Plain Layout
12766 \begin_layout Plain Layout
12780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12783 \begin_layout Plain Layout
12784 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12797 \begin_layout Plain Layout
12804 \begin_layout Plain Layout
12818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12821 \begin_layout Plain Layout
12822 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12835 \begin_layout Plain Layout
12842 \begin_layout Plain Layout
12852 \begin_inset Formula $\to$
12856 \begin_inset Formula $\to$
12869 \begin_layout Plain Layout
12879 \begin_inset Formula $\downarrow$
12887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12890 \begin_layout Plain Layout
12891 \begin_inset Formula $\raisebox{6mm}{}$
12895 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12899 \begin_inset Formula $\raisebox{-4mm}{}$
12915 \begin_layout Standard
12916 The frame thickness can also be adjusted.
12917 To do this the following commands have to be inserted in TeX-mode before
12921 \begin_layout Standard
12931 \begin_inset Quotes eld
12935 \begin_inset Quotes erd
12949 \begin_inset Quotes eld
12953 \begin_inset Quotes erd
12959 \begin_layout Standard
12960 \begin_inset Quotes eld
12964 \begin_inset Quotes erd
12967 specifies the minimal distance between the frame and the first character
12969 An example for this is the following framed formula:
12973 \begin_layout Plain Layout
12985 \begin_inset Formula \[
12990 Before this formula the commands
12993 \begin_layout Standard
13015 \begin_layout Standard
13016 were inserted in TeX-mode.
13017 The given values are used for all following boxes.
13020 \begin_layout Standard
13021 To return to the standard frame size, the command
13024 \begin_layout Standard
13049 \begin_layout Plain Layout
13063 \begin_layout Standard
13064 is inserted in TeX-mode before the next formula.
13067 \begin_layout Subsection
13068 Boxes without Frame
13069 \begin_inset CommandInset label
13071 name "sub:Boxes-without-Frame"
13079 \begin_layout Plain Layout
13080 Boxes ! without frame
13088 \begin_layout Standard
13089 For boxes without a frame there are the following box commands:
13099 \begin_layout Plain Layout
13117 \begin_layout Plain Layout
13135 \begin_layout Plain Layout
13146 \begin_layout Standard
13153 a box can be super- or subscripted.
13154 But in contrary to normal super- and subscripting, the characters in the
13155 box keep their font size.
13162 is used in the following scheme:
13165 \begin_layout Standard
13170 raisebox{height}{box content}
13173 \begin_layout Standard
13174 When the box should contain a formula, an extra formula is needed like for
13185 \begin_inset Note Greyedout
13188 \begin_layout Plain Layout
13199 this extra formula is created by pressing
13203 twice instead of once because LyX doesn't yet support
13217 \begin_layout Standard
13219 \begin_inset Tabular
13220 <lyxtabular version="3" rows="4" columns="2">
13222 <column alignment="center" valignment="top" width="0">
13223 <column alignment="center" valignment="top" width="0">
13225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13228 \begin_layout Plain Layout
13234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13237 \begin_layout Plain Layout
13245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13248 \begin_layout Plain Layout
13252 \begin_inset Formula $\to$
13258 \begin_inset Formula $\to$
13266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13269 \begin_layout Plain Layout
13270 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13283 \begin_layout Plain Layout
13287 \begin_inset Formula $\to$
13293 \begin_inset Formula $\to$
13301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13304 \begin_layout Plain Layout
13305 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13318 \begin_layout Plain Layout
13322 \begin_inset Formula $\to$
13341 \begin_layout Plain Layout
13355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13358 \begin_layout Plain Layout
13359 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13375 \begin_layout Standard
13400 , with the difference that there is no frame.
13403 \begin_layout Subsection
13405 \begin_inset CommandInset label
13407 name "sub:Colored-Boxes"
13415 \begin_layout Plain Layout
13424 \begin_layout Standard
13425 To be able to use all commands explained in this section, the LaTeX-package
13434 \begin_layout Plain Layout
13439 is part of every LaTeX standard installation.
13448 \begin_layout Plain Layout
13454 has to be loaded in the LaTeX-preamble with the line
13458 \begin_layout Plain Layout
13459 When text is colored somewhere in the document with a predefined color,
13460 LyX loads the LaTeX-package
13465 Thus it is possible that the package is loaded twice, but this doesn't
13472 \begin_inset Note Note
13475 \begin_layout Plain Layout
13476 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13485 \begin_layout Standard
13493 \begin_layout Standard
13494 \begin_inset VSpace medskip
13497 To color boxes, the command
13507 \begin_layout Plain Layout
13515 is used in the following scheme:
13518 \begin_layout Standard
13523 colorbox{color}{box content}
13526 \begin_layout Standard
13527 The box content can also be a box and a
13533 can also be part of another box (see the 2nd and 3rd example).
13534 When the box should contain a formula, an extra formula has to be created,
13535 the same way as for
13545 \begin_layout Plain Layout
13546 This also applies for the command
13560 \begin_layout Standard
13561 One of the following predefined colors can be chosen:
13564 \begin_layout Standard
13598 \begin_layout Standard
13600 \begin_inset Tabular
13601 <lyxtabular version="3" rows="4" columns="2">
13603 <column alignment="center" valignment="top" width="0">
13604 <column alignment="center" valignment="top" width="0">
13606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13609 \begin_layout Plain Layout
13615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13618 \begin_layout Plain Layout
13620 \begin_inset Note Note
13623 \begin_layout Plain Layout
13630 is only used as spacer.
13642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13645 \begin_layout Plain Layout
13649 \begin_inset Formula $\to$
13659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13662 \begin_layout Plain Layout
13663 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13676 \begin_layout Plain Layout
13680 \begin_inset Formula $\to$
13691 \begin_layout Plain Layout
13705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13708 \begin_layout Plain Layout
13709 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13722 \begin_layout Plain Layout
13729 \begin_layout Plain Layout
13741 \begin_inset Formula $\to$
13760 \begin_layout Plain Layout
13774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13777 \begin_layout Plain Layout
13778 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13794 \begin_layout Standard
13801 only colors the box but not the characters in the box.
13802 To color all characters, the whole formula is highlighted and the wanted
13803 color is chosen in the
13806 \begin_inset space ~
13812 The dialog can be called with the toolbar button
13813 \begin_inset Graphics
13814 filename ../images/dialog-show_character.png
13821 Edit\SpecialChar \menuseparator
13823 \begin_inset space ~
13826 Style\SpecialChar \menuseparator
13830 The formula number has then the same color as the formula.
13831 When the formula number should get another color than the formula characters,
13832 the color must be changed within the formula.
13835 \begin_layout Standard
13839 \begin_layout Standard
13842 \begin_inset Formula \begin{equation}
13843 \int A=B\label{eq:red}\end{equation}
13850 \begin_inset Formula \begin{equation}
13851 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13858 \begin_layout Standard
13860 \begin_inset CommandInset ref
13866 is completely colored red.
13867 \begin_inset Newline newline
13871 \begin_inset CommandInset ref
13873 reference "eq:redgreen"
13877 was first completely colored green to set the color for the formula number.
13878 Subsequently the formula characters were colored red.
13881 \begin_layout Standard
13882 \begin_inset VSpace bigskip
13885 To color the frame different than the rest of the box, the command
13895 \begin_layout Plain Layout
13903 is used in the following scheme:
13906 \begin_layout Standard
13911 fcolorbox{frame color}{color}{box content}
13914 \begin_layout Standard
13921 is an extension of the command
13928 The frame width is set, like for
13951 \begin_layout Plain Layout
13963 \begin_inset Formula \[
13964 \fcolorbox{cyan}{magenta}{A=B}\]
13972 \begin_layout Plain Layout
13986 \begin_layout Standard
13987 This formula was created with the command
13988 \begin_inset Newline newline
13996 \begin_inset Formula $\to$
14002 \begin_inset Formula $\to$
14012 \begin_layout Standard
14013 \begin_inset VSpace bigskip
14016 To use other colors than the predefined ones, they have to be defined first.
14019 \begin_layout Standard
14020 One can for example define the color
14021 \begin_inset Quotes eld
14029 \begin_inset Quotes erd
14032 with the LaTeX-preamble line:
14035 \begin_layout Standard
14040 definecolor{darkgreen}{cmyk}{0.5,
14058 \begin_layout Plain Layout
14069 \begin_layout Standard
14074 is the color space that denotes the colors
14091 The four comma separated numbers are the portion factor for the corresponding
14092 colors of the color space.
14093 The factors can be in the range of 0
14094 \begin_inset space \thinspace{}
14098 \begin_inset space \thinspace{}
14106 also the color space
14110 can be used for definitions.
14127 , so that there are in this case three portion factors for the corresponding
14129 Furthermore there is the color space
14133 with one portion factor for the gray value.
14136 \begin_layout Standard
14137 As example a framed box with the new defined color
14141 where the characters have been colored
14146 \begin_inset Formula \begin{equation}
14147 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14154 \begin_layout Standard
14155 Self-defined colors can also be used for text with the help of the command
14166 \begin_layout Plain Layout
14175 \begin_layout Standard
14179 \begin_layout Plain Layout
14183 textcolor{darkgreen}{
14189 \begin_inset Quotes eld
14193 \begin_inset Quotes erd
14200 \begin_layout Plain Layout
14210 \begin_layout Standard
14221 \begin_layout Plain Layout
14229 is used in the scheme
14233 textcolor{color}{characters to color}
14238 \begin_layout Subsection
14240 \begin_inset CommandInset label
14242 name "sub:Paragraph-Boxes"
14250 \begin_layout Plain Layout
14251 Boxes ! as paragraph
14259 \begin_layout Standard
14260 A box that can contain several lines and paragraphs, a so called paragraph
14261 box (parbox), can be created with the menu
14263 Insert\SpecialChar \menuseparator
14266 or the toolbar button
14267 \begin_inset Graphics
14268 filename ../images/box-insert.png
14276 \begin_layout Standard
14277 The following example shows a framed parbox in a line:
14280 \begin_layout Standard
14281 \begin_inset VSpace medskip
14285 \begin_inset Box Boxed
14294 height_special "totalheight"
14297 \begin_layout Plain Layout
14298 This is a paragraph box.
14300 \begin_inset space \thinspace{}
14303 cm long and can also contain formulas:
14304 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14315 \begin_layout Standard
14316 \begin_inset VSpace medskip
14322 \begin_layout Standard
14323 Such a box is created by right-clicking on the gray box inset.
14324 A dialog pops up showing the box properties.
14338 \begin_inset space \thinspace{}
14343 Vertical Box Alignment
14348 \begin_layout Standard
14349 \begin_inset VSpace medskip
14352 In LaTeX a parbox is created with the command
14362 \begin_layout Plain Layout
14370 that has the following scheme:
14373 \begin_layout Standard
14378 parbox[position]{width}{box content}
14381 \begin_layout Standard
14395 for bottom means that the box is aligned within the surrounding text with
14401 for top this is done with the first line.
14402 When no position is given, the box will be vertically centered, see section
14410 \begin_inset space ~
14415 manual for examples.
14418 \begin_layout Standard
14419 \begin_inset VSpace bigskip
14422 To frame formulas completely, including the formula number, the formula
14423 must be set into a parbox.
14424 To do this, the command
14438 is inserted in TeX-mode before the formula.
14447 \begin_layout Plain Layout
14457 is hereby the line width set for the document.
14458 Because the frame is outside the parbox, 2
14459 \begin_inset space \thinspace{}
14462 times the frame separation and the frame thickness must be subtracted from
14464 As this is not automatically done by LyX due to a bug
14468 \begin_layout Plain Layout
14469 \begin_inset CommandInset href
14471 name "LyX-bug #4483"
14472 target "http://www.lyx.org/trac/ticket/4483"
14481 , TeX-mode has to be used.
14482 To be able to multiply and subtract in arguments, the LaTeX-package
14490 \begin_layout Plain Layout
14495 is part of every LaTeX standard installation.
14504 \begin_layout Plain Layout
14510 must be loaded in the LaTeX-preamble with the line
14513 \begin_layout Standard
14521 \begin_layout Standard
14522 Behind the formula both boxes are closed by entering
14527 Here is an example:
14531 \begin_layout Plain Layout
14545 \begin_layout Standard
14549 \begin_layout Plain Layout
14567 \begin_inset Formula \begin{equation}
14568 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14576 \begin_layout Plain Layout
14587 \begin_layout Plain Layout
14601 \begin_layout Standard
14602 \begin_inset VSpace medskip
14605 As a parbox is used as argument of
14611 , there is in this case no difference between
14626 \begin_layout Standard
14627 \begin_inset VSpace bigskip
14630 Paragraph boxes are very useful to comment formulas directly.
14637 is used in combination with the command
14651 \begin_inset CommandInset ref
14653 reference "sub:User-defined-Numbering"
14660 \begin_layout Standard
14661 An example of a formula commented with
14670 \begin_layout Standard
14674 \begin_layout Plain Layout
14687 This is a description.
14688 It is distinctly separated from the formula and multiline.
14692 \begin_layout Plain Layout
14704 \begin_layout Standard
14705 Such a formula must be inserted completely in TeX-mode because LyX does
14706 not yet support the command
14713 The formula is created with the following command sequence:
14716 \begin_layout Standard
14729 is inserted in TeX-mode.
14733 \begin_layout Plain Layout
14734 When the formula style
14746 can also be replaced by
14753 (formula styles see
14754 \begin_inset CommandInset ref
14756 reference "sec:Formula-Styles"
14765 Then the description follows as normal text, and finally
14771 is inserted in TeX-mode.
14784 hereby create a displayed formula.
14787 \begin_layout Standard
14794 can be seen in this example that was
14795 \begin_inset Quotes eld
14799 \begin_inset Quotes erd
14802 using the mathematical textmode:
14803 \begin_inset Formula \[
14804 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14811 \begin_layout Section
14816 \begin_layout Plain Layout
14825 \begin_layout Subsection
14827 \begin_inset CommandInset label
14829 name "sub:Big-Operators"
14837 \begin_layout Plain Layout
14847 \begin_layout Plain Layout
14857 \begin_layout Plain Layout
14866 \begin_layout Standard
14867 To be able to use all integral operators listed here, the option
14869 Use esint package automatically
14871 must be set in the document settings under
14874 \begin_inset space ~
14882 \begin_layout Standard
14883 \begin_inset space \hfill{}
14887 \begin_inset Tabular
14888 <lyxtabular version="3" rows="11" columns="2">
14890 <column alignment="center" valignment="top" width="0pt">
14891 <column alignment="center" valignment="top" width="0pt">
14893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14896 \begin_layout Plain Layout
14902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14905 \begin_layout Plain Layout
14913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14916 \begin_layout Plain Layout
14923 \begin_layout Plain Layout
14936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14939 \begin_layout Plain Layout
14940 \begin_inset Formula $\int$
14950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14953 \begin_layout Plain Layout
14961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14964 \begin_layout Plain Layout
14965 \begin_inset Formula $\oint$
14975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14978 \begin_layout Plain Layout
14986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14989 \begin_layout Plain Layout
14990 \begin_inset Formula $\ointctrclockwise$
15000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15003 \begin_layout Plain Layout
15011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15014 \begin_layout Plain Layout
15015 \begin_inset Formula $\ointclockwise$
15025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15028 \begin_layout Plain Layout
15036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15039 \begin_layout Plain Layout
15040 \begin_inset Formula $\sqint$
15050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15053 \begin_layout Plain Layout
15061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15064 \begin_layout Plain Layout
15066 \begin_inset Formula $\fint$
15076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15079 \begin_layout Plain Layout
15087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15090 \begin_layout Plain Layout
15092 \begin_inset Formula $\landupint$
15102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15105 \begin_layout Plain Layout
15113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15116 \begin_layout Plain Layout
15118 \begin_inset Formula $\landdownint$
15128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15131 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15142 \begin_layout Plain Layout
15143 \begin_inset Formula $\bigcap$
15153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15156 \begin_layout Plain Layout
15164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15167 \begin_layout Plain Layout
15168 \begin_inset Formula $\bigcup$
15182 \begin_inset space \hfill{}
15186 \begin_inset Tabular
15187 <lyxtabular version="3" rows="11" columns="2">
15189 <column alignment="center" valignment="top" width="0pt">
15190 <column alignment="center" valignment="top" width="0pt">
15192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15195 \begin_layout Plain Layout
15201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15204 \begin_layout Plain Layout
15212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15215 \begin_layout Plain Layout
15222 \begin_layout Plain Layout
15235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15238 \begin_layout Plain Layout
15239 \begin_inset Formula $\sum$
15249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15252 \begin_layout Plain Layout
15259 \begin_layout Plain Layout
15272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15275 \begin_layout Plain Layout
15276 \begin_inset Formula $\prod$
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15289 \begin_layout Plain Layout
15297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15300 \begin_layout Plain Layout
15301 \begin_inset Formula $\coprod$
15311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15314 \begin_layout Plain Layout
15322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15325 \begin_layout Plain Layout
15326 \begin_inset Formula $\bigodot$
15336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15339 \begin_layout Plain Layout
15347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15350 \begin_layout Plain Layout
15351 \begin_inset Formula $\bigotimes$
15361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15364 \begin_layout Plain Layout
15372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15375 \begin_layout Plain Layout
15376 \begin_inset Formula $\bigoplus$
15386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15389 \begin_layout Plain Layout
15397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15400 \begin_layout Plain Layout
15401 \begin_inset Formula $\bigwedge$
15411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15414 \begin_layout Plain Layout
15422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15425 \begin_layout Plain Layout
15426 \begin_inset Formula $\bigvee$
15436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15439 \begin_layout Plain Layout
15447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15450 \begin_layout Plain Layout
15451 \begin_inset Formula $\bigsqcup$
15461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15464 \begin_layout Plain Layout
15472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15475 \begin_layout Plain Layout
15476 \begin_inset Formula $\biguplus$
15490 \begin_inset space \hfill{}
15496 \begin_layout Standard
15497 All big operators can also be inserted via the math toolbar button
15498 \begin_inset Graphics
15499 filename ../images/math/intop.png
15507 \begin_layout Standard
15508 The operators are called big because they are bigger than the sometimes
15509 equal looking binary operators.
15510 All big operators can have limits as described in the next subsection.
15513 \begin_layout Standard
15514 For all integral operators there is a second version available, ending on
15532 These operators are different from
15539 \begin_inset space \space{}
15542 in the style the operator limits are displayed, see
15543 \begin_inset CommandInset ref
15545 reference "sub:Operator-Limits"
15553 \begin_layout Subsubsection*
15554 Advice for Integrals
15557 \begin_layout Standard
15562 in an integral is an operator, that therefore has to be set upright.
15563 This is done by highlighting the
15567 and using the keyboard shortcut
15577 \begin_layout Plain Layout
15583 \begin_inset CommandInset ref
15585 reference "sub:Font-Styles"
15595 Finally the smallest space is inserted before the
15599 , as this is usual for operators.
15603 \begin_layout Standard
15605 \begin_inset Formula $\int A(x)dx$
15609 \begin_inset Newline newline
15616 \begin_layout Plain Layout
15626 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15632 \begin_layout Standard
15633 For multiple integrals there are the following commands:
15634 \begin_inset VSpace medskip
15640 \begin_layout Standard
15641 \begin_inset space \hfill{}
15645 \begin_inset Tabular
15646 <lyxtabular version="3" rows="4" columns="2">
15648 <column alignment="center" valignment="top" width="0">
15649 <column alignment="center" valignment="top" width="0">
15651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15654 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15663 \begin_layout Plain Layout
15665 \begin_inset Note Note
15668 \begin_layout Plain Layout
15675 is only used as spacer.
15687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15690 \begin_layout Plain Layout
15698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15701 \begin_layout Plain Layout
15702 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15715 \begin_layout Plain Layout
15723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15726 \begin_layout Plain Layout
15727 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15740 \begin_layout Plain Layout
15748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15751 \begin_layout Plain Layout
15752 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15766 \begin_inset space \hfill{}
15770 \begin_inset Tabular
15771 <lyxtabular version="3" rows="4" columns="2">
15773 <column alignment="center" valignment="top" width="0">
15774 <column alignment="center" valignment="top" width="0">
15776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15779 \begin_layout Plain Layout
15785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15788 \begin_layout Plain Layout
15796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15799 \begin_layout Plain Layout
15807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15810 \begin_layout Plain Layout
15811 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15824 \begin_layout Plain Layout
15832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15835 \begin_layout Plain Layout
15836 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15849 \begin_layout Plain Layout
15857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15860 \begin_layout Plain Layout
15861 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15875 \begin_inset space \hfill{}
15881 \begin_layout Subsection
15883 \begin_inset CommandInset label
15885 name "sub:Operator-Limits"
15893 \begin_layout Plain Layout
15902 \begin_layout Standard
15903 Limits are created by super- and subscripts:
15906 \begin_layout Standard
15908 \begin_inset Tabular
15909 <lyxtabular version="3" rows="2" columns="2">
15911 <column alignment="center" valignment="top" width="0pt">
15912 <column alignment="center" valignment="top" width="0pt">
15914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15917 \begin_layout Plain Layout
15923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15926 \begin_layout Plain Layout
15928 \begin_inset Note Note
15931 \begin_layout Plain Layout
15938 is only used as spacer.
15950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15953 \begin_layout Plain Layout
15962 \begin_layout Plain Layout
15972 \begin_inset Formula $\to$
15976 \begin_inset Formula $\to$
15984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15987 \begin_layout Plain Layout
15988 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16004 \begin_layout Standard
16005 Limits of inline formulas are set right beside the operator.
16006 Limits in displayed formulas are set above or below the operator, except
16007 for integral limits.
16010 \begin_layout Standard
16011 To force that the limits are set beside the operator, the cursor is set
16012 directly behind the operator and the limits type is changed with the menu
16015 Edit\SpecialChar \menuseparator
16016 Math\SpecialChar \menuseparator
16035 \begin_layout Standard
16036 The default limits type is this:
16037 \begin_inset Formula \[
16038 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16042 This is how it looks when the limits type was changed to
16049 \begin_inset Formula \[
16050 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16054 For integrals, except those ending with
16070 etc., the limits are by default set beside the operator.
16071 But for multiple integrals the limits are often set below the operator.
16072 In the following example the limits type was therefore set to
16076 and so set below the integrals:
16077 \begin_inset Formula \begin{equation}
16078 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16085 \begin_layout Standard
16086 \begin_inset VSpace medskip
16089 To specify conditions for limits, the commands
16099 \begin_layout Plain Layout
16117 \begin_layout Plain Layout
16126 To create for example this expression
16127 \begin_inset Formula \begin{equation}
16128 \sum_{\begin{subarray}{c}
16130 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16137 \begin_layout Standard
16138 the following has to be done:
16139 \begin_inset Newline newline
16154 \begin_layout Plain Layout
16166 One is now in a blue box under the summation operator and insert there
16175 \begin_layout Plain Layout
16187 The blue box is now within a purple box and now several lines can be written
16189 A new line is created by inserting a line break (
16192 arg "newline-insert newline"
16197 \begin_inset Newline newline
16202 0<k<1000 Ctrl+Return
16203 \begin_inset Newline newline
16208 is typed in, a new box appears below for the new line.
16211 \begin_layout Standard
16212 The alignment of the lines can be changed to left aligned with the
16222 Edit\SpecialChar \menuseparator
16226 To get right alignment,
16234 \begin_layout Plain Layout
16245 is inserted at the beginning of the line.
16248 \begin_layout Standard
16261 with the difference that the lines are always centered.
16264 \begin_layout Standard
16265 \begin_inset VSpace bigskip
16269 \begin_inset CommandInset ref
16271 reference "eq:substack"
16275 there can be too much space beside an operator, because the characters
16276 following the operator are set beside the limits.
16279 \begin_layout Standard
16280 To avoid this, the following macro can be used in the LaTeX-preamble:
16283 \begin_layout Standard
16297 \begin_inset Newline newline
16309 \begin_inset Newline newline
16316 mathclapinternal #1#2{
16320 mathsurround =0pt #1{#2}$}}
16323 \begin_layout Standard
16324 This defines the command
16334 \begin_layout Plain Layout
16342 that sets the width of the limit to 0
16343 \begin_inset space \thinspace{}
16347 The command scheme is
16350 \begin_layout Standard
16358 \begin_layout Standard
16359 where the limit can consist of several conditions.
16362 \begin_layout Standard
16364 \begin_inset CommandInset ref
16366 reference "eq:substack"
16370 , one uses the command
16373 \begin_layout Standard
16386 \begin_layout Plain Layout
16395 0<k<1000 Ctrl+Return
16398 \begin_layout Standard
16399 to create the lower limit.
16400 The summand is now directly behind the summation operator:
16401 \begin_inset Formula \[
16402 \sum_{\mathclap{\substack{0<k<1000\\
16403 \\k\,\in\,\mathbb{N}}
16411 \begin_layout Standard
16412 \begin_inset VSpace bigskip
16415 How to use one limit for several operators is described in
16416 \begin_inset CommandInset ref
16418 reference "sub:Self-defined-Operators"
16425 \begin_layout Subsection
16427 \begin_inset CommandInset label
16429 name "sub:Binary-Operators"
16437 \begin_layout Plain Layout
16446 \begin_layout Standard
16447 Binary operators are surrounded by space when there is a character before
16449 \begin_inset VSpace medskip
16455 \begin_layout Standard
16456 \begin_inset space \hfill{}
16460 \begin_inset Tabular
16461 <lyxtabular version="3" rows="13" columns="2">
16463 <column alignment="center" valignment="top" width="0pt">
16464 <column alignment="center" valignment="top" width="0pt">
16466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16469 \begin_layout Plain Layout
16471 \begin_inset Note Note
16474 \begin_layout Plain Layout
16481 is only used as spacer.
16491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16494 \begin_layout Plain Layout
16502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16505 \begin_layout Plain Layout
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16514 \begin_layout Plain Layout
16515 \begin_inset Formula $+$
16525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16528 \begin_layout Plain Layout
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16537 \begin_layout Plain Layout
16538 \begin_inset Formula $-$
16548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16551 \begin_layout Plain Layout
16559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16562 \begin_layout Plain Layout
16563 \begin_inset Formula $\pm$
16573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16576 \begin_layout Plain Layout
16584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16587 \begin_layout Plain Layout
16588 \begin_inset Formula $\mp$
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16601 \begin_layout Plain Layout
16609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16612 \begin_layout Plain Layout
16613 \begin_inset Formula $\cdot$
16623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16626 \begin_layout Plain Layout
16634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16637 \begin_layout Plain Layout
16638 \begin_inset Formula $\times$
16648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16651 \begin_layout Plain Layout
16659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16662 \begin_layout Plain Layout
16663 \begin_inset Formula $\div$
16673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16676 \begin_layout Plain Layout
16680 \begin_layout Plain Layout
16693 \begin_layout Plain Layout
16705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16708 \begin_layout Plain Layout
16709 \begin_inset Formula $*$
16719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16722 \begin_layout Plain Layout
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16733 \begin_layout Plain Layout
16734 \begin_inset Formula $\star$
16744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16747 \begin_layout Plain Layout
16755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16758 \begin_layout Plain Layout
16759 \begin_inset Formula $\circ$
16769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16772 \begin_layout Plain Layout
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16783 \begin_layout Plain Layout
16784 \begin_inset Formula $\diamond$
16794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16797 \begin_layout Plain Layout
16805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16808 \begin_layout Plain Layout
16809 \begin_inset Formula $\bullet$
16823 \begin_inset space \hfill{}
16827 \begin_inset Tabular
16828 <lyxtabular version="3" rows="13" columns="2">
16830 <column alignment="center" valignment="top" width="0pt">
16831 <column alignment="center" valignment="top" width="0pt">
16833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16836 \begin_layout Plain Layout
16842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16845 \begin_layout Plain Layout
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16856 \begin_layout Plain Layout
16864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16867 \begin_layout Plain Layout
16868 \begin_inset Formula $\nabla$
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16881 \begin_layout Plain Layout
16889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16892 \begin_layout Plain Layout
16893 \begin_inset Formula $\bigtriangledown$
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16906 \begin_layout Plain Layout
16914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16917 \begin_layout Plain Layout
16918 \begin_inset Formula $\bigtriangleup$
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16931 \begin_layout Plain Layout
16939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16942 \begin_layout Plain Layout
16943 \begin_inset Formula $\Box$
16953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16956 \begin_layout Plain Layout
16964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16967 \begin_layout Plain Layout
16968 \begin_inset Formula $\cap$
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16981 \begin_layout Plain Layout
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16992 \begin_layout Plain Layout
16993 \begin_inset Formula $\cup$
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17006 \begin_layout Plain Layout
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17018 \begin_inset Formula $\dagger$
17028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17031 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17042 \begin_layout Plain Layout
17043 \begin_inset Formula $\ddagger$
17053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17067 \begin_layout Plain Layout
17068 \begin_inset Formula $\wr$
17078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17081 \begin_layout Plain Layout
17089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17092 \begin_layout Plain Layout
17093 \begin_inset Formula $\bigcirc$
17103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17106 \begin_layout Plain Layout
17114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17117 \begin_layout Plain Layout
17118 \begin_inset Formula $\wedge$
17128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17131 \begin_layout Plain Layout
17139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17142 \begin_layout Plain Layout
17143 \begin_inset Formula $\vee$
17157 \begin_inset space \hfill{}
17161 \begin_inset Tabular
17162 <lyxtabular version="3" rows="13" columns="2">
17164 <column alignment="center" valignment="top" width="0pt">
17165 <column alignment="center" valignment="top" width="0pt">
17167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17170 \begin_layout Plain Layout
17176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17179 \begin_layout Plain Layout
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17190 \begin_layout Plain Layout
17198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17201 \begin_layout Plain Layout
17202 \begin_inset Formula $\oplus$
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17215 \begin_layout Plain Layout
17223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17226 \begin_layout Plain Layout
17227 \begin_inset Formula $\ominus$
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17240 \begin_layout Plain Layout
17248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17251 \begin_layout Plain Layout
17252 \begin_inset Formula $\otimes$
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17265 \begin_layout Plain Layout
17273 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17276 \begin_layout Plain Layout
17277 \begin_inset Formula $\oslash$
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17290 \begin_layout Plain Layout
17298 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17301 \begin_layout Plain Layout
17302 \begin_inset Formula $\odot$
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17315 \begin_layout Plain Layout
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17326 \begin_layout Plain Layout
17327 \begin_inset Formula $\amalg$
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17340 \begin_layout Plain Layout
17348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17351 \begin_layout Plain Layout
17352 \begin_inset Formula $\uplus$
17362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17365 \begin_layout Plain Layout
17373 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17376 \begin_layout Plain Layout
17377 \begin_inset Formula $\setminus$
17387 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17390 \begin_layout Plain Layout
17398 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17401 \begin_layout Plain Layout
17402 \begin_inset Formula $\sqcap$
17412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17415 \begin_layout Plain Layout
17423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17426 \begin_layout Plain Layout
17427 \begin_inset Formula $\sqcup$
17437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17440 \begin_layout Plain Layout
17448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17451 \begin_layout Plain Layout
17452 \begin_inset Formula $\triangleleft$
17462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17465 \begin_layout Plain Layout
17473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17476 \begin_layout Plain Layout
17477 \begin_inset Formula $\triangleright$
17491 \begin_inset space \hfill{}
17497 \begin_layout Standard
17498 All binary operators can also be inserted via the math toolbar button
17499 \begin_inset Graphics
17500 filename ../images/math/pm.png
17508 \begin_layout Standard
17509 To typeset the Laplace operator also
17526 \begin_inset Formula $\nabla^{2}$
17529 ) can be used instead of
17538 \begin_layout Standard
17545 Insert\SpecialChar \menuseparator
17557 \begin_layout Subsection
17558 Self-defined Operators
17559 \begin_inset CommandInset label
17561 name "sub:Self-defined-Operators"
17569 \begin_layout Plain Layout
17570 Operators ! self-defined
17578 \begin_layout Standard
17579 With the help of the command
17583 DeclareMathOperator
17589 \begin_layout Plain Layout
17594 DeclareMathOperator
17599 custom operators can be defined in the LaTeX-preamble.
17600 Its command scheme is:
17603 \begin_layout Standard
17608 DeclareMathOperator{new command}{display}
17611 \begin_layout Standard
17612 Display can be characters or symbols that define how the operator looks
17614 To define a big operator a * is set behind the command.
17615 All self-defined big operators can have limits as described in
17616 \begin_inset CommandInset ref
17618 reference "sub:Operator-Limits"
17625 \begin_layout Standard
17626 For example the LaTeX-preamble line
17629 \begin_layout Standard
17634 DeclareMathOperator*{
17641 \begin_layout Standard
17642 defines the command
17648 , that inserts a big operator consisting of the lozenge symbol from
17649 \begin_inset CommandInset ref
17651 reference "sub:Miscellaneous-Symbols"
17656 \begin_inset Formula \[
17657 \Lozenge_{n=1}^{\infty}\]
17661 The command for this formula is:
17672 \begin_inset Formula $\to$
17678 \begin_layout Standard
17679 \begin_inset VSpace bigskip
17682 When self-defined operators are not used several times in the document,
17683 they can also be defined with the commands
17693 \begin_layout Plain Layout
17711 \begin_layout Plain Layout
17719 , which have the following scheme:
17722 \begin_layout Standard
17736 \begin_layout Standard
17743 defines big operators,
17752 \begin_layout Standard
17760 \begin_inset space \thinspace{}
17764 \begin_inset space \space{}
17767 be used to use one limit for several operators:
17770 \begin_layout Standard
17771 \begin_inset Formula \[
17772 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17779 \begin_layout Standard
17780 The command for the formula above is:
17781 \begin_inset Newline newline
17800 \begin_layout Plain Layout
17812 \begin_inset Formula $\to$
17821 \begin_layout Plain Layout
17835 \begin_layout Section
17840 \begin_layout Plain Layout
17849 \begin_layout Subsection
17851 \begin_inset CommandInset label
17853 name "sub:Font-Styles"
17861 \begin_layout Plain Layout
17870 \begin_layout Standard
17871 Latin letters in formulas can be set in one of the following font styles:
17872 \begin_inset VSpace -2mm
17878 \begin_layout Standard
17880 \begin_inset Tabular
17881 <lyxtabular version="3" rows="6" columns="3">
17883 <column alignment="center" valignment="top" width="0">
17884 <column alignment="center" valignment="top" width="0">
17885 <column alignment="center" valignment="top" width="0">
17887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17890 \begin_layout Plain Layout
17896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17899 \begin_layout Plain Layout
17905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17908 \begin_layout Plain Layout
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17919 \begin_layout Plain Layout
17928 \begin_layout Plain Layout
17944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17947 \begin_layout Plain Layout
17948 \begin_inset Formula $\mathbb{ABC}$
17956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17959 \begin_layout Plain Layout
17972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17975 \begin_layout Plain Layout
17984 \begin_layout Plain Layout
18000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18003 \begin_layout Plain Layout
18004 \begin_inset Formula $\mathbf{AbC}$
18012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18015 \begin_layout Plain Layout
18028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18031 \begin_layout Plain Layout
18040 \begin_layout Plain Layout
18056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18059 \begin_layout Plain Layout
18060 \begin_inset Formula $\boldsymbol{AbC}$
18068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18071 \begin_layout Plain Layout
18074 arg "font-boldsymbol"
18084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18087 \begin_layout Plain Layout
18096 \begin_layout Plain Layout
18112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18115 \begin_layout Plain Layout
18116 \begin_inset Formula $\mathcal{ABC}$
18124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18127 \begin_layout Plain Layout
18140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18143 \begin_layout Plain Layout
18152 \begin_layout Plain Layout
18168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18171 \begin_layout Plain Layout
18172 \begin_inset Formula $\mathfrak{AbC}$
18180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18183 \begin_layout Plain Layout
18197 \begin_layout Standard
18199 \begin_inset Tabular
18200 <lyxtabular version="3" rows="5" columns="3">
18202 <column alignment="center" valignment="top" width="0">
18203 <column alignment="center" valignment="top" width="0">
18204 <column alignment="center" valignment="top" width="0">
18206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18209 \begin_layout Plain Layout
18215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18218 \begin_layout Plain Layout
18224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18227 \begin_layout Plain Layout
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18238 \begin_layout Plain Layout
18247 \begin_layout Plain Layout
18263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18266 \begin_layout Plain Layout
18267 \begin_inset Formula $\mathit{AbC}$
18275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18278 \begin_layout Plain Layout
18286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18289 \begin_layout Plain Layout
18298 \begin_layout Plain Layout
18314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18317 \begin_layout Plain Layout
18318 \begin_inset Formula $\mathrm{AbC}$
18326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18329 \begin_layout Plain Layout
18342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18345 \begin_layout Plain Layout
18354 \begin_layout Plain Layout
18370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18373 \begin_layout Plain Layout
18374 \begin_inset Formula $\mathsf{AbC}$
18382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18385 \begin_layout Plain Layout
18398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18401 \begin_layout Plain Layout
18410 \begin_layout Plain Layout
18426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18429 \begin_layout Plain Layout
18430 \begin_inset Formula $\mathtt{AbC}$
18438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18441 \begin_layout Plain Layout
18444 arg "font-typewriter"
18460 \begin_layout Standard
18461 \begin_inset Note Greyedout
18464 \begin_layout Plain Layout
18481 can only be used for big letters.
18489 \begin_layout Standard
18490 Predefined is the style
18499 \begin_layout Standard
18500 The style commands work also for letters in mathematical constructs:
18501 \begin_inset Formula \[
18502 \mathfrak{A=\frac{b}{C}}\]
18509 \begin_layout Standard
18510 Characters in mathematical text don't appear in a math font style but in
18511 the text font style
18518 That their style can't be set correctly via the text style dialog is a
18523 \begin_layout Plain Layout
18524 \begin_inset CommandInset href
18526 name "LyX-bug #4629"
18527 target "http://www.lyx.org/trac/ticket/4629"
18539 \begin_layout Standard
18540 Instead of the style commands the dialog
18542 Edit\SpecialChar \menuseparator
18543 Math\SpecialChar \menuseparator
18546 or the toolbar button
18547 \begin_inset Graphics
18548 filename ../images/math/font.png
18556 \begin_layout Subsection
18558 \begin_inset CommandInset label
18560 name "sub:Bold-Formulas"
18568 \begin_layout Plain Layout
18577 \begin_layout Standard
18578 To make a complete formula bold, the command
18584 from the previous subsection cannot be used, because it doesn't work for
18585 small Greek letters.
18586 Furthermore it prints Latin letters always upright, like in the following
18590 \begin_layout Standard
18591 \begin_inset Formula \[
18592 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18599 \begin_layout Standard
18600 To display the formula correctly, the command
18607 \begin_inset Formula \[
18608 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18612 It is also possible to set the formula in a
18614 boldmath environment
18617 This environment is created by inserting the command
18625 \begin_layout Plain Layout
18636 To end the environment, the command
18644 \begin_layout Plain Layout
18654 is inserted in TeX-mode.
18658 \begin_layout Plain Layout
18668 \begin_inset Formula \[
18669 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18677 \begin_layout Plain Layout
18689 \begin_layout Subsection
18694 \begin_layout Plain Layout
18703 \begin_layout Standard
18704 Formulas can be colored like normal text: Highlight a formula or a formula
18710 Here is a formula in magenta:
18711 \begin_inset Formula \[
18712 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18719 \begin_layout Standard
18720 You can also define your own colors as described in
18721 \begin_inset CommandInset ref
18723 reference "sub:Colored-Boxes"
18728 They can be used with the TeX code command
18738 \begin_layout Plain Layout
18749 \begin_layout Standard
18754 textcolor{color}{characters or formula}
18757 \begin_layout Standard
18758 The following example was colored completely dark green and partly red:
18761 \begin_layout Standard
18765 \begin_layout Plain Layout
18769 textcolor{darkgreen}{
18775 \begin_inset Formula \[
18776 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18784 \begin_layout Plain Layout
18794 \begin_layout Standard
18795 Due to a bug in LyX only complete formulas can be colored with self-defined
18800 \begin_layout Plain Layout
18801 \begin_inset CommandInset href
18803 name "LyX-bug #5269"
18804 target "http://www.lyx.org/trac/ticket/5269"
18816 \begin_layout Subsection
18818 \begin_inset CommandInset label
18820 name "sub:Font-Sizes"
18828 \begin_layout Plain Layout
18837 \begin_layout Standard
18838 For characters in formulas there are, analog to characters in text, the
18839 following size commands:
18842 \begin_layout Standard
18886 \begin_inset Newline newline
18908 \begin_layout Standard
18909 The size produced by the commands depends on the document font size, that
18910 corresponds with the command
18917 The other commands produce smaller or larger sizes than
18924 The font size can however not exceed a certain value.
18925 Is for example the document font size 12
18926 \begin_inset space \thinspace{}
18935 switches to the same size as
18945 \begin_layout Standard
18946 A size command is inserted in TeX-mode before the formula and sets the size
18947 for all following formula and text characters.
18948 To switch back to the initial size, the command
18954 is inserted behind the formula in TeX-mode.
18957 \begin_layout Standard
18958 Within a formula the size can only be changed for symbols or letters in
18960 To do this, the size command is inserted in mathematical text.
18961 All following characters until the end of the mathematical text or until
18962 another size command will have the selected size.
18964 \begin_inset VSpace -2mm
18970 \begin_layout Standard
18974 \begin_layout Plain Layout
18984 \begin_inset Formula \[
18985 A=\frac{B}{c}\cdot\maltese\]
18990 \begin_inset Formula \[
18991 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18999 \begin_layout Plain Layout
19011 \begin_layout Standard
19012 \begin_inset VSpace medskip
19015 Before both formulas the command
19022 The command for the second formula is:
19023 \begin_inset Newline newline
19034 \begin_layout Plain Layout
19049 \begin_layout Plain Layout
19064 \begin_layout Plain Layout
19079 \begin_layout Plain Layout
19089 \begin_inset Formula $\to$
19093 \begin_inset Formula $\to$
19097 \begin_inset Newline newline
19101 \begin_inset space \hspace*{}
19115 \begin_layout Plain Layout
19130 \begin_layout Plain Layout
19145 \begin_layout Plain Layout
19157 \begin_layout Standard
19158 If a symbol cannot be displayed in different sizes, it will always be displayed
19159 in the default size.
19162 \begin_layout Section
19167 \begin_layout Plain Layout
19176 \begin_layout Standard
19177 All Greek letters can also be inserted via the toolbar button
19178 \begin_inset Graphics
19179 filename ../images/math/alpha.png
19187 \begin_layout Subsection
19192 \begin_layout Plain Layout
19193 Greek letters ! small
19201 \begin_layout Standard
19202 \begin_inset space \hfill{}
19206 \begin_inset Tabular
19207 <lyxtabular version="3" rows="11" columns="2">
19209 <column alignment="center" valignment="top" width="0pt">
19210 <column alignment="center" valignment="top" width="0pt">
19212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19215 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19235 \begin_layout Plain Layout
19243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19246 \begin_layout Plain Layout
19247 \begin_inset Formula $\alpha$
19257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19260 \begin_layout Plain Layout
19268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19271 \begin_layout Plain Layout
19272 \begin_inset Formula $\beta$
19282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19285 \begin_layout Plain Layout
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19296 \begin_layout Plain Layout
19297 \begin_inset Formula $\gamma$
19307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19310 \begin_layout Plain Layout
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19321 \begin_layout Plain Layout
19322 \begin_inset Formula $\delta$
19332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19335 \begin_layout Plain Layout
19343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19346 \begin_layout Plain Layout
19347 \begin_inset Formula $\epsilon$
19357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19360 \begin_layout Plain Layout
19368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19371 \begin_layout Plain Layout
19372 \begin_inset Formula $\varepsilon$
19382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19385 \begin_layout Plain Layout
19393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19396 \begin_layout Plain Layout
19397 \begin_inset Formula $\zeta$
19407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19410 \begin_layout Plain Layout
19418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19421 \begin_layout Plain Layout
19422 \begin_inset Formula $\eta$
19432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19435 \begin_layout Plain Layout
19443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19446 \begin_layout Plain Layout
19447 \begin_inset Formula $\theta$
19457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19460 \begin_layout Plain Layout
19468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19471 \begin_layout Plain Layout
19472 \begin_inset Formula $\vartheta$
19486 \begin_inset space \hfill{}
19490 \begin_inset Tabular
19491 <lyxtabular version="3" rows="12" columns="2">
19493 <column alignment="center" valignment="top" width="0pt">
19494 <column alignment="center" valignment="top" width="0pt">
19496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19499 \begin_layout Plain Layout
19505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19508 \begin_layout Plain Layout
19516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19519 \begin_layout Plain Layout
19527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19530 \begin_layout Plain Layout
19531 \begin_inset Formula $\iota$
19541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19544 \begin_layout Plain Layout
19552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19555 \begin_layout Plain Layout
19556 \begin_inset Formula $\kappa$
19566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19569 \begin_layout Plain Layout
19577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19580 \begin_layout Plain Layout
19581 \begin_inset Formula $\varkappa$
19591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19594 \begin_layout Plain Layout
19602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19605 \begin_layout Plain Layout
19606 \begin_inset Formula $\lambda$
19616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19619 \begin_layout Plain Layout
19627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19630 \begin_layout Plain Layout
19631 \begin_inset Formula $\mu$
19641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19644 \begin_layout Plain Layout
19652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19655 \begin_layout Plain Layout
19656 \begin_inset Formula $\nu$
19666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19669 \begin_layout Plain Layout
19677 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19680 \begin_layout Plain Layout
19681 \begin_inset Formula $\xi$
19691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19694 \begin_layout Plain Layout
19700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19703 \begin_layout Plain Layout
19704 \begin_inset Formula $o$
19714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19717 \begin_layout Plain Layout
19725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19728 \begin_layout Plain Layout
19729 \begin_inset Formula $\pi$
19739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19742 \begin_layout Plain Layout
19750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19753 \begin_layout Plain Layout
19754 \begin_inset Formula $\varpi$
19764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19767 \begin_layout Plain Layout
19775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19778 \begin_layout Plain Layout
19779 \begin_inset Formula $\rho$
19793 \begin_inset space \hfill{}
19797 \begin_inset Tabular
19798 <lyxtabular version="3" rows="11" columns="2">
19800 <column alignment="center" valignment="top" width="0pt">
19801 <column alignment="center" valignment="top" width="0pt">
19803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19806 \begin_layout Plain Layout
19812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19815 \begin_layout Plain Layout
19823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19826 \begin_layout Plain Layout
19834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19837 \begin_layout Plain Layout
19838 \begin_inset Formula $\varrho$
19848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19851 \begin_layout Plain Layout
19859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19862 \begin_layout Plain Layout
19863 \begin_inset Formula $\sigma$
19873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19876 \begin_layout Plain Layout
19884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19887 \begin_layout Plain Layout
19888 \begin_inset Formula $\varsigma$
19898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19901 \begin_layout Plain Layout
19909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19912 \begin_layout Plain Layout
19913 \begin_inset Formula $\tau$
19923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19926 \begin_layout Plain Layout
19934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19937 \begin_layout Plain Layout
19938 \begin_inset Formula $\upsilon$
19948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19951 \begin_layout Plain Layout
19959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19962 \begin_layout Plain Layout
19963 \begin_inset Formula $\phi$
19973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19976 \begin_layout Plain Layout
19984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19987 \begin_layout Plain Layout
19988 \begin_inset Formula $\varphi$
19998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20001 \begin_layout Plain Layout
20009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20012 \begin_layout Plain Layout
20013 \begin_inset Formula $\chi$
20023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20026 \begin_layout Plain Layout
20034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20037 \begin_layout Plain Layout
20038 \begin_inset Formula $\psi$
20048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20051 \begin_layout Plain Layout
20059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20062 \begin_layout Plain Layout
20063 \begin_inset Formula $\omega$
20077 \begin_inset space \hfill{}
20083 \begin_layout Standard
20084 \begin_inset VSpace medskip
20090 \begin_layout Standard
20091 How to create upright Greek letters is explained in
20092 \begin_inset CommandInset ref
20094 reference "sub:Upright-small-Greek"
20101 \begin_layout Subsection
20106 \begin_layout Plain Layout
20107 Greek letters ! big
20115 \begin_layout Standard
20116 \begin_inset space \hfill{}
20120 \begin_inset Tabular
20121 <lyxtabular version="3" rows="7" columns="2">
20123 <column alignment="center" valignment="top" width="0pt">
20124 <column alignment="center" valignment="top" width="0pt">
20126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20129 \begin_layout Plain Layout
20135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20138 \begin_layout Plain Layout
20146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20149 \begin_layout Plain Layout
20157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20160 \begin_layout Plain Layout
20161 \begin_inset Formula $\Gamma$
20171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20174 \begin_layout Plain Layout
20182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20185 \begin_layout Plain Layout
20186 \begin_inset Formula $\Delta$
20196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20199 \begin_layout Plain Layout
20207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20210 \begin_layout Plain Layout
20211 \begin_inset Formula $\Theta$
20221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20224 \begin_layout Plain Layout
20232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20235 \begin_layout Plain Layout
20236 \begin_inset Formula $\Lambda$
20246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20249 \begin_layout Plain Layout
20257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20260 \begin_layout Plain Layout
20261 \begin_inset Formula $\Xi$
20271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20285 \begin_layout Plain Layout
20286 \begin_inset Formula $\Pi$
20300 \begin_inset space \hfill{}
20304 \begin_inset Tabular
20305 <lyxtabular version="3" rows="6" columns="2">
20307 <column alignment="center" valignment="top" width="0pt">
20308 <column alignment="center" valignment="top" width="0pt">
20310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20313 \begin_layout Plain Layout
20319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20333 \begin_layout Plain Layout
20341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20344 \begin_layout Plain Layout
20345 \begin_inset Formula $\Sigma$
20355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20358 \begin_layout Plain Layout
20366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20369 \begin_layout Plain Layout
20370 \begin_inset Formula $\Upsilon$
20380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20383 \begin_layout Plain Layout
20391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20394 \begin_layout Plain Layout
20395 \begin_inset Formula $\Phi$
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Plain Layout
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Plain Layout
20420 \begin_inset Formula $\Psi$
20430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20433 \begin_layout Plain Layout
20441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Plain Layout
20445 \begin_inset Formula $\Omega$
20459 \begin_inset space \hfill{}
20465 \begin_layout Standard
20466 \begin_inset VSpace medskip
20469 That the big Greek letters appear upright is caused by a design bug when
20471 To get correct italic big letters, begin every command with
20476 For example the command
20483 \begin_inset Formula $\varGamma$
20489 \begin_layout Subsection
20494 \begin_layout Plain Layout
20495 Greek letters ! bold
20503 \begin_layout Standard
20504 Greek letters cannot be set with different font styles like Latin letters.
20505 They can only be made bold with the command
20515 \begin_layout Plain Layout
20526 \begin_layout Standard
20528 \begin_inset Tabular
20529 <lyxtabular version="3" rows="3" columns="2">
20531 <column alignment="center" valignment="top" width="0">
20532 <column alignment="center" valignment="top" width="0">
20534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20537 \begin_layout Plain Layout
20543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20546 \begin_layout Plain Layout
20554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20557 \begin_layout Plain Layout
20569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20572 \begin_layout Plain Layout
20573 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20586 \begin_layout Plain Layout
20598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20601 \begin_layout Plain Layout
20602 \begin_inset Formula $\theta\boldsymbol{\theta}$
20618 \begin_layout Section
20623 \begin_layout Plain Layout
20636 \begin_layout Plain Layout
20637 A list with all symbols of most of the LaTeX-packages can be found in
20638 \begin_inset CommandInset citation
20653 \begin_layout Plain Layout
20661 \begin_inset Note Note
20664 \begin_layout Plain Layout
20667 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20670 \begin_layout Plain Layout
20673 texorpdfstring is in section
20674 \begin_inset CommandInset ref
20676 reference "sub:Formulas-in-Section"
20689 \begin_layout Plain Layout
20698 \begin_layout Standard
20699 Many of the symbols listed in this section can also be inserted via the
20701 \begin_inset Graphics
20702 filename ../images/math/nabla.png
20708 \begin_inset Graphics
20709 filename ../images/math/digamma.png
20717 \begin_layout Subsection
20718 Mathematical Symbols
20719 \begin_inset CommandInset label
20721 name "sub:Mathematical-Symbols"
20729 \begin_layout Plain Layout
20730 Symbols ! mathematical
20738 \begin_layout Standard
20739 \begin_inset space \hfill{}
20743 \begin_inset Tabular
20744 <lyxtabular version="3" rows="10" columns="2">
20746 <column alignment="center" valignment="top" width="0pt">
20747 <column alignment="center" valignment="top" width="0pt">
20749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20752 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20772 \begin_layout Plain Layout
20780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20783 \begin_layout Plain Layout
20784 \begin_inset Formula $\neg$
20794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20797 \begin_layout Plain Layout
20805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20808 \begin_layout Plain Layout
20809 \begin_inset Formula $\Im$
20819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20822 \begin_layout Plain Layout
20830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20833 \begin_layout Plain Layout
20834 \begin_inset Formula $\Re$
20844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20847 \begin_layout Plain Layout
20855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20858 \begin_layout Plain Layout
20859 \begin_inset Formula $\aleph$
20869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20872 \begin_layout Plain Layout
20880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20883 \begin_layout Plain Layout
20884 \begin_inset Formula $\partial$
20894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20897 \begin_layout Plain Layout
20905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20908 \begin_layout Plain Layout
20909 \begin_inset Formula $\infty$
20919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20922 \begin_layout Plain Layout
20930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20933 \begin_layout Plain Layout
20934 \begin_inset Formula $\wp$
20944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20947 \begin_layout Plain Layout
20955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20958 \begin_layout Plain Layout
20959 \begin_inset Formula $\imath$
20969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20972 \begin_layout Plain Layout
20980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20983 \begin_layout Plain Layout
20984 \begin_inset Formula $\jmath$
20998 \begin_inset space \hfill{}
21002 \begin_inset Tabular
21003 <lyxtabular version="3" rows="10" columns="2">
21005 <column alignment="center" valignment="top" width="0pt">
21006 <column alignment="center" valignment="top" width="0pt">
21008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21011 \begin_layout Plain Layout
21017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21020 \begin_layout Plain Layout
21022 \begin_inset Note Note
21025 \begin_layout Plain Layout
21032 is only used as spacer.
21044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21047 \begin_layout Plain Layout
21055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21058 \begin_layout Plain Layout
21059 \begin_inset Formula $\forall$
21069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21072 \begin_layout Plain Layout
21080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21083 \begin_layout Plain Layout
21084 \begin_inset Formula $\exists$
21094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21097 \begin_layout Plain Layout
21105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21108 \begin_layout Plain Layout
21109 \begin_inset Formula $\nexists$
21119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21122 \begin_layout Plain Layout
21130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21133 \begin_layout Plain Layout
21134 \begin_inset Formula $\emptyset$
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21159 \begin_inset Formula $\varnothing$
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21183 \begin_layout Plain Layout
21184 \begin_inset Formula $\dag$
21194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21197 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21209 \begin_inset Formula $\ddag$
21219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21237 \begin_layout Plain Layout
21247 \begin_inset Formula $\complement$
21254 \begin_layout Plain Layout
21268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21271 \begin_layout Plain Layout
21279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21282 \begin_layout Plain Layout
21283 \begin_inset Formula $\Bbbk$
21297 \begin_inset space \hfill{}
21301 \begin_inset Tabular
21302 <lyxtabular version="3" rows="10" columns="2">
21304 <column alignment="center" valignment="top" width="0pt">
21305 <column alignment="center" valignment="top" width="0pt">
21307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21310 \begin_layout Plain Layout
21316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21319 \begin_layout Plain Layout
21327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21330 \begin_layout Plain Layout
21338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21341 \begin_layout Plain Layout
21342 \begin_inset Formula $\prime$
21352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21355 \begin_layout Plain Layout
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21366 \begin_layout Plain Layout
21367 \begin_inset Formula $\backprime$
21377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21380 \begin_layout Plain Layout
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21391 \begin_layout Plain Layout
21392 \begin_inset Formula $\mho$
21402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21405 \begin_layout Plain Layout
21413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21416 \begin_layout Plain Layout
21417 \begin_inset Formula $\triangle$
21427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21430 \begin_layout Plain Layout
21438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21441 \begin_layout Plain Layout
21442 \begin_inset Formula $\angle$
21452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21455 \begin_layout Plain Layout
21463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21466 \begin_layout Plain Layout
21467 \begin_inset Formula $\measuredangle$
21477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21480 \begin_layout Plain Layout
21488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21491 \begin_layout Plain Layout
21492 \begin_inset Formula $\sphericalangle$
21502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21505 \begin_layout Plain Layout
21513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21516 \begin_layout Plain Layout
21517 \begin_inset Formula $\top$
21527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21530 \begin_layout Plain Layout
21538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21541 \begin_layout Plain Layout
21542 \begin_inset Formula $\bot$
21556 \begin_inset space \hfill{}
21562 \begin_layout Subsection
21563 Miscellaneous Symbols
21564 \begin_inset CommandInset label
21566 name "sub:Miscellaneous-Symbols"
21574 \begin_layout Plain Layout
21575 Symbols ! miscellaneous
21583 \begin_layout Standard
21586 \begin_inset Tabular
21587 <lyxtabular version="3" rows="10" columns="2">
21589 <column alignment="center" valignment="top" width="0pt">
21590 <column alignment="center" valignment="top" width="0pt">
21592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21595 \begin_layout Plain Layout
21601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21604 \begin_layout Plain Layout
21612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21615 \begin_layout Plain Layout
21623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21626 \begin_layout Plain Layout
21627 \begin_inset Formula $\flat$
21637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21640 \begin_layout Plain Layout
21648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21651 \begin_layout Plain Layout
21652 \begin_inset Formula $\natural$
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21665 \begin_layout Plain Layout
21673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21676 \begin_layout Plain Layout
21677 \begin_inset Formula $\sharp$
21687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Plain Layout
21702 \begin_inset Formula $\surd$
21712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21715 \begin_layout Plain Layout
21723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21726 \begin_layout Plain Layout
21727 \begin_inset Formula $\checkmark$
21737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21752 \begin_inset Formula $\yen$
21762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\pounds$
21787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21799 \begin_layout Plain Layout
21800 \begin_inset Formula $\$$
21810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21813 \begin_layout Plain Layout
21819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Plain Layout
21823 \begin_inset Formula $§$
21837 \begin_inset Tabular
21838 <lyxtabular version="3" rows="10" columns="2">
21840 <column alignment="center" valignment="top" width="0">
21841 <column alignment="center" valignment="top" width="0">
21843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21846 \begin_layout Plain Layout
21852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21855 \begin_layout Plain Layout
21863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21866 \begin_layout Plain Layout
21874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21877 \begin_layout Plain Layout
21878 \begin_inset Formula $\hbar$
21888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21891 \begin_layout Plain Layout
21899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21902 \begin_layout Plain Layout
21903 \begin_inset Formula $\hslash$
21913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21916 \begin_layout Plain Layout
21924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21927 \begin_layout Plain Layout
21928 \begin_inset Formula $\clubsuit$
21938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21941 \begin_layout Plain Layout
21949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21952 \begin_layout Plain Layout
21953 \begin_inset Formula $\spadesuit$
21963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21966 \begin_layout Plain Layout
21974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21977 \begin_layout Plain Layout
21978 \begin_inset Formula $\bigstar$
21988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21991 \begin_layout Plain Layout
21999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22002 \begin_layout Plain Layout
22003 \begin_inset Formula $\blacklozenge$
22013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22016 \begin_layout Plain Layout
22024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22027 \begin_layout Plain Layout
22028 \begin_inset Formula $\blacktriangle$
22038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22041 \begin_layout Plain Layout
22049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22052 \begin_layout Plain Layout
22053 \begin_inset Formula $\blacktriangledown$
22063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22066 \begin_layout Plain Layout
22074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22077 \begin_layout Plain Layout
22078 \begin_inset Formula $\bullet$
22092 \begin_inset Tabular
22093 <lyxtabular version="3" rows="10" columns="2">
22095 <column alignment="center" valignment="top" width="0pt">
22096 <column alignment="center" valignment="top" width="0pt">
22098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22101 \begin_layout Plain Layout
22107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22110 \begin_layout Plain Layout
22118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22121 \begin_layout Plain Layout
22129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22132 \begin_layout Plain Layout
22133 \begin_inset Formula $\diamondsuit$
22143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22146 \begin_layout Plain Layout
22154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22157 \begin_layout Plain Layout
22158 \begin_inset Formula $\Diamond$
22168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22171 \begin_layout Plain Layout
22179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22182 \begin_layout Plain Layout
22183 \begin_inset Formula $\heartsuit$
22193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22196 \begin_layout Plain Layout
22204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22207 \begin_layout Plain Layout
22208 \begin_inset Formula $\P$
22218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22221 \begin_layout Plain Layout
22229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22232 \begin_layout Plain Layout
22233 \begin_inset Formula $\copyright$
22243 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22246 \begin_layout Plain Layout
22254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22257 \begin_layout Plain Layout
22258 \begin_inset Formula $\circledR$
22268 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22271 \begin_layout Plain Layout
22279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22282 \begin_layout Plain Layout
22283 \begin_inset Formula $\maltese$
22293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22296 \begin_layout Plain Layout
22304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22307 \begin_layout Plain Layout
22308 \begin_inset Formula $\diagup$
22318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22321 \begin_layout Plain Layout
22329 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22332 \begin_layout Plain Layout
22333 \begin_inset Formula $\diagdown$
22349 \begin_layout Standard
22350 \begin_inset VSpace medskip
22353 More symbols are listed in
22354 \begin_inset CommandInset ref
22356 reference "sub:Miscellaneous-special-Characters"
22363 \begin_layout Standard
22364 Some symbols can be displayed in different sizes, see
22365 \begin_inset CommandInset ref
22367 reference "sub:Font-Sizes"
22374 \begin_layout Subsection
22379 \begin_layout Plain Layout
22380 Symbols ! Euro-symbol
22389 \begin_layout Plain Layout
22396 \begin_layout Plain Layout
22413 \begin_layout Standard
22414 To use the Euro symbol in formulas, the LaTeX-package
22422 \begin_layout Plain Layout
22428 must be installed and loaded with the LaTeX-preamble line
22431 \begin_layout Standard
22436 usepackage[gennarrow]{eurosym}
22439 \begin_layout Standard
22440 The Euro symbol can now be inserted with the command
22450 \begin_layout Plain Layout
22461 \begin_layout Standard
22462 The Euro symbol can directly be inserted with the € key in mathematical
22463 text, without having
22478 can also be inserted in TeX-mode.
22479 The official currency symbol can then be inserted with the command
22489 \begin_layout Plain Layout
22497 , that is only available in TeX-mode.
22500 \begin_layout Standard
22504 \begin_layout Plain Layout
22514 \begin_inset Note Note
22517 \begin_layout Plain Layout
22518 The following table will only be displayed when the LaTeX-package
22530 \begin_layout Standard
22531 An overview about the different Euro symbols:
22534 \begin_layout Standard
22536 \begin_inset Tabular
22537 <lyxtabular version="3" rows="4" columns="3">
22539 <column alignment="center" valignment="top" width="0pt">
22540 <column alignment="center" valignment="top" width="0pt">
22541 <column alignment="center" valignment="top" width="0pt">
22543 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22546 \begin_layout Plain Layout
22552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22555 \begin_layout Plain Layout
22561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22564 \begin_layout Plain Layout
22572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22575 \begin_layout Plain Layout
22581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22584 \begin_layout Plain Layout
22592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22595 \begin_layout Plain Layout
22596 \begin_inset Formula $\euro$
22606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22609 \begin_layout Plain Layout
22615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22618 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22627 \begin_layout Plain Layout
22628 \begin_inset Formula $\mbox{€}$
22638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22641 \begin_layout Plain Layout
22647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22650 \begin_layout Plain Layout
22658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22661 \begin_layout Plain Layout
22665 \begin_layout Plain Layout
22687 \begin_layout Standard
22691 \begin_layout Plain Layout
22701 \begin_inset Note Note
22704 \begin_layout Plain Layout
22705 The following will be displayed when the LaTeX-package
22717 \begin_layout Standard
22718 You need to install the LaTeX-package
22722 to see the rest of this subsection in the output.
22725 \begin_layout Standard
22729 \begin_layout Plain Layout
22741 \begin_layout Standard
22742 \begin_inset Newpage newpage
22748 \begin_layout Section
22750 \begin_inset CommandInset label
22752 name "sec:Relations"
22760 \begin_layout Plain Layout
22770 \begin_layout Plain Layout
22775 \begin_layout Plain Layout
22786 \begin_layout Plain Layout
22801 \begin_layout Standard
22802 All relations can also be inserted via the toolbar button
22803 \begin_inset Graphics
22804 filename ../images/math/leq.png
22812 \begin_layout Standard
22813 \begin_inset space \hfill{}
22817 \begin_inset Tabular
22818 <lyxtabular version="3" rows="17" columns="2">
22820 <column alignment="center" valignment="top" width="0pt">
22821 <column alignment="center" valignment="top" width="0pt">
22823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22826 \begin_layout Plain Layout
22832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22835 \begin_layout Plain Layout
22843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22846 \begin_layout Plain Layout
22852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22855 \begin_layout Plain Layout
22856 \begin_inset Formula $<$
22866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22869 \begin_layout Plain Layout
22877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22880 \begin_layout Plain Layout
22881 \begin_inset Formula $\le$
22891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22894 \begin_layout Plain Layout
22902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22905 \begin_layout Plain Layout
22906 \begin_inset Formula $\ll$
22916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22919 \begin_layout Plain Layout
22927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22930 \begin_layout Plain Layout
22931 \begin_inset Formula $\prec$
22941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22944 \begin_layout Plain Layout
22952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22955 \begin_layout Plain Layout
22956 \begin_inset Formula $\preceq$
22966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22969 \begin_layout Plain Layout
22977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22980 \begin_layout Plain Layout
22981 \begin_inset Formula $\subset$
22991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22994 \begin_layout Plain Layout
23002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23005 \begin_layout Plain Layout
23006 \begin_inset Formula $\subseteq$
23016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23019 \begin_layout Plain Layout
23027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23030 \begin_layout Plain Layout
23031 \begin_inset Formula $\sqsubseteq$
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23044 \begin_layout Plain Layout
23052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23055 \begin_layout Plain Layout
23056 \begin_inset Formula $\in$
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23069 \begin_layout Plain Layout
23077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23080 \begin_layout Plain Layout
23081 \begin_inset Formula $\vdash$
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23094 \begin_layout Plain Layout
23102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23105 \begin_layout Plain Layout
23106 \begin_inset Formula $\smile$
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23119 \begin_layout Plain Layout
23127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23130 \begin_layout Plain Layout
23131 \begin_inset Formula $\lhd$
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23144 \begin_layout Plain Layout
23152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23155 \begin_layout Plain Layout
23156 \begin_inset Formula $\unlhd$
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23169 \begin_layout Plain Layout
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23180 \begin_layout Plain Layout
23181 \begin_inset Formula $\gtrless$
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23194 \begin_layout Plain Layout
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23205 \begin_layout Plain Layout
23206 \begin_inset Formula $\mid$
23216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23219 \begin_layout Plain Layout
23227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23230 \begin_layout Plain Layout
23231 \begin_inset Formula $\nmid$
23245 \begin_inset space \hfill{}
23249 \begin_inset Tabular
23250 <lyxtabular version="3" rows="17" columns="2">
23252 <column alignment="center" valignment="top" width="0pt">
23253 <column alignment="center" valignment="top" width="0pt">
23255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23258 \begin_layout Plain Layout
23264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23267 \begin_layout Plain Layout
23275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23278 \begin_layout Plain Layout
23284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23287 \begin_layout Plain Layout
23288 \begin_inset Formula $=$
23298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23301 \begin_layout Plain Layout
23309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23312 \begin_layout Plain Layout
23313 \begin_inset Formula $\not=$
23323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23326 \begin_layout Plain Layout
23334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23337 \begin_layout Plain Layout
23338 \begin_inset Formula $\equiv$
23348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23351 \begin_layout Plain Layout
23359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23362 \begin_layout Plain Layout
23363 \begin_inset Formula $\sim$
23373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23376 \begin_layout Plain Layout
23384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23387 \begin_layout Plain Layout
23388 \begin_inset Formula $\simeq$
23398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23401 \begin_layout Plain Layout
23409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23412 \begin_layout Plain Layout
23413 \begin_inset Formula $\approx$
23423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23426 \begin_layout Plain Layout
23434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23437 \begin_layout Plain Layout
23438 \begin_inset Formula $\cong$
23448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23451 \begin_layout Plain Layout
23459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23462 \begin_layout Plain Layout
23463 \begin_inset Formula $\bowtie$
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23476 \begin_layout Plain Layout
23484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23487 \begin_layout Plain Layout
23488 \begin_inset Formula $\notin$
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23501 \begin_layout Plain Layout
23509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23512 \begin_layout Plain Layout
23513 \begin_inset Formula $\perp$
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23526 \begin_layout Plain Layout
23534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23537 \begin_layout Plain Layout
23538 \begin_inset Formula $\propto$
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23551 \begin_layout Plain Layout
23559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23562 \begin_layout Plain Layout
23563 \begin_inset Formula $\asymp$
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23576 \begin_layout Plain Layout
23584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23587 \begin_layout Plain Layout
23588 \begin_inset Formula $\doteq$
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23601 \begin_layout Plain Layout
23609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23612 \begin_layout Plain Layout
23613 \begin_inset Formula $\circeq$
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23626 \begin_layout Plain Layout
23634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23637 \begin_layout Plain Layout
23638 \begin_inset Formula $\models$
23648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23651 \begin_layout Plain Layout
23659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23662 \begin_layout Plain Layout
23663 \begin_inset Formula $\widehat{=}$
23677 \begin_inset space \hfill{}
23681 \begin_inset Tabular
23682 <lyxtabular version="3" rows="17" columns="2">
23684 <column alignment="center" valignment="top" width="0pt">
23685 <column alignment="center" valignment="top" width="0pt">
23687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23699 \begin_layout Plain Layout
23707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23710 \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 $>$
23730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23733 \begin_layout Plain Layout
23741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23744 \begin_layout Plain Layout
23745 \begin_inset Formula $\ge$
23755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23758 \begin_layout Plain Layout
23766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23769 \begin_layout Plain Layout
23770 \begin_inset Formula $\gg$
23780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23783 \begin_layout Plain Layout
23791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23794 \begin_layout Plain Layout
23795 \begin_inset Formula $\succ$
23805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23808 \begin_layout Plain Layout
23816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23819 \begin_layout Plain Layout
23820 \begin_inset Formula $\succeq$
23830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23833 \begin_layout Plain Layout
23841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23844 \begin_layout Plain Layout
23845 \begin_inset Formula $\supset$
23855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23858 \begin_layout Plain Layout
23866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23869 \begin_layout Plain Layout
23870 \begin_inset Formula $\supseteq$
23880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23883 \begin_layout Plain Layout
23891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23894 \begin_layout Plain Layout
23895 \begin_inset Formula $\sqsupseteq$
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23908 \begin_layout Plain Layout
23916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23919 \begin_layout Plain Layout
23920 \begin_inset Formula $\ni$
23930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23933 \begin_layout Plain Layout
23941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23944 \begin_layout Plain Layout
23945 \begin_inset Formula $\dashv$
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23958 \begin_layout Plain Layout
23966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23969 \begin_layout Plain Layout
23970 \begin_inset Formula $\frown$
23980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23983 \begin_layout Plain Layout
23991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23994 \begin_layout Plain Layout
23995 \begin_inset Formula $\rhd$
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24008 \begin_layout Plain Layout
24016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24019 \begin_layout Plain Layout
24020 \begin_inset Formula $\unrhd$
24030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24033 \begin_layout Plain Layout
24041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24044 \begin_layout Plain Layout
24045 \begin_inset Formula $\lessgtr$
24055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24058 \begin_layout Plain Layout
24066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24069 \begin_layout Plain Layout
24070 \begin_inset Formula $\parallel$
24080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24083 \begin_layout Plain Layout
24091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24094 \begin_layout Plain Layout
24095 \begin_inset Formula $\nparallel$
24109 \begin_inset space \hfill{}
24115 \begin_layout Standard
24116 \begin_inset VSpace medskip
24131 are bigger than the equal looking operators
24146 \begin_layout Standard
24147 Relations are, in contrary to symbols, always surrounded by space.
24150 \begin_layout Standard
24151 Relations with labels can be created with the command
24161 \begin_layout Plain Layout
24172 \begin_layout Standard
24174 \begin_inset Tabular
24175 <lyxtabular version="3" rows="2" columns="2">
24177 <column alignment="center" valignment="top" width="0">
24178 <column alignment="center" valignment="top" width="0">
24180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24183 \begin_layout Plain Layout
24189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24192 \begin_layout Plain Layout
24194 \begin_inset Note Note
24197 \begin_layout Plain Layout
24204 is only used as spacer.
24216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24219 \begin_layout Plain Layout
24226 \begin_layout Plain Layout
24243 \begin_layout Plain Layout
24253 \begin_inset Formula $\downarrow$
24262 \begin_layout Plain Layout
24275 \begin_layout Plain Layout
24289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24292 \begin_layout Plain Layout
24293 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24309 \begin_layout Section
24313 \begin_layout Subsection
24314 Predefined Functions
24315 \begin_inset CommandInset label
24317 name "sub:Predefined-Functions"
24325 \begin_layout Plain Layout
24326 Functions ! predefined
24334 \begin_layout Standard
24335 In general, variables are set
24339 in mathematical expressions, but not function names, because
24340 \begin_inset Formula $sin$
24343 could be misunderstood as
24344 \begin_inset Formula $s\cdot i\cdot n$
24348 Therefore there are predefined functions, that are additionally a bit separated
24350 They are inserted as commands starting with a backslash before their name.
24353 \begin_layout Standard
24355 \begin_inset Tabular
24356 <lyxtabular version="3" rows="2" columns="4">
24358 <column alignment="center" valignment="top" width="0pt">
24359 <column alignment="center" valignment="top" width="0pt">
24360 <column alignment="center" valignment="top" width="0pt">
24361 <column alignment="center" valignment="top" width="0pt">
24363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24366 \begin_layout Plain Layout
24372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24375 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24384 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24413 \begin_layout Plain Layout
24414 \begin_inset Formula $Asin(x)+B$
24422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24425 \begin_layout Plain Layout
24433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24436 \begin_layout Plain Layout
24437 \begin_inset Formula $A\sin(x)+B$
24453 \begin_layout Standard
24454 The following functions are predefined:
24457 \begin_layout Standard
24458 \begin_inset VSpace -2mm
24464 \begin_layout Standard
24466 \begin_inset Tabular
24467 <lyxtabular version="3" rows="9" columns="4">
24469 <column alignment="center" valignment="top" width="0pt">
24470 <column alignment="center" valignment="top" width="0pt">
24471 <column alignment="center" valignment="top" width="0pt">
24472 <column alignment="center" valignment="top" width="0pt">
24474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24504 \begin_layout Plain Layout
24512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24515 \begin_layout Plain Layout
24523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24526 \begin_layout Plain Layout
24534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24537 \begin_layout Plain Layout
24545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24548 \begin_layout Plain Layout
24558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24561 \begin_layout Plain Layout
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" usebox="none">
24583 \begin_layout Plain Layout
24591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24594 \begin_layout Plain Layout
24604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24607 \begin_layout Plain Layout
24615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24618 \begin_layout Plain Layout
24626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24629 \begin_layout Plain Layout
24637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24640 \begin_layout Plain Layout
24650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24653 \begin_layout Plain Layout
24661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24664 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24675 \begin_layout Plain Layout
24683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24686 \begin_layout Plain Layout
24696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24699 \begin_layout Plain Layout
24707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24710 \begin_layout Plain Layout
24718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24721 \begin_layout Plain Layout
24729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24732 \begin_layout Plain Layout
24742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24745 \begin_layout Plain Layout
24753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24756 \begin_layout Plain Layout
24764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24767 \begin_layout Plain Layout
24775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24778 \begin_layout Plain Layout
24788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24791 \begin_layout Plain Layout
24799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24802 \begin_layout Plain Layout
24810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24813 \begin_layout Plain Layout
24821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24824 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24848 \begin_layout Plain Layout
24856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24859 \begin_layout Plain Layout
24867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24870 \begin_layout Plain Layout
24886 \begin_layout Standard
24887 They can also be inserted with the math toolbar button
24888 \begin_inset Graphics
24889 filename ../images/math/functions.png
24897 \begin_layout Subsection
24898 Self-defined Functions
24902 \begin_layout Plain Layout
24903 Functions ! self-defined
24911 \begin_layout Standard
24912 To use a function that is not predefined, like for example the sign function
24913 sgn(x), there are two possibilities:
24916 \begin_layout Itemize
24917 Define the function by inserting the following line to the LaTeX-preamble
24921 \begin_layout Plain Layout
24926 DeclareMathOperator
24929 \begin_inset CommandInset ref
24931 reference "sub:Self-defined-Operators"
24941 \begin_inset Newline newline
24945 \begin_inset VSpace -3mm
24949 \begin_inset Newline newline
24956 DeclareMathOperator{
24964 \begin_layout Plain Layout
24969 DeclareMathOperator
24975 \begin_inset Newline newline
24979 \begin_inset VSpace -2mm
24983 \begin_inset Newline newline
24986 Now the new defined function can be called with the command
24995 \begin_layout Itemize
24996 Write the the formula as usual, mark the formula name, in our example the
25001 , and change it to mathematical text.
25002 At last a space is inserted between prefactor and function.
25005 \begin_layout Standard
25006 The result is the same with both methods as with a predefined function
25010 \begin_layout Plain Layout
25011 In LyX self-defined functions are displayed red, predefined ones black.
25019 \begin_layout Standard
25021 \begin_inset Tabular
25022 <lyxtabular version="3" rows="3" columns="2">
25024 <column alignment="center" valignment="top" width="0pt">
25025 <column alignment="center" valignment="top" width="0pt">
25027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25030 \begin_layout Plain Layout
25036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25039 \begin_layout Plain Layout
25047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25050 \begin_layout Plain Layout
25058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25061 \begin_layout Plain Layout
25062 \begin_inset Formula $A\sgn(x)+B$
25072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25075 \begin_layout Plain Layout
25079 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25090 \begin_layout Plain Layout
25091 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25107 \begin_layout Standard
25108 The first method is more suitable when the self-defined function should
25109 be used several times.
25112 \begin_layout Subsection
25117 \begin_layout Plain Layout
25126 \begin_layout Standard
25127 For limits there are defined besides
25137 \begin_layout Plain Layout
25157 furthermore the following functions:
25160 \begin_layout Standard
25162 \begin_inset Tabular
25163 <lyxtabular version="3" rows="5" columns="2">
25165 <column alignment="center" valignment="top" width="0">
25166 <column alignment="center" valignment="top" width="0">
25168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25171 \begin_layout Plain Layout
25177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25180 \begin_layout Plain Layout
25182 \begin_inset Note Note
25185 \begin_layout Plain Layout
25192 is only used as spacer.
25204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25207 \begin_layout Plain Layout
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25218 \begin_layout Plain Layout
25219 \begin_inset Formula $\varliminf$
25229 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25232 \begin_layout Plain Layout
25240 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25243 \begin_layout Plain Layout
25244 \begin_inset Formula $\varlimsup$
25254 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25257 \begin_layout Plain Layout
25265 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25268 \begin_layout Plain Layout
25269 \begin_inset Formula $\varprojlim$
25279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25282 \begin_layout Plain Layout
25290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25293 \begin_layout Plain Layout
25294 \begin_inset Formula $\varinjlim$
25298 \begin_inset Formula $\raisebox{-2.5mm}{}$
25314 \begin_layout Standard
25315 \begin_inset VSpace medskip
25318 The limit is created by inserting a subscript.
25319 It is set right beside the function in an inline formula:
25322 \begin_layout Standard
25324 \begin_inset Tabular
25325 <lyxtabular version="3" rows="2" columns="2">
25327 <column alignment="center" valignment="top" width="0pt">
25328 <column alignment="center" valignment="top" width="0pt">
25330 <cell alignment="center" valignment="top" usebox="none">
25333 \begin_layout Plain Layout
25339 <cell alignment="center" valignment="top" usebox="none">
25342 \begin_layout Plain Layout
25343 \begin_inset space \hspace{}
25348 \begin_inset Note Note
25351 \begin_layout Plain Layout
25358 are used here as spacer.
25370 <cell alignment="center" valignment="top" usebox="none">
25373 \begin_layout Plain Layout
25382 \begin_layout Plain Layout
25395 \begin_layout Plain Layout
25409 <cell alignment="center" valignment="top" usebox="none">
25412 \begin_layout Plain Layout
25413 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25429 \begin_layout Standard
25430 In a displayed formula the limit is set below the formula, as usual:
25431 \begin_inset Formula \[
25439 \begin_layout Subsection
25444 \begin_layout Plain Layout
25445 Functions ! modulo-
25453 \begin_layout Standard
25454 The modulo-function is special, because it exists in four variants.
25457 \begin_layout Standard
25458 The variants in a displayed formula:
25459 \begin_inset Formula \begin{align*}
25460 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25461 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25462 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25463 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25464 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25471 \begin_layout Standard
25472 In an inline formula less space is set before the function names for all
25476 \begin_layout Standard
25477 \begin_inset Newpage newpage
25483 \begin_layout Section
25488 \begin_layout Plain Layout
25497 \begin_layout Subsection
25498 Special Characters in Mathematical Text
25501 \begin_layout Standard
25502 The following commands can only be used in mathematical text or in TeX-mode:
25505 \begin_layout Standard
25506 \begin_inset space \hfill{}
25510 \begin_inset Tabular
25511 <lyxtabular version="3" rows="8" columns="2">
25513 <column alignment="block" valignment="top" width="0">
25514 <column alignment="block" valignment="top" width="0">
25516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25519 \begin_layout Plain Layout
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25539 \begin_layout Plain Layout
25547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25550 \begin_layout Plain Layout
25551 \begin_inset Formula $\textrm{œ}$
25561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25564 \begin_layout Plain Layout
25572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25575 \begin_layout Plain Layout
25576 \begin_inset Formula $\textrm{Œ}$
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25600 \begin_layout Plain Layout
25601 \begin_inset Formula $\textrm{æ}$
25611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25625 \begin_layout Plain Layout
25626 \begin_inset Formula $\textrm{Æ}$
25636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25639 \begin_layout Plain Layout
25647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25650 \begin_layout Plain Layout
25651 \begin_inset Formula $\textrm{\aa}$
25661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25664 \begin_layout Plain Layout
25671 \begin_layout Plain Layout
25678 \begin_layout Plain Layout
25699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25702 \begin_layout Plain Layout
25703 \begin_inset Formula $\textrm{Å}$
25713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25716 \begin_layout Plain Layout
25724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25727 \begin_layout Plain Layout
25728 \begin_inset Formula $\textrm{ı}$
25742 \begin_inset space \hfill{}
25746 \begin_inset Tabular
25747 <lyxtabular version="3" rows="8" columns="2">
25749 <column alignment="block" valignment="top" width="0">
25750 <column alignment="center" valignment="top" width="0">
25752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25755 \begin_layout Plain Layout
25757 \begin_inset Note Note
25760 \begin_layout Plain Layout
25762 \begin_inset space \thinspace{}
25765 mm is used for separation, because otherwise the output will be ¡ and ¿
25776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25779 \begin_layout Plain Layout
25787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25790 \begin_layout Plain Layout
25798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25801 \begin_layout Plain Layout
25802 \begin_inset Formula $\textrm{ø}$
25812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25815 \begin_layout Plain Layout
25823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25826 \begin_layout Plain Layout
25827 \begin_inset Formula $\textrm{Ø}$
25837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25840 \begin_layout Plain Layout
25848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25851 \begin_layout Plain Layout
25852 \begin_inset Formula $\textrm{ł}$
25862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25865 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25876 \begin_layout Plain Layout
25877 \begin_inset Formula $\textrm{Ł}$
25887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25890 \begin_layout Plain Layout
25892 \begin_inset space \hspace{}
25900 \begin_layout Plain Layout
25914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25917 \begin_layout Plain Layout
25918 \begin_inset Formula $\textrm{!`}$
25928 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25931 \begin_layout Plain Layout
25933 \begin_inset space \hspace{}
25941 \begin_layout Plain Layout
25955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25958 \begin_layout Plain Layout
25959 \begin_inset Formula $\textrm{?`}$
25969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25972 \begin_layout Plain Layout
25980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25983 \begin_layout Plain Layout
25984 \begin_inset Formula $\textrm{ȷ}$
25998 \begin_inset space \hfill{}
26004 \begin_layout Standard
26006 \begin_inset Formula $\textrm{\textrm{Å}}$
26010 \begin_inset Formula $\textrm{\textrm{Ø}}$
26013 can also be inserted via the math toolbar button
26014 \begin_inset Graphics
26015 filename ../images/math/digamma.png
26023 \begin_layout Standard
26024 An exception are the commands
26027 \begin_inset space \hspace{}
26036 \begin_inset space \hspace{}
26042 , because they can be inserted in LyX directly to text.
26045 \begin_layout Subsection
26047 \begin_inset CommandInset label
26049 name "sub:Accents-in-Text"
26057 \begin_layout Plain Layout
26066 \begin_layout Standard
26067 With the following commands all letters can be accented.
26068 The commands must be inserted in TeX-mode.
26071 \begin_layout Standard
26072 \begin_inset space \hfill{}
26076 \begin_inset Tabular
26077 <lyxtabular version="3" rows="8" columns="2">
26079 <column alignment="block" valignment="top" width="0">
26080 <column alignment="block" valignment="top" width="0">
26082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26085 \begin_layout Plain Layout
26091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26094 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26105 \begin_layout Plain Layout
26109 \begin_inset Quotes grd
26117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26120 \begin_layout Plain Layout
26124 \begin_layout Plain Layout
26140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26143 \begin_layout Plain Layout
26151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26154 \begin_layout Plain Layout
26158 \begin_layout Plain Layout
26174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26177 \begin_layout Plain Layout
26184 \begin_layout Plain Layout
26198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26201 \begin_layout Plain Layout
26205 \begin_layout Plain Layout
26221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26224 \begin_layout Plain Layout
26232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26235 \begin_layout Plain Layout
26239 \begin_layout Plain Layout
26255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26258 \begin_layout Plain Layout
26265 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26282 \begin_layout Plain Layout
26286 \begin_layout Plain Layout
26302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26305 \begin_layout Plain Layout
26312 \begin_layout Plain Layout
26326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26329 \begin_layout Plain Layout
26333 \begin_layout Plain Layout
26349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26352 \begin_layout Plain Layout
26359 \begin_layout Plain Layout
26373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26376 \begin_layout Plain Layout
26380 \begin_layout Plain Layout
26400 \begin_inset space \hfill{}
26404 \begin_inset Tabular
26405 <lyxtabular version="3" rows="8" columns="2">
26407 <column alignment="block" valignment="top" width="0">
26408 <column alignment="center" valignment="top" width="0">
26410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26413 \begin_layout Plain Layout
26419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26422 \begin_layout Plain Layout
26430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26433 \begin_layout Plain Layout
26440 \begin_layout Plain Layout
26454 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26457 \begin_layout Plain Layout
26461 \begin_layout Plain Layout
26477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26480 \begin_layout Plain Layout
26488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26491 \begin_layout Plain Layout
26495 \begin_layout Plain Layout
26511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26514 \begin_layout Plain Layout
26521 \begin_layout Plain Layout
26532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26535 \begin_layout Plain Layout
26539 \begin_layout Plain Layout
26555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26558 \begin_layout Plain Layout
26566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26569 \begin_layout Plain Layout
26573 \begin_layout Plain Layout
26589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26592 \begin_layout Plain Layout
26599 \begin_layout Plain Layout
26613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26616 \begin_layout Plain Layout
26620 \begin_layout Plain Layout
26636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26639 \begin_layout Plain Layout
26646 \begin_layout Plain Layout
26660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26663 \begin_layout Plain Layout
26667 \begin_layout Plain Layout
26683 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26686 \begin_layout Plain Layout
26693 \begin_layout Plain Layout
26707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26710 \begin_layout Plain Layout
26714 \begin_layout Plain Layout
26734 \begin_inset space \hfill{}
26740 \begin_layout Standard
26741 \begin_inset VSpace medskip
26750 also two different characters can be accented.
26759 \begin_layout Plain Layout
26774 \begin_layout Plain Layout
26786 \begin_layout Standard
26799 can in combination with vowels directly be inserted with the keyboard without
26801 The same applies for the tilde
26805 \begin_layout Plain Layout
26806 This only applies for keyboards where the tilde is defined as accent.
26815 in combination with
26830 \begin_layout Standard
26873 , and accents inserted directly with the keyboard are also available in
26875 For the other accents there are special math commands to be used in formulas,
26877 \begin_inset CommandInset ref
26879 reference "sub:Accents-for-one"
26886 \begin_layout Standard
26887 \begin_inset VSpace bigskip
26890 Furthermore, with the command
26900 \begin_layout Plain Layout
26908 all numbers and letters can be set into a circle, quasi accented with a
26909 circle, similar to the the copyright symbol.
26912 \begin_layout Standard
26914 \begin_inset Tabular
26915 <lyxtabular version="3" rows="3" columns="2">
26917 <column alignment="center" valignment="top" width="0">
26918 <column alignment="center" valignment="top" width="0">
26920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26923 \begin_layout Plain Layout
26929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26932 \begin_layout Plain Layout
26934 \begin_inset Note Note
26937 \begin_layout Plain Layout
26944 is only used as spacer.
26956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26959 \begin_layout Plain Layout
26967 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26974 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26993 \begin_layout Plain Layout
27004 raisebox{-1.5pt}{W}}
27009 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27012 \begin_layout Plain Layout
27013 \begin_inset Formula $\raisebox{4.5mm}{}$
27020 \begin_layout Plain Layout
27038 \begin_inset Formula $\raisebox{-2mm}{}$
27054 \begin_layout Standard
27055 One has to take care that the character fits in the circle.
27066 \begin_layout Plain Layout
27068 \begin_inset CommandInset ref
27070 reference "sub:Font-Sizes"
27079 specifies thereby the size of the circle.
27090 \begin_layout Plain Layout
27092 \begin_inset CommandInset ref
27094 reference "sub:Boxes-without-Frame"
27103 the character can be centered.
27106 \begin_layout Subsection
27111 \begin_layout Plain Layout
27120 \begin_layout Standard
27121 Minuscule numbers are created with the command
27131 \begin_layout Plain Layout
27140 The command can be used in formulas and in TeX-mode.
27141 The command scheme is:
27144 \begin_layout Standard
27149 oldstylenums{number}
27152 \begin_layout Standard
27157 oldstylenums{0123456789
27160 \begin_inset Formula $\oldstylenums{0123456789}$
27166 \begin_layout Subsection
27167 Miscellaneous special Characters
27168 \begin_inset CommandInset label
27170 name "sub:Miscellaneous-special-Characters"
27178 \begin_layout Plain Layout
27179 Special characters ! miscellaneous
27187 \begin_layout Standard
27188 The following characters can only be inserted to formulas by using commands:
27191 \begin_layout Standard
27193 \begin_inset Tabular
27194 <lyxtabular version="3" rows="4" columns="2">
27196 <column alignment="center" valignment="top" width="0">
27197 <column alignment="center" valignment="top" width="0">
27199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27202 \begin_layout Plain Layout
27208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27211 \begin_layout Plain Layout
27219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27222 \begin_layout Plain Layout
27229 \begin_layout Plain Layout
27243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27246 \begin_layout Plain Layout
27247 \begin_inset Formula $\mathcircumflex$
27257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27260 \begin_layout Plain Layout
27268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27271 \begin_layout Plain Layout
27272 \begin_inset Formula $\_$
27282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27285 \begin_layout Plain Layout
27290 \begin_layout Plain Layout
27305 \begin_layout Plain Layout
27318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27321 \begin_layout Plain Layout
27322 \begin_inset Formula $^{\circ}$
27338 \begin_layout Standard
27339 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27340 contains the following line
27344 \begin_layout Plain Layout
27345 More about this is described in
27346 \begin_inset CommandInset ref
27348 reference "sub:Text-Characters-in"
27360 \begin_layout Standard
27365 DeclareInputtext{176}{
27378 \begin_layout Standard
27379 \begin_inset Newpage newpage
27385 \begin_layout Section
27387 \begin_inset CommandInset label
27389 name "sec:Formula-Styles"
27397 \begin_layout Plain Layout
27406 \begin_layout Itemize
27407 There are two different alignment styles:
27411 \begin_layout Description
27412 Centered is the predefined standard
27415 \begin_layout Description
27416 Indented for this the option
27420 must be inserted in the menu
27422 Document\SpecialChar \menuseparator
27428 \begin_inset space ~
27434 \begin_layout Standard
27439 is used, the indentation can be adjusted with the length
27449 \begin_layout Plain Layout
27458 Should the distance be 15
27459 \begin_inset space \thinspace{}
27462 mm, the following command line is inserted in the LaTeX-preamble
27465 \begin_layout Standard
27475 \begin_layout Standard
27476 When no length is specified, the predefined value of 30
27477 \begin_inset space \thinspace{}
27484 \begin_layout Itemize
27485 And two different numbering styles:
27489 \begin_layout Description
27490 Right is the predefined standard
27493 \begin_layout Description
27494 Left for this the option
27498 must be inserted in the menu
27500 Document\SpecialChar \menuseparator
27506 \begin_inset space ~
27513 \begin_layout Standard
27522 can also be used together.
27523 In this case both options are inserted, separated by a comma.
27526 \begin_layout Standard
27527 The chosen styles are used for all displayed formulas of the document.
27528 When both, centered and indented formulas should be created in a document,
27534 The indented formulas are then set in a flalign environment, see
27535 \begin_inset CommandInset ref
27537 reference "sub:Flalign-Environment"
27544 \begin_layout Section
27546 \begin_inset CommandInset label
27548 name "sec:Multiline-Formulas"
27556 \begin_layout Plain Layout
27557 Formula ! multiline
27565 \begin_layout Subsection
27569 \begin_layout Standard
27570 In LyX multiline formulas are created by pressing
27575 arg "newline-insert newline"
27581 This creates either an
27583 eqnarray environment
27585 that is described in
27586 \begin_inset CommandInset ref
27588 reference "sub:Eqnarray-Environment"
27592 or, when the option
27594 Use AMS math package
27596 in the document settings is selected, an
27600 that is described in
27601 \begin_inset CommandInset ref
27603 reference "sub:Standard-align-Environment"
27610 \begin_layout Standard
27611 There are other multiline formula environments that can be created via the
27614 Insert\SpecialChar \menuseparator
27618 These environments are described in the following sections.
27621 \begin_layout Standard
27622 In all multiline formula environments a new line is created by pressing
27626 arg "newline-insert newline"
27630 To add or delete lines, the math toolbar buttons
27631 \begin_inset Graphics
27632 filename ../images/tabular-feature_append-row.png
27638 \begin_inset Graphics
27639 filename ../images/tabular-feature_delete-row.png
27644 , respectively, or the menu
27646 Edit\SpecialChar \menuseparator
27652 \begin_layout Subsubsection
27654 \begin_inset CommandInset label
27656 name "sub:Line-Separation"
27664 \begin_layout Plain Layout
27665 Formula ! multiline ! Line separation
27673 \begin_layout Standard
27674 There is sometimes not enough space in multiline formulas between the lines:
27675 \begin_inset Formula \begin{eqnarray*}
27676 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}\\
27677 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\end{eqnarray*}
27684 \begin_layout Standard
27685 In LaTeX additional line space is specified as optional argument of the
27687 This is not yet possible in LyX
27691 \begin_layout Plain Layout
27693 \begin_inset CommandInset href
27695 name "LyX-bug #1505"
27696 target "http://www.lyx.org/trac/ticket/1505"
27705 , therefore the whole formula must be inserted in TeX-mode.
27706 To add in our example space, the command
27714 is inserted at the end of the first line.
27719 \begin_layout Plain Layout
27726 \begin_layout Plain Layout
27728 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27731 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27738 \begin_layout Plain Layout
27742 left(B^{2}+x_{0}^{2}
27750 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27755 \begin_layout Plain Layout
27767 \begin_layout Standard
27768 \begin_inset VSpace bigskip
27771 To set the the line separation for all lines in a formula, the length
27781 \begin_layout Plain Layout
27791 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27802 \begin_inset space \thinspace{}
27807 \begin_inset space \thinspace{}
27810 mm additional line separation as in the previous example, the command
27813 \begin_layout Standard
27823 \begin_layout Standard
27824 is inserted in TeX-mode before the formula.
27825 This requires that the LaTeX-package
27833 \begin_layout Plain Layout
27838 is part of every LaTeX standard installation.
27847 \begin_layout Plain Layout
27853 was loaded in LaTeX-preamble with the line
27856 \begin_layout Standard
27864 \begin_layout Standard
27869 \begin_layout Plain Layout
27881 \begin_inset Formula \begin{eqnarray*}
27882 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}\\
27883 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\end{eqnarray*}
27890 \begin_layout Standard
27894 \begin_layout Plain Layout
27905 To get back to the predefined distance,
27911 is set to the value 3
27912 \begin_inset space \thinspace{}
27918 \begin_layout Subsubsection
27920 \begin_inset CommandInset label
27922 name "sub:Column-Separation"
27930 \begin_layout Plain Layout
27931 Formula ! multiline ! Column separation
27939 \begin_layout Standard
27940 Multiline formulas form a matrix.
27941 A formula in the eqnarray environment is for example a matrix with three
27943 By changing the column separation in this environment, the space beside
27944 the relation sign can be changed.
27947 \begin_layout Standard
27948 The column separation is specified with the length
27958 \begin_layout Plain Layout
27967 \begin_inset Newline newline
27970 column separation = 2
27971 \begin_inset space \thinspace{}
27981 \begin_inset Newline newline
27987 \begin_layout Standard
27997 \begin_layout Standard
27998 inserted in TeX-mode, sets for all following formulas a column separation
28000 \begin_inset space \thinspace{}
28004 To get back to the predefined distance,
28011 \begin_inset space \thinspace{}
28017 \begin_layout Standard
28019 \begin_inset space \thinspace{}
28022 cm column separation:
28026 \begin_layout Plain Layout
28038 \begin_inset Formula \begin{eqnarray*}
28040 C & \ne & A\end{eqnarray*}
28044 A formula with the predefined column separation for matrices of 10
28045 \begin_inset space \thinspace{}
28052 \begin_layout Plain Layout
28064 \begin_inset Formula \begin{eqnarray*}
28066 C & \ne & A\end{eqnarray*}
28073 \begin_layout Subsubsection
28078 \begin_layout Plain Layout
28087 \begin_layout Standard
28088 Long formulas can be typeset using these methods:
28091 \begin_layout Itemize
28092 When one side of the equation is much shorther than the line width, this
28093 one is chosen for the left side and the right side is typeset over two
28095 \begin_inset Formula \begin{eqnarray}
28096 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 \\
28097 & & -\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}\end{eqnarray}
28101 The minus sign at the beginning of the second line does normally not appear
28102 as operator because it is the first character of the line.
28103 Thus it would not be surrounded by space and could not be distinguished
28104 from the fraction bar.
28106 \begin_inset space \thinspace{}
28109 pt space was inserted behind the minus sign with the command
28119 \begin_layout Plain Layout
28127 \begin_inset CommandInset ref
28129 reference "sub:Variable-Space"
28142 \begin_layout Plain Layout
28153 \begin_layout Itemize
28154 When both sides of the equation are too long, the command
28164 \begin_layout Plain Layout
28173 It is inserted to the first column of the first line and effects that all
28174 further insertions overwrite the following columns:
28175 \begin_inset Formula \begin{eqnarray}
28176 \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 \\
28177 & & -\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 \\
28178 & & =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}\end{eqnarray}
28182 After the insertion of
28188 , the cursor is in a purple box that is a bit shifted to the left from the
28190 In this the formula is inserted.
28191 \begin_inset Newline newline
28194 The content of the further lines is inserted to the second or another formula
28196 The greater the column number where it was inserted, the larger the indentation.
28197 \begin_inset VSpace medskip
28201 \begin_inset Newline newline
28205 \begin_inset Note Greyedout
28208 \begin_layout Plain Layout
28209 Note the following when using
28218 \begin_layout Itemize
28219 The formula doesn't use the full page width.
28221 \begin_inset space \thinspace{}
28225 \begin_inset space \space{}
28229 \begin_inset Formula $-B^{2}$
28232 is added to the first line in the above example, it would have been outside
28234 To better use the width, negative space can be inserted at the beginning
28238 \begin_layout Itemize
28239 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28244 \begin_layout Plain Layout
28245 \begin_inset CommandInset href
28247 name "LyX-bug #1429"
28248 target "http://www.lyx.org/trac/ticket/1429"
28257 One can only set the cursor at the beginning of the line and move it with
28266 \begin_layout Itemize
28267 Other methods to set long formulas are offered by the environments described
28269 \begin_inset CommandInset ref
28271 reference "sub:Multline-Environment"
28276 \begin_inset CommandInset ref
28278 reference "sub:Multiline-Formula-Parts"
28285 \begin_layout Subsubsection
28287 \begin_inset CommandInset label
28289 name "sub:Multiline-Brackets"
28297 \begin_layout Plain Layout
28298 Brackets ! for multiline expressions
28306 \begin_layout Standard
28307 For brackets spanning multiple lines the following problem occurs:
28308 \begin_inset Formula \begin{eqnarray*}
28309 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28310 & & \left.\cdots+B-D\right]\end{eqnarray*}
28317 \begin_layout Standard
28318 The closing bracket is smaller than the opening bracket because brackets
28319 with variable size may not span multiple lines.
28322 \begin_layout Standard
28323 To set the bracket size for the second line correctly, the first line is
28334 \begin_layout Plain Layout
28342 and the second line with
28350 \begin_layout Plain Layout
28364 \begin_inset CommandInset ref
28366 reference "sub:Automatic-Bracket-Size"
28381 \begin_layout Plain Layout
28407 \begin_layout Plain Layout
28426 \begin_layout Plain Layout
28445 \begin_layout Plain Layout
28457 \begin_inset Formula $\downarrow$
28466 \begin_layout Plain Layout
28474 is inserted, because the multiplication operator with its limits is the
28475 largest symbol in the first line and this should be the size for the bracket
28476 in the second line.
28479 \begin_layout Standard
28480 The result is this:
28481 \begin_inset Formula \begin{eqnarray*}
28482 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28483 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28490 \begin_layout Subsection
28494 \begin_layout Standard
28495 Align environments can be used for every kind of multiline formulas.
28496 They are specially useful to set several formulas side by side.
28499 \begin_layout Standard
28500 Align environments consist of columns.
28501 The odd columns are right aligned, the even ones left aligned.
28502 Every line in an Align environment can be numbered.
28505 \begin_layout Standard
28506 Align environments are created via the menu
28508 Insert\SpecialChar \menuseparator
28514 Edit\SpecialChar \menuseparator
28515 Math\SpecialChar \menuseparator
28516 Change Formula Type
28518 already existing formulas can be converted to Align environments.
28521 \begin_layout Standard
28522 To add or delete columns, the math toolbar buttons
28523 \begin_inset Graphics
28524 filename ../images/tabular-feature_append-column.png
28530 \begin_inset Graphics
28531 filename ../images/tabular-feature_delete-column.png
28536 , respectively, or the menu
28538 Edit\SpecialChar \menuseparator
28544 \begin_layout Subsubsection
28545 Standard align Environment
28546 \begin_inset CommandInset label
28548 name "sub:Standard-align-Environment"
28556 \begin_layout Plain Layout
28557 Formula ! multiline ! align environment
28565 \begin_layout Standard
28566 This Align environment is created by presssing
28569 arg "newline-insert newline"
28572 in a formula or by the menu
28574 Insert\SpecialChar \menuseparator
28575 Math\SpecialChar \menuseparator
28576 AMS align Environment
28581 \begin_layout Standard
28582 An example for two formulas set side by side, that are created with a four
28583 column align environment:
28584 \begin_inset Formula \begin{align*}
28585 A & =\sin(B) & C & =D\\
28586 C & \ne A & B & \ne D\end{align*}
28590 As it can be seen, the formulas in this environment are placed so as if
28599 \begin_layout Plain Layout
28607 \begin_inset CommandInset ref
28609 reference "sub:Variable-Space"
28620 before the first and after every even column.
28621 When the formula style
28627 \begin_layout Plain Layout
28629 \begin_inset CommandInset ref
28631 reference "sec:Formula-Styles"
28642 is used, the formula is set without the
28648 before the first column.
28651 \begin_layout Subsubsection
28652 Alignat Environment
28656 \begin_layout Plain Layout
28657 Formula ! multiline ! alignat environment
28665 \begin_layout Standard
28666 The alignat environment has no predefined column separation.
28667 It can be inserted manually with the spaces that are described
28668 \begin_inset CommandInset ref
28670 reference "sub:Space"
28677 \begin_layout Standard
28678 The above example in the alignat environment where 1
28679 \begin_inset space \thinspace{}
28682 cm space was inserted at the beginning of the second formula:
28683 \begin_inset Formula \begin{alignat*}{2}
28684 A & =\sin(B) & \hspace{1cm}C & =D\\
28685 C & \ne A & B & \ne D\end{alignat*}
28689 Because the column separation can be set separately for every column, this
28690 environment is especially suitable to set three and more formulas side
28694 \begin_layout Subsubsection
28695 Flalign Environment
28696 \begin_inset CommandInset label
28698 name "sub:Flalign-Environment"
28706 \begin_layout Plain Layout
28707 Formula ! multiline ! flalign environment
28715 \begin_layout Standard
28716 In this environment the first two columns are always set as much as possible
28717 to the left and the last two ones to the right.
28719 \begin_inset Formula \begin{flalign*}
28720 A & =1 & B & =2 & C & =3\\
28721 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28728 \begin_layout Standard
28729 By creating a flalign environment with an odd number of columns where an
28730 empty TeX-brace is inserted to the last column, several formulas in a document
28731 can be set to the left, although the formula style
28736 As example the indented formula
28737 \begin_inset CommandInset ref
28739 reference "eq:VolInt"
28744 \begin_inset Formula \begin{flalign}
28745 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28749 The first two columns contain the formula.
28750 To indent it as with the formula style
28755 \begin_inset space \thinspace{}
28758 pt space was inserted at the beginning of the first column.
28761 \begin_layout Subsection
28762 Eqnarray Environment
28763 \begin_inset CommandInset label
28765 name "sub:Eqnarray-Environment"
28773 \begin_layout Plain Layout
28774 Formula ! multiline ! eqnarray environment
28782 \begin_layout Standard
28783 When this environment has been created, three blue boxes appear.
28784 The content of the first box is right aligned, the content of the last
28786 The content of the middle box appears centered and a bit smaller, because
28787 it is designed to insert there only relation characters.
28788 \begin_inset Formula \begin{eqnarray*}
28789 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28791 A & = & A\end{eqnarray*}
28798 \begin_layout Subsection
28803 \begin_layout Plain Layout
28804 Formula ! multiline ! gather environment
28812 \begin_layout Standard
28813 This environment consists of only one centered column.
28814 Every line can be numbered.
28815 \begin_inset Formula \begin{gather}
28817 X=\textrm{-}1\end{gather}
28824 \begin_layout Subsection
28825 Multline Environment
28826 \begin_inset CommandInset label
28828 name "sub:Multline-Environment"
28836 \begin_layout Plain Layout
28837 Formula ! multiline ! multline environment
28845 \begin_layout Standard
28846 The multline environment consists, like the gather environment, of only
28848 But the first line is left aligned, the last one right aligned.
28849 All other lines are centered.
28850 Therefore this environment is suitable for long formulas.
28852 \begin_inset CommandInset ref
28854 reference "eq:lefteqn"
28858 in the multline environment:
28859 \begin_inset Formula \begin{multline}
28860 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}\\
28861 -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}\\
28862 =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}}\end{multline}
28869 \begin_layout Standard
28870 In the output only the last (first) line of a multline environment appears
28871 numbered when the document numbering is right (left).
28875 \begin_layout Plain Layout
28876 numbering styles see
28877 \begin_inset CommandInset ref
28879 reference "sec:Formula-Styles"
28891 \begin_layout Standard
28900 \begin_layout Plain Layout
28918 \begin_layout Plain Layout
28928 a centered line can be right or left aligned, respectively.
28929 The commands are used as follows:
28932 \begin_layout Standard
28937 shoveright{line content}
28943 shoveleft{line content}
28946 \begin_layout Standard
28947 \begin_inset VSpace medskip
28958 \begin_layout Plain Layout
28968 specifies the distance of the first line from the left page margin.
28969 Predefined is the length 0
28970 \begin_inset space \thinspace{}
28976 \begin_layout Standard
28977 As example the above formula where the command
28980 \begin_layout Standard
28990 \begin_layout Standard
28991 was inserted in TeX-mode before:
28995 \begin_layout Plain Layout
29007 \begin_inset Formula \begin{multline}
29008 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}\\
29009 \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}}\\
29010 =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}}\end{multline}
29018 \begin_layout Plain Layout
29029 The second line was left aligned using
29038 \begin_layout Subsection
29039 Multiline Formula Parts
29040 \begin_inset CommandInset label
29042 name "sub:Multiline-Formula-Parts"
29050 \begin_layout Plain Layout
29051 Formula ! multiline ! formula parts
29059 \begin_layout Standard
29060 To display only parts of a formula with multiple lines, one of the following
29061 environments are used:
29078 They can be inserted via the menu
29080 Insert\SpecialChar \menuseparator
29083 or by using the commands described in this section.
29086 \begin_layout Standard
29087 The first three have the same properties as the corresponding multiline
29088 formula environments, but it is possible to set further formula parts beside
29091 \begin_inset Formula \[
29092 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29093 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29094 \right\} \textrm{Uncertainty relations}\]
29101 \begin_layout Standard
29102 To get this formula, a displayed formula is created where the command
29110 \begin_layout Plain Layout
29121 A purple box appears around the blue formula box where now columns and
29122 lines can be added.
29123 Outside the multiline environment other formula parts can be set, like
29127 \begin_layout Standard
29128 The aligned environment is also suitable for long formulas whose lines are
29129 horizontally aligned.
29130 Using aligned in a displayed formula has the advantage that the formula
29131 number is vertically centered behind the lines.
29133 \begin_inset CommandInset ref
29135 reference "eq:shortlong"
29139 in the aligned environment:
29140 \begin_inset Formula \begin{equation}
29141 \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}|}\\
29142 & -\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}|}\end{aligned}
29150 \begin_layout Standard
29151 To use the environments
29173 \begin_layout Plain Layout
29191 \begin_layout Plain Layout
29209 \begin_layout Plain Layout
29217 are inserted, respectively.
29218 The split environment has the same properties as the aligned environment
29219 but it can only have two columns.
29222 \begin_layout Subsection
29223 Text in multiline Formulas
29224 \begin_inset CommandInset label
29226 name "sub:Text-in-multiline"
29234 \begin_layout Plain Layout
29244 \begin_layout Plain Layout
29245 Formula ! multiline ! text
29253 \begin_layout Standard
29254 In the Align environments, and the multline and gather environment, text
29255 can be inserted that will appear in a separate line and doesn't affect
29256 the column alignment.
29257 To do this, the command
29265 \begin_layout Plain Layout
29275 is used in the following scheme:
29278 \begin_layout Standard
29286 \begin_layout Standard
29287 The text should not be longer than a line because it cannot be hyphenated.
29288 As LyX doesn't yet support
29294 directly, the text is written as mathematical text.
29301 must hereby be at the beginning of a line and appears in the output above
29303 An example where the text was inserted at the beginning of the second line:
29304 \begin_inset Formula \begin{align}
29305 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29306 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29313 \begin_layout Section
29318 \begin_layout Plain Layout
29328 \begin_layout Plain Layout
29329 Formula ! numbering|see
29333 \begin_layout Plain Layout
29344 \begin_layout Plain Layout
29359 \begin_layout Subsection
29363 \begin_layout Standard
29364 Numbered formulas can be created with the menu
29366 Insert\SpecialChar \menuseparator
29367 Math\SpecialChar \menuseparator
29369 \begin_inset space ~
29377 \begin_inset space ~
29383 Existing formulas can be numbered with the menu
29385 Edit\SpecialChar \menuseparator
29386 Math\SpecialChar \menuseparator
29388 \begin_inset space ~
29396 arg "math-number-toggle"
29400 The formula number is displayed in LyX behind the formula as number sign
29402 The number sign is replaced in the output by the formula number.
29405 \begin_layout Standard
29406 When numbering is turned on in multiline formulas, all lines will be numbered.
29407 But the numbering can be controlled with the menu
29409 Edit\SpecialChar \menuseparator
29410 Math\SpecialChar \menuseparator
29412 \begin_inset space ~
29416 \begin_inset space ~
29420 \begin_inset space ~
29428 arg "math-number-line-toggle"
29434 \begin_layout Standard
29435 Except for inline formulas, all formulas can be numbered with two different
29437 \begin_inset CommandInset ref
29439 reference "sec:Formula-Styles"
29446 \begin_layout Subsection
29451 \begin_layout Plain Layout
29452 Cross-references ! to formulas
29460 \begin_layout Standard
29461 All labeled formulas can be cross-referenced.
29462 A label is added by the menu
29464 Insert\SpecialChar \menuseparator
29467 or the toolbar button
29468 \begin_inset Graphics
29469 filename ../images/label-insert.png
29475 The cursor must hereby be inside a displayed formula.
29476 A dialog pops up displaying the prefix
29481 The label is inserted there behind the prefix.
29482 The predefined prefix means
29483 \begin_inset Quotes eld
29487 \begin_inset Quotes erd
29490 and makes it easier to find labels in large documents because it marks
29491 it as formula label to divide it from e.
29492 \begin_inset space \thinspace{}
29496 \begin_inset space \space{}
29500 To change a label, the menu
29502 Insert\SpecialChar \menuseparator
29508 \begin_layout Standard
29509 The name of the label is displayed in LyX within two parentheses behind
29511 A formula with a label is always numbered.
29514 \begin_layout Standard
29515 Cross-references are inserted via the menu
29517 Insert\SpecialChar \menuseparator
29520 or with the toolbar button
29521 \begin_inset Graphics
29522 filename ../images/dialog-show-new-inset_ref.png
29528 A formula cross-reference appears in the output as formula number.
29529 When in the cross-reference dialog window the format
29533 is chosen, the cross-reference appears in the output as formula number
29535 \begin_inset Newline newline
29538 By right-clicking on a cross-reference in LyX, one jumps to the formula
29539 that is referenced.
29542 \begin_layout Standard
29543 Here are as examples cross-references to formulas of the following subsections:
29544 \begin_inset Note Note
29547 \begin_layout Plain Layout
29548 Note the different cross-reference types.
29556 \begin_layout Standard
29558 \begin_inset CommandInset ref
29565 \begin_inset CommandInset ref
29573 \begin_inset CommandInset ref
29579 ) big Latin letters are used for the numbering in contrary to (
29580 \begin_inset CommandInset ref
29589 \begin_layout Standard
29590 \begin_inset VSpace medskip
29593 When the argument of
29601 \begin_layout Plain Layout
29609 \begin_inset CommandInset ref
29611 reference "sub:User-defined-Numbering"
29622 contains a box like in
29623 \begin_inset CommandInset ref
29625 reference "sub:Paragraph-Boxes"
29629 , the formula cannot be referenced.
29632 \begin_layout Subsection
29637 \begin_layout Plain Layout
29638 Formula numbering ! subnumbering
29646 \begin_layout Standard
29647 With the help of the commands
29651 begin{subequations}
29659 formulas can be subnumbered.
29660 Both commands are inserted in TeX-mode.
29663 \begin_layout Standard
29665 \begin_inset Formula \begin{equation}
29666 A=C-B\label{eq:a}\end{equation}
29674 \begin_layout Plain Layout
29678 addtocounter{equation}{-1}
29687 \begin_layout Plain Layout
29691 begin{subequations}
29697 \begin_inset VSpace -5mm
29701 \begin_inset Formula \begin{equation}
29702 B=C-A\label{eq:b}\end{equation}
29707 \begin_inset Formula \begin{equation}
29708 C=A+B\label{eq:c}\end{equation}
29715 \begin_layout Standard
29719 \begin_layout Plain Layout
29731 \begin_layout Standard
29732 To create the example, the following is done:
29735 \begin_layout Enumerate
29736 first formula is inserted
29739 \begin_layout Enumerate
29744 addtocounter{equation}{-1}
29746 begin{subequations}
29750 \begin_layout Plain Layout
29759 \begin_inset Newline newline
29764 is inserted after the first formula
29767 \begin_layout Enumerate
29768 second formula is inserted
29771 \begin_layout Enumerate
29772 third formula is inserted
29775 \begin_layout Enumerate
29782 is inserted after the third formula
29785 \begin_layout Standard
29786 Every formula between the commands
29798 is subnumbered as a, b,
29799 \begin_inset Newline linebreak
29802 c, \SpecialChar \ldots{}
29803 For multiline formulas every line will be subnumbered.
29804 All subnumbered formulas are treated as
29809 But as every numbered formula increases the counter
29813 by one, the command
29819 is needed to decrease it.
29820 Otherwise the formulas
29821 \begin_inset CommandInset ref
29828 \begin_inset CommandInset ref
29835 \begin_inset CommandInset ref
29841 would be numbered as
29842 \begin_inset CommandInset ref
29849 \begin_inset CommandInset ref
29856 \begin_inset CommandInset ref
29865 \begin_layout Standard
29866 By inserting the commands in TeX-mode, a space is created between the first
29869 \begin_inset space \thinspace{}
29872 mm vertical space is inserted after the command
29876 begin{subequations}
29879 When the formula style
29885 \begin_layout Plain Layout
29887 \begin_inset CommandInset ref
29889 reference "sec:Formula-Styles"
29901 \begin_inset space \thinspace{}
29904 mm space is inserted instead.
29907 \begin_layout Standard
29908 Here is an example for a multiline formula where the numbering was turned
29909 off for the second line:
29913 \begin_layout Plain Layout
29917 begin{subequations}
29923 \begin_inset Formula \begin{eqnarray}
29924 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29925 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29926 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29934 \begin_layout Plain Layout
29946 \begin_layout Subsection
29947 User-defined Numbering
29948 \begin_inset CommandInset label
29950 name "sub:User-defined-Numbering"
29958 \begin_layout Plain Layout
29959 Formula numbering ! user-defined
29967 \begin_layout Standard
29971 \begin_layout Plain Layout
29972 Formula numbering ! self-defined delimiters
29977 With the standard numbering parentheses are set around the formula number.
29978 To replace the parentheses for example by vertical bars, the following
29979 line is added to the LaTeX-preamble:
29982 \begin_layout Standard
29994 \begin_inset Note Note
29997 \begin_layout Plain Layout
29998 This macro is already declared in the LaTeX-preamble for testing.
29999 To activate it, remove the percent sign at the beginning.
30007 \begin_layout Standard
30008 To use other characters, the vertical bars besides the
30012 are replaced by one ore more characters.
30013 To get only the formula number the vertical bars are omitted.
30016 \begin_layout Standard
30017 \begin_inset VSpace bigskip
30020 When there should be an expression of your choice instead of the consecutive
30021 formula number in parentheses behind the formula, the command
30031 \begin_layout Plain Layout
30040 \begin_inset Formula \begin{equation}
30041 A+B=C\tag{something}\label{eq:tag}\end{equation}
30045 In this example the command
30053 \begin_layout Plain Layout
30064 was inserted to the formula.
30067 \begin_layout Standard
30076 \begin_layout Plain Layout
30087 is inserted instead, the star prevents the parentheses around the expression:
30088 \begin_inset Formula \[
30089 A+B=C\tag*{something}\]
30096 \begin_layout Standard
30097 \begin_inset VSpace bigskip
30100 To restart the formula numbering with new document parts or sections, the
30101 following command is used:
30104 \begin_layout Standard
30109 @addtoreset{equation}{part}
30115 \begin_layout Plain Layout
30120 \begin_layout Plain Layout
30131 \begin_layout Plain Layout
30144 \begin_layout Plain Layout
30155 \begin_layout Plain Layout
30168 \begin_inset Newline newline
30172 \begin_inset Newline newline
30179 @addtoreset{equation}{section}
30182 \begin_layout Standard
30183 To be able to use these commands in TeX-mode, the
30184 \begin_inset Quotes eld
30188 \begin_inset Quotes erd
30191 character has to be made
30192 \begin_inset Quotes eld
30196 \begin_inset Quotes erd
30199 for LaTeX using the command
30213 So the command sequence in TeX-mode is:
30216 \begin_layout Standard
30222 \begin_inset Newline newline
30227 @addtoreset{equation}{section}
30228 \begin_inset Newline newline
30236 \begin_layout Standard
30237 In the LaTeX-preamble
30249 can be omitted as they are automatically internally inserted by LyX.
30252 \begin_layout Standard
30267 \begin_layout Plain Layout
30272 is part of the LaTeX-package
30280 \begin_layout Plain Layout
30281 Packages ! carlisle
30286 that is part of every LaTeX standard installation.
30295 \begin_layout Plain Layout
30296 Packages ! remreset
30301 has to be loaded in the LaTeX-preamble with the line
30304 \begin_layout Standard
30309 usepackage{remreset}
30312 \begin_layout Standard
30323 \begin_layout Plain Layout
30328 \begin_layout Plain Layout
30339 \begin_layout Plain Layout
30352 \begin_layout Plain Layout
30363 \begin_layout Plain Layout
30375 can be used with the same scheme as
30384 \begin_layout Standard
30385 \begin_inset VSpace bigskip
30388 Sometimes formulas should be numbered in the following form:
30391 \begin_layout Standard
30394 (section number.formula number)
30397 \begin_layout Standard
30398 The formula number should start with every section with
30399 \begin_inset Quotes eld
30403 \begin_inset Quotes erd
30409 \begin_layout Standard
30410 For this case there is the command
30420 \begin_layout Plain Layout
30428 , which is used with the following scheme:
30431 \begin_layout Standard
30436 numberwithin{counter}{sectioning}
30439 \begin_layout Standard
30440 Counter denotes what kind of numbering is affected, sectioning denotes what
30441 number is before the dot.
30444 \begin_layout Standard
30445 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30448 \begin_layout Standard
30453 numberwithin{equation}{section}
30456 \begin_layout Standard
30457 This is the result:
30461 \begin_layout Plain Layout
30465 numberwithin{equation}{section}
30471 \begin_inset Formula \begin{equation}
30472 A+B=C\end{equation}
30479 \begin_layout Standard
30481 \begin_inset space \thinspace{}
30485 \begin_inset space \space{}
30488 tables so that the number of the part is the sectioning,
30489 \begin_inset Newline newline
30496 numberwithin{table}{part}
30501 \begin_layout Standard
30502 To go back to the standard numbering or to prevent this kind of numbering
30503 when it is defined by the document class, the following command is inserted
30504 as TeX-Code or to the LaTeX-preamble:
30507 \begin_layout Standard
30520 \begin_layout Plain Layout
30534 \begin_layout Plain Layout
30550 \begin_inset Newline newline
30558 \begin_inset Newline newline
30570 \begin_layout Standard
30577 uses internally the command
30583 , described above, that also needs to be reverted.
30587 \begin_layout Plain Layout
30594 \begin_layout Plain Layout
30598 @removefromreset{equation}{section}
30601 \begin_layout Plain Layout
30613 \begin_layout Subsection
30614 Numbering with Roman Numbers and Letters
30618 \begin_layout Plain Layout
30619 Formula numbering ! with letters
30628 \begin_layout Plain Layout
30629 Formula numbering ! with Roman numbers
30637 \begin_layout Standard
30638 Formulas can also be numbered with Roman numbers and Latin letters.
30639 To number for example with small Roman numbers, the command
30642 \begin_layout Standard
30654 \begin_layout Standard
30655 is inserted before the formula in TeX-mode.
30666 \begin_layout Plain Layout
30674 redefines the predefined command
30690 \begin_layout Plain Layout
30697 has the same scheme like the command
30703 that is described in
30704 \begin_inset CommandInset ref
30706 reference "sub:The-Command-newcommand"
30719 is the formula counter.
30726 is used as prefix for a counter, the value of the counter is output as
30728 When a formula is numbered, LaTeX sets internally the command
30734 behind the formula.
30743 \begin_layout Plain Layout
30753 outputs the counter as small Roman number.
30756 \begin_layout Standard
30757 All formulas behind the command
30767 are now numbered Roman.
30768 To switch to numbering with big Roman numbers, the command is inserted
30785 \begin_layout Plain Layout
30797 \begin_inset Quotes eld
30801 \begin_inset Quotes erd
30804 with small Latin letters there is the command
30814 \begin_layout Plain Layout
30822 , for big ones there is the command
30832 \begin_layout Plain Layout
30845 \begin_layout Standard
30846 \begin_inset Note Greyedout
30849 \begin_layout Plain Layout
30854 Only maximal 26 formulas can be numbered with Latin letters in one document.
30862 \begin_layout Standard
30863 \begin_inset Newpage pagebreak
30869 \begin_layout Standard
30873 \begin_layout Plain Layout
30889 \begin_layout Standard
30890 \begin_inset Formula \begin{equation}
30891 A=\textrm{small roman}\end{equation}
30899 \begin_layout Plain Layout
30913 \begin_inset Formula \begin{equation}
30914 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30922 \begin_layout Plain Layout
30936 \begin_inset Formula \begin{equation}
30937 C=\textrm{small Latin}\end{equation}
30945 \begin_layout Plain Layout
30959 \begin_inset Formula \begin{equation}
30960 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30967 \begin_layout Standard
30968 To switch back to the default numbering, insert the command:
30971 \begin_layout Standard
30984 \begin_layout Plain Layout
30995 \begin_layout Standard
30999 \begin_layout Plain Layout
31013 \begin_inset Formula \begin{equation}
31014 E=\textrm{Arabic}\end{equation}
31021 \begin_layout Standard
31022 \begin_inset VSpace medskip
31025 As you see, formulas are numbered serially independent from the numbering
31027 When then numbering should start with
31028 \begin_inset Quotes eld
31032 \begin_inset Quotes erd
31035 when the style is changed, new equation counters have to be defined.
31036 A description about this can be found in the file
31037 \begin_inset CommandInset href
31039 name "Formula-numbering.lyx"
31040 target "run:Formula-numbering.lyx"
31047 \begin_layout Section
31048 Chemical Symbols and Equations
31049 \begin_inset CommandInset label
31051 name "sub:Chemical-Symbols-and"
31059 \begin_layout Plain Layout
31060 Chemical characters ! Symbols
31069 \begin_layout Plain Layout
31079 \begin_layout Plain Layout
31088 \begin_layout Standard
31089 An example text from chemistry:
31092 \begin_layout Quote
31094 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31097 -ion reacts with two
31098 \begin_inset Formula $\mathrm{Na^{+}}$
31101 -ions to sodium sulfate
31102 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31106 The chemical equation for this is:
31107 \begin_inset Formula \begin{equation}
31108 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31115 \begin_layout Standard
31116 This chemical equation can directly be created as formula.
31117 To avoid that the symbols appear italic, everything is highlighted and
31118 changed by the shortcut
31124 to the upright font style.
31128 \begin_layout Plain Layout
31134 \begin_inset CommandInset ref
31136 reference "sub:Font-Styles"
31148 \begin_layout Standard
31149 A more convenient way to typeset chemical formulas is to use the command
31160 \begin_layout Plain Layout
31168 that is available when the LaTeX-package
31176 \begin_layout Plain Layout
31187 \begin_layout Plain Layout
31197 \begin_inset Note Note
31200 \begin_layout Plain Layout
31201 The following will only be displayed when the LaTeX-package
31216 to a formula a new blue box appears where chemical formulas can be inserted
31217 in an intuitive way.
31220 \begin_layout Standard
31222 \begin_inset Tabular
31223 <lyxtabular version="3" rows="9" columns="2">
31225 <column alignment="center" valignment="top" width="0">
31226 <column alignment="center" valignment="top" width="0">
31228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31231 \begin_layout Plain Layout
31237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31240 \begin_layout Plain Layout
31242 \begin_inset Note Note
31245 \begin_layout Plain Layout
31252 is only used as spacer.
31264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31267 \begin_layout Plain Layout
31274 \begin_layout Plain Layout
31288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31291 \begin_layout Plain Layout
31292 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31305 \begin_layout Plain Layout
31312 \begin_layout Plain Layout
31326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31329 \begin_layout Plain Layout
31330 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31343 \begin_layout Plain Layout
31350 \begin_layout Plain Layout
31364 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31367 \begin_layout Plain Layout
31368 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31381 \begin_layout Plain Layout
31388 \begin_layout Plain Layout
31402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31405 \begin_layout Plain Layout
31406 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31419 \begin_layout Plain Layout
31426 \begin_layout Plain Layout
31441 \begin_layout Plain Layout
31456 \begin_layout Plain Layout
31470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31473 \begin_layout Plain Layout
31474 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31487 \begin_layout Plain Layout
31494 \begin_layout Plain Layout
31504 \begin_inset Formula $\downarrow$
31508 \begin_inset Formula $\to$
31516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31519 \begin_layout Plain Layout
31520 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31533 \begin_layout Plain Layout
31540 \begin_layout Plain Layout
31553 \begin_layout Plain Layout
31566 \begin_layout Plain Layout
31579 \begin_layout Plain Layout
31592 \begin_layout Plain Layout
31606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31609 \begin_layout Plain Layout
31610 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31623 \begin_layout Plain Layout
31630 \begin_layout Plain Layout
31643 \begin_layout Plain Layout
31656 \begin_layout Plain Layout
31669 \begin_layout Plain Layout
31686 \begin_layout Plain Layout
31700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31703 \begin_layout Plain Layout
31704 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31720 \begin_layout Standard
31721 \begin_inset Note Greyedout
31724 \begin_layout Plain Layout
31729 Inserting a formula to a
31735 box will lead to LaTeX errors.
31736 In this case TeX code has to be used like for
31750 \begin_layout Plain Layout
31771 \begin_layout Standard
31778 the command for equation
31779 \begin_inset space ~
31783 \begin_inset CommandInset ref
31785 reference "eq:chem-reaction"
31790 \begin_inset Newline newline
31801 \begin_layout Plain Layout
31814 \begin_layout Plain Layout
31827 \begin_layout Plain Layout
31840 \begin_layout Plain Layout
31853 \begin_layout Plain Layout
31866 \begin_layout Plain Layout
31878 \begin_layout Standard
31879 To create multiline chemical equations first a multiline formula is created
31881 \begin_inset CommandInset ref
31883 reference "sec:Multiline-Formulas"
31888 Afterwards the command
31894 is used in every small blue box of the formula.
31896 \begin_inset CommandInset ref
31898 reference "eq:TEOS-reaction-1"
31903 \begin_inset CommandInset ref
31905 reference "eq:TEOS-reaction-2"
31909 are an example of a multi-stage chemical reaction where every equation
31910 has its own number.
31911 \begin_inset Formula \begin{eqnarray}
31912 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31913 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
31920 \begin_layout Standard
31931 package provides the command
31941 \begin_layout Plain Layout
31949 that has to be used for special cases.
31950 For more information about
31956 and more examples have a look at the documentation of
31961 \begin_inset CommandInset citation
31970 \begin_layout Standard
31974 \begin_layout Plain Layout
31984 \begin_inset Note Note
31987 \begin_layout Plain Layout
31988 The following will be displayed when the LaTeX-package
32000 \begin_layout Standard
32001 You need to install the package
32005 to see the content of this section in the output.
32008 \begin_layout Standard
32012 \begin_layout Plain Layout
32024 \begin_layout Section
32028 \begin_layout Standard
32029 LyX supports two types of commutative diagrams:
32037 that are explained in the following.
32040 \begin_layout Subsection
32045 \begin_layout Plain Layout
32054 \begin_layout Standard
32055 Diagrams of this type visualize relations by vertical and horizontal lines
32057 \begin_inset Formula \[
32058 \begin{CD}A@>>>B@>>>C\\
32060 F@<<<E@<<<D\end{CD}\]
32067 \begin_layout Standard
32068 To get them, the command
32076 \begin_layout Plain Layout
32086 is inserted to a formula.
32087 A blue box appears with two dashed lines where further commands can be
32092 arg "newline-insert newline"
32095 a new line is created.
32096 Horizontal relations are inserted in odd, vertical in even formula lines.
32099 \begin_layout Standard
32100 To create the relations there are the following commands:
32103 \begin_layout Itemize
32108 creates a left arrow,
32119 \begin_layout Itemize
32124 creates an up arrow,
32132 a vertical equal sign
32135 \begin_layout Itemize
32141 is a placeholder for non-existent relations
32144 \begin_layout Standard
32145 All arrows can be labeled as follows:
32148 \begin_layout Itemize
32149 Is text inserted between the first and second < or >, resp., it is placed
32151 When it is inserted between the second and third one, it appears under
32155 \begin_layout Itemize
32156 When text for vertical arrows is inserted between the first and second A
32157 or V, resp., it is placed left beside the arrow.
32158 When it is inserted between the second and third one, it appears right
32160 If the text contains an A or V, these letters must be set into a TeX-brace.
32163 \begin_layout Standard
32164 As example a diagram with all possible relations:
32167 \begin_layout Standard
32168 \begin_inset Formula \[
32169 \begin{CD}A@>j>>B@>>k>C@=F\\
32171 D@<<j<E@>k>>F@=C\end{CD}\]
32178 \begin_layout Standard
32179 The command for this is:
32180 \begin_inset Newline newline
32191 \begin_layout Plain Layout
32200 A@>j>>B@>>k>C@=F Ctrl+Return
32201 \begin_inset Newline newline
32208 \begin_layout Plain Layout
32223 \begin_layout Plain Layout
32236 \begin_layout Plain Layout
32248 \begin_inset Formula $\to$
32254 \begin_inset Newline newline
32261 \begin_layout Plain Layout
32276 \begin_layout Plain Layout
32289 \begin_layout Plain Layout
32299 \begin_layout Subsection
32304 \begin_layout Plain Layout
32305 Diagrams ! xymatrix
32313 \begin_layout Standard
32314 To be able to use xymatrices, the LaTeX-package
32319 A xymatrix is created by inserting the command
32326 Then you are able to add new matrix columns and rows like for normal matrices,
32328 \begin_inset CommandInset ref
32330 reference "sec:Matrices"
32337 \begin_layout Standard
32338 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32340 All possibilities to create commutative diagrams and decorations are explained
32345 that you find in the menu
32347 Help\SpecialChar \menuseparator
32349 \begin_inset space ~
32352 Manuals\SpecialChar \menuseparator
32354 \begin_inset space ~
32362 \begin_layout Standard
32363 \begin_inset Newpage newpage
32369 \begin_layout Section
32370 User-defined Commands
32374 \begin_layout Plain Layout
32375 User-defined commands
32383 \begin_layout Standard
32384 \begin_inset Note Greyedout
32387 \begin_layout Plain Layout
32392 The names of user-defined commands and macros may only consist of Latin
32401 \begin_layout Subsection
32405 \begin_inset CommandInset label
32407 name "sub:The-Command-newcommand"
32415 \begin_layout Plain Layout
32416 User-defined commands !
32427 \begin_layout Plain Layout
32438 \begin_layout Standard
32439 Many LaTeX-commands are too long to be used frequently.
32440 But it is possible to define with the command
32446 new shorter commands.
32449 \begin_layout Standard
32450 The command scheme of
32459 \begin_layout Standard
32464 newcommand{new command name}[number of arguments][optional
32469 \begin_inset Newline newline
32476 \begin_layout Plain Layout
32491 \begin_layout Plain Layout
32498 {command definition}
32501 \begin_layout Standard
32502 \begin_inset Note Greyedout
32505 \begin_layout Plain Layout
32510 Assure that the name of the new command is not already used in your document
32511 or by LaTeX-packages that you use.
32512 When you for example define the command
32524 , you get an error message because
32530 is already defined as command for
32531 \begin_inset Quotes eld
32535 \begin_inset Formula $\le$
32539 \begin_inset Quotes erd
32550 \begin_layout Standard
32551 The number of arguments is an integer in the range 0
32552 \begin_inset space \thinspace{}
32556 \begin_inset space \thinspace{}
32559 9 and specifies how many arguments the new command should have.
32560 With the optional value a value for an optional argument can be predefined.
32561 When this is done, the
32569 rgument of the new command is automatically an optional one.
32572 \begin_layout Standard
32573 Here are some examples:
32576 \begin_layout Itemize
32577 To define the command
32589 , the LaTeX-preamble line is:
32590 \begin_inset VSpace medskip
32594 \begin_inset Newline newline
32608 \begin_layout Itemize
32609 To define the command
32621 , the argument (that should be underlined) must be taken into account.
32622 For this the preamble line is:
32623 \begin_inset VSpace medskip
32627 \begin_inset Newline newline
32641 \begin_inset VSpace medskip
32645 \begin_inset Newline newline
32652 acts as argument placeholder, the
32656 behind it denotes that it is the placeholder for the first argument.
32659 \begin_layout Itemize
32667 \begin_inset space \thinspace{}
32671 \begin_inset space \space{}
32681 \begin_inset VSpace medskip
32685 \begin_inset Newline newline
32696 framebox#1#2{$#3$}}
32699 \begin_inset VSpace medskip
32703 \begin_inset Newline newline
32706 The two Dollar signs creates the extra formula needed for
32713 \begin_inset CommandInset ref
32715 reference "sub:Boxes-with-Frame"
32722 \begin_layout Itemize
32723 To create a new command for
32729 where the color for the box needn't to be specified, the argument for the
32730 color is defined optional:
32731 \begin_inset VSpace medskip
32735 \begin_inset Newline newline
32746 fcolorbox{#2}{#1}{$#3$}}
32749 \begin_inset VSpace medskip
32753 \begin_inset Newline newline
32756 When the color is not specified when using
32762 , the predefined color
32769 \begin_layout Standard
32770 A test of the new defined commands:
32773 \begin_layout Standard
32775 \begin_inset Tabular
32776 <lyxtabular version="3" rows="6" columns="2">
32778 <column alignment="center" valignment="top" width="0">
32779 <column alignment="center" valignment="top" width="0">
32781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32784 \begin_layout Plain Layout
32790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32793 \begin_layout Plain Layout
32795 \begin_inset Note Note
32798 \begin_layout Plain Layout
32805 is only used as spacer.
32817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32820 \begin_layout Plain Layout
32827 \begin_layout Plain Layout
32841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32844 \begin_layout Plain Layout
32845 \begin_inset Formula $A\gr B$
32855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32858 \begin_layout Plain Layout
32866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32869 \begin_layout Plain Layout
32870 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32883 \begin_layout Plain Layout
32887 \begin_inset Formula $\to$
32893 \begin_inset Formula $\to$
32904 \begin_layout Plain Layout
32918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32921 \begin_layout Plain Layout
32922 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32935 \begin_layout Plain Layout
32939 \begin_inset Formula $\to$
32950 \begin_layout Plain Layout
32964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32967 \begin_layout Plain Layout
32968 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32981 \begin_layout Plain Layout
32987 \begin_inset Formula $\to$
32998 \begin_layout Plain Layout
33012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33015 \begin_layout Plain Layout
33016 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33032 \begin_layout Subsection
33037 \begin_layout Plain Layout
33038 User-defined commands! Math macros
33047 \begin_layout Plain Layout
33056 \begin_layout Standard
33057 User-defined commands are especially convenient for complex expressions.
33058 When you are for example dealing in a document with quadratic equations,
33059 the same solution type occurs several times.
33060 The general form of a quadratic equation is
33061 \begin_inset Formula \[
33062 0=\lambda^{2}+p\lambda+q\]
33066 The general form of the solution is
33067 \begin_inset Formula \[
33068 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33075 \begin_layout Standard
33076 To define a command for the solution formula where only the three parameters
33078 \begin_inset Formula $\lambda$
33082 \begin_inset Formula $p$
33086 \begin_inset Formula $q$
33089 need to be specified and the index of
33090 \begin_inset Formula $\lambda$
33093 can be given optionally, the LaTeX-preamble line is
33094 \begin_inset Newline newline
33110 \begin_inset Newline newline
33117 \begin_layout Plain Layout
33132 \begin_layout Plain Layout
33143 frac{#3^{2}}{4}-#4}}
33146 \begin_layout Standard
33147 To create with this the solution formula, the command
33148 \begin_inset Newline newline
33158 \begin_inset Formula $\to$
33164 \begin_inset Formula $\to$
33171 is inserted to a formula
33176 \begin_layout Standard
33177 The definition of the new command is unintuitive because one has to know
33178 the schemes of all used LaTeX commands, e.
33179 \begin_inset space \thinspace{}
33183 \begin_inset space \space{}
33186 that a fraction is inserted in LaTeX as
33190 frac{numerator}{denominator}
33193 Furthermore one can easily forget a brace in the definition and cannot
33194 see in LyX what the new command is doing.
33195 To avoid these problems LyX offers the possibility to use math macros instead
33205 \begin_layout Standard
33206 A math macro is created by using the menu
33208 Insert\SpecialChar \menuseparator
33209 Math\SpecialChar \menuseparator
33212 or the toolbar button
33213 \begin_inset Graphics
33214 filename ../images/math-macro_newmacroname_newcommand.png
33220 The math macro toolbar appears together with the following box where the
33222 \begin_inset Newline newline
33226 \begin_inset space \hspace*{\fill}
33230 \begin_inset Graphics
33231 filename clipart/macrobox.png
33236 \begin_inset space \hspace*{\fill}
33240 \begin_inset Newline newline
33244 \begin_inset FormulaMacro
33245 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33250 newmacroname is the default name of the macro that should be changed to
33251 something sensible.
33252 The wanted formula is inserted in the first blue box.
33253 An argument placeholder is inserted with the command
33260 \begin_inset space \thinspace{}
33264 \begin_inset space \space{}
33273 or by using the macro toolbar button
33274 \begin_inset Graphics
33275 filename ../images/math-macro-add-param.png
33281 Argument placeholders are displayed red.
33282 Maximum 9 arguments are possible.
33283 Optional arguments are created with the toolbar button
33284 \begin_inset Graphics
33285 filename ../images/math-macro-add-optional-param.png
33291 The first non-optional argument can be transformed to an optional one with
33293 \begin_inset Graphics
33294 filename ../images/math-macro-make-optional.png
33300 In the second blue box the appearance of the macro in LyX can be defined.
33301 Normally you want to see it as it is defined, so the box is kept empty.
33302 But when you have created a macro that needs lot of space on the screen,
33303 you can insert in the box for example
33304 \begin_inset Newline newline
33334 \begin_inset Newline newline
33339 For the macro only the arguments with the macro name in front of them will
33340 then be displayed in LyX, leading to a better overview.
33341 The formula appears in the output as defined in the first box.
33342 \begin_inset Newline newline
33345 The appearance of macros in formulas can furthermore be changed for single
33346 macros by setting the cursor in the macro and using the menu
33348 View\SpecialChar \menuseparator
33350 \begin_inset space ~
33354 \begin_inset space ~
33362 \begin_layout Standard
33363 To use a macro, the macro name is inserted as command to a formula, in our
33371 Our macro looks in LyX like this:
33372 \begin_inset Newline newline
33376 \begin_inset space \hspace*{\fill}
33380 \begin_inset Graphics
33381 filename clipart/macrouse.png
33386 \begin_inset space \hspace*{\fill}
33390 \begin_inset Newline newline
33393 Here is our macro example with the arguments
33394 \begin_inset Formula $x$
33398 \begin_inset Formula $\ln(x)$
33402 \begin_inset Formula $B$
33408 \begin_layout Standard
33409 \begin_inset Formula \[
33417 \begin_layout Standard
33418 LyX offers in the menu
33420 Tools\SpecialChar \menuseparator
33421 Preferences\SpecialChar \menuseparator
33422 Editing\SpecialChar \menuseparator
33425 different styles to edit macros.
33426 To find the style that suits you the most, choose a style and set the cursor
33427 in a macro formula to see the difference.
33430 \begin_layout Standard
33431 A math macro is transformed internally to a
33437 command when exporting the document.
33444 command is not placed in the LaTeX-preamble, therefore macros can only
33445 be used in formulas that are in the document below the macro definition
33449 \begin_layout Standard
33450 Math macros can also be directly be created from a
33457 When writing for example the command
33460 \begin_inset Newline newline
33469 xleftarrow[#2]{#1}}
33470 \begin_inset Newline newline
33475 in LyX as normal text, highlighting it completely and using then the shortcut
33480 , the command will be transformed to a math macro.
33481 Using this method you need to be careful that the
33487 command is typed correctly, otherwise you get a faulty macro leading to
33491 \begin_layout Standard
33492 Math macros currently yet have the problem that further formulas in macro
33493 definitions are handled wrongly.
33494 Therefore the example
33501 \begin_inset CommandInset ref
33503 reference "sub:The-Command-newcommand"
33507 cannot be created as macro.
33510 \begin_layout Standard
33511 When the cursor is in a macro definition box, you will see the macro toolbar
33515 \begin_layout Standard
33516 \begin_inset VSpace defskip
33522 \begin_layout Standard
33523 \begin_inset Graphics
33524 filename clipart/MacroToolbar.png
33532 \begin_layout Plain Layout
33541 \begin_layout Standard
33542 \begin_inset VSpace defskip
33548 \begin_layout Standard
33549 The macro toolbar contains from left to right the following buttons:
33552 \begin_layout Standard
33553 \begin_inset VSpace defskip
33559 \begin_layout Standard
33560 \begin_inset Tabular
33561 <lyxtabular version="3" rows="9" columns="2">
33562 <features islongtable="true">
33563 <column alignment="left" valignment="top" width="0">
33564 <column alignment="left" valignment="top" width="85col%">
33565 <row interlinespace="2.5mm">
33566 <cell alignment="center" valignment="top" usebox="none">
33569 \begin_layout Plain Layout
33570 \begin_inset Graphics
33571 filename ../images/math-macro-remove-param.png
33572 BoundingBox 0bp 5bp 20bp 25bp
33573 rotateOrigin center
33582 <cell alignment="center" valignment="top" usebox="none">
33585 \begin_layout Plain Layout
33588 Edit\SpecialChar \menuseparator
33589 Math\SpecialChar \menuseparator
33591 \begin_inset space ~
33594 Definition\SpecialChar \menuseparator
33595 Remove Last Argument
33601 <row interlinespace="2.5mm">
33602 <cell alignment="center" valignment="top" usebox="none">
33605 \begin_layout Plain Layout
33606 \begin_inset Graphics
33607 filename ../images/math-macro-add-param.png
33608 BoundingBox 0bp 5bp 20bp 25bp
33609 rotateOrigin center
33618 <cell alignment="center" valignment="top" usebox="none">
33621 \begin_layout Plain Layout
33624 Edit\SpecialChar \menuseparator
33625 Math\SpecialChar \menuseparator
33627 \begin_inset space ~
33630 Definition\SpecialChar \menuseparator
33637 <row interlinespace="2.5mm">
33638 <cell alignment="center" valignment="top" usebox="none">
33641 \begin_layout Plain Layout
33642 \begin_inset Graphics
33643 filename ../images/math-macro-make-optional.png
33644 BoundingBox 0bp 5bp 20bp 25bp
33645 rotateOrigin center
33654 <cell alignment="center" valignment="top" usebox="none">
33657 \begin_layout Plain Layout
33660 Edit\SpecialChar \menuseparator
33661 Math\SpecialChar \menuseparator
33663 \begin_inset space ~
33666 Definition\SpecialChar \menuseparator
33667 Make First Non-Optional into
33668 \begin_inset Newline newline
33675 \begin_layout Plain Layout
33684 Edit\SpecialChar \menuseparator
33685 Math\SpecialChar \menuseparator
33687 \begin_inset space ~
33690 Definition\SpecialChar \menuseparator
33695 \begin_layout Plain Layout
33708 <row interlinespace="2.5mm">
33709 <cell alignment="center" valignment="top" usebox="none">
33712 \begin_layout Plain Layout
33713 \begin_inset Graphics
33714 filename ../images/math-macro-make-nonoptional.png
33715 BoundingBox 0bp 5bp 20bp 25bp
33716 rotateOrigin center
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33731 Edit\SpecialChar \menuseparator
33732 Math\SpecialChar \menuseparator
33734 \begin_inset space ~
33737 Definition\SpecialChar \menuseparator
33738 Make Last Optional into
33739 \begin_inset Newline newline
33746 \begin_layout Plain Layout
33755 Edit\SpecialChar \menuseparator
33756 Math\SpecialChar \menuseparator
33758 \begin_inset space ~
33761 Definition\SpecialChar \menuseparator
33766 \begin_layout Plain Layout
33773 Non-Optional Argument
33779 <row interlinespace="2.5mm">
33780 <cell alignment="center" valignment="top" usebox="none">
33783 \begin_layout Plain Layout
33784 \begin_inset Graphics
33785 filename ../images/math-macro-remove-optional-param.png
33786 BoundingBox 0bp 5bp 20bp 25bp
33787 rotateOrigin center
33796 <cell alignment="center" valignment="top" usebox="none">
33799 \begin_layout Plain Layout
33802 Edit\SpecialChar \menuseparator
33803 Math\SpecialChar \menuseparator
33805 \begin_inset space ~
33808 Definition\SpecialChar \menuseparator
33809 Remove Optional Argument
33815 <row interlinespace="2.5mm">
33816 <cell alignment="center" valignment="top" usebox="none">
33819 \begin_layout Plain Layout
33820 \begin_inset Graphics
33821 filename ../images/math-macro-add-optional-param.png
33822 BoundingBox 0bp 5bp 20bp 25bp
33823 rotateOrigin center
33832 <cell alignment="center" valignment="top" usebox="none">
33835 \begin_layout Plain Layout
33838 Edit\SpecialChar \menuseparator
33839 Math\SpecialChar \menuseparator
33841 \begin_inset space ~
33844 Definition\SpecialChar \menuseparator
33845 Insert Optional Argument
33851 <row interlinespace="2.5mm">
33852 <cell alignment="center" valignment="top" usebox="none">
33855 \begin_layout Plain Layout
33856 \begin_inset Graphics
33857 filename ../images/math-macro-remove-greedy-param.png
33858 BoundingBox 0bp 5bp 20bp 25bp
33859 rotateOrigin center
33868 <cell alignment="center" valignment="top" usebox="none">
33871 \begin_layout Plain Layout
33874 Edit\SpecialChar \menuseparator
33875 Math\SpecialChar \menuseparator
33877 \begin_inset space ~
33880 Definition\SpecialChar \menuseparator
33881 Remove Last Argument
33882 \begin_inset Newline newline
33889 \begin_layout Plain Layout
33898 Edit\SpecialChar \menuseparator
33899 Math\SpecialChar \menuseparator
33901 \begin_inset space ~
33904 Definition\SpecialChar \menuseparator
33909 \begin_layout Plain Layout
33916 Spitting Out To The Right
33922 <row interlinespace="2.5mm">
33923 <cell alignment="center" valignment="top" usebox="none">
33926 \begin_layout Plain Layout
33927 \begin_inset Graphics
33928 filename ../images/math-macro-append-greedy-param.png
33929 BoundingBox 0bp 5bp 20bp 25bp
33930 rotateOrigin center
33939 <cell alignment="center" valignment="top" usebox="none">
33942 \begin_layout Plain Layout
33945 Edit\SpecialChar \menuseparator
33946 Math\SpecialChar \menuseparator
33948 \begin_inset space ~
33951 Definition\SpecialChar \menuseparator
33953 \begin_inset Newline newline
33960 \begin_layout Plain Layout
33969 Edit\SpecialChar \menuseparator
33970 Math\SpecialChar \menuseparator
33972 \begin_inset space ~
33975 Definition\SpecialChar \menuseparator
33980 \begin_layout Plain Layout
33987 Eating From The Right
33993 <row interlinespace="2.5mm">
33994 <cell alignment="center" valignment="top" usebox="none">
33997 \begin_layout Plain Layout
33998 \begin_inset Graphics
33999 filename ../images/math-macro-add-greedy-optional-param.png
34000 BoundingBox 0bp 5bp 20bp 25bp
34001 rotateOrigin center
34010 <cell alignment="center" valignment="top" usebox="none">
34013 \begin_layout Plain Layout
34016 Edit\SpecialChar \menuseparator
34017 Math\SpecialChar \menuseparator
34019 \begin_inset space ~
34022 Definition\SpecialChar \menuseparator
34023 Append Optional Argument
34024 \begin_inset Newline newline
34031 \begin_layout Plain Layout
34040 Edit\SpecialChar \menuseparator
34041 Math\SpecialChar \menuseparator
34043 \begin_inset space ~
34046 Definition\SpecialChar \menuseparator
34051 \begin_layout Plain Layout
34058 Eating From The Right
34071 \begin_layout Standard
34072 \begin_inset Newpage newpage
34078 \begin_layout Section
34083 \begin_layout Plain Layout
34096 \begin_layout Plain Layout
34097 Other useful math tips can be found in
34098 \begin_inset CommandInset citation
34113 \begin_layout Plain Layout
34121 \begin_inset Note Note
34124 \begin_layout Plain Layout
34127 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
34130 \begin_layout Plain Layout
34133 texorpdfstring is in section
34134 \begin_inset CommandInset ref
34136 reference "sub:Formulas-in-Section"
34149 \begin_layout Plain Layout
34159 \begin_layout Plain Layout
34164 \begin_layout Plain Layout
34171 Chemical characters
34175 \begin_layout Plain Layout
34190 \begin_layout Subsection
34195 \begin_layout Plain Layout
34204 \begin_layout Standard
34205 Negative numbers often look ugly in formulas because the minus sign before
34206 the number is set with the same length as the minus operator sign.
34207 When writing the negative number in normal text, the minus sign appears
34211 \begin_layout Standard
34212 Thus, the problem disappears when converting the minus sign to mathematical
34216 \begin_layout Standard
34217 An example to visualize the problem:
34220 \begin_layout Standard
34222 \begin_inset Tabular
34223 <lyxtabular version="3" rows="3" columns="2">
34225 <column alignment="right" valignment="top" width="0">
34226 <column alignment="left" valignment="top" width="0">
34228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34231 \begin_layout Plain Layout
34237 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34240 \begin_layout Plain Layout
34248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34251 \begin_layout Plain Layout
34257 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34260 \begin_layout Plain Layout
34261 \begin_inset Formula $x=-2$
34271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34274 \begin_layout Plain Layout
34280 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34283 \begin_layout Plain Layout
34284 \begin_inset Formula $x=\textrm{-}2$
34300 \begin_layout Subsection
34301 Comma as decimal Separator
34305 \begin_layout Plain Layout
34314 \begin_layout Standard
34315 In LaTeX a comma inside a formula is used, according to the English convention,
34316 as number group separator.
34317 So there will be space added behind all commas in formulas.
34320 \begin_layout Standard
34321 To avoid this, the comma is highlighted and changed to mathematical text
34331 \begin_layout Standard
34332 To use all formula commas in the document as decimal separator, the file
34341 \begin_layout Plain Layout
34346 is part of the LaTeX-package
34354 \begin_layout Plain Layout
34359 \begin_layout Plain Layout
34382 \begin_layout Plain Layout
34388 is loaded with the LaTeX-preamble line
34391 \begin_layout Standard
34399 \begin_layout Subsection
34401 \begin_inset CommandInset label
34403 name "sub:Physical-Vectors"
34411 \begin_layout Plain Layout
34420 \begin_layout Standard
34421 Predefined vectors are offered by the LaTeX-package
34429 \begin_layout Plain Layout
34434 should be part of every LaTeX standard installation.
34443 \begin_layout Plain Layout
34449 that is loaded with the LaTeX-preamble line
34452 \begin_layout Standard
34460 \begin_layout Standard
34464 \begin_layout Plain Layout
34474 \begin_inset Note Note
34477 \begin_layout Plain Layout
34478 The following table will only be displayed when the LaTeX-package
34487 The following commands are defined:
34490 \begin_layout Standard
34492 \begin_inset Tabular
34493 <lyxtabular version="3" rows="4" columns="2">
34495 <column alignment="center" valignment="top" width="0">
34496 <column alignment="center" valignment="top" width="0">
34498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34501 \begin_layout Plain Layout
34507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34510 \begin_layout Plain Layout
34518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34521 \begin_layout Plain Layout
34531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34534 \begin_layout Plain Layout
34535 \begin_inset Formula $\Bra{\psi}$
34545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34548 \begin_layout Plain Layout
34558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34561 \begin_layout Plain Layout
34562 \begin_inset Formula $\Ket{\psi}$
34572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34575 \begin_layout Plain Layout
34587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34590 \begin_layout Plain Layout
34591 \begin_inset Formula $\Braket{\psi|\phi}$
34607 \begin_layout Standard
34614 assures that all vertical bars are set in the size of the surrounding brackets:
34615 \begin_inset Formula \[
34616 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34624 \begin_layout Plain Layout
34634 \begin_inset Note Note
34637 \begin_layout Plain Layout
34638 The following will be displayed when the LaTeX-package
34650 \begin_layout Standard
34651 You need to install the LaTeX-package
34655 to see the rest of this subsection in the output.
34658 \begin_layout Standard
34662 \begin_layout Plain Layout
34674 \begin_layout Standard
34681 can also be achieved using the command
34687 , that is described in
34688 \begin_inset CommandInset ref
34690 reference "sub:Automatic-Bracket-Size"
34697 \begin_layout Subsection
34698 Self-defined Fractions
34699 \begin_inset CommandInset label
34701 name "sub:Self-defined-Fractions"
34709 \begin_layout Plain Layout
34710 Fractions ! self-defined
34718 \begin_layout Standard
34719 To define custom commands for fractions, the command
34729 \begin_layout Plain Layout
34737 is used in the following scheme:
34740 \begin_layout Standard
34753 bracket}{fraction bar thickness}{style}
34754 \begin_inset Newline newline
34761 \begin_layout Plain Layout
34776 \begin_layout Plain Layout
34783 {numerator}{denominator}
34786 \begin_layout Standard
34787 The style is a number in the range of 0
34788 \begin_inset space \thinspace{}
34792 \begin_inset space \thinspace{}
34798 \begin_layout Standard
34800 \begin_inset Tabular
34801 <lyxtabular version="3" rows="5" columns="2">
34803 <column alignment="center" valignment="top" width="0">
34804 <column alignment="center" valignment="top" width="0">
34806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34809 \begin_layout Plain Layout
34815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34818 \begin_layout Plain Layout
34826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34829 \begin_layout Plain Layout
34835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34838 \begin_layout Plain Layout
34839 display style formula
34846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34849 \begin_layout Plain Layout
34855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34858 \begin_layout Plain Layout
34866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34869 \begin_layout Plain Layout
34875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34878 \begin_layout Plain Layout
34886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34889 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34898 \begin_layout Plain Layout
34912 \begin_layout Standard
34913 When no style is given, the size is adjusted to the surrounding environment
34914 like for the command
34923 \begin_layout Standard
34924 When no fraction bar thickness is given, the predefined value of 0.4
34925 \begin_inset space \thinspace{}
34931 \begin_layout Standard
34932 \begin_inset VSpace medskip
34935 For example, the commands
34948 \begin_inset CommandInset ref
34950 reference "sub:Fractions"
34954 are defined with the commands
34957 \begin_layout Standard
34966 genfrac{}{}{}{0}{#1}{#2}}
34969 \begin_layout Standard
34973 \begin_layout Standard
34982 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34985 \begin_layout Standard
34986 \begin_inset VSpace medskip
34989 To define a fraction where the fraction bar thickness can be given as optional
34990 argument, the following line is inserted to the LaTeX-preamble:
34993 \begin_layout Standard
35002 genfrac{}{}{#1}{}{#2}{#3}}
35005 \begin_layout Standard
35007 \begin_inset Formula \begin{align*}
35008 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35009 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
35013 As one can see, the distance of the numerator and the denominator to the
35014 fraction bar is round about three times the bar thickness.
35017 \begin_layout Subsection
35022 \begin_layout Plain Layout
35031 \begin_layout Standard
35032 To cancel formulas or formula parts, the LaTeX-package
35040 \begin_layout Plain Layout
35045 is part of every LaTeX standard installation.
35054 \begin_layout Plain Layout
35060 has to be loaded with the LaTeX-preamble line
35063 \begin_layout Standard
35068 usepackage[samesize]{cancel}
35071 \begin_layout Standard
35072 There are four ways to cancel formulas:
35075 \begin_layout Standard
35077 \begin_inset Tabular
35078 <lyxtabular version="3" rows="5" columns="2">
35080 <column alignment="center" valignment="top" width="0">
35081 <column alignment="center" valignment="top" width="0">
35083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35086 \begin_layout Plain Layout
35092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35095 \begin_layout Plain Layout
35097 \begin_inset Note Note
35100 \begin_layout Plain Layout
35107 are used here as spacer.
35119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35122 \begin_layout Plain Layout
35131 \begin_layout Plain Layout
35145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35148 \begin_layout Plain Layout
35149 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35162 \begin_layout Plain Layout
35171 \begin_layout Plain Layout
35185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35188 \begin_layout Plain Layout
35189 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35202 \begin_layout Plain Layout
35211 \begin_layout Plain Layout
35225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35228 \begin_layout Plain Layout
35229 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35242 \begin_layout Plain Layout
35246 \begin_inset Formula $\to$
35257 \begin_layout Plain Layout
35271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35274 \begin_layout Plain Layout
35275 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35291 \begin_layout Standard
35298 is especially suitable to visualize the reduction of fractions within formulas:
35299 \begin_inset Formula \[
35300 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35307 \begin_layout Subsection
35308 Formulas in Section Headings
35309 \begin_inset CommandInset label
35311 name "sub:Formulas-in-Section"
35319 \begin_layout Plain Layout
35320 Formula ! in section headings
35328 \begin_layout Standard
35329 When formulas are used in section headings, the following has to be taken
35333 \begin_layout Standard
35334 \begin_inset Note Greyedout
35337 \begin_layout Plain Layout
35346 \begin_layout Plain Layout
35347 Packages ! hyperref
35352 support is enabled in the document settings dialog under
35355 \begin_inset space ~
35360 , PDF-bookmarks are created for every section heading in the table of contents.
35361 If a section heading contains formulas, they are incorrectly displayed
35362 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35371 \begin_layout Standard
35372 Both problems can be solved by inserting at the end of the section heading
35373 a short title with the menu
35375 Insert\SpecialChar \menuseparator
35377 \begin_inset space ~
35383 Short titles are used as alternative for multiline section headings to
35384 keep the table of contents clearly arranged.
35385 Only the short title appears in the table of contents and therefore also
35386 in the PDF-bookmark.
35389 \begin_layout Standard
35390 When formulas should be used in the table of contents but
35394 is used, one can use the following command in TeX-mode:
35397 \begin_layout Standard
35402 texorpdfstring{part}{alternative}
35406 \begin_layout Plain Layout
35417 \begin_layout Standard
35418 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35419 This can be characters, formulas, footnotes, but also cross-references.
35420 The alternative is used instead of the part for the bookmark.
35423 \begin_layout Standard
35424 Here are two example headings:
35425 \begin_inset VSpace -3mm
35432 \begin_layout Plain Layout
35444 \begin_layout Subsubsection
35445 Heading without formula in table of contents
35446 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35450 \begin_inset OptArg
35453 \begin_layout Plain Layout
35454 Heading without formula in table of contents
35462 \begin_layout Subsubsection
35463 Heading with formula in table of contents
35467 \begin_layout Plain Layout
35477 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35484 \begin_layout Plain Layout
35494 \begin_layout Standard
35498 \begin_layout Plain Layout
35507 In the first heading a short title was used, in the second one
35516 \begin_layout Standard
35517 To get the same formatting as for the other headings, the complete heading
35526 \begin_layout Plain Layout
35528 \begin_inset CommandInset ref
35530 reference "sub:Bold-Formulas"
35542 \begin_layout Subsection
35543 Formulas in multi-column Text
35547 \begin_layout Plain Layout
35548 Formula ! in multi-column text
35556 \begin_layout Standard
35557 Formulas in multi-column text are often too wide to fit into a column and
35558 thus need to be set over the whole page width.
35559 This is done by using the LaTeX-package
35567 \begin_layout Plain Layout
35572 is part of every LaTeX standard installation.
35581 \begin_layout Plain Layout
35582 Packages ! multicol
35587 , that is loaded with the LaTeX-preamble line
35590 \begin_layout Standard
35595 usepackage{multicol}
35598 \begin_layout Standard
35599 \begin_inset Note Greyedout
35602 \begin_layout Plain Layout
35603 Note herby that the setting
35606 \begin_inset space ~
35613 Document\SpecialChar \menuseparator
35619 \begin_inset space ~
35639 \begin_layout Standard
35640 Before the multi-column text the command
35643 \begin_layout Standard
35648 begin{multicols}{column number}
35651 \begin_layout Standard
35652 is written in TeX-mode.
35653 The column number is a number in the range of 2
35654 \begin_inset space \thinspace{}
35658 \begin_inset space \thinspace{}
35662 Before the formula the multi-column text is ended by inserting the command
35665 \begin_layout Standard
35673 \begin_layout Standard
35677 \begin_layout Standard
35678 Due to the command some space is automatically added before the formula.
35680 \begin_inset space \thinspace{}
35683 mm vertical space is inserted before the formula.
35684 When the formula style
35690 \begin_layout Plain Layout
35692 \begin_inset CommandInset ref
35694 reference "sec:Formula-Styles"
35706 \begin_inset space \thinspace{}
35709 mm space is inserted instead.
35712 \begin_layout Standard
35713 As example a multi-column text with a displayed formula:
35716 \begin_layout Standard
35722 \begin_layout Plain Layout
35726 begin{multicols}{2}
35731 Das Spektrum wird fouriertransformiert.
35732 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35733 , Lösungsmittel) zu trennen.
35734 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35735 nun das Aussehen des Ausgangssignals.
35736 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35737 über alle Phasen integrieren muss.
35739 \begin_inset Formula $S$
35742 unser normiertes Ausgangssignal und
35743 \begin_inset Formula $P$
35746 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35750 \begin_layout Plain Layout
35760 \begin_inset VSpace -6mm
35764 \begin_inset Formula \begin{equation}
35765 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35773 \begin_layout Plain Layout
35777 begin{multicols}{2}
35783 \begin_inset Formula $S_{0}$
35786 das Signal ohne Gradient ist und die Normierungsbedingung
35787 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35791 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35793 \begin_inset Formula $\nicefrac{\pi}{2}$
35797 \begin_inset space \thinspace{}
35800 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35801 das Signal zusätzlich abschwächt.
35802 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35804 \begin_inset Formula $T_{2}$
35810 \begin_layout Standard
35816 \begin_layout Plain Layout
35828 \begin_layout Subsection
35829 Formulas with Description of Variables
35833 \begin_layout Plain Layout
35834 Formula ! with description of variables
35842 \begin_layout Standard
35843 To describe variables within a formula, like in formula
35844 \begin_inset CommandInset ref
35846 reference "eq:within"
35855 \begin_inset Formula $n$
35859 \begin_inset space ~
35862 matrix is used with left aligned columns for the
35863 \begin_inset Formula $n$
35870 \begin_layout Plain Layout
35872 \begin_inset CommandInset ref
35874 reference "sec:Matrices"
35883 To set the description in a smaller size, before the matrix e.
35884 \begin_inset space \thinspace{}
35888 \begin_inset space \space{}
35901 \begin_layout Plain Layout
35903 \begin_inset CommandInset ref
35905 reference "sub:Font-Sizes"
35917 \begin_layout Standard
35918 When the formula style
35924 \begin_layout Plain Layout
35926 \begin_inset CommandInset ref
35928 reference "sec:Formula-Styles"
35949 \begin_layout Plain Layout
35956 only works in formulas with the style
35961 \begin_inset CommandInset ref
35963 reference "sub:Variable-Space"
35972 is inserted before and after the matrix to have the same separation of
35973 the matrix from the equation and the side margin.
35976 \begin_layout Standard
35977 When the formula style
35981 is used, the method described in
35982 \begin_inset CommandInset ref
35984 reference "sub:Flalign-Environment"
35988 is used to indent formulas.
35990 \begin_inset CommandInset ref
35992 reference "eq:within"
35996 consists of five columns whereas in the first two columns contain the equation,
35997 the third the matrix, and the last one an empty TeX-brace.
35998 \begin_inset Formula \begin{flalign}
35999 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36000 \rho & \textrm{density}\\
36001 V & \textrm{volume}\\
36002 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
36009 \begin_layout Subsection
36010 Upright small Greek Letters
36011 \begin_inset CommandInset label
36013 name "sub:Upright-small-Greek"
36021 \begin_layout Plain Layout
36022 Greek letters ! upright
36030 \begin_layout Standard
36031 Most of the math fonts only provide italic small Greek letters.
36032 But for symbols of elementary particles like pions and neutrinos, upright
36033 Greek letters are needed.
36042 \begin_layout Plain Layout
36047 is part of the LaTeX-package
36055 \begin_layout Plain Layout
36060 \begin_layout Plain Layout
36083 \begin_layout Plain Layout
36089 that is loaded with the LaTeX-preamble line
36092 \begin_layout Standard
36097 usepackage{upgreek}
36100 \begin_layout Standard
36106 \begin_layout Plain Layout
36116 \begin_inset Note Note
36119 \begin_layout Plain Layout
36120 The following table will only be displayed when the LaTeX-package
36129 They are created when the command for a small Greek letters is started
36135 For example the command
36142 \begin_inset Formula $\uptau$
36148 \begin_layout Standard
36149 With these commands reactions of elementary particles can be typeset:
36150 \begin_inset Formula \[
36151 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36158 \begin_layout Standard
36159 The upright letters are more bold and wider than the italic ones.
36160 They should therefore not be used for units like
36161 \begin_inset Quotes eld
36165 \begin_inset Quotes erd
36171 \begin_layout Standard
36175 \begin_layout Plain Layout
36185 \begin_inset Note Note
36188 \begin_layout Plain Layout
36189 The following will be displayed when the LaTeX-package
36201 \begin_layout Standard
36202 You need to install the LaTeX-package
36206 to see the rest of this subsection in the output.
36209 \begin_layout Standard
36213 \begin_layout Plain Layout
36225 \begin_layout Subsection
36226 Text Characters in Formulas
36227 \begin_inset CommandInset label
36229 name "sub:Text-Characters-in"
36237 \begin_layout Plain Layout
36246 \begin_layout Standard
36247 In some cases you might want to insert text characters directly into formulas.
36248 When for example the centered dot · is often used in formulas like
36249 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36252 , one would have to insert the command
36262 \begin_layout Plain Layout
36264 \begin_inset CommandInset ref
36266 reference "sub:Binary-Operators"
36275 all the time, because this character is defined in all encodings as text
36277 But the encoding can be changed by this LaTeX-preamble line:
36280 \begin_layout Standard
36285 Declare Inputtext{183}{
36295 f\SpecialChar \textcompwordmark{}
36299 \begin_layout Standard
36300 The character encoding (menu
36302 Document\SpecialChar \menuseparator
36303 Settings\SpecialChar \menuseparator
36306 ) specifies what character appears when a keyboard key is pressed.
36307 When the key for the character '·' is pressed, internally the command
36314 But this command is not available in a formula so that you would get LaTeX-erro
36316 With the changed encoding the right command is chosen automatically, depending
36317 on if the character was inserted into a formula or not.
36320 \begin_layout Standard
36321 The encoding of several characters is saved in definition files.
36322 Fore example the encoding
36326 is defined in the file
36330 that is in the installation folder of LaTeX.
36331 Encodings should only be changed via the LaTeX-preamble and not in the
36333 Otherwise own documents could not be edited by other LyX users working
36334 on other computers.
36337 \begin_layout Standard
36338 \begin_inset VSpace medskip
36341 Besides the centered dot, in this document the degree sign ° is defined
36342 with the following LaTeX-preamble line so that it can directly be inserted
36346 \begin_layout Standard
36351 DeclareInputtext{176}{
36361 f\SpecialChar \textcompwordmark{}
36365 \begin_layout Standard
36366 \begin_inset Newpage newpage
36372 \begin_layout Section
36378 \begin_layout Plain Layout
36387 \begin_layout Standard
36388 This section is a summary of the most important typographic rules, listed
36393 \begin_layout Plain Layout
36394 This collection was partly taken from the German semi-official dictionary
36396 \begin_inset Quotes eld
36400 \begin_inset Quotes erd
36404 \begin_inset CommandInset citation
36410 that lists some of the ISO rules.
36418 \begin_layout Itemize
36427 \begin_layout Plain Layout
36428 done with font styles, see
36429 \begin_inset CommandInset ref
36431 reference "sub:Font-Styles"
36441 \begin_inset space \thinspace{}
36445 \begin_inset Newline newline
36448 Between the value and the unit is the smallest space, see
36449 \begin_inset CommandInset ref
36451 reference "sub:Predefined-Space"
36456 \begin_inset Newline newline
36459 This convention is automatically fulfilled when the command
36466 When it is entered to a formula, two boxes appear.
36467 In the first one the value is inserted, in the second one the unit, and
36469 \begin_inset Formula $\unit[30]{km/h}$
36473 \begin_inset space \thinspace{}
36483 is not a real LaTeX command but the command
36489 , therefore you cannot use it in TeX code.
36492 \begin_layout Itemize
36493 Percent and perthousand signs are set like physical units:
36494 \begin_inset Newline newline
36498 \begin_inset space \thinspace{}
36504 \begin_layout Itemize
36505 The degree sign follows directly on the value: 15°, but not when it is used
36507 \begin_inset space \thinspace{}
36513 \begin_layout Itemize
36514 In numbers with more than four digits the smallest space is inserted before
36515 every third digit to group them:
36525 \begin_inset space \thinspace{}
36529 \begin_inset space \thinspace{}
36535 \begin_layout Itemize
36536 For dimensions like 120×90×40
36537 \begin_inset space \thinspace{}
36540 cm the multiplication sign
36541 \begin_inset Quotes eld
36545 \begin_inset Quotes erd
36549 It is available either via the command
36557 Insert\SpecialChar \menuseparator
36558 Special Character\SpecialChar \menuseparator
36564 \begin_layout Itemize
36565 Functions with names consisting of several letters are set upright to avoid
36567 \begin_inset CommandInset ref
36569 reference "sub:Predefined-Functions"
36576 \begin_layout Itemize
36577 Indices consisting of several letters, are set upright:
36578 \begin_inset Formula $E_{\mathrm{kin}}$
36582 \begin_inset Newline newline
36585 Components of matrices are set italic:
36586 \begin_inset Formula $\hat{H}_{kl}$
36592 \begin_layout Itemize
36593 The differentiation/integration operator 'd', the Euler's number 'e', and
36594 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36598 \begin_layout Itemize
36599 The character that denotes a
36603 transformation is inserted either by the command
36611 \begin_layout Plain Layout
36628 \begin_layout Plain Layout
36638 Insert\SpecialChar \menuseparator
36639 Special Character\SpecialChar \menuseparator
36640 Symbols\SpecialChar \menuseparator
36642 \begin_inset space ~
36648 \begin_inset Formula $\mathscr{F}$
36652 \begin_inset Newline newline
36655 To be able to use the command
36661 , the LaTeX package
36669 \begin_layout Plain Layout
36670 Packages ! mathrsfs
36675 needs to be loaded with the LaTeX-preamble line
36679 usepackage{mathrsfs}
36684 \begin_layout Standard
36685 \begin_inset Newpage newpage
36691 \begin_layout Section
36696 \begin_layout Plain Layout
36705 \begin_layout Standard
36706 Some characters and symbols can be created with several commands.
36707 Here is a list of the synonym commands:
36710 \begin_layout Standard
36711 \begin_inset VSpace bigskip
36715 \begin_inset space \hfill{}
36719 \begin_inset Tabular
36720 <lyxtabular version="3" rows="12" columns="2">
36722 <column alignment="center" valignment="top" width="0pt">
36723 <column alignment="center" valignment="top" width="0pt">
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