1 #LyX 1.6.2svn 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 % center multirows (e.g. in sec. 13.3)
86 \renewcommand{\multirowsetup}{\centering}
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % redefine the greyed out note
113 \renewenvironment{lyxgreyedout}
114 {\textcolor{blue}\bgroup}{\egroup}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % needed in sec. 22.4
129 % check for package braket
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % needed in sec. 22.10
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
145 \use_default_options false
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pdfusetitle false
174 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
181 \paperorientation portrait
184 \paragraph_separation skip
186 \quotes_language english
189 \paperpagestyle plain
193 \tracking_changes false
194 \output_changes false
202 LyX's detailed Math manual
210 \begin_layout Plain Layout
212 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_inset CommandInset href
218 name "lyx-docs@lists.lyx.org"
219 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
230 \begin_inset Note Note
233 \begin_layout Plain Layout
240 \begin_inset Newline newline
244 \begin_inset Newline newline
252 \begin_layout Standard
253 \begin_inset CommandInset toc
254 LatexCommand tableofcontents
261 \begin_layout Standard
262 \begin_inset Note Note
265 \begin_layout Plain Layout
266 To export this document to PDF, PS, or DVI the LaTeX-packages
279 If they are not installed you can export the document anyway but the sections
280 where the packages are required won't appear in the output.
283 \begin_layout Plain Layout
284 The latest PDF-version of this document can be found here:
285 \begin_inset Newline newline
290 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
298 \begin_layout Standard
299 \begin_inset Newpage newpage
305 \begin_layout Section
309 \begin_layout Standard
310 This document explains LyX's math features and is furthermore a collection
311 of LaTeX-commands used for mathematical characters and constructs.
312 The explanations are designed for the usage of commands.
313 It is therefore required that you have read the section
324 \begin_layout Standard
325 Most of the characters and many constructs explained in this manual are
326 also accessible via the menu
330 \SpecialChar \menuseparator
346 But everybody who has to write lots of formulas will notice that it is
347 much faster to use commands instead of the math toolbar.
348 Therefore this manual is focused on commands but also mentions the correspondin
349 g toolbar buttons when available.
352 \begin_layout Standard
353 If not specially mentioned the commands are only available within formulas.
354 To be able to use all commands explained in this document, the option
358 must be used in the document settings (menu
360 Document\SpecialChar \menuseparator
361 Settings\SpecialChar \menuseparator
372 \begin_layout Plain Layout
375 Use AMS math package automatically
381 \begin_layout Plain Layout
390 -math when math constructs are found that are supported by LyX.
398 \begin_layout Standard
399 This document doesn't list all
403 \begin_layout Plain Layout
416 \begin_layout Plain Layout
421 \begin_layout Plain Layout
430 -math commands is in the file
433 \begin_inset CommandInset href
436 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
442 , which is part of every LaTeX standard installation.
447 for lucidity reasons.
450 \begin_layout Section
454 \begin_layout Standard
455 To create an inline formula
459 \begin_layout Plain Layout
465 that is embedded into a text line, use one of the shortcuts
471 or the toolbar button
472 \begin_inset Graphics
473 filename ../images/math-mode.png
479 \begin_inset Newline newline
482 To create a display style formula
486 \begin_layout Plain Layout
487 Formula ! display style
492 that will appear bigger and in an own paragraph, use one of these shortcuts:
502 \begin_layout Standard
503 To change a display style formula to an inline formula, set the cursor into
504 the formula and use one of the shortcuts
512 Edit\SpecialChar \menuseparator
513 Math\SpecialChar \menuseparator
517 The same way is used to change an inline formula to a display style formula.
520 \begin_layout Standard
521 To display parts of an inline formula in the size of a display style formula,
530 \begin_layout Plain Layout
541 Then a new blue box appears in which the desired formula part is inserted.
544 \begin_layout Standard
545 Only inline formulas are allowed inside tables.
548 \begin_layout Standard
553 can be turned on in the menu
555 View\SpecialChar \menuseparator
559 When you click there on
560 \begin_inset Quotes eld
564 \begin_inset Quotes erd
567 the toolbar will be shown permanently at the bottom; this state is visualized
572 menu with a checkmark.
573 When you click in this state again on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
589 is only shown when the cursor is within a formula; this state is visualized
590 by the renaming of the menu entry from
591 \begin_inset Quotes eld
595 \begin_inset Quotes erd
599 \begin_inset Quotes eld
607 \begin_inset Quotes erd
613 \begin_layout Standard
618 \begin_layout Plain Layout
624 is invoked by pressing the toolbar button
625 \begin_inset Graphics
626 filename ../images/ert-insert.png
633 Insert\SpecialChar \menuseparator
638 \begin_layout Plain Layout
654 \begin_inset Note Note
657 \begin_layout Plain Layout
658 In LyX there are three
659 \begin_inset Quotes eld
663 \begin_inset Quotes erd
666 that appear in the output with sub- and superscript letters: TeX, LaTeX,
670 \begin_layout Plain Layout
671 To avoid that these names are recognized as proper names, a TeX-brace pair
680 \begin_layout Standard
681 To change the LaTeX-preamble
685 \begin_layout Plain Layout
693 Document\SpecialChar \menuseparator
694 Settings\SpecialChar \menuseparator
699 \begin_layout Plain Layout
715 \begin_layout Standard
716 To edit matrices, case differentiations, and multiline formulas subsequently,
719 Edit\SpecialChar \menuseparator
724 Edit\SpecialChar \menuseparator
726 \begin_inset space \thinspace{}
730 \begin_inset space \thinspace{}
740 When lines and columns are swapped via the menu, the column or line where
741 the cursor is in is exchanged with the column to the right or the line
743 Is the cursor in the last column or row, the exchange is done with the
744 column to the left or the line above.
747 \begin_layout Standard
748 To write text in formulas
752 \begin_layout Plain Layout
753 For multiline formulas the command
760 \begin_inset CommandInset ref
762 reference "sub:Text-in-multiline"
779 \begin_layout Plain Layout
789 \begin_layout Plain Layout
796 This mode is invoked with the the shortcut
802 or by the insertion of the command
810 \begin_layout Plain Layout
821 The text appears black in LyX and can therefore be distinguished from the
822 other formula parts that appear blue.
823 In the output mathematical text is set upright, in contrary to other formula
827 \begin_layout Subsection*
831 \begin_layout Standard
832 Most of the LaTeX-commands for math constructs have the following scheme:
835 \begin_layout Standard
851 \begin_layout Standard
852 A command starts always with a backslash
853 \begin_inset Quotes gld
863 \begin_inset Quotes grd
867 To omit optional arguments, also omit the associated brackets.
868 The braces around the required arguments are named in this document as
873 \begin_layout Plain Layout
880 If you add in a formula a left brace to a command name, LyX creates automatical
882 In all other cases TeX-braces are created in formulas with the command
890 TeX-braces appear red in LyX, in contrary to normal braces that appear
892 In TeX-mode no command is needed to get TeX-braces.
893 TeX-braces don't appear in the output.
896 \begin_layout Standard
897 When commands without arguments, like commands for symbols are entered in
898 TeX-mode, a space character must
902 be behind the command to end it.
903 This space doesn't appear in the output.
904 When the space should appear in the output, the space must be followed
905 by a protected space in normal text.
908 \begin_layout Standard
909 A protected space is inserted with
912 arg "space-insert protected"
918 \begin_layout Subsection*
919 \begin_inset Newpage newpage
925 \begin_layout Itemize
930 \begin_layout Plain Layout
931 This visible space character can be created with the command
941 \begin_layout Plain Layout
949 , inserted in TeX-mode.
958 \begin_layout Plain Layout
971 denotes a space character to be input.
974 \begin_layout Itemize
976 \begin_inset Formula $\to$
979 denotes the usage of the corresponding arrow key on the keyboard.
982 \begin_layout Subsection*
986 \begin_layout Standard
988 \begin_inset Float table
994 \begin_layout Plain Layout
998 \begin_layout Plain Layout
999 \begin_inset CommandInset label
1001 name "tab:Available-units"
1013 \begin_layout Plain Layout
1015 \begin_inset Tabular
1016 <lyxtabular version="3" rows="13" columns="2">
1018 <column alignment="center" valignment="top" width="0">
1019 <column alignment="center" valignment="top" width="0">
1021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1084 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1093 \begin_layout Plain Layout
1095 \begin_inset space \thinspace{}
1099 \begin_inset space \thinspace{}
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset Formula $\approx$
1243 \begin_inset space \thinspace{}
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1256 \begin_layout Plain Layout
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1265 \begin_layout Plain Layout
1267 \begin_inset space \thinspace{}
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1297 \begin_inset Quotes eld
1303 \begin_inset Quotes erd
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1316 \begin_layout Plain Layout
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1325 \begin_layout Plain Layout
1327 \begin_inset Quotes eld
1335 \begin_inset Quotes erd
1345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1348 \begin_layout Plain Layout
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1357 \begin_layout Plain Layout
1359 \begin_inset space \thinspace{}
1363 \begin_inset Formula $\nicefrac{1}{18}$
1367 \begin_inset space \thinspace{}
1388 \begin_layout Standard
1389 \begin_inset Newpage newpage
1395 \begin_layout Section
1399 \begin_layout Subsection
1404 \begin_layout Plain Layout
1414 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1487 \begin_layout Standard
1488 Indices are created with an underscore
1489 \begin_inset Quotes eld
1493 \begin_inset Quotes erd
1496 or via the math toolbar button
1497 \begin_inset Graphics
1498 filename ../images/math-subscript.png
1503 , exponents with a caret
1504 \begin_inset Quotes eld
1508 \begin_inset Quotes erd
1511 or via the math toolbar button
1512 \begin_inset Graphics
1513 filename ../images/math-superscript.png
1521 \begin_layout Standard
1523 \begin_inset Tabular
1524 <lyxtabular version="3" rows="4" columns="2">
1526 <column alignment="center" valignment="top" width="0pt">
1527 <column alignment="center" valignment="top" width="0pt">
1529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1541 \begin_layout Plain Layout
1543 \begin_inset Note Note
1546 \begin_layout Plain Layout
1553 is only used as spacer.
1565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1568 \begin_layout Plain Layout
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1577 \begin_layout Plain Layout
1578 \begin_inset Formula $B_{V}$
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1591 \begin_layout Plain Layout
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1619 \begin_layout Plain Layout
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1636 \begin_layout Plain Layout
1637 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1653 \begin_layout Standard
1654 As the caret is in some languages an accent, vowels will be accentuated
1655 in this case and not set as exponents
1659 \begin_layout Plain Layout
1660 Depending on the used keyboard settings this can also happen for other character
1667 To get in this case exponents, press
1671 after the caret as in the last example.
1674 \begin_layout Subsection
1676 \begin_inset CommandInset label
1678 name "sub:Fractions"
1686 \begin_layout Plain Layout
1695 \begin_layout Standard
1696 Fractions are generated with the command
1706 \begin_layout Plain Layout
1714 or via the math toolbar button
1715 \begin_inset Graphics
1716 filename ../images/math/frac.png
1722 The font size is adjusted automatically, depending on whether the fraction
1723 is in an inline or display style formula.
1724 With the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac-square.png
1731 you can select different fraction types.
1734 \begin_layout Standard
1743 \begin_layout Plain Layout
1753 a fraction can be created that has in any case the size of a display style
1763 \begin_layout Plain Layout
1773 the fraction appears always with the size of an inline formula.
1777 \begin_layout Standard
1778 A line with the fraction
1779 \begin_inset Formula $\frac{1}{2}$
1782 that was created with the command
1791 \begin_layout Standard
1792 A line with the fraction
1793 \begin_inset Formula $\dfrac{1}{2}$
1796 that was created with the command
1805 \begin_layout Standard
1807 \begin_inset Tabular
1808 <lyxtabular version="3" rows="4" columns="2">
1810 <column alignment="center" valignment="top" width="0pt">
1811 <column alignment="center" valignment="top" width="0pt">
1813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1816 \begin_layout Plain Layout
1822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1825 \begin_layout Plain Layout
1827 \begin_inset Note Note
1830 \begin_layout Plain Layout
1837 is only used as spacer.
1849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1852 \begin_layout Plain Layout
1859 \begin_layout Plain Layout
1869 \begin_inset Formula $\downarrow$
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1894 \begin_layout Plain Layout
1901 \begin_layout Plain Layout
1911 \begin_inset Formula $\downarrow$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1922 \begin_layout Plain Layout
1923 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1936 \begin_layout Plain Layout
1943 \begin_layout Plain Layout
1956 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow\downarrow$
1993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1996 \begin_layout Plain Layout
1997 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2013 \begin_layout Standard
2014 \begin_inset VSpace bigskip
2018 \begin_inset Newpage newpage
2021 For nested fractions the command
2031 \begin_layout Plain Layout
2041 \begin_inset VSpace -3mm
2047 \begin_layout Standard
2048 \begin_inset Formula \begin{align*}
2049 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2050 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2057 \begin_layout Standard
2058 The command for the example above is:
2061 \begin_layout Standard
2067 \begin_inset Formula $\to$
2077 \begin_inset Formula $\to$
2083 \begin_inset Formula $\to\to$
2091 \begin_layout Standard
2092 \begin_inset VSpace medskip
2098 \begin_layout Standard
2105 sets the fraction always in the size of a displayed formula, also when
2106 it is part of another fraction.
2113 has the following command scheme:
2116 \begin_layout Standard
2121 cfrac[numerator position]{numerator}{denominator}
2124 \begin_layout Standard
2125 The numerator position can be
2138 l or r aligns the numerator to the left or right, resp.
2139 \begin_inset space ~
2142 with the fraction stroke.
2147 or no position is given, the numerator appears centered.
2148 These fractions demonstrate the different alignments:
2149 \begin_inset Newline newline
2155 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2159 \begin_inset Formula $\cfrac{A}{B+C}$
2163 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2169 \begin_layout Standard
2170 \begin_inset VSpace medskip
2173 It is often advantageous to combine
2186 \begin_inset Formula \[
2187 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2194 \begin_layout Standard
2195 For inline fractions with a sloped fraction stroke you can use the command
2206 \begin_layout Plain Layout
2215 \begin_inset Formula $\nicefrac{5}{31}$
2228 \begin_layout Plain Layout
2237 \begin_inset Formula $\unitfrac{5}{31}$
2240 There is furthermore the command
2246 that offers to write a fraction in combination with a number:
2247 \begin_inset Formula $\unitfrac[2]{1}{3}$
2251 \begin_inset Newline newline
2260 is not a real LaTeX command but the command
2261 \begin_inset Newline newline
2268 unitfrac[number]{numerator}{denominator}
2270 , therefore you cannot use it in TeX code.
2273 \begin_layout Standard
2274 How to define own fractions where the fraction stroke can be changed, is
2276 \begin_inset CommandInset ref
2278 reference "sub:Self-defined-Fractions"
2285 \begin_layout Subsection
2290 \begin_layout Plain Layout
2299 \begin_layout Standard
2300 Square roots are created with
2310 \begin_layout Plain Layout
2318 or the math toolbar button
2319 \begin_inset Graphics
2320 filename ../images/math/sqrt.png
2325 , all other roots with the command
2335 \begin_layout Plain Layout
2343 or with the math toolbar button
2344 \begin_inset Graphics
2345 filename ../images/math/root.png
2353 \begin_layout Standard
2355 \begin_inset Tabular
2356 <lyxtabular version="3" rows="3" columns="2">
2358 <column alignment="center" valignment="top" width="0pt">
2359 <column alignment="center" valignment="top" width="0pt">
2361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2364 \begin_layout Plain Layout
2370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2373 \begin_layout Plain Layout
2375 \begin_inset Note Note
2378 \begin_layout Plain Layout
2385 is only used as spacer.
2397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2400 \begin_layout Plain Layout
2407 \begin_layout Plain Layout
2421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2424 \begin_layout Plain Layout
2425 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2438 \begin_layout Plain Layout
2445 \begin_layout Plain Layout
2455 \begin_inset Formula $\downarrow$
2463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2466 \begin_layout Plain Layout
2467 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2483 \begin_layout Standard
2484 A square root can also be created with
2490 when the root index field is left empty.
2493 \begin_layout Standard
2494 With certain indices the distance to the root is too small, like in this
2496 \begin_inset Formula $\sqrt[\beta]{B}$
2500 \begin_inset Newline newline
2504 \begin_inset Formula $\beta$
2508 To avoid this, the commands
2518 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2544 are used with the following scheme:
2547 \begin_layout Standard
2561 \begin_layout Standard
2562 Distance is the number of Big Points (unit bp;
2563 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2566 ), that the index should be moved to the left or top, resp..
2567 The commands are written to the index.
2568 This way the command
2569 \begin_inset Newline newline
2579 \begin_inset Formula $\to$
2585 \begin_inset Formula $\to$
2594 \begin_layout Plain Layout
2604 \begin_inset Formula $\to$
2608 \begin_inset Newline newline
2613 produces a correct typeset formula:
2614 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2620 \begin_layout Subsection
2621 Binomial Coefficients
2625 \begin_layout Plain Layout
2626 Binomial coefficients
2634 \begin_layout Standard
2635 Binomial coefficients are inserted with the command
2645 \begin_layout Plain Layout
2653 or with the submenu of the math toolbar button
2654 \begin_inset Graphics
2655 filename ../images/math/frac-square.png
2661 Analog to fractions (
2681 \begin_layout Plain Layout
2701 \begin_layout Plain Layout
2710 For other brackets around binomial coeficients there are the commands
2720 \begin_layout Plain Layout
2738 \begin_layout Plain Layout
2749 \begin_layout Standard
2751 \begin_inset Tabular
2752 <lyxtabular version="3" rows="6" columns="2">
2754 <column alignment="center" valignment="top" width="0pt">
2755 <column alignment="center" valignment="top" width="0pt">
2757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2760 \begin_layout Plain Layout
2766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2769 \begin_layout Plain Layout
2771 \begin_inset Note Note
2774 \begin_layout Plain Layout
2781 is only used as spacer.
2793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2796 \begin_layout Plain Layout
2803 \begin_layout Plain Layout
2813 \begin_inset Formula $\downarrow$
2821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2824 \begin_layout Plain Layout
2825 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2838 \begin_layout Plain Layout
2845 \begin_layout Plain Layout
2855 \begin_inset Formula $\downarrow$
2863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2866 \begin_layout Plain Layout
2867 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2880 \begin_layout Plain Layout
2887 \begin_layout Plain Layout
2897 \begin_inset Formula $\downarrow$
2905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2908 \begin_layout Plain Layout
2909 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2922 \begin_layout Plain Layout
2929 \begin_layout Plain Layout
2939 \begin_inset Formula $\downarrow$
2947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2950 \begin_layout Plain Layout
2951 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2964 \begin_layout Plain Layout
2971 \begin_layout Plain Layout
2981 \begin_inset Formula $\downarrow$
2989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2992 \begin_layout Plain Layout
2993 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3009 \begin_layout Subsection
3010 Case Differentiations
3014 \begin_layout Plain Layout
3015 Case differentiations
3023 \begin_layout Standard
3025 \begin_inset Tabular
3026 <lyxtabular version="3" rows="3" columns="2">
3028 <column alignment="center" valignment="top" width="0pt">
3029 <column alignment="center" valignment="top" width="0pt">
3031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3034 \begin_layout Plain Layout
3040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3043 \begin_layout Plain Layout
3051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3054 \begin_layout Plain Layout
3061 \begin_layout Plain Layout
3071 \begin_inset Formula $\to$
3078 \begin_layout Plain Layout
3091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3094 \begin_layout Plain Layout
3095 \begin_inset Formula $\begin{cases}
3106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3109 \begin_layout Plain Layout
3116 \begin_layout Plain Layout
3128 arg "newline-insert newline"
3136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3139 \begin_layout Plain Layout
3140 \begin_inset Formula $\begin{cases}
3141 A & \textrm{for }x>0\\
3142 B & \textrm{for }x=0\end{cases}$
3158 \begin_layout Standard
3165 or the usage of the math toolbar button
3166 \begin_inset Graphics
3167 filename ../images/math/cases.png
3172 you can create new lines with the shortcut
3175 arg "newline-insert newline"
3178 or the table toolbar button
3179 \begin_inset Graphics
3180 filename ../images/tabular-feature_append-row.png
3188 \begin_layout Standard
3195 is also available via the menu
3197 Insert\SpecialChar \menuseparator
3198 Math\SpecialChar \menuseparator
3204 \begin_layout Subsection
3209 \begin_layout Plain Layout
3218 \begin_layout Standard
3229 \begin_layout Plain Layout
3237 every character can be displayed canceled.
3238 The characters are quasi accentuated by a slash.
3241 \begin_layout Standard
3243 \begin_inset Tabular
3244 <lyxtabular version="3" rows="4" columns="2">
3246 <column alignment="center" valignment="top" width="0pt">
3247 <column alignment="center" valignment="top" width="0pt">
3249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3252 \begin_layout Plain Layout
3258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3261 \begin_layout Plain Layout
3269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3272 \begin_layout Plain Layout
3280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3283 \begin_layout Plain Layout
3284 \begin_inset Formula $\not=$
3294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3297 \begin_layout Plain Layout
3307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3310 \begin_layout Plain Layout
3311 \begin_inset Formula $\not\le$
3321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3324 \begin_layout Plain Layout
3334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3337 \begin_layout Plain Layout
3338 \begin_inset Formula $\not\parallel$
3354 \begin_layout Standard
3355 The last example shows, that not all negations look good.
3356 Therefore there are for some negations special commands (see
3357 \begin_inset CommandInset ref
3359 reference "sub:Mathematical-Symbols"
3364 \begin_inset CommandInset ref
3366 reference "sec:Relations"
3373 \begin_layout Subsection
3375 \begin_inset CommandInset label
3377 name "sub:Placeholders"
3385 \begin_layout Plain Layout
3395 \begin_layout Plain Layout
3396 Chemical characters ! Isotopes
3405 \begin_layout Plain Layout
3410 \begin_layout Plain Layout
3421 \begin_layout Plain Layout
3436 \begin_layout Standard
3438 \begin_inset space \thinspace{}
3442 \begin_inset space \space{}
3449 \begin_layout Plain Layout
3450 More about chemical symbols is written in
3451 \begin_inset CommandInset ref
3453 reference "sub:Chemical-Symbols-and"
3462 the following problem occurs:
3465 \begin_layout Standard
3467 \begin_inset Tabular
3468 <lyxtabular version="3" rows="2" columns="2">
3470 <column alignment="center" valignment="top" width="0pt">
3471 <column alignment="center" valignment="top" width="0pt">
3473 <cell alignment="center" valignment="top" usebox="none">
3476 \begin_layout Plain Layout
3477 Indices created with sub- and superscripts:
3482 <cell alignment="center" valignment="top" usebox="none">
3485 \begin_layout Plain Layout
3486 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3496 <cell alignment="center" valignment="top" usebox="none">
3499 \begin_layout Plain Layout
3505 <cell alignment="center" valignment="top" usebox="none">
3508 \begin_layout Plain Layout
3509 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3523 \begin_inset Note Note
3526 \begin_layout Plain Layout
3533 is only used as spacer.
3541 \begin_layout Standard
3542 The shorter index is by default placed below or above the first character
3543 of the longer index.
3544 To avoid this there is the command
3554 \begin_layout Plain Layout
3562 or the math toolbar button
3563 \begin_inset space \thinspace{}
3570 \begin_layout Plain Layout
3571 can be found in the submenu of the toolbar button
3572 \begin_inset Graphics
3573 filename ../images/math/space.png
3584 \begin_inset Graphics
3585 filename ../images/math/phantom.png
3590 that creates one or more phantom characters.
3597 a small blue box appears that is superposed with two red arrows.
3598 The arrows indicate that the complete width and height of the box content
3599 will be created as placeholder.
3600 Phantom characters are accordingly placeholders with the size of the characters.
3603 \begin_layout Standard
3605 \begin_inset Tabular
3606 <lyxtabular version="3" rows="4" columns="2">
3608 <column alignment="center" valignment="top" width="0">
3609 <column alignment="center" valignment="top" width="0">
3611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3614 \begin_layout Plain Layout
3620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3623 \begin_layout Plain Layout
3625 \begin_inset Note Note
3628 \begin_layout Plain Layout
3635 is only used as spacer.
3647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3650 \begin_layout Plain Layout
3655 \begin_layout Plain Layout
3670 \begin_layout Plain Layout
3680 \begin_inset Formula $\to$
3687 \begin_layout Plain Layout
3701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3704 \begin_layout Plain Layout
3705 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3718 \begin_layout Plain Layout
3723 \begin_layout Plain Layout
3738 \begin_layout Plain Layout
3748 \begin_inset Formula $\to$
3755 \begin_layout Plain Layout
3769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3772 \begin_layout Plain Layout
3773 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3786 \begin_layout Plain Layout
3793 \begin_layout Plain Layout
3808 \begin_layout Plain Layout
3818 \begin_inset Formula $\to$
3825 \begin_layout Plain Layout
3839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3842 \begin_layout Plain Layout
3843 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3859 \begin_layout Standard
3860 Furthermore there are the commands
3870 \begin_layout Plain Layout
3879 \begin_inset space ~
3883 \begin_inset Graphics
3884 filename ../images/math/vphantom.png
3899 \begin_layout Plain Layout
3908 \begin_inset space ~
3912 \begin_inset Graphics
3913 filename ../images/math/hphantom.png
3925 creates only space for the maximal height of the characters in the box
3926 but not for its width.
3933 creates only space for the width of the box content.
3934 Therefore the boxes of both commands have only one red arrow.
3937 \begin_layout Standard
3948 \begin_layout Plain Layout
3963 space for the height of the integral sign,
3967 \begin_layout Plain Layout
3974 creates an integral sign, see
3975 \begin_inset CommandInset ref
3977 reference "sub:Big-Operators"
3986 because this is the larger character.
3987 An example application is in
3988 \begin_inset CommandInset ref
3990 reference "sub:Multiline-Brackets"
3997 \begin_layout Subsection
4002 \begin_layout Plain Layout
4012 \begin_layout Plain Layout
4013 Formula ! underlined
4021 \begin_layout Standard
4023 \begin_inset Tabular
4024 <lyxtabular version="3" rows="4" columns="2">
4026 <column alignment="center" valignment="top" width="0pt">
4027 <column alignment="center" valignment="top" width="0pt">
4029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4032 \begin_layout Plain Layout
4038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4041 \begin_layout Plain Layout
4043 \begin_inset Note Note
4046 \begin_layout Plain Layout
4053 is only used as spacer.
4065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4068 \begin_layout Plain Layout
4075 \begin_layout Plain Layout
4088 \begin_layout Plain Layout
4101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4104 \begin_layout Plain Layout
4105 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4118 \begin_layout Plain Layout
4125 \begin_layout Plain Layout
4138 \begin_layout Plain Layout
4151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4154 \begin_layout Plain Layout
4155 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4168 \begin_layout Plain Layout
4175 \begin_layout Plain Layout
4190 \begin_layout Plain Layout
4204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4207 \begin_layout Plain Layout
4208 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4224 \begin_layout Standard
4225 In the last example it doesn't matter if first
4240 \begin_layout Standard
4241 To double underline e.
4242 \begin_inset space \thinspace{}
4246 \begin_inset space \space{}
4258 \begin_layout Standard
4259 It is possible to place up to 6 lines above or below characters.
4262 \begin_layout Standard
4263 \begin_inset VSpace bigskip
4266 Custom lines can be created using the command
4276 \begin_layout Plain Layout
4284 which has the following scheme:
4287 \begin_layout Standard
4292 rule[vertical offset]{length}{thickness}
4295 \begin_layout Standard
4296 The optional vertical offset shifts the line upwards (or downwards, when
4297 the value is negative).
4299 \begin_inset CommandInset ref
4301 reference "tab:Available-units"
4305 can be used for the values.
4306 Here are two example lines created with the commands
4307 \begin_inset Newline newline
4314 rule[-2ex]{3cm}{2pt}
4325 \begin_layout Standard
4327 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4333 \begin_layout Standard
4340 can also be used for text when it is inserted in TeX-mode.
4343 \begin_layout Subsection
4345 \begin_inset CommandInset label
4355 \begin_layout Plain Layout
4364 \begin_layout Standard
4365 There are different types of ellipses available.
4369 \begin_layout Plain Layout
4370 In the math toolbar in the submenu of the button
4371 \begin_inset Graphics
4372 filename ../images/math/ldots.png
4382 For listings dots at the baseline are used (
4392 \begin_layout Plain Layout
4400 ), while for operations dots are needed that are on the same height as the
4411 \begin_layout Plain Layout
4420 When using the command
4430 \begin_layout Plain Layout
4438 , LaTeX decides on the basis of the next character what type is used.
4441 \begin_layout Standard
4443 \begin_inset Tabular
4444 <lyxtabular version="3" rows="8" columns="2">
4446 <column alignment="center" valignment="top" width="0pt">
4447 <column alignment="center" valignment="top" width="0pt">
4449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4452 \begin_layout Plain Layout
4458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4461 \begin_layout Plain Layout
4469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4472 \begin_layout Plain Layout
4477 \begin_layout Plain Layout
4492 \begin_layout Plain Layout
4506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4509 \begin_layout Plain Layout
4510 \begin_inset Formula $A_{1},\dots,A_{n}$
4520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4523 \begin_layout Plain Layout
4528 \begin_layout Plain Layout
4543 \begin_layout Plain Layout
4557 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4560 \begin_layout Plain Layout
4561 \begin_inset Formula $A_{1}+\dots+A_{n}$
4571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4574 \begin_layout Plain Layout
4579 \begin_layout Plain Layout
4594 \begin_layout Plain Layout
4608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4611 \begin_layout Plain Layout
4612 \begin_inset Formula $A_{1},\ldots,A_{n}$
4622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4625 \begin_layout Plain Layout
4630 \begin_layout Plain Layout
4645 \begin_layout Plain Layout
4659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4662 \begin_layout Plain Layout
4663 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4676 \begin_layout Plain Layout
4684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4687 \begin_layout Plain Layout
4688 \begin_inset Formula $\vdots$
4698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4701 \begin_layout Plain Layout
4709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4712 \begin_layout Plain Layout
4713 \begin_inset Formula $\ddots$
4723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4726 \begin_layout Plain Layout
4728 \begin_inset space \thinspace{}
4731 matrix with the different dots
4736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4739 \begin_layout Plain Layout
4740 \begin_inset Formula $\begin{array}{ccc}
4741 A_{11} & \cdots & A_{1m}\\
4742 \vdots & \ddots & \vdots\\
4743 A_{n1} & \cdots & A_{nm}\end{array}$
4759 \begin_layout Standard
4760 The ellipses available in menu
4762 Insert\SpecialChar \menuseparator
4764 \begin_inset space ~
4778 \begin_layout Standard
4779 \begin_inset VSpace medskip
4782 Specially for matrices there are ellipses that span over several columns.
4783 They are created with the command
4793 \begin_layout Plain Layout
4801 , that has the following scheme:
4804 \begin_layout Standard
4809 hdotsfor[distance]{number of columns}
4812 \begin_layout Standard
4813 The number of columns specifies how many columns should be spanned.
4814 Distance is a factor for the distance between the dots.
4817 \begin_layout Standard
4818 In the following matrix the command
4824 was inserted in the first box of the second line, to get an ellipsis with
4825 a dot distance twice as long as with the command
4832 \begin_inset Formula \[
4833 \left(\begin{array}{cccc}
4836 q & w & e & r\end{array}\right)\]
4840 Note that the matrix fields that should be spanned must be empty, otherwise
4841 you get LaTeX-errors.
4844 \begin_layout Standard
4845 \begin_inset VSpace bigskip
4848 Furthermore you can fill with the command
4858 \begin_layout Plain Layout
4866 the rest of a line with dots.
4867 The effect of these commands is the same like with
4874 \begin_inset CommandInset ref
4876 reference "sub:Variable-Space"
4883 \begin_layout Standard
4884 For example the command
4892 \begin_layout Plain Layout
4906 \begin_layout Standard
4907 \begin_inset Formula $A\dotfill B$
4913 \begin_layout Standard
4920 there is for a line the command
4930 \begin_layout Plain Layout
4941 \begin_layout Standard
4942 \begin_inset Formula $A\hrulefill B$
4948 \begin_layout Standard
4949 To use the commands for text, they have to be inserted in TeX-mode.
4952 \begin_layout Section
4954 \begin_inset CommandInset label
4964 \begin_layout Plain Layout
4973 \begin_layout Standard
4974 Matrices can be inserted via the math toolbar button
4975 \begin_inset Graphics
4976 filename ../images/dialog-show_mathmatrix.png
4983 Insert\SpecialChar \menuseparator
4984 Math\SpecialChar \menuseparator
4988 You will be asked for the number of matrix columns and rows, and the alignment.
4989 The vertical alignment is hereby only of importance for matrices in inline
4993 \begin_layout Standard
4994 The first matrix is top
4995 \begin_inset Formula $\begin{array}[t]{cccc}
4998 C & F & I & L\end{array}$
5002 \begin_inset Formula $\begin{array}{cccc}
5005 C & F & I & L\end{array}$
5008 , and the third bottom
5009 \begin_inset Formula $\begin{array}[b]{cccc}
5012 C & F & I & L\end{array}$
5018 \begin_layout Standard
5019 The horizontal alignment specifies how the column entries should be aligned.
5020 It is set by entering a letter for every column.
5025 denotes left aligned,
5034 To create for example a 4
5039 \begin_inset space ~
5042 matrix where the first column is left aligned, the second and third are
5043 centered, and the last one is right aligned, one enters for the horizontal
5049 Normally are in a matrix all columns centered, therefore the default is
5050 for every column is a
5057 \begin_layout Standard
5058 Horizontal alignment:
5061 \begin_layout Standard
5067 \begin_inset Formula $\begin{array}{lll}
5070 C & F & 10000\end{array}$
5078 \begin_inset Formula $\begin{array}{ccc}
5081 C & F & 10000\end{array}$
5089 \begin_inset Formula $\begin{array}{rrr}
5092 C & F & 10000\end{array}$
5098 \begin_layout Standard
5099 To add or delete rows and columns subsequently, the math toolbar buttons
5101 \begin_inset Graphics
5102 filename ../images/tabular-feature_append-row.png
5108 \begin_inset Graphics
5109 filename ../images/tabular-feature_delete-row.png
5115 \begin_inset space \thinspace{}
5120 Edit\SpecialChar \menuseparator
5124 New rows can also be created with
5127 arg "newline-insert newline"
5133 \begin_layout Standard
5134 \begin_inset VSpace bigskip
5137 Parentheses around a matrix can can either be created with the commands
5148 \begin_layout Plain Layout
5166 \begin_layout Plain Layout
5177 \begin_inset space ~
5183 \begin_inset CommandInset ref
5185 reference "sub:Automatic-Bracket-Size"
5189 , or by using the following commands:
5190 \begin_inset VSpace medskip
5196 \begin_layout Standard
5197 \begin_inset space \hfill{}
5201 \begin_inset Tabular
5202 <lyxtabular version="3" rows="4" columns="2">
5204 <column alignment="center" valignment="top" width="0">
5205 <column alignment="center" valignment="top" width="0">
5207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5210 \begin_layout Plain Layout
5216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5219 \begin_layout Plain Layout
5221 \begin_inset Note Note
5224 \begin_layout Plain Layout
5231 is only used as spacer.
5243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5246 \begin_layout Plain Layout
5253 \begin_layout Plain Layout
5267 \begin_inset space \thinspace{}
5275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5278 \begin_layout Plain Layout
5279 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5280 0 & \textrm{-}\mathrm{i}\\
5281 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5294 \begin_layout Plain Layout
5301 \begin_layout Plain Layout
5315 \begin_inset space \thinspace{}
5323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5326 \begin_layout Plain Layout
5327 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5328 0 & \textrm{-}\mathrm{i}\\
5329 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5342 \begin_layout Plain Layout
5349 \begin_layout Plain Layout
5363 \begin_inset space \thinspace{}
5371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5374 \begin_layout Plain Layout
5375 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5376 0 & \textrm{-}\mathrm{i}\\
5377 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5391 \begin_inset space \hfill{}
5395 \begin_inset Tabular
5396 <lyxtabular version="3" rows="4" columns="2">
5398 <column alignment="center" valignment="top" width="0">
5399 <column alignment="center" valignment="top" width="0">
5401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5404 \begin_layout Plain Layout
5410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5413 \begin_layout Plain Layout
5421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5424 \begin_layout Plain Layout
5431 \begin_layout Plain Layout
5445 \begin_inset space \thinspace{}
5453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5456 \begin_layout Plain Layout
5457 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5458 0 & \textrm{-}\mathrm{i}\\
5459 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5472 \begin_layout Plain Layout
5479 \begin_layout Plain Layout
5493 \begin_inset space \thinspace{}
5501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5504 \begin_layout Plain Layout
5505 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5506 0 & \textrm{-}\mathrm{i}\\
5507 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5517 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5520 \begin_layout Plain Layout
5527 \begin_layout Plain Layout
5541 \begin_inset space \thinspace{}
5549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5552 \begin_layout Plain Layout
5553 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5554 0 & \textrm{-}\mathrm{i}\\
5555 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5569 \begin_inset space \hfill{}
5575 \begin_layout Standard
5576 \begin_inset VSpace medskip
5580 \begin_inset space \thinspace{}
5584 \begin_inset space \space{}
5593 is inserted, a blue box appears between two vertical lines where the matrix
5597 \begin_layout Standard
5598 \begin_inset VSpace bigskip
5601 As all multiline formulas are matrices, the length
5611 \begin_layout Plain Layout
5619 that is described in
5620 \begin_inset CommandInset ref
5622 reference "sub:Column-Separation"
5626 can also be used to change the column separation of matrices.
5629 \begin_layout Standard
5630 To change the row separation, the command
5640 \begin_layout Plain Layout
5649 It is used as follows:
5652 \begin_layout Standard
5659 arraystretch}{stretch factor}
5663 \begin_layout Plain Layout
5674 \begin_layout Standard
5681 assigns the stretch factor to the predefined command
5689 \begin_inset space \thinspace{}
5693 \begin_inset space \space{}
5696 the row separation, use the factor 2.
5697 This is then used for all following matrices.
5698 To go back to the original separation, assign the factor 1 to
5707 \begin_layout Standard
5708 To set matrices into a text line, the command
5718 \begin_layout Plain Layout
5727 When it is inserted a blue box with two dashed lines appears.
5728 In this box the matrix is inserted.
5731 \begin_layout Standard
5733 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5734 C & D\end{smallmatrix}\right)$
5740 \begin_layout Section
5741 Brackets and Delimiters
5745 \begin_layout Plain Layout
5755 \begin_layout Plain Layout
5764 \begin_layout Subsection
5765 Vertical Brackets and Delimiters
5769 \begin_layout Plain Layout
5778 \begin_layout Standard
5779 \begin_inset space \hfill{}
5783 \begin_inset Tabular
5784 <lyxtabular version="3" rows="9" columns="2">
5786 <column alignment="center" valignment="top" width="0pt">
5787 <column alignment="center" valignment="top" width="0pt">
5789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5792 \begin_layout Plain Layout
5798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5801 \begin_layout Plain Layout
5809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5812 \begin_layout Plain Layout
5818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5821 \begin_layout Plain Layout
5822 \begin_inset Formula $($
5832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5835 \begin_layout Plain Layout
5841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5844 \begin_layout Plain Layout
5845 \begin_inset Formula $\{$
5855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5858 \begin_layout Plain Layout
5864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5867 \begin_layout Plain Layout
5868 \begin_inset Formula $[$
5878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5881 \begin_layout Plain Layout
5889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5892 \begin_layout Plain Layout
5893 \begin_inset Formula $\langle$
5903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5906 \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 $\lceil$
5928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5931 \begin_layout Plain Layout
5939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5942 \begin_layout Plain Layout
5943 \begin_inset Formula $\lfloor$
5953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5956 \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 $/$
5976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5979 \begin_layout Plain Layout
5985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5988 \begin_layout Plain Layout
5989 \begin_inset Formula $|$
6003 \begin_inset space \hfill{}
6007 \begin_inset Tabular
6008 <lyxtabular version="3" rows="9" columns="2">
6010 <column alignment="center" valignment="top" width="0pt">
6011 <column alignment="center" valignment="top" width="0pt">
6013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6016 \begin_layout Plain Layout
6022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6025 \begin_layout Plain Layout
6033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6036 \begin_layout Plain Layout
6042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6045 \begin_layout Plain Layout
6046 \begin_inset Formula $)$
6056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6059 \begin_layout Plain Layout
6065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6068 \begin_layout Plain Layout
6069 \begin_inset Formula $\}$
6079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6082 \begin_layout Plain Layout
6088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6091 \begin_layout Plain Layout
6092 \begin_inset Formula $]$
6102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6105 \begin_layout Plain Layout
6113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6116 \begin_layout Plain Layout
6117 \begin_inset Formula $\rangle$
6127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6130 \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 $\rceil$
6152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6155 \begin_layout Plain Layout
6163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6166 \begin_layout Plain Layout
6167 \begin_inset Formula $\rfloor$
6177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6180 \begin_layout Plain Layout
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6193 \begin_layout Plain Layout
6194 \begin_inset Formula $\backslash$
6204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6207 \begin_layout Plain Layout
6215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6218 \begin_layout Plain Layout
6219 \begin_inset Formula $\|$
6233 \begin_inset space \hfill{}
6239 \begin_layout Standard
6242 \begin_inset Note Greyedout
6245 \begin_layout Plain Layout
6250 In TeX-mode the command
6260 \begin_layout Plain Layout
6268 must be used for the backslash, because the command
6276 produces there a line break.
6284 \begin_layout Standard
6285 For all characters listed above the size can be adjusted with the commands
6286 described in the following two subsections.
6287 When using these commands, the characters < and > can directly be used
6288 instead of the commands
6303 \begin_layout Subsubsection
6305 \begin_inset CommandInset label
6307 name "sub:Manual-Bracket-Size"
6315 \begin_layout Plain Layout
6316 Bracket size ! manual
6324 \begin_layout Standard
6325 The bracket size can be specified manually by the LaTeX-commands
6335 \begin_layout Plain Layout
6368 denotes the smallest and
6374 the largest bracket size.
6377 \begin_layout Standard
6378 These commands are used to emphasize levels of brackets:
6381 \begin_layout Standard
6383 \begin_inset Tabular
6384 <lyxtabular version="3" rows="2" columns="2">
6386 <column alignment="center" valignment="top" width="0pt">
6387 <column alignment="center" valignment="top" width="0pt">
6389 <cell alignment="center" valignment="top" usebox="none">
6392 \begin_layout Plain Layout
6393 all brackets in the same size:
6398 <cell alignment="center" valignment="top" usebox="none">
6401 \begin_layout Plain Layout
6402 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6412 <cell alignment="center" valignment="top" usebox="none">
6415 \begin_layout Plain Layout
6421 <cell alignment="center" valignment="top" usebox="none">
6424 \begin_layout Plain Layout
6425 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6439 \begin_inset Note Note
6442 \begin_layout Plain Layout
6449 is only used as spacer.
6457 \begin_layout Standard
6458 For the second formula the command
6468 \begin_layout Plain Layout
6482 \begin_layout Standard
6483 Here is an overview about all bracket sizes:
6486 \begin_layout Standard
6506 \begin_layout Plain Layout
6523 \begin_layout Plain Layout
6536 \begin_layout Plain Layout
6552 \begin_layout Standard
6554 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6560 \begin_layout Standard
6567 -commands there is the variant
6577 \begin_layout Plain Layout
6585 that adds a bit more space between the bracket and its content, and the
6602 \begin_layout Plain Layout
6612 , that don't add additional space.
6617 at the end of the command
6623 is for a left bracket; for a right bracket this will be replaced by an
6629 A left or right bracket can each be an opening or closing bracket.
6632 \begin_layout Standard
6633 In the following table is a comparison of the variants:
6636 \begin_layout Standard
6638 \begin_inset Tabular
6639 <lyxtabular version="3" rows="5" columns="2">
6641 <column alignment="center" valignment="middle" width="0">
6642 <column alignment="center" valignment="middle" width="0">
6644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6647 \begin_layout Plain Layout
6653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6656 \begin_layout Plain Layout
6658 \begin_inset Note Note
6661 \begin_layout Plain Layout
6668 is only used as spacer.
6680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6683 \begin_layout Plain Layout
6698 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6719 \begin_layout Plain Layout
6720 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6733 \begin_layout Plain Layout
6748 \begin_layout Plain Layout
6766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6769 \begin_layout Plain Layout
6770 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6783 \begin_layout Plain Layout
6798 \begin_layout Plain Layout
6816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6819 \begin_layout Plain Layout
6820 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6833 \begin_layout Plain Layout
6845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6848 \begin_layout Plain Layout
6849 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6865 \begin_layout Subsubsection
6866 Automatic Bracket Size
6867 \begin_inset CommandInset label
6869 name "sub:Automatic-Bracket-Size"
6877 \begin_layout Plain Layout
6878 Bracket size ! automatic
6886 \begin_layout Standard
6887 Brackets with variable size can be inserted with the commands
6897 \begin_layout Plain Layout
6915 \begin_layout Plain Layout
6923 or via the math toolbar button
6924 \begin_inset Graphics
6925 filename ../images/dialog-show_mathdelimiter.png
6943 the wanted bracket must be inserted.
6944 The bracket size will then automatically be calculated for the output.
6947 \begin_layout Standard
6949 normal bracket: The command
6959 \begin_layout Plain Layout
6969 \begin_inset Formula $\downarrow$
6976 \begin_layout Plain Layout
6988 \begin_inset Formula \[
6996 \begin_layout Standard
6998 multiline bracket: The command
7010 \begin_layout Plain Layout
7020 \begin_inset Formula $\downarrow$
7027 \begin_layout Plain Layout
7041 \begin_inset Formula \[
7042 \ln\left(\frac{A}{C}\right)\]
7049 \begin_layout Standard
7065 \begin_inset space ~
7071 This has the advantage that you can see in LyX immediately the real bracket
7072 size and that the matching right bracket will be created too.
7073 \begin_inset Newline newline
7076 The command for the last example would then be:
7090 \begin_layout Plain Layout
7100 \begin_inset Formula $\downarrow$
7106 \begin_layout Standard
7107 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7108 For example the command
7118 \begin_layout Plain Layout
7128 \begin_inset Formula $\downarrow$
7135 \begin_layout Plain Layout
7151 \begin_inset Formula \[
7152 \left.\frac{A}{B}\right\} \]
7170 will be converted by LyX to brackets in the right size when the document
7171 is reloaded and an omitted bracket will appear as dashed line.
7174 \begin_layout Standard
7175 \begin_inset VSpace bigskip
7178 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7189 \begin_layout Plain Layout
7197 is additionally available for all brackets and limits.
7198 With this command the height of the following character is adapted to the
7199 one of the surrounding brackets, what is e.
7200 \begin_inset space \thinspace{}
7204 \begin_inset space \space{}
7207 needed for physical vectors:
7208 \begin_inset Formula \[
7209 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7213 For physical vectors there is a special LaTeX-package, described in
7214 \begin_inset CommandInset ref
7216 reference "sub:Physical-Vectors"
7223 \begin_layout Subsection
7228 \begin_layout Plain Layout
7229 Brackets ! horizontal
7237 \begin_layout Standard
7239 \begin_inset Tabular
7240 <lyxtabular version="3" rows="4" columns="2">
7242 <column alignment="center" valignment="top" width="0pt">
7243 <column alignment="center" valignment="top" width="0pt">
7245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7248 \begin_layout Plain Layout
7250 \begin_inset Note Note
7253 \begin_layout Plain Layout
7260 is only used as spacer.
7270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7273 \begin_layout Plain Layout
7281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7284 \begin_layout Plain Layout
7288 \begin_layout Plain Layout
7303 \begin_layout Plain Layout
7316 \begin_layout Plain Layout
7329 \begin_layout Plain Layout
7342 \begin_layout Plain Layout
7353 \begin_layout Plain Layout
7366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7369 \begin_layout Plain Layout
7370 \begin_inset Formula $\overbrace{A+B}^{3}$
7380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7383 \begin_layout Plain Layout
7387 \begin_layout Plain Layout
7402 \begin_layout Plain Layout
7415 \begin_layout Plain Layout
7428 \begin_layout Plain Layout
7439 \begin_layout Plain Layout
7452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7455 \begin_layout Plain Layout
7456 \begin_inset Formula $\underbrace{A+B}_{5}$
7466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7469 \begin_layout Plain Layout
7476 \begin_layout Plain Layout
7491 \begin_layout Plain Layout
7504 \begin_layout Plain Layout
7517 \begin_layout Plain Layout
7530 \begin_layout Plain Layout
7543 \begin_layout Plain Layout
7556 \begin_layout Plain Layout
7570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7573 \begin_layout Plain Layout
7574 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7590 \begin_layout Standard
7591 In the last example it doesn't matter if
7603 is inserted at first.
7606 \begin_layout Standard
7607 \begin_inset VSpace bigskip
7610 When brackets are needed that overlap each other, multiline formulas, as
7612 \begin_inset CommandInset ref
7614 reference "sec:Multiline-Formulas"
7619 \begin_inset Formula \begin{eqnarray*}
7620 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7621 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7625 In the first row the formula is inserted together with the first brace.
7626 It is hereby important that the space command
7630 \begin_layout Plain Layout
7631 Space commands are explained in
7632 \begin_inset CommandInset ref
7634 reference "sub:Predefined-Space"
7649 is inserted before the first
7650 \begin_inset Formula $d$
7653 , because the brace that ends behind the
7654 \begin_inset Formula $q$
7657 prevents that the following
7658 \begin_inset Quotes eld
7662 \begin_inset Quotes erd
7665 is surrounded by space.
7669 \begin_layout Plain Layout
7670 because a bracket is not handled as character, see
7671 \begin_inset CommandInset ref
7673 reference "sub:Binary-Operators"
7682 In the second row the second brace is inserted.
7683 As it should begin before the
7684 \begin_inset Formula $b$
7699 \begin_layout Plain Layout
7707 \begin_inset CommandInset ref
7709 reference "sub:Placeholders"
7718 This space is needed because the
7719 \begin_inset Quotes eld
7723 \begin_inset Quotes erd
7726 is also surrounded by space in the formula.
7727 The brace is placed under the command
7736 \begin_layout Standard
7737 It gets more complicated when brackets overlap each other, like in the following
7742 \begin_layout Plain Layout
7754 \begin_inset Formula \begin{eqnarray*}
7755 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7756 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7764 \begin_layout Plain Layout
7775 The first formula row is the same as the second row of the previous example,
7776 with the difference that the brace is above.
7777 The second row contains the formula together with the second brace.
7778 To avoid that there is space between the upper brace in the first row and
7779 the formula, the row spacing need to be reduced.
7780 This is not easily possible due to a bug in LyX
7784 \begin_layout Plain Layout
7785 \begin_inset CommandInset href
7787 name "LyX-bug #1505"
7788 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7798 As solution for the problem, the global formula row separation
7808 \begin_layout Plain Layout
7816 must be changed to -6
7817 \begin_inset space \thinspace{}
7820 pt before the formula with the command
7835 is set back after the formula to the standard value of 3
7836 \begin_inset space \thinspace{}
7839 pt using the same command.
7840 More about the row separation in formulas is explained in
7841 \begin_inset CommandInset ref
7843 reference "sub:Line-Separation"
7850 \begin_layout Section
7855 \begin_layout Plain Layout
7864 \begin_layout Standard
7865 Arrows can be inserted via the math toolbar button
7866 \begin_inset Graphics
7867 filename ../images/math/leftarrow.png
7872 or the commands listed in the following subsections.
7875 \begin_layout Standard
7876 \begin_inset Newpage newpage
7882 \begin_layout Subsection
7887 \begin_layout Plain Layout
7896 \begin_layout Standard
7897 \begin_inset space \hfill{}
7901 \begin_inset Tabular
7902 <lyxtabular version="3" rows="8" columns="2">
7904 <column alignment="center" valignment="top" width="0pt">
7905 <column alignment="center" valignment="top" width="0pt">
7907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7910 \begin_layout Plain Layout
7916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7919 \begin_layout Plain Layout
7927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7930 \begin_layout Plain Layout
7938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7941 \begin_layout Plain Layout
7942 \begin_inset Formula $\gets$
7952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7955 \begin_layout Plain Layout
7963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7966 \begin_layout Plain Layout
7967 \begin_inset Formula $\Leftarrow$
7977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7980 \begin_layout Plain Layout
7988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7991 \begin_layout Plain Layout
7992 \begin_inset Formula $\longleftarrow$
8002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8005 \begin_layout Plain Layout
8013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8016 \begin_layout Plain Layout
8017 \begin_inset Formula $\Longleftarrow$
8027 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8030 \begin_layout Plain Layout
8038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8041 \begin_layout Plain Layout
8042 \begin_inset Formula $\leftharpoonup$
8052 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8055 \begin_layout Plain Layout
8063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8066 \begin_layout Plain Layout
8067 \begin_inset Formula $\leftharpoondown$
8077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8080 \begin_layout Plain Layout
8088 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8091 \begin_layout Plain Layout
8092 \begin_inset Formula $\hookleftarrow$
8106 \begin_inset space \hfill{}
8110 \begin_inset Tabular
8111 <lyxtabular version="3" rows="8" columns="2">
8113 <column alignment="center" valignment="top" width="0pt">
8114 <column alignment="center" valignment="top" width="0pt">
8116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8119 \begin_layout Plain Layout
8125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8128 \begin_layout Plain Layout
8136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8139 \begin_layout Plain Layout
8147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8150 \begin_layout Plain Layout
8151 \begin_inset Formula $\to$
8161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8164 \begin_layout Plain Layout
8172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8175 \begin_layout Plain Layout
8176 \begin_inset Formula $\Rightarrow$
8186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8189 \begin_layout Plain Layout
8197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8200 \begin_layout Plain Layout
8201 \begin_inset Formula $\longrightarrow$
8211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8214 \begin_layout Plain Layout
8222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8225 \begin_layout Plain Layout
8226 \begin_inset Formula $\Longrightarrow$
8236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8239 \begin_layout Plain Layout
8247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8250 \begin_layout Plain Layout
8251 \begin_inset Formula $\rightharpoonup$
8261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8264 \begin_layout Plain Layout
8272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8275 \begin_layout Plain Layout
8276 \begin_inset Formula $\rightharpoondown$
8286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8289 \begin_layout Plain Layout
8297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8300 \begin_layout Plain Layout
8301 \begin_inset Formula $\hookrightarrow$
8315 \begin_inset space \hfill{}
8321 \begin_layout Standard
8322 \begin_inset space \hfill{}
8326 \begin_inset Tabular
8327 <lyxtabular version="3" rows="6" columns="2">
8329 <column alignment="center" valignment="top" width="0pt">
8330 <column alignment="center" valignment="top" width="0pt">
8332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8335 \begin_layout Plain Layout
8341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8344 \begin_layout Plain Layout
8352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8355 \begin_layout Plain Layout
8363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8366 \begin_layout Plain Layout
8367 \begin_inset Formula $\leftrightarrow$
8377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8380 \begin_layout Plain Layout
8388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8391 \begin_layout Plain Layout
8392 \begin_inset Formula $\Leftrightarrow$
8402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8405 \begin_layout Plain Layout
8413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8416 \begin_layout Plain Layout
8417 \begin_inset Formula $\longleftrightarrow$
8427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8430 \begin_layout Plain Layout
8438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8441 \begin_layout Plain Layout
8442 \begin_inset Formula $\Longleftrightarrow$
8452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8455 \begin_layout Plain Layout
8463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8466 \begin_layout Plain Layout
8467 \begin_inset Formula $\rightleftharpoons$
8481 \begin_inset space \hspace{}
8486 \begin_inset space \hfill{}
8490 \begin_inset Tabular
8491 <lyxtabular version="3" rows="5" columns="2">
8493 <column alignment="center" valignment="top" width="0pt">
8494 <column alignment="center" valignment="top" width="0pt">
8496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8499 \begin_layout Plain Layout
8505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8508 \begin_layout Plain Layout
8516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8519 \begin_layout Plain Layout
8527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8530 \begin_layout Plain Layout
8531 \begin_inset Formula $\mapsto$
8541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8544 \begin_layout Plain Layout
8552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8555 \begin_layout Plain Layout
8556 \begin_inset Formula $\longmapsto$
8566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8569 \begin_layout Plain Layout
8577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8580 \begin_layout Plain Layout
8581 \begin_inset Formula $\leadsto$
8591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8594 \begin_layout Plain Layout
8602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8605 \begin_layout Plain Layout
8606 \begin_inset Formula $\dasharrow$
8620 \begin_inset space \hfill{}
8626 \begin_layout Standard
8627 \begin_inset VSpace medskip
8630 Arrows used as accent like e.
8631 \begin_inset space \thinspace{}
8635 \begin_inset space \space{}
8638 vector arrows are listed in
8639 \begin_inset CommandInset ref
8641 reference "sec:Accents"
8648 \begin_layout Standard
8649 \begin_inset VSpace bigskip
8652 Furthermore there are the labeled arrows
8656 \begin_layout Plain Layout
8672 \begin_layout Plain Layout
8690 \begin_layout Plain Layout
8697 \begin_layout Plain Layout
8712 When inserting one of these commands in a formula, an arrow with two blue
8713 boxes appear where the label can be inserted.
8714 The length of the arrow adapts to the label width.
8717 \begin_layout Standard
8719 \begin_inset Tabular
8720 <lyxtabular version="3" rows="3" columns="2">
8722 <column alignment="center" valignment="top" width="0pt">
8723 <column alignment="center" valignment="top" width="0pt">
8725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8728 \begin_layout Plain Layout
8734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8737 \begin_layout Plain Layout
8739 \begin_inset Note Note
8742 \begin_layout Plain Layout
8749 is only used as spacer.
8761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8764 \begin_layout Plain Layout
8771 \begin_layout Plain Layout
8781 \begin_inset Formula $\downarrow$
8785 \begin_inset Formula $\to$
8793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8796 \begin_layout Plain Layout
8797 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8810 \begin_layout Plain Layout
8817 \begin_layout Plain Layout
8827 \begin_inset Formula $\downarrow$
8831 \begin_inset Formula $\to$
8839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8842 \begin_layout Plain Layout
8843 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8859 \begin_layout Subsection
8860 Vertical and diagonal Arrows
8864 \begin_layout Plain Layout
8874 \begin_layout Plain Layout
8883 \begin_layout Standard
8884 \begin_inset space \hfill{}
8888 \begin_inset Tabular
8889 <lyxtabular version="3" rows="7" columns="2">
8891 <column alignment="center" valignment="top" width="0pt">
8892 <column alignment="center" valignment="top" width="0pt">
8894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8897 \begin_layout Plain Layout
8903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8906 \begin_layout Plain Layout
8914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8917 \begin_layout Plain Layout
8925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8928 \begin_layout Plain Layout
8929 \begin_inset Formula $\uparrow$
8939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8942 \begin_layout Plain Layout
8950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8953 \begin_layout Plain Layout
8954 \begin_inset Formula $\Uparrow$
8964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8967 \begin_layout Plain Layout
8975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8978 \begin_layout Plain Layout
8979 \begin_inset Formula $\updownarrow$
8989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8992 \begin_layout Plain Layout
9000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9003 \begin_layout Plain Layout
9004 \begin_inset Formula $\Updownarrow$
9014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9017 \begin_layout Plain Layout
9025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9028 \begin_layout Plain Layout
9029 \begin_inset Formula $\Downarrow$
9039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9042 \begin_layout Plain Layout
9050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9053 \begin_layout Plain Layout
9054 \begin_inset Formula $\downarrow$
9068 \begin_inset space \hfill{}
9072 \begin_inset Tabular
9073 <lyxtabular version="3" rows="5" columns="2">
9075 <column alignment="center" valignment="top" width="0pt">
9076 <column alignment="center" valignment="top" width="0pt">
9078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9081 \begin_layout Plain Layout
9087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9090 \begin_layout Plain Layout
9098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9101 \begin_layout Plain Layout
9109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9112 \begin_layout Plain Layout
9113 \begin_inset Formula $\nearrow$
9123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9126 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9138 \begin_inset Formula $\searrow$
9148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9151 \begin_layout Plain Layout
9159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9162 \begin_layout Plain Layout
9163 \begin_inset Formula $\swarrow$
9173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9176 \begin_layout Plain Layout
9184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9187 \begin_layout Plain Layout
9188 \begin_inset Formula $\nwarrow$
9202 \begin_inset space \hfill{}
9208 \begin_layout Standard
9209 \begin_inset VSpace medskip
9212 Vertical arrows can be used also as delimiter together with the commands
9214 \begin_inset CommandInset ref
9216 reference "sub:Manual-Bracket-Size"
9221 \begin_inset CommandInset ref
9223 reference "sub:Automatic-Bracket-Size"
9230 \begin_layout Standard
9231 \begin_inset Newpage newpage
9237 \begin_layout Section
9239 \begin_inset CommandInset label
9249 \begin_layout Plain Layout
9258 \begin_layout Standard
9259 Accents can be inserted via the math toolbar button
9260 \begin_inset Graphics
9261 filename ../images/math/hat.png
9266 or the commands listed in the following subsections.
9269 \begin_layout Subsection
9270 Accents for one Character
9274 \begin_layout Plain Layout
9287 \begin_layout Plain Layout
9289 \begin_inset CommandInset ref
9291 reference "sub:Accents-in-Text"
9304 \begin_layout Plain Layout
9312 \begin_inset Note Note
9315 \begin_layout Plain Layout
9318 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9321 \begin_layout Plain Layout
9324 texorpdfstring is in section
9325 \begin_inset CommandInset ref
9327 reference "sub:Formulas-in-Section"
9337 \begin_inset CommandInset label
9339 name "sub:Accents-for-one"
9347 \begin_layout Plain Layout
9348 Accents ! for one character
9356 \begin_layout Standard
9357 \begin_inset space \hfill{}
9361 \begin_inset Tabular
9362 <lyxtabular version="3" rows="8" columns="2">
9364 <column alignment="center" valignment="top" width="0pt">
9365 <column alignment="center" valignment="top" width="0pt">
9367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9370 \begin_layout Plain Layout
9376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9379 \begin_layout Plain Layout
9381 \begin_inset Note Note
9384 \begin_layout Plain Layout
9391 is only used as spacer.
9403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9406 \begin_layout Plain Layout
9413 \begin_layout Plain Layout
9427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9430 \begin_layout Plain Layout
9431 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9441 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9444 \begin_layout Plain Layout
9451 \begin_layout Plain Layout
9465 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9468 \begin_layout Plain Layout
9469 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9482 \begin_layout Plain Layout
9489 \begin_layout Plain Layout
9503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9506 \begin_layout Plain Layout
9507 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9520 \begin_layout Plain Layout
9528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9531 \begin_layout Plain Layout
9532 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9545 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9565 \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 $\raisebox{5mm}{}\vec{A}$
9590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9593 \begin_layout Plain Layout
9600 \begin_layout Plain Layout
9614 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9617 \begin_layout Plain Layout
9618 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9628 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9631 \begin_layout Plain Layout
9638 \begin_layout Plain Layout
9652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9655 \begin_layout Plain Layout
9656 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9670 \begin_inset space \hfill{}
9674 \begin_inset Tabular
9675 <lyxtabular version="3" rows="7" columns="2">
9677 <column alignment="center" valignment="top" width="0pt">
9678 <column alignment="center" valignment="top" width="0pt">
9680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9683 \begin_layout Plain Layout
9689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9692 \begin_layout Plain Layout
9700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9703 \begin_layout Plain Layout
9710 \begin_layout Plain Layout
9724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9727 \begin_layout Plain Layout
9728 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9741 \begin_layout Plain Layout
9748 \begin_layout Plain Layout
9762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9765 \begin_layout Plain Layout
9766 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9786 \begin_layout Plain Layout
9800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9803 \begin_layout Plain Layout
9804 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9817 \begin_layout Plain Layout
9824 \begin_layout Plain Layout
9838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9841 \begin_layout Plain Layout
9842 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9855 \begin_layout Plain Layout
9862 \begin_layout Plain Layout
9876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9879 \begin_layout Plain Layout
9880 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9893 \begin_layout Plain Layout
9900 \begin_layout Plain Layout
9914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9917 \begin_layout Plain Layout
9918 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9932 \begin_inset space \hfill{}
9938 \begin_layout Standard
9939 \begin_inset VSpace bigskip
9945 \begin_layout Standard
9946 You can directly insert accents like é to formulas.
9947 LyX will transform them to the corresponding accent command.
9952 \begin_layout Plain Layout
9958 it is better to insert a quotation mark before the vowel.
9959 These two characters are then treated by LaTeX as
9963 character when the formula part with the umlaut is marked as German.
9971 \begin_inset Quotes eld
9975 \begin_inset Quotes erd
9978 umlauts are created as demonstrated in the following example:
9981 \begin_layout Standard
9982 \begin_inset VSpace -2mm
9988 \begin_layout Standard
9990 \begin_inset Tabular
9991 <lyxtabular version="3" rows="3" columns="2">
9993 <column alignment="center" valignment="top" width="0">
9994 <column alignment="center" valignment="top" width="0">
9996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9999 \begin_layout Plain Layout
10005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10008 \begin_layout Plain Layout
10010 \begin_inset Note Note
10013 \begin_layout Plain Layout
10021 \begin_inset space \thinspace{}
10024 pt space are only used as spacer.
10036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10039 \begin_layout Plain Layout
10042 \begin_inset Quotes grd
10050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10053 \begin_layout Plain Layout
10054 \begin_inset space \hspace{}
10061 \begin_inset Formula $"i$
10071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10074 \begin_layout Plain Layout
10081 \begin_layout Plain Layout
10095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10098 \begin_layout Plain Layout
10099 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10115 \begin_layout Standard
10116 Another advantage to
10122 is that umlauts can directly be converted to mathematical text because
10123 the accent commands above are
10129 in mathematical text
10132 To convert an accented character to mathematical text, only the character
10133 under the accent may be converted.
10134 This applies also for all other conversions, e.
10135 \begin_inset space \thinspace{}
10139 \begin_inset space \space{}
10145 \begin_layout Standard
10146 In mathematical text, umlauts and other accented characters can directly
10150 \begin_layout Subsection
10151 Accents for Operators
10155 \begin_layout Plain Layout
10156 Accents ! for operators
10164 \begin_layout Standard
10175 \begin_layout Plain Layout
10193 \begin_layout Plain Layout
10201 characters can be placed above or below an operator, respectively, to accent
10213 \begin_layout Plain Layout
10221 characters can be set before and behind an operator.
10222 The command scheme is:
10225 \begin_layout Standard
10241 \begin_layout Standard
10248 must always be before the operator that should be accented.
10249 You can accent with several characters and even with other operators and
10257 for example only characters behind an operator, write nothing between the
10258 first braces but don't omit the braces.
10261 \begin_layout Standard
10262 For example the command
10267 \begin_inset Formula $\to$
10277 \begin_inset Formula $\to$
10286 \begin_layout Plain Layout
10302 \begin_inset Formula \[
10303 \sideset{}{'}\sum_{k=1}^{n}\]
10310 \begin_layout Standard
10319 \begin_layout Plain Layout
10334 \begin_layout Plain Layout
10346 \begin_inset Formula $\uparrow$
10354 \begin_inset Formula \[
10355 \overset{a}{\maltese}\]
10359 As seen in the last example, with
10371 also symbols and characters can be accented; with
10377 this is not possible.
10380 \begin_layout Subsection
10381 Accents for several Characters
10385 \begin_layout Plain Layout
10386 Accents ! for several characters
10394 \begin_layout Standard
10395 \begin_inset space \hfill{}
10399 \begin_inset Tabular
10400 <lyxtabular version="3" rows="5" columns="2">
10402 <column alignment="center" valignment="top" width="0pt">
10403 <column alignment="center" valignment="top" width="0pt">
10405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10408 \begin_layout Plain Layout
10414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10417 \begin_layout Plain Layout
10419 \begin_inset Note Note
10422 \begin_layout Plain Layout
10429 is only used as spacer.
10441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10444 \begin_layout Plain Layout
10451 \begin_layout Plain Layout
10465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10468 \begin_layout Plain Layout
10469 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10482 \begin_layout Plain Layout
10489 \begin_layout Plain Layout
10503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10506 \begin_layout Plain Layout
10507 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10520 \begin_layout Plain Layout
10527 \begin_layout Plain Layout
10541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10544 \begin_layout Plain Layout
10545 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10558 \begin_layout Plain Layout
10561 underleftrightarrow
10565 \begin_layout Plain Layout
10579 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10582 \begin_layout Plain Layout
10583 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10597 \begin_inset space \hfill{}
10601 \begin_inset Tabular
10602 <lyxtabular version="3" rows="5" columns="2">
10604 <column alignment="center" valignment="top" width="0pt">
10605 <column alignment="center" valignment="top" width="0pt">
10607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10610 \begin_layout Plain Layout
10616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10619 \begin_layout Plain Layout
10627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10630 \begin_layout Plain Layout
10637 \begin_layout Plain Layout
10651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10654 \begin_layout Plain Layout
10655 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10668 \begin_layout Plain Layout
10675 \begin_layout Plain Layout
10689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10692 \begin_layout Plain Layout
10693 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10703 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10706 \begin_layout Plain Layout
10713 \begin_layout Plain Layout
10727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10730 \begin_layout Plain Layout
10731 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10741 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10744 \begin_layout Plain Layout
10751 \begin_layout Plain Layout
10765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10768 \begin_layout Plain Layout
10769 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10783 \begin_inset space \hfill{}
10789 \begin_layout Standard
10790 \begin_inset VSpace medskip
10793 With these commands as many characters as you like can be accented.
10806 will only be set in the output with a length of three characters, as shown
10807 in the following example:
10808 \begin_inset Formula \[
10809 \widetilde{A+B=C-D}\]
10816 \begin_layout Standard
10827 \begin_layout Plain Layout
10845 \begin_layout Plain Layout
10853 described in the previous subsection it is also possible to accent several
10863 \begin_layout Plain Layout
10873 \begin_inset Formula $\downarrow$
10879 \begin_inset Formula \[
10880 \underset{***}{A=B}\]
10887 \begin_layout Section
10889 \begin_inset CommandInset label
10899 \begin_layout Plain Layout
10908 \begin_layout Subsection
10910 \begin_inset CommandInset label
10912 name "sub:Predefined-Space"
10920 \begin_layout Plain Layout
10921 Space ! horizontal ! predefined
10929 \begin_layout Standard
10930 Sometimes it is necessary to insert horizontal space to a formula.
10931 This is done by inserting a protected space (shortcut
10934 arg "space-insert protected"
10939 \begin_inset Quotes eld
10949 \begin_layout Plain Layout
10962 \begin_inset Quotes erd
10965 appears and by pressing
10969 several times one can select one of eight different space sizes.
10970 The spaces can also be inserted using the math toolbar button
10971 \begin_inset Graphics
10972 filename ../images/math/space.png
10977 or special commands.
10978 Independent from the inserted command, one can select the size again by
10986 \begin_layout Standard
10989 \begin_inset VSpace -5mm
10993 \begin_inset Tabular
10994 <lyxtabular version="3" rows="3" columns="7">
10996 <column alignment="center" valignment="middle" width="6.8cm">
10997 <column alignment="center" valignment="top" width="0">
10998 <column alignment="center" valignment="top" width="0">
10999 <column alignment="center" valignment="top" width="0">
11000 <column alignment="center" valignment="top" width="0">
11001 <column alignment="center" valignment="top" width="0">
11002 <column alignment="center" valignment="top" width="0">
11004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11007 \begin_layout Plain Layout
11013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11016 \begin_layout Plain Layout
11024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11027 \begin_layout Plain Layout
11035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11038 \begin_layout Plain Layout
11046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11049 \begin_layout Plain Layout
11057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11060 \begin_layout Plain Layout
11068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11071 \begin_layout Plain Layout
11081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11084 \begin_layout Plain Layout
11089 keystrokes after inserting the protected space
11094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11097 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11106 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11133 \begin_layout Plain Layout
11139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11142 \begin_layout Plain Layout
11150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11153 \begin_layout Plain Layout
11159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11162 \begin_layout Plain Layout
11163 \begin_inset Formula $A\, B$
11171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11174 \begin_layout Plain Layout
11175 \begin_inset Formula $A\: B$
11183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11186 \begin_layout Plain Layout
11187 \begin_inset Formula $A\; B$
11195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11198 \begin_layout Plain Layout
11199 \begin_inset Formula $A\quad B$
11207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11210 \begin_layout Plain Layout
11211 \begin_inset Formula $A\qquad B$
11219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11223 \begin_inset Formula $A\! B$
11239 \begin_layout Standard
11240 The last size seem to produce no space.
11241 It is displayed red in LyX contrary to the other sizes, because it is a
11243 There are two more negative spaces:
11246 \begin_layout Standard
11248 \begin_inset Tabular
11249 <lyxtabular version="3" rows="3" columns="3">
11251 <column alignment="center" valignment="middle" width="6.8cm">
11252 <column alignment="center" valignment="top" width="0pt">
11253 <column alignment="center" valignment="top" width="0pt">
11255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11258 \begin_layout Plain Layout
11264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11267 \begin_layout Plain Layout
11275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11278 \begin_layout Plain Layout
11288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11291 \begin_layout Plain Layout
11296 keystrokes after inserting the protected space
11301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11304 \begin_layout Plain Layout
11310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11313 \begin_layout Plain Layout
11321 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11324 \begin_layout Plain Layout
11330 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11333 \begin_layout Plain Layout
11334 \begin_inset Formula $A\negmedspace B$
11342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11345 \begin_layout Plain Layout
11346 \begin_inset Formula $A\negthickspace B$
11362 \begin_layout Standard
11363 Negative spaces can lead to characters overlapping each other.
11364 Thus they can be used to enforce ligatures, what is e.
11365 \begin_inset space \thinspace{}
11369 \begin_inset space \space{}
11372 useful for summation operators:
11375 \begin_layout Standard
11377 \begin_inset Tabular
11378 <lyxtabular version="3" rows="3" columns="2">
11380 <column alignment="center" valignment="top" width="0">
11381 <column alignment="center" valignment="top" width="0">
11383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11386 \begin_layout Plain Layout
11392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11395 \begin_layout Plain Layout
11397 \begin_inset Note Note
11400 \begin_layout Plain Layout
11407 is only used as spacer.
11419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11422 \begin_layout Plain Layout
11431 \begin_layout Plain Layout
11445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11448 \begin_layout Plain Layout
11449 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11462 \begin_layout Plain Layout
11473 \begin_layout Plain Layout
11487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11490 \begin_layout Plain Layout
11491 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11507 \begin_layout Standard
11508 Relations like for example equal signs, are always surrounded by space.
11509 To suppress this, the equal sign is placed into a TeX-brace.
11510 The following example demonstrates this:
11513 \begin_layout Standard
11515 \begin_inset Tabular
11516 <lyxtabular version="3" rows="2" columns="2">
11518 <column alignment="center" valignment="top" width="0pt">
11519 <column alignment="center" valignment="top" width="0pt">
11521 <cell alignment="center" valignment="top" usebox="none">
11524 \begin_layout Plain Layout
11530 <cell alignment="center" valignment="top" usebox="none">
11533 \begin_layout Plain Layout
11534 \begin_inset Formula $A=B$
11544 <cell alignment="center" valignment="top" usebox="none">
11547 \begin_layout Plain Layout
11548 \begin_inset Note Note
11551 \begin_layout Plain Layout
11558 is only used as spacer.
11564 \begin_inset Formula $\raisebox{5mm}{}$
11567 equation without space
11572 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11575 \begin_layout Plain Layout
11576 \begin_inset Formula $A{=}B$
11592 \begin_layout Standard
11594 The command for the last formula is:
11599 \begin_inset Formula $\to$
11605 \begin_layout Standard
11606 \begin_inset VSpace bigskip
11609 Spaces are needed for physical units, because the space between the value
11610 and the unit is the smallest one and not a normal space.
11611 For units in text, the smallest space is inserted via the menu
11613 Insert\SpecialChar \menuseparator
11614 Formatting\SpecialChar \menuseparator
11616 \begin_inset space ~
11624 arg "space-insert thin"
11630 \begin_layout Standard
11631 An example to visualize the difference:
11634 \begin_layout Standard
11635 \begin_inset Tabular
11636 <lyxtabular version="3" rows="2" columns="2">
11638 <column alignment="left" valignment="top" width="0">
11639 <column alignment="left" valignment="top" width="0">
11641 <cell alignment="center" valignment="top" usebox="none">
11644 \begin_layout Plain Layout
11646 \begin_inset Formula $\cdot$
11654 <cell alignment="center" valignment="top" usebox="none">
11657 \begin_layout Plain Layout
11658 space between value and unit
11665 <cell alignment="center" valignment="top" usebox="none">
11668 \begin_layout Plain Layout
11670 \begin_inset space \thinspace{}
11674 \begin_inset Formula $\cdot$
11682 <cell alignment="center" valignment="top" usebox="none">
11685 \begin_layout Plain Layout
11686 smallest space between value and unit
11699 \begin_layout Subsection
11704 \begin_layout Plain Layout
11717 \begin_layout Plain Layout
11718 for vertical space in formulas see
11719 \begin_inset CommandInset ref
11721 reference "sub:Line-Separation"
11734 \begin_layout Plain Layout
11742 \begin_inset Note Note
11745 \begin_layout Plain Layout
11748 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11751 \begin_layout Plain Layout
11754 texorpdfstring is in section
11755 \begin_inset CommandInset ref
11757 reference "sub:Formulas-in-Section"
11767 \begin_inset CommandInset label
11769 name "sub:Variable-Space"
11777 \begin_layout Plain Layout
11778 Space ! horizontal ! variable
11786 \begin_layout Standard
11787 Space with a defined length can be inserted in LyX with the command
11788 \begin_inset Newline newline
11801 \begin_layout Plain Layout
11810 For the length all units listed in
11811 \begin_inset CommandInset ref
11813 reference "tab:Available-units"
11817 are allowed, except of the unit
11818 \begin_inset Quotes eld
11822 \begin_inset Quotes erd
11826 The length may also be negative.
11827 To insert so many space that the formula uses all available space, the
11838 \begin_layout Plain Layout
11849 \begin_layout Standard
11850 \begin_inset VSpace -1mm
11856 \begin_layout Standard
11858 \begin_inset Tabular
11859 <lyxtabular version="3" rows="4" columns="2">
11861 <column alignment="center" valignment="top" width="0">
11862 <column alignment="center" valignment="top" width="0">
11864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11867 \begin_layout Plain Layout
11873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11876 \begin_layout Plain Layout
11884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11887 \begin_layout Plain Layout
11891 \begin_inset Formula $\to$
11901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11904 \begin_layout Plain Layout
11905 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11918 \begin_layout Plain Layout
11922 \begin_inset Formula $\to$
11932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11935 \begin_layout Plain Layout
11936 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11949 \begin_layout Plain Layout
11956 \begin_layout Plain Layout
11970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11973 \begin_layout Plain Layout
11974 \begin_inset Formula $A=A\hfill B=B$
11990 \begin_layout Standard
11991 In the last example the available space is given by the longest column entry
11993 In an inline formula the space depends on the length of the line in which
12001 Thus, when the line uses the full width, no space will be created.
12008 only has an effect on displayed formulas when the formula style
12013 (Formula styles are explained in
12014 \begin_inset CommandInset ref
12016 reference "sec:Formula-Styles"
12023 \begin_layout Standard
12030 , there are the commands
12042 that fill the space with a pattern, see
12043 \begin_inset CommandInset ref
12045 reference "sub:Ellipses"
12052 \begin_layout Standard
12053 For text, variable space can be inserted via the menu
12055 Insert\SpecialChar \menuseparator
12056 Formatting\SpecialChar \menuseparator
12058 \begin_inset space ~
12063 , what is not possible in formulas:
12066 \begin_layout Standard
12067 This is a line with
12068 \begin_inset space \hspace{}
12073 \begin_inset space \thinspace{}
12079 \begin_layout Standard
12080 This is a line with
12081 \begin_inset space \hfill{}
12087 \begin_layout Subsection
12088 Space besides inline Formulas
12092 \begin_layout Plain Layout
12093 Space ! besides inline formulas
12101 \begin_layout Standard
12102 The space that surrounds inline formulas can be adjusted with the length
12111 \begin_layout Plain Layout
12122 The value of a length is set with the command
12130 \begin_layout Plain Layout
12140 that has the following scheme:
12143 \begin_layout Standard
12148 setlength{length name}{value}
12151 \begin_layout Standard
12159 \begin_inset space \thinspace{}
12165 \begin_layout Standard
12175 \begin_layout Standard
12176 is inserted in TeX-mode.
12178 \begin_inset space \thinspace{}
12181 mm space will now be set around all inline formulas:
12185 \begin_layout Plain Layout
12199 \begin_layout Standard
12200 This is a line with an inline formula
12201 \begin_inset Formula $A=B$
12205 \begin_inset space \thinspace{}
12208 mm surrounding space.
12212 \begin_layout Plain Layout
12226 \begin_layout Standard
12227 To return to the predefined value,
12233 is set to the value 0
12234 \begin_inset space \thinspace{}
12240 \begin_layout Section
12245 \begin_layout Plain Layout
12255 \begin_layout Plain Layout
12260 \begin_layout Plain Layout
12271 \begin_layout Plain Layout
12286 \begin_layout Standard
12287 Boxes for text are described in chapter
12294 \begin_inset space ~
12302 \begin_layout Subsection
12304 \begin_inset CommandInset label
12306 name "sub:Boxes-with-Frame"
12314 \begin_layout Plain Layout
12323 \begin_layout Standard
12324 It is possible to frame formulas or parts of it with the commands
12334 \begin_layout Plain Layout
12352 \begin_layout Plain Layout
12363 \begin_layout Standard
12364 When one of these commands is inserted to a formula, a blue box appears
12365 within a frame to enter formula parts.
12372 an additional formula has to be created by
12380 \begin_layout Plain Layout
12381 Due to a bug in LyX it is not possible to create a new formula with
12386 \begin_inset CommandInset href
12388 name "LyX-bug #1435"
12389 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12398 , because the box content will otherwise be treated as mathematical text.
12405 is used, a new formula is automatically created inside the frame.
12408 \begin_layout Standard
12415 is not suitable to frame displayed formulas, because the formula will always
12416 be set in the size of the text.
12423 is in contrary not suitable to frame inline formulas, because the formula
12424 will always be set in the size of a displayed formula.
12427 \begin_layout Standard
12434 there is the command
12444 \begin_layout Plain Layout
12452 where additionally the frame width and the alignment can be specified.
12459 is used in the following scheme:
12462 \begin_layout Standard
12467 framebox[frame width][position]{box content}
12470 \begin_layout Standard
12471 The position can either be
12488 right aligns the formula in the box.
12489 When no position is given, the formula will be centered.
12490 \begin_inset Newline newline
12493 Is no width given, also no position can be given.
12494 In this case the frame width is adjusted to the box content like for
12503 \begin_layout Standard
12510 is inserted, a box appears containing three blue boxes.
12511 The first two boxes are surrounded by brackets and denote the two optional
12513 The third box is for formula parts like for
12522 \begin_layout Standard
12524 \begin_inset Note Note
12527 \begin_layout Plain Layout
12528 The table has been set into a minipage to make the footnote appearing.
12529 Otherwise the footnote text would not be displayed.
12535 \begin_inset Box Frameless
12544 height_special "totalheight"
12547 \begin_layout Plain Layout
12549 \begin_inset Tabular
12550 <lyxtabular version="3" rows="5" columns="2">
12552 <column alignment="center" valignment="top" width="0">
12553 <column alignment="center" valignment="top" width="0">
12555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12558 \begin_layout Plain Layout
12563 \begin_layout Plain Layout
12564 Due to a bug in LyX it is not possible to create a new formula with
12569 \begin_inset CommandInset href
12571 name "LyX-bug #1435"
12572 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12589 \begin_layout Plain Layout
12591 \begin_inset Note Note
12594 \begin_layout Plain Layout
12601 is only used as spacer.
12613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12616 \begin_layout Plain Layout
12623 \begin_layout Plain Layout
12642 \begin_layout Plain Layout
12656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12659 \begin_layout Plain Layout
12660 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12673 \begin_layout Plain Layout
12680 \begin_layout Plain Layout
12695 \begin_layout Plain Layout
12709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12712 \begin_layout Plain Layout
12713 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12726 \begin_layout Plain Layout
12733 \begin_layout Plain Layout
12747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12750 \begin_layout Plain Layout
12751 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12764 \begin_layout Plain Layout
12771 \begin_layout Plain Layout
12781 \begin_inset Formula $\to$
12785 \begin_inset Formula $\to$
12798 \begin_layout Plain Layout
12808 \begin_inset Formula $\downarrow$
12816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12819 \begin_layout Plain Layout
12820 \begin_inset Formula $\raisebox{6mm}{}$
12824 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12828 \begin_inset Formula $\raisebox{-4mm}{}$
12849 \begin_layout Standard
12850 The frame thickness can also be adjusted.
12851 To do this the following commands have to be inserted in TeX-mode before
12855 \begin_layout Standard
12865 \begin_inset Quotes eld
12869 \begin_inset Quotes erd
12883 \begin_inset Quotes eld
12887 \begin_inset Quotes erd
12893 \begin_layout Standard
12894 \begin_inset Quotes eld
12898 \begin_inset Quotes erd
12901 specifies the minimal distance between the frame and the first character
12903 An example for this is the following framed formula:
12907 \begin_layout Plain Layout
12919 \begin_inset Formula \[
12924 Before this formula the commands
12927 \begin_layout Standard
12949 \begin_layout Standard
12950 were inserted in TeX-mode.
12951 The given values are used for all following boxes.
12954 \begin_layout Standard
12955 To return to the standard frame size, the command
12958 \begin_layout Standard
12983 \begin_layout Plain Layout
12997 \begin_layout Standard
12998 is inserted in TeX-mode before the next formula.
13001 \begin_layout Subsection
13002 Boxes without Frame
13003 \begin_inset CommandInset label
13005 name "sub:Boxes-without-Frame"
13013 \begin_layout Plain Layout
13014 Boxes ! without frame
13022 \begin_layout Standard
13023 For boxes without a frame there are the following box commands:
13033 \begin_layout Plain Layout
13051 \begin_layout Plain Layout
13069 \begin_layout Plain Layout
13080 \begin_layout Standard
13087 a box can be super- or subscripted.
13088 But in contrary to normal super- and subscripting, the characters in the
13089 box keep their font size.
13096 is used in the following scheme:
13099 \begin_layout Standard
13104 raisebox{height}{box content}
13107 \begin_layout Standard
13108 When the box should contain a formula, an extra formula is needed like for
13118 \begin_layout Standard
13120 \begin_inset Tabular
13121 <lyxtabular version="3" rows="4" columns="2">
13123 <column alignment="center" valignment="top" width="0">
13124 <column alignment="center" valignment="top" width="0">
13126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13129 \begin_layout Plain Layout
13135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13138 \begin_layout Plain Layout
13146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13149 \begin_layout Plain Layout
13153 \begin_inset Formula $\to$
13159 \begin_inset Formula $\to$
13167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13170 \begin_layout Plain Layout
13171 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13184 \begin_layout Plain Layout
13188 \begin_inset Formula $\to$
13194 \begin_inset Formula $\to$
13202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13205 \begin_layout Plain Layout
13206 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13219 \begin_layout Plain Layout
13223 \begin_inset Formula $\to$
13238 \begin_layout Plain Layout
13252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13255 \begin_layout Plain Layout
13259 \begin_layout Plain Layout
13283 \begin_layout Standard
13284 The last formula can currently only be created using TeX-mode because LyX
13285 inserts a box instead of the needed extra formula.
13289 \begin_layout Plain Layout
13291 \begin_inset CommandInset href
13293 name "LyX-bug #1435"
13294 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13306 \begin_layout Standard
13331 , with the difference that there is no frame.
13334 \begin_layout Subsection
13336 \begin_inset CommandInset label
13338 name "sub:Colored-Boxes"
13346 \begin_layout Plain Layout
13355 \begin_layout Standard
13356 To be able to use all commands explained in this section, the LaTeX-package
13365 \begin_layout Plain Layout
13370 is part of every LaTeX standard installation.
13379 \begin_layout Plain Layout
13385 has to be loaded in the LaTeX-preamble with the line
13389 \begin_layout Plain Layout
13390 When text is colored somewhere in the document with a predefined color,
13391 LyX loads the LaTeX-package
13396 Thus it is possible that the package is loaded twice, but this doesn't
13403 \begin_inset Note Note
13406 \begin_layout Plain Layout
13407 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13416 \begin_layout Standard
13424 \begin_layout Standard
13425 \begin_inset VSpace medskip
13428 To color boxes, the command
13438 \begin_layout Plain Layout
13446 is used in the following scheme:
13449 \begin_layout Standard
13454 colorbox{color}{box content}
13457 \begin_layout Standard
13458 The box content can also be a box and a
13464 can also be part of another box (see the 2nd and 3rd example).
13465 When the box should contain a formula, an extra formula has to be created,
13476 \begin_layout Plain Layout
13477 This also applies for the command
13485 \begin_inset CommandInset href
13487 name "LyX-bug #1435"
13488 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13500 \begin_layout Standard
13501 One of the following predefined colors can be chosen:
13504 \begin_layout Standard
13538 \begin_layout Standard
13540 \begin_inset Tabular
13541 <lyxtabular version="3" rows="4" columns="2">
13543 <column alignment="center" valignment="top" width="0">
13544 <column alignment="center" valignment="top" width="0">
13546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13549 \begin_layout Plain Layout
13555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13558 \begin_layout Plain Layout
13560 \begin_inset Note Note
13563 \begin_layout Plain Layout
13570 is only used as spacer.
13582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13585 \begin_layout Plain Layout
13589 \begin_inset Formula $\to$
13599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13602 \begin_layout Plain Layout
13603 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13616 \begin_layout Plain Layout
13620 \begin_inset Formula $\to$
13631 \begin_layout Plain Layout
13645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13648 \begin_layout Plain Layout
13649 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13662 \begin_layout Plain Layout
13669 \begin_layout Plain Layout
13681 \begin_inset Formula $\to$
13691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13694 \begin_layout Plain Layout
13695 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13711 \begin_layout Standard
13718 only colors the box but not the characters in the box.
13719 To color all characters, the whole formula is highlighted and the wanted
13720 color is chosen in the
13723 \begin_inset space ~
13729 The dialog can be called with the toolbar button
13730 \begin_inset Graphics
13731 filename ../images/dialog-show_character.png
13738 Edit\SpecialChar \menuseparator
13740 \begin_inset space ~
13743 Style\SpecialChar \menuseparator
13747 The formula number has then the same color as the formula.
13748 When the formula number should get another color than the formula characters,
13749 the color must be changed within the formula.
13752 \begin_layout Standard
13756 \begin_layout Standard
13759 \begin_inset Formula \begin{equation}
13760 \int A=B\label{eq:red}\end{equation}
13767 \begin_inset Formula \begin{equation}
13768 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13775 \begin_layout Standard
13777 \begin_inset CommandInset ref
13783 is completely colored red.
13784 \begin_inset Newline newline
13788 \begin_inset CommandInset ref
13790 reference "eq:redgreen"
13794 was first completely colored green to set the color for the formula number.
13795 Subsequently the formula characters were colored red.
13798 \begin_layout Standard
13799 \begin_inset VSpace bigskip
13802 To color the frame different than the rest of the box, the command
13812 \begin_layout Plain Layout
13820 is used in the following scheme:
13823 \begin_layout Standard
13828 fcolorbox{frame color}{color}{box content}
13831 \begin_layout Standard
13838 is an extension of the command
13845 The frame width is set, like for
13868 \begin_layout Plain Layout
13880 \begin_inset Formula \[
13881 \fcolorbox{cyan}{magenta}{A=B}\]
13889 \begin_layout Plain Layout
13903 \begin_layout Standard
13904 This formula was created with the command
13905 \begin_inset Newline newline
13913 \begin_inset Formula $\to$
13919 \begin_inset Formula $\to$
13929 \begin_layout Standard
13930 \begin_inset VSpace bigskip
13933 To use other colors than the predefined ones, they have to be defined first.
13936 \begin_layout Standard
13937 One can for example define the color
13938 \begin_inset Quotes eld
13946 \begin_inset Quotes erd
13949 with the LaTeX-preamble line:
13952 \begin_layout Standard
13957 definecolor{darkgreen}{cmyk}{0.5,
13975 \begin_layout Plain Layout
13986 \begin_layout Standard
13991 is the color space that denotes the colors
14008 The four comma separated numbers are the portion factor for the corresponding
14009 colors of the color space.
14010 The factors can be in the range of 0
14011 \begin_inset space \thinspace{}
14015 \begin_inset space \thinspace{}
14023 also the color space
14027 can be used for definitions.
14044 , so that there are in this case three portion factors for the corresponding
14046 Furthermore there is the color space
14050 with one portion factor for the gray value.
14053 \begin_layout Standard
14054 As example a framed box with the new defined color
14058 where the characters have been colored
14063 \begin_inset Formula \begin{equation}
14064 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14071 \begin_layout Standard
14072 Self-defined colors can also be used for text with the help of the command
14083 \begin_layout Plain Layout
14092 \begin_layout Standard
14096 \begin_layout Plain Layout
14100 textcolor{darkgreen}{
14106 \begin_inset Quotes eld
14110 \begin_inset Quotes erd
14117 \begin_layout Plain Layout
14127 \begin_layout Standard
14138 \begin_layout Plain Layout
14146 is used in the scheme
14150 textcolor{color}{characters to color}
14155 \begin_layout Subsection
14157 \begin_inset CommandInset label
14159 name "sub:Paragraph-Boxes"
14167 \begin_layout Plain Layout
14168 Boxes ! as paragraph
14176 \begin_layout Standard
14177 A box that can contain several lines and paragraphs, a so called paragraph
14178 box (parbox), can be created with the menu
14180 Insert\SpecialChar \menuseparator
14183 or the toolbar button
14184 \begin_inset Graphics
14185 filename ../images/box-insert.png
14193 \begin_layout Standard
14194 The following example shows a framed parbox in a line:
14197 \begin_layout Standard
14198 \begin_inset VSpace medskip
14202 \begin_inset Box Boxed
14211 height_special "totalheight"
14214 \begin_layout Plain Layout
14215 This is a paragraph box.
14217 \begin_inset space \thinspace{}
14220 cm long and can also contain formulas:
14221 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14232 \begin_layout Standard
14233 \begin_inset VSpace medskip
14239 \begin_layout Standard
14240 Such a box is created by right-clicking on the gray box inset.
14241 A dialog pops up showing the box properties.
14255 \begin_inset space \thinspace{}
14260 Vertical Box Alignment
14265 \begin_layout Standard
14266 \begin_inset VSpace medskip
14269 In LaTeX a parbox is created with the command
14279 \begin_layout Plain Layout
14287 that has the following scheme:
14290 \begin_layout Standard
14295 parbox[position]{width}{box content}
14298 \begin_layout Standard
14312 for bottom means that the box is aligned within the surrounding text with
14318 for top this is done with the first line.
14319 When no position is given, the box will be vertically centered, see section
14327 \begin_inset space ~
14332 manual for examples.
14335 \begin_layout Standard
14336 \begin_inset VSpace bigskip
14339 To frame formulas completely, including the formula number, the formula
14340 must be set into a parbox.
14341 To do this, the command
14355 is inserted in TeX-mode before the formula.
14364 \begin_layout Plain Layout
14374 is hereby the line width set for the document.
14375 Because the frame is outside the parbox, 2
14376 \begin_inset space \thinspace{}
14379 times the frame separation and the frame thickness must be subtracted from
14381 As this is not automatically done by LyX due to a bug
14385 \begin_layout Plain Layout
14386 \begin_inset CommandInset href
14388 name "LyX-bug #4483"
14389 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14398 , TeX-mode has to be used.
14399 To be able to multiply and subtract in arguments, the LaTeX-package
14407 \begin_layout Plain Layout
14412 is part of every LaTeX standard installation.
14421 \begin_layout Plain Layout
14427 must be loaded in the LaTeX-preamble with the line
14430 \begin_layout Standard
14438 \begin_layout Standard
14439 Behind the formula both boxes are closed by entering
14444 Here is an example:
14448 \begin_layout Plain Layout
14462 \begin_layout Standard
14466 \begin_layout Plain Layout
14484 \begin_inset Formula \begin{equation}
14485 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14493 \begin_layout Plain Layout
14504 \begin_layout Plain Layout
14518 \begin_layout Standard
14519 \begin_inset VSpace medskip
14522 As a parbox is used as argument of
14528 , there is in this case no difference between
14543 \begin_layout Standard
14544 \begin_inset VSpace bigskip
14547 Paragraph boxes are very useful to comment formulas directly.
14554 is used in combination with the command
14568 \begin_inset CommandInset ref
14570 reference "sub:User-defined-Numbering"
14577 \begin_layout Standard
14578 An example of a formula commented with
14587 \begin_layout Standard
14591 \begin_layout Plain Layout
14604 This is a description.
14605 It is distinctly separated from the formula and multiline.
14609 \begin_layout Plain Layout
14621 \begin_layout Standard
14622 Such a formula must be inserted completely in TeX-mode because LyX does
14623 not yet support the command
14630 The formula is created with the following command sequence:
14633 \begin_layout Standard
14646 is inserted in TeX-mode.
14650 \begin_layout Plain Layout
14651 When the formula style
14663 can also be replaced by
14670 (formula styles see
14671 \begin_inset CommandInset ref
14673 reference "sec:Formula-Styles"
14682 Then the description follows as normal text, and finally
14688 is inserted in TeX-mode.
14701 hereby create a displayed formula.
14704 \begin_layout Standard
14711 can be seen in this example that was
14712 \begin_inset Quotes eld
14716 \begin_inset Quotes erd
14719 using the mathematical textmode:
14720 \begin_inset Formula \[
14721 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14728 \begin_layout Section
14733 \begin_layout Plain Layout
14742 \begin_layout Subsection
14744 \begin_inset CommandInset label
14746 name "sub:Big-Operators"
14754 \begin_layout Plain Layout
14764 \begin_layout Plain Layout
14774 \begin_layout Plain Layout
14783 \begin_layout Standard
14784 To be able to use all integral operators listed here, the option
14786 Use esint package automatically
14788 must be set in the document settings under
14791 \begin_inset space ~
14799 \begin_layout Standard
14800 \begin_inset space \hfill{}
14804 \begin_inset Tabular
14805 <lyxtabular version="3" rows="11" columns="2">
14807 <column alignment="center" valignment="top" width="0pt">
14808 <column alignment="center" valignment="top" width="0pt">
14810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14813 \begin_layout Plain Layout
14819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14822 \begin_layout Plain Layout
14830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14833 \begin_layout Plain Layout
14840 \begin_layout Plain Layout
14853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14856 \begin_layout Plain Layout
14857 \begin_inset Formula $\sum$
14867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14870 \begin_layout Plain Layout
14877 \begin_layout Plain Layout
14890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14893 \begin_layout Plain Layout
14894 \begin_inset Formula $\int$
14904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14907 \begin_layout Plain Layout
14915 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14918 \begin_layout Plain Layout
14919 \begin_inset Formula $\intop$
14929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14932 \begin_layout Plain Layout
14940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14943 \begin_layout Plain Layout
14944 \begin_inset Formula $\oint$
14954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14957 \begin_layout Plain Layout
14965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14968 \begin_layout Plain Layout
14969 \begin_inset Formula $\ointop$
14979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14982 \begin_layout Plain Layout
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14993 \begin_layout Plain Layout
14994 \begin_inset Formula $\ointctrclockwise$
15004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15007 \begin_layout Plain Layout
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15018 \begin_layout Plain Layout
15019 \begin_inset Formula $\ointclockwise$
15029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15032 \begin_layout Plain Layout
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15043 \begin_layout Plain Layout
15044 \begin_inset Formula $\sqint$
15054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15057 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\bigcap$
15079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\bigcup$
15108 \begin_inset space \hfill{}
15112 \begin_inset Tabular
15113 <lyxtabular version="3" rows="10" columns="2">
15115 <column alignment="center" valignment="top" width="0pt">
15116 <column alignment="center" valignment="top" width="0pt">
15118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15130 \begin_layout Plain Layout
15138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15141 \begin_layout Plain Layout
15148 \begin_layout Plain Layout
15161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15164 \begin_layout Plain Layout
15165 \begin_inset Formula $\prod$
15175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15189 \begin_layout Plain Layout
15190 \begin_inset Formula $\coprod$
15200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15203 \begin_layout Plain Layout
15211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15214 \begin_layout Plain Layout
15215 \begin_inset Formula $\bigodot$
15225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15228 \begin_layout Plain Layout
15236 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15239 \begin_layout Plain Layout
15240 \begin_inset Formula $\bigotimes$
15250 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15253 \begin_layout Plain Layout
15261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15264 \begin_layout Plain Layout
15265 \begin_inset Formula $\bigoplus$
15275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15278 \begin_layout Plain Layout
15286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15289 \begin_layout Plain Layout
15290 \begin_inset Formula $\bigwedge$
15300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15303 \begin_layout Plain Layout
15311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15314 \begin_layout Plain Layout
15315 \begin_inset Formula $\bigvee$
15325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15328 \begin_layout Plain Layout
15336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15339 \begin_layout Plain Layout
15340 \begin_inset Formula $\bigsqcup$
15350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15353 \begin_layout Plain Layout
15361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15364 \begin_layout Plain Layout
15365 \begin_inset Formula $\biguplus$
15379 \begin_inset space \hfill{}
15385 \begin_layout Standard
15386 All big operators can also be inserted via the math toolbar button
15387 \begin_inset Graphics
15388 filename ../images/math/intop.png
15396 \begin_layout Standard
15397 The operators are called big because they are bigger than the sometimes
15398 equal looking binary operators.
15399 All big operators can have limits as described in the next subsection.
15402 \begin_layout Standard
15428 \begin_inset space ~
15431 in the style the operator limits are displayed, see
15432 \begin_inset CommandInset ref
15434 reference "sub:Operator-Limits"
15442 \begin_layout Subsubsection*
15443 Advices for Integrals
15446 \begin_layout Standard
15451 in an integral is an operator, that therefore has to be set upright.
15452 This is done by highlighting the
15456 and using the keyboard shortcut
15466 \begin_layout Plain Layout
15472 \begin_inset CommandInset ref
15474 reference "sub:Font-Styles"
15484 Finally the smallest space is inserted before the
15488 , as this is usual for operators.
15492 \begin_layout Standard
15494 \begin_inset Formula $\int A(x)dx$
15498 \begin_inset Newline newline
15505 \begin_layout Plain Layout
15515 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15521 \begin_layout Standard
15522 For multiple integrals there are the following commands:
15523 \begin_inset VSpace medskip
15529 \begin_layout Standard
15530 \begin_inset space \hfill{}
15534 \begin_inset Tabular
15535 <lyxtabular version="3" rows="4" columns="2">
15537 <column alignment="center" valignment="top" width="0">
15538 <column alignment="center" valignment="top" width="0">
15540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15543 \begin_layout Plain Layout
15549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15552 \begin_layout Plain Layout
15554 \begin_inset Note Note
15557 \begin_layout Plain Layout
15564 is only used as spacer.
15576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15579 \begin_layout Plain Layout
15587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15590 \begin_layout Plain Layout
15591 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15604 \begin_layout Plain Layout
15612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15615 \begin_layout Plain Layout
15616 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15629 \begin_layout Plain Layout
15637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15640 \begin_layout Plain Layout
15641 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15655 \begin_inset space \hfill{}
15659 \begin_inset Tabular
15660 <lyxtabular version="3" rows="4" columns="2">
15662 <column alignment="center" valignment="top" width="0">
15663 <column alignment="center" valignment="top" width="0">
15665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15668 \begin_layout Plain Layout
15674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15677 \begin_layout Plain Layout
15685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15688 \begin_layout Plain Layout
15696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15699 \begin_layout Plain Layout
15700 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15713 \begin_layout Plain Layout
15721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15724 \begin_layout Plain Layout
15725 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15738 \begin_layout Plain Layout
15746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15749 \begin_layout Plain Layout
15750 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15764 \begin_inset space \hfill{}
15770 \begin_layout Subsection
15772 \begin_inset CommandInset label
15774 name "sub:Operator-Limits"
15782 \begin_layout Plain Layout
15791 \begin_layout Standard
15792 Limits are created by super- and subscripts:
15795 \begin_layout Standard
15797 \begin_inset Tabular
15798 <lyxtabular version="3" rows="2" columns="2">
15800 <column alignment="center" valignment="top" width="0pt">
15801 <column alignment="center" valignment="top" width="0pt">
15803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15806 \begin_layout Plain Layout
15812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15815 \begin_layout Plain Layout
15817 \begin_inset Note Note
15820 \begin_layout Plain Layout
15827 is only used as spacer.
15839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15842 \begin_layout Plain Layout
15851 \begin_layout Plain Layout
15861 \begin_inset Formula $\to$
15865 \begin_inset Formula $\to$
15873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15876 \begin_layout Plain Layout
15877 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15893 \begin_layout Standard
15894 Limits of inline formulas are set right beside the operator.
15895 Limits in displayed formulas are set above or below the operator, except
15896 of integral limits.
15899 \begin_layout Standard
15900 To force that the limits are set beside the operator, the cursor is set
15901 directly behind the operator and the limits type is changed with the menu
15904 Edit\SpecialChar \menuseparator
15905 Math\SpecialChar \menuseparator
15924 \begin_layout Standard
15925 The default limits type is this:
15926 \begin_inset Formula \[
15927 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15931 This is how it looks when the limits type was changed to
15938 \begin_inset Formula \[
15939 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15943 For integrals, except of
15955 , the limits are by default set beside the operator.
15956 But for multiple integrals the limits are often set below the operator.
15957 In the following example the limits type was therefore set to
15961 and so set below the integrals:
15962 \begin_inset Formula \begin{equation}
15963 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15970 \begin_layout Standard
15971 \begin_inset VSpace medskip
15974 To specify conditions for limits, the commands
15984 \begin_layout Plain Layout
16002 \begin_layout Plain Layout
16011 To create for example this expression
16012 \begin_inset Formula \begin{equation}
16013 \sum_{\begin{subarray}{c}
16015 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16022 \begin_layout Standard
16023 the following has to be done:
16024 \begin_inset Newline newline
16039 \begin_layout Plain Layout
16051 One is now in a blue box under the summation operator and insert there
16060 \begin_layout Plain Layout
16072 The blue box is now within a purple box and now several lines can be written
16074 A new line is created by inserting a line break (
16077 arg "newline-insert newline"
16082 \begin_inset Newline newline
16087 0<k<1000 Ctrl+Return
16088 \begin_inset Newline newline
16093 is typed in, a new box appears below for the new line.
16096 \begin_layout Standard
16097 The alignment of the lines can be changed to left aligned with the
16107 Edit\SpecialChar \menuseparator
16111 To get right alignment,
16119 \begin_layout Plain Layout
16130 is inserted at the beginning of the line.
16133 \begin_layout Standard
16146 with the difference that the lines are always centered.
16149 \begin_layout Standard
16150 \begin_inset VSpace bigskip
16154 \begin_inset CommandInset ref
16156 reference "eq:substack"
16160 there can be too much space beside an operator, because the characters
16161 following the operator are set beside the limits.
16164 \begin_layout Standard
16165 To avoid this, the following macro can be used in the LaTeX-preamble:
16168 \begin_layout Standard
16182 \begin_inset Newline newline
16194 \begin_inset Newline newline
16201 mathclapinternal #1#2{
16205 mathsurround =0pt #1{#2}$}}
16208 \begin_layout Standard
16209 This defines the command
16219 \begin_layout Plain Layout
16227 that sets the width of the limit to 0
16228 \begin_inset space \thinspace{}
16232 The command scheme is
16235 \begin_layout Standard
16243 \begin_layout Standard
16244 where the limit can consist of several conditions.
16247 \begin_layout Standard
16249 \begin_inset CommandInset ref
16251 reference "eq:substack"
16255 , one uses the command
16258 \begin_layout Standard
16271 \begin_layout Plain Layout
16280 0<k<1000 Ctrl+Return
16283 \begin_layout Standard
16284 to create the lower limit.
16285 The summand is now directly behind the summation operator:
16286 \begin_inset Formula \[
16287 \sum_{\mathclap{\substack{0<k<1000\\
16288 \\k\,\in\,\mathbb{N}}
16296 \begin_layout Standard
16297 \begin_inset VSpace bigskip
16300 How to use one limit for several operators is described in
16301 \begin_inset CommandInset ref
16303 reference "sub:Self-defined-Operators"
16310 \begin_layout Standard
16311 \begin_inset Newpage newpage
16317 \begin_layout Subsection
16319 \begin_inset CommandInset label
16321 name "sub:Binary-Operators"
16329 \begin_layout Plain Layout
16338 \begin_layout Standard
16339 Binary operators are surrounded by space when there is a character before
16341 \begin_inset VSpace medskip
16347 \begin_layout Standard
16348 \begin_inset space \hfill{}
16352 \begin_inset Tabular
16353 <lyxtabular version="3" rows="13" columns="2">
16355 <column alignment="center" valignment="top" width="0pt">
16356 <column alignment="center" valignment="top" width="0pt">
16358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16361 \begin_layout Plain Layout
16363 \begin_inset Note Note
16366 \begin_layout Plain Layout
16373 is only used as spacer.
16383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16386 \begin_layout Plain Layout
16394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16397 \begin_layout Plain Layout
16403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16406 \begin_layout Plain Layout
16407 \begin_inset Formula $+$
16417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16420 \begin_layout Plain Layout
16426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16429 \begin_layout Plain Layout
16430 \begin_inset Formula $-$
16440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16443 \begin_layout Plain Layout
16451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16454 \begin_layout Plain Layout
16455 \begin_inset Formula $\pm$
16465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16468 \begin_layout Plain Layout
16476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16479 \begin_layout Plain Layout
16480 \begin_inset Formula $\mp$
16490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16493 \begin_layout Plain Layout
16501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16504 \begin_layout Plain Layout
16505 \begin_inset Formula $\cdot$
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16518 \begin_layout Plain Layout
16526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16529 \begin_layout Plain Layout
16530 \begin_inset Formula $\times$
16540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16543 \begin_layout Plain Layout
16551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16554 \begin_layout Plain Layout
16555 \begin_inset Formula $\div$
16565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16568 \begin_layout Plain Layout
16572 \begin_layout Plain Layout
16585 \begin_layout Plain Layout
16597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16600 \begin_layout Plain Layout
16601 \begin_inset Formula $*$
16611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16614 \begin_layout Plain Layout
16622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16625 \begin_layout Plain Layout
16626 \begin_inset Formula $\star$
16636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16639 \begin_layout Plain Layout
16647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16650 \begin_layout Plain Layout
16651 \begin_inset Formula $\circ$
16661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16664 \begin_layout Plain Layout
16672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16675 \begin_layout Plain Layout
16676 \begin_inset Formula $\diamond$
16686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16689 \begin_layout Plain Layout
16697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16700 \begin_layout Plain Layout
16701 \begin_inset Formula $\bullet$
16715 \begin_inset space \hfill{}
16719 \begin_inset Tabular
16720 <lyxtabular version="3" rows="13" columns="2">
16722 <column alignment="center" valignment="top" width="0pt">
16723 <column alignment="center" valignment="top" width="0pt">
16725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16728 \begin_layout Plain Layout
16734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16737 \begin_layout Plain Layout
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16748 \begin_layout Plain Layout
16756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16759 \begin_layout Plain Layout
16760 \begin_inset Formula $\nabla$
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16773 \begin_layout Plain Layout
16781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16784 \begin_layout Plain Layout
16785 \begin_inset Formula $\bigtriangledown$
16795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16798 \begin_layout Plain Layout
16806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16809 \begin_layout Plain Layout
16810 \begin_inset Formula $\bigtriangleup$
16820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16823 \begin_layout Plain Layout
16831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16834 \begin_layout Plain Layout
16835 \begin_inset Formula $\Box$
16845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16848 \begin_layout Plain Layout
16856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16859 \begin_layout Plain Layout
16860 \begin_inset Formula $\cap$
16870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16873 \begin_layout Plain Layout
16881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16884 \begin_layout Plain Layout
16885 \begin_inset Formula $\cup$
16895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16898 \begin_layout Plain Layout
16906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16909 \begin_layout Plain Layout
16910 \begin_inset Formula $\dagger$
16920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16923 \begin_layout Plain Layout
16931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16934 \begin_layout Plain Layout
16935 \begin_inset Formula $\ddagger$
16945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16948 \begin_layout Plain Layout
16956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16959 \begin_layout Plain Layout
16960 \begin_inset Formula $\wr$
16970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16973 \begin_layout Plain Layout
16981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16984 \begin_layout Plain Layout
16985 \begin_inset Formula $\bigcirc$
16995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16998 \begin_layout Plain Layout
17006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17009 \begin_layout Plain Layout
17010 \begin_inset Formula $\wedge$
17020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17023 \begin_layout Plain Layout
17031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17034 \begin_layout Plain Layout
17035 \begin_inset Formula $\vee$
17049 \begin_inset space \hfill{}
17053 \begin_inset Tabular
17054 <lyxtabular version="3" rows="13" columns="2">
17056 <column alignment="center" valignment="top" width="0pt">
17057 <column alignment="center" valignment="top" width="0pt">
17059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17062 \begin_layout Plain Layout
17068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17082 \begin_layout Plain Layout
17090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17093 \begin_layout Plain Layout
17094 \begin_inset Formula $\oplus$
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17107 \begin_layout Plain Layout
17115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17118 \begin_layout Plain Layout
17119 \begin_inset Formula $\ominus$
17129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17132 \begin_layout Plain Layout
17140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17143 \begin_layout Plain Layout
17144 \begin_inset Formula $\otimes$
17154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17157 \begin_layout Plain Layout
17165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17168 \begin_layout Plain Layout
17169 \begin_inset Formula $\oslash$
17179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17182 \begin_layout Plain Layout
17190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17193 \begin_layout Plain Layout
17194 \begin_inset Formula $\odot$
17204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17207 \begin_layout Plain Layout
17215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17218 \begin_layout Plain Layout
17219 \begin_inset Formula $\amalg$
17229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17232 \begin_layout Plain Layout
17240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17243 \begin_layout Plain Layout
17244 \begin_inset Formula $\uplus$
17254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17257 \begin_layout Plain Layout
17265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17268 \begin_layout Plain Layout
17269 \begin_inset Formula $\setminus$
17279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17282 \begin_layout Plain Layout
17290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17293 \begin_layout Plain Layout
17294 \begin_inset Formula $\sqcap$
17304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17307 \begin_layout Plain Layout
17315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17318 \begin_layout Plain Layout
17319 \begin_inset Formula $\sqcup$
17329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17332 \begin_layout Plain Layout
17340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17343 \begin_layout Plain Layout
17344 \begin_inset Formula $\triangleleft$
17354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17357 \begin_layout Plain Layout
17365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17368 \begin_layout Plain Layout
17369 \begin_inset Formula $\triangleright$
17383 \begin_inset space \hfill{}
17389 \begin_layout Standard
17390 All binary operators can also be inserted via the math toolbar button
17391 \begin_inset Graphics
17392 filename ../images/math/pm.png
17400 \begin_layout Standard
17401 To typeset the Laplace operator also
17418 \begin_inset Formula $\nabla^{2}$
17421 ) can be used instead of
17430 \begin_layout Standard
17437 Insert\SpecialChar \menuseparator
17449 \begin_layout Subsection
17450 Self-defined Operators
17451 \begin_inset CommandInset label
17453 name "sub:Self-defined-Operators"
17461 \begin_layout Plain Layout
17462 Operators ! self-defined
17470 \begin_layout Standard
17471 With the help of the command
17475 DeclareMathOperator
17481 \begin_layout Plain Layout
17486 DeclareMathOperator
17491 custom operators can be defined in the LaTeX-preamble.
17492 Its command scheme is:
17495 \begin_layout Standard
17500 DeclareMathOperator{new command}{display}
17503 \begin_layout Standard
17504 Display can be characters or symbols that define how the operator looks
17506 To define a big operator a * is set behind the command.
17507 All self-defined big operators can have limits as described in
17508 \begin_inset CommandInset ref
17510 reference "sub:Operator-Limits"
17517 \begin_layout Standard
17518 For example the LaTeX-preamble line
17521 \begin_layout Standard
17526 DeclareMathOperator*{
17533 \begin_layout Standard
17534 defines the command
17540 , that inserts a big operator consisting of the lozenge symbol from
17541 \begin_inset CommandInset ref
17543 reference "sub:Miscellaneous-Symbols"
17548 \begin_inset Formula \[
17549 \Lozenge_{n=1}^{\infty}\]
17553 The command for this formula is:
17564 \begin_inset Formula $\to$
17570 \begin_layout Standard
17571 \begin_inset VSpace bigskip
17574 When self-defined operators are not used several times in the document,
17575 they can also be defined with the commands
17585 \begin_layout Plain Layout
17603 \begin_layout Plain Layout
17611 , which have the following scheme:
17614 \begin_layout Standard
17628 \begin_layout Standard
17635 defines big operators,
17644 \begin_layout Standard
17652 \begin_inset space \thinspace{}
17656 \begin_inset space \space{}
17659 be used to use one limit for several operators:
17662 \begin_layout Standard
17663 \begin_inset Formula \[
17664 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17671 \begin_layout Standard
17672 The command for the formula above is:
17673 \begin_inset Newline newline
17692 \begin_layout Plain Layout
17704 \begin_inset Formula $\to$
17713 \begin_layout Plain Layout
17727 \begin_layout Section
17732 \begin_layout Plain Layout
17741 \begin_layout Subsection
17743 \begin_inset CommandInset label
17745 name "sub:Font-Styles"
17753 \begin_layout Plain Layout
17762 \begin_layout Standard
17763 Latin letters in formulas can be set in one of the following font styles:
17764 \begin_inset VSpace -2mm
17770 \begin_layout Standard
17772 \begin_inset Tabular
17773 <lyxtabular version="3" rows="6" columns="3">
17775 <column alignment="center" valignment="top" width="0">
17776 <column alignment="center" valignment="top" width="0">
17777 <column alignment="center" valignment="top" width="0">
17779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17782 \begin_layout Plain Layout
17788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17791 \begin_layout Plain Layout
17797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Plain Layout
17808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17820 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17840 \begin_inset Formula $\mathbb{ABC}$
17848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17867 \begin_layout Plain Layout
17876 \begin_layout Plain Layout
17892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17895 \begin_layout Plain Layout
17896 \begin_inset Formula $\mathbf{AbC}$
17904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17907 \begin_layout Plain Layout
17920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17932 \begin_layout Plain Layout
17948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17951 \begin_layout Plain Layout
17952 \begin_inset Formula $\boldsymbol{AbC}$
17960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17963 \begin_layout Plain Layout
17966 arg "font-boldsymbol"
17976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17979 \begin_layout Plain Layout
17988 \begin_layout Plain Layout
18004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18007 \begin_layout Plain Layout
18008 \begin_inset Formula $\mathcal{ABC}$
18016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18019 \begin_layout Plain Layout
18032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18035 \begin_layout Plain Layout
18044 \begin_layout Plain Layout
18060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18063 \begin_layout Plain Layout
18064 \begin_inset Formula $\mathfrak{AbC}$
18072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18075 \begin_layout Plain Layout
18089 \begin_layout Standard
18091 \begin_inset Tabular
18092 <lyxtabular version="3" rows="5" columns="3">
18094 <column alignment="center" valignment="top" width="0">
18095 <column alignment="center" valignment="top" width="0">
18096 <column alignment="center" valignment="top" width="0">
18098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18101 \begin_layout Plain Layout
18107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18110 \begin_layout Plain Layout
18116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18119 \begin_layout Plain Layout
18127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18130 \begin_layout Plain Layout
18139 \begin_layout Plain Layout
18155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18158 \begin_layout Plain Layout
18159 \begin_inset Formula $\mathit{AbC}$
18167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18170 \begin_layout Plain Layout
18178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18181 \begin_layout Plain Layout
18190 \begin_layout Plain Layout
18206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18209 \begin_layout Plain Layout
18210 \begin_inset Formula $\mathrm{AbC}$
18218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18221 \begin_layout Plain Layout
18234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18237 \begin_layout Plain Layout
18246 \begin_layout Plain Layout
18262 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18265 \begin_layout Plain Layout
18266 \begin_inset Formula $\mathsf{AbC}$
18274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18277 \begin_layout Plain Layout
18290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18293 \begin_layout Plain Layout
18302 \begin_layout Plain Layout
18318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18321 \begin_layout Plain Layout
18322 \begin_inset Formula $\mathtt{AbC}$
18330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18333 \begin_layout Plain Layout
18336 arg "font-typewriter"
18352 \begin_layout Standard
18353 \begin_inset Note Greyedout
18356 \begin_layout Plain Layout
18373 can only be used for big letters.
18381 \begin_layout Standard
18382 Predefined is the style
18391 \begin_layout Standard
18392 The style commands work also for letters in mathematical constructs:
18393 \begin_inset Formula \[
18394 \mathfrak{A=\frac{b}{C}}\]
18401 \begin_layout Standard
18402 Characters in mathematical text don't appear in a math font style but in
18403 the text font style
18410 That their style can't be set correctly via the text style dialog is a
18415 \begin_layout Plain Layout
18416 \begin_inset CommandInset href
18418 name "LyX-bug #4091"
18419 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18431 \begin_layout Standard
18432 Instead of the style commands the dialog
18434 Edit\SpecialChar \menuseparator
18435 Math\SpecialChar \menuseparator
18438 or the toolbar button
18439 \begin_inset Graphics
18440 filename ../images/math/font.png
18448 \begin_layout Subsection
18450 \begin_inset CommandInset label
18452 name "sub:Bold-Formulas"
18460 \begin_layout Plain Layout
18469 \begin_layout Standard
18470 To make a complete formula bold, the command
18476 from the previous subsection cannot be used, because it doesn't work for
18477 small Greek letters.
18478 Furthermore it prints Latin letters always upright, like in the following
18482 \begin_layout Standard
18483 \begin_inset Formula \[
18484 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18491 \begin_layout Standard
18492 To display the formula correctly, the command
18499 \begin_inset Formula \[
18500 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18504 It is also possible to set the formula in a
18506 boldmath environment
18509 This environment is created by inserting the command
18517 \begin_layout Plain Layout
18528 To end the environment, the command
18536 \begin_layout Plain Layout
18546 is inserted in TeX-mode.
18550 \begin_layout Plain Layout
18560 \begin_inset Formula \[
18561 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18569 \begin_layout Plain Layout
18581 \begin_layout Subsection
18586 \begin_layout Plain Layout
18595 \begin_layout Standard
18596 Formulas can be colored like normal text: Highlight a formula or a formula
18602 Here is a formula in magenta:
18603 \begin_inset Formula \[
18604 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18611 \begin_layout Standard
18612 You can also define your own colors as described in
18613 \begin_inset CommandInset ref
18615 reference "sub:Colored-Boxes"
18620 They can be used with the TeX code command
18630 \begin_layout Plain Layout
18641 \begin_layout Standard
18646 textcolor{color}{characters or formula}
18649 \begin_layout Standard
18650 The following example was colored completely dark green and partly red:
18653 \begin_layout Standard
18657 \begin_layout Plain Layout
18661 textcolor{darkgreen}{
18667 \begin_inset Formula \[
18668 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18676 \begin_layout Plain Layout
18686 \begin_layout Standard
18687 Due to a bug in LyX only complete formulas can be colored with self-defined
18692 \begin_layout Plain Layout
18693 \begin_inset CommandInset href
18695 name "LyX-bug #5269"
18696 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18708 \begin_layout Subsection
18710 \begin_inset CommandInset label
18712 name "sub:Font-Sizes"
18720 \begin_layout Plain Layout
18729 \begin_layout Standard
18730 For characters in formulas there are, analog to characters in text, the
18731 following size commands:
18734 \begin_layout Standard
18778 \begin_inset Newline newline
18800 \begin_layout Standard
18801 The size produced by the commands depends on the document font size, that
18802 corresponds with the command
18809 The other commands produce smaller or larger sizes than
18816 The font size can however not exceed a certain value.
18817 Is for example the document font size 12
18818 \begin_inset space \thinspace{}
18827 switches to the same size as
18837 \begin_layout Standard
18838 A size command is inserted in TeX-mode before the formula and sets the size
18839 for all following formula and text characters.
18840 To switch back to the initial size, the command
18846 is inserted behind the formula in TeX-mode.
18849 \begin_layout Standard
18850 Within a formula the size can only be changed for symbols or letters in
18852 To do this, the size command is inserted in mathematical text.
18853 All following characters until the end of the mathematical text or until
18854 another size command will have the selected size.
18856 \begin_inset VSpace -2mm
18862 \begin_layout Standard
18866 \begin_layout Plain Layout
18876 \begin_inset Formula \[
18877 A=\frac{B}{c}\cdot\maltese\]
18882 \begin_inset Formula \[
18883 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18891 \begin_layout Plain Layout
18903 \begin_layout Standard
18904 \begin_inset VSpace medskip
18907 Before both formulas the command
18914 The command for the second formula is:
18915 \begin_inset Newline newline
18926 \begin_layout Plain Layout
18941 \begin_layout Plain Layout
18956 \begin_layout Plain Layout
18971 \begin_layout Plain Layout
18981 \begin_inset Formula $\to$
18985 \begin_inset Formula $\to$
18989 \begin_inset Newline newline
18993 \begin_inset space \hspace*{}
19007 \begin_layout Plain Layout
19022 \begin_layout Plain Layout
19037 \begin_layout Plain Layout
19049 \begin_layout Standard
19050 If a symbol cannot be displayed in different sizes, it will always be displayed
19051 in the default size.
19054 \begin_layout Section
19059 \begin_layout Plain Layout
19068 \begin_layout Standard
19069 All Greek letters can also be inserted via the toolbar button
19070 \begin_inset Graphics
19071 filename ../images/math/alpha.png
19079 \begin_layout Subsection
19084 \begin_layout Plain Layout
19085 Greek letters ! small
19093 \begin_layout Standard
19094 \begin_inset space \hfill{}
19098 \begin_inset Tabular
19099 <lyxtabular version="3" rows="11" columns="2">
19101 <column alignment="center" valignment="top" width="0pt">
19102 <column alignment="center" valignment="top" width="0pt">
19104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19107 \begin_layout Plain Layout
19113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19116 \begin_layout Plain Layout
19124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19127 \begin_layout Plain Layout
19135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19138 \begin_layout Plain Layout
19139 \begin_inset Formula $\alpha$
19149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19152 \begin_layout Plain Layout
19160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19163 \begin_layout Plain Layout
19164 \begin_inset Formula $\beta$
19174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19177 \begin_layout Plain Layout
19185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19188 \begin_layout Plain Layout
19189 \begin_inset Formula $\gamma$
19199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19202 \begin_layout Plain Layout
19210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19213 \begin_layout Plain Layout
19214 \begin_inset Formula $\delta$
19224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19227 \begin_layout Plain Layout
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19238 \begin_layout Plain Layout
19239 \begin_inset Formula $\epsilon$
19249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19252 \begin_layout Plain Layout
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19263 \begin_layout Plain Layout
19264 \begin_inset Formula $\varepsilon$
19274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19277 \begin_layout Plain Layout
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19288 \begin_layout Plain Layout
19289 \begin_inset Formula $\zeta$
19299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19302 \begin_layout Plain Layout
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19313 \begin_layout Plain Layout
19314 \begin_inset Formula $\eta$
19324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19327 \begin_layout Plain Layout
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19338 \begin_layout Plain Layout
19339 \begin_inset Formula $\theta$
19349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19363 \begin_layout Plain Layout
19364 \begin_inset Formula $\vartheta$
19378 \begin_inset space \hfill{}
19382 \begin_inset Tabular
19383 <lyxtabular version="3" rows="12" columns="2">
19385 <column alignment="center" valignment="top" width="0pt">
19386 <column alignment="center" valignment="top" width="0pt">
19388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19391 \begin_layout Plain Layout
19397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19400 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $\iota$
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\kappa$
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Plain Layout
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Plain Layout
19473 \begin_inset Formula $\varkappa$
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19486 \begin_layout Plain Layout
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Plain Layout
19498 \begin_inset Formula $\lambda$
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Plain Layout
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Plain Layout
19523 \begin_inset Formula $\mu$
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Plain Layout
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Plain Layout
19548 \begin_inset Formula $\nu$
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Plain Layout
19573 \begin_inset Formula $\xi$
19583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19595 \begin_layout Plain Layout
19596 \begin_inset Formula $o$
19606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19609 \begin_layout Plain Layout
19617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19620 \begin_layout Plain Layout
19621 \begin_inset Formula $\pi$
19631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19645 \begin_layout Plain Layout
19646 \begin_inset Formula $\varpi$
19656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19659 \begin_layout Plain Layout
19667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19670 \begin_layout Plain Layout
19671 \begin_inset Formula $\rho$
19685 \begin_inset space \hfill{}
19689 \begin_inset Tabular
19690 <lyxtabular version="3" rows="11" columns="2">
19692 <column alignment="center" valignment="top" width="0pt">
19693 <column alignment="center" valignment="top" width="0pt">
19695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19698 \begin_layout Plain Layout
19704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19707 \begin_layout Plain Layout
19715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19718 \begin_layout Plain Layout
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19729 \begin_layout Plain Layout
19730 \begin_inset Formula $\varrho$
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19743 \begin_layout Plain Layout
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19754 \begin_layout Plain Layout
19755 \begin_inset Formula $\sigma$
19765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19768 \begin_layout Plain Layout
19776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19779 \begin_layout Plain Layout
19780 \begin_inset Formula $\varsigma$
19790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19793 \begin_layout Plain Layout
19801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19804 \begin_layout Plain Layout
19805 \begin_inset Formula $\tau$
19815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19818 \begin_layout Plain Layout
19826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19829 \begin_layout Plain Layout
19830 \begin_inset Formula $\upsilon$
19840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19843 \begin_layout Plain Layout
19851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19854 \begin_layout Plain Layout
19855 \begin_inset Formula $\phi$
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\varphi$
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\chi$
19915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\psi$
19940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\omega$
19969 \begin_inset space \hfill{}
19975 \begin_layout Standard
19976 \begin_inset VSpace medskip
19982 \begin_layout Standard
19983 How to create upright Greek letters is explained in
19984 \begin_inset CommandInset ref
19986 reference "sub:Upright-small-Greek"
19993 \begin_layout Subsection
19998 \begin_layout Plain Layout
19999 Greek letters ! big
20007 \begin_layout Standard
20008 \begin_inset space \hfill{}
20012 \begin_inset Tabular
20013 <lyxtabular version="3" rows="7" columns="2">
20015 <column alignment="center" valignment="top" width="0pt">
20016 <column alignment="center" valignment="top" width="0pt">
20018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20021 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20041 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Plain Layout
20053 \begin_inset Formula $\Gamma$
20063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20066 \begin_layout Plain Layout
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20077 \begin_layout Plain Layout
20078 \begin_inset Formula $\Delta$
20088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20091 \begin_layout Plain Layout
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20102 \begin_layout Plain Layout
20103 \begin_inset Formula $\Theta$
20113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20127 \begin_layout Plain Layout
20128 \begin_inset Formula $\Lambda$
20138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20141 \begin_layout Plain Layout
20149 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20152 \begin_layout Plain Layout
20153 \begin_inset Formula $\Xi$
20163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20166 \begin_layout Plain Layout
20174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20177 \begin_layout Plain Layout
20178 \begin_inset Formula $\Pi$
20192 \begin_inset space \hfill{}
20196 \begin_inset Tabular
20197 <lyxtabular version="3" rows="6" columns="2">
20199 <column alignment="center" valignment="top" width="0pt">
20200 <column alignment="center" valignment="top" width="0pt">
20202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20205 \begin_layout Plain Layout
20211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20225 \begin_layout Plain Layout
20233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20236 \begin_layout Plain Layout
20237 \begin_inset Formula $\Sigma$
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20250 \begin_layout Plain Layout
20258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20261 \begin_layout Plain Layout
20262 \begin_inset Formula $\Upsilon$
20272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20275 \begin_layout Plain Layout
20283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20286 \begin_layout Plain Layout
20287 \begin_inset Formula $\Phi$
20297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20300 \begin_layout Plain Layout
20308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20311 \begin_layout Plain Layout
20312 \begin_inset Formula $\Psi$
20322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20325 \begin_layout Plain Layout
20333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20336 \begin_layout Plain Layout
20337 \begin_inset Formula $\Omega$
20351 \begin_inset space \hfill{}
20357 \begin_layout Standard
20358 \begin_inset VSpace medskip
20361 That the big Greek letters appear upright is caused by a design bug when
20363 To get correct italic big letters, begin every command with
20368 For example the command
20375 \begin_inset Formula $\varGamma$
20381 \begin_layout Subsection
20386 \begin_layout Plain Layout
20387 Greek letters ! bold
20395 \begin_layout Standard
20396 Greek letters cannot be set with different font styles like Latin letters.
20397 They can only be made bold with the command
20407 \begin_layout Plain Layout
20418 \begin_layout Standard
20420 \begin_inset Tabular
20421 <lyxtabular version="3" rows="3" columns="2">
20423 <column alignment="center" valignment="top" width="0">
20424 <column alignment="center" valignment="top" width="0">
20426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20429 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20449 \begin_layout Plain Layout
20461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20464 \begin_layout Plain Layout
20465 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20478 \begin_layout Plain Layout
20490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20493 \begin_layout Plain Layout
20494 \begin_inset Formula $\theta\boldsymbol{\theta}$
20510 \begin_layout Section
20515 \begin_layout Plain Layout
20528 \begin_layout Plain Layout
20529 A list with all symbols of most of the LaTeX-packages can be found in
20530 \begin_inset CommandInset citation
20545 \begin_layout Plain Layout
20553 \begin_inset Note Note
20556 \begin_layout Plain Layout
20559 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20562 \begin_layout Plain Layout
20565 texorpdfstring is in section
20566 \begin_inset CommandInset ref
20568 reference "sub:Formulas-in-Section"
20581 \begin_layout Plain Layout
20590 \begin_layout Standard
20591 Many of the symbols listed in this section can also be inserted via the
20593 \begin_inset Graphics
20594 filename ../images/math/nabla.png
20600 \begin_inset Graphics
20601 filename ../images/math/digamma.png
20609 \begin_layout Subsection
20610 Mathematical Symbols
20611 \begin_inset CommandInset label
20613 name "sub:Mathematical-Symbols"
20621 \begin_layout Plain Layout
20622 Symbols ! mathematical
20630 \begin_layout Standard
20631 \begin_inset space \hfill{}
20635 \begin_inset Tabular
20636 <lyxtabular version="3" rows="10" columns="2">
20638 <column alignment="center" valignment="top" width="0pt">
20639 <column alignment="center" valignment="top" width="0pt">
20641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20644 \begin_layout Plain Layout
20650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20653 \begin_layout Plain Layout
20661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20676 \begin_inset Formula $\neg$
20686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20689 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20701 \begin_inset Formula $\Im$
20711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20714 \begin_layout Plain Layout
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20725 \begin_layout Plain Layout
20726 \begin_inset Formula $\Re$
20736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20739 \begin_layout Plain Layout
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20750 \begin_layout Plain Layout
20751 \begin_inset Formula $\aleph$
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\partial$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\infty$
20811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\wp$
20836 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20850 \begin_layout Plain Layout
20851 \begin_inset Formula $\imath$
20861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20875 \begin_layout Plain Layout
20876 \begin_inset Formula $\jmath$
20890 \begin_inset space \hfill{}
20894 \begin_inset Tabular
20895 <lyxtabular version="3" rows="10" columns="2">
20897 <column alignment="center" valignment="top" width="0pt">
20898 <column alignment="center" valignment="top" width="0pt">
20900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20903 \begin_layout Plain Layout
20909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20912 \begin_layout Plain Layout
20914 \begin_inset Note Note
20917 \begin_layout Plain Layout
20924 is only used as spacer.
20936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20939 \begin_layout Plain Layout
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Plain Layout
20951 \begin_inset Formula $\forall$
20961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20964 \begin_layout Plain Layout
20972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20975 \begin_layout Plain Layout
20976 \begin_inset Formula $\exists$
20986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20989 \begin_layout Plain Layout
20997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21000 \begin_layout Plain Layout
21001 \begin_inset Formula $\nexists$
21011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21014 \begin_layout Plain Layout
21022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21025 \begin_layout Plain Layout
21026 \begin_inset Formula $\emptyset$
21036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21039 \begin_layout Plain Layout
21047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21050 \begin_layout Plain Layout
21051 \begin_inset Formula $\varnothing$
21061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21064 \begin_layout Plain Layout
21072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21075 \begin_layout Plain Layout
21076 \begin_inset Formula $\dag$
21086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21089 \begin_layout Plain Layout
21097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21100 \begin_layout Plain Layout
21101 \begin_inset Formula $\ddag$
21111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21114 \begin_layout Plain Layout
21122 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21125 \begin_layout Plain Layout
21129 \begin_layout Plain Layout
21139 \begin_inset Formula $\complement$
21146 \begin_layout Plain Layout
21160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21163 \begin_layout Plain Layout
21171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21174 \begin_layout Plain Layout
21175 \begin_inset Formula $\Bbbk$
21189 \begin_inset space \hfill{}
21193 \begin_inset Tabular
21194 <lyxtabular version="3" rows="10" columns="2">
21196 <column alignment="center" valignment="top" width="0pt">
21197 <column alignment="center" valignment="top" width="0pt">
21199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21202 \begin_layout Plain Layout
21208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21211 \begin_layout Plain Layout
21219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21234 \begin_inset Formula $\prime$
21244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21247 \begin_layout Plain Layout
21255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21258 \begin_layout Plain Layout
21259 \begin_inset Formula $\backprime$
21269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21272 \begin_layout Plain Layout
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21283 \begin_layout Plain Layout
21284 \begin_inset Formula $\mho$
21294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21297 \begin_layout Plain Layout
21305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21308 \begin_layout Plain Layout
21309 \begin_inset Formula $\triangle$
21319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21322 \begin_layout Plain Layout
21330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21333 \begin_layout Plain Layout
21334 \begin_inset Formula $\angle$
21344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21347 \begin_layout Plain Layout
21355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21358 \begin_layout Plain Layout
21359 \begin_inset Formula $\measuredangle$
21369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21372 \begin_layout Plain Layout
21380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21383 \begin_layout Plain Layout
21384 \begin_inset Formula $\sphericalangle$
21394 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21397 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $\top$
21419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21422 \begin_layout Plain Layout
21430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21433 \begin_layout Plain Layout
21434 \begin_inset Formula $\bot$
21448 \begin_inset space \hfill{}
21454 \begin_layout Subsection
21455 Miscellaneous Symbols
21456 \begin_inset CommandInset label
21458 name "sub:Miscellaneous-Symbols"
21466 \begin_layout Plain Layout
21467 Symbols ! miscellaneous
21475 \begin_layout Standard
21478 \begin_inset Tabular
21479 <lyxtabular version="3" rows="10" columns="2">
21481 <column alignment="center" valignment="top" width="0pt">
21482 <column alignment="center" valignment="top" width="0pt">
21484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21487 \begin_layout Plain Layout
21493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21496 \begin_layout Plain Layout
21504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21507 \begin_layout Plain Layout
21515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21518 \begin_layout Plain Layout
21519 \begin_inset Formula $\flat$
21529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21532 \begin_layout Plain Layout
21540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21543 \begin_layout Plain Layout
21544 \begin_inset Formula $\natural$
21554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21557 \begin_layout Plain Layout
21565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21568 \begin_layout Plain Layout
21569 \begin_inset Formula $\sharp$
21579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21582 \begin_layout Plain Layout
21590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21593 \begin_layout Plain Layout
21594 \begin_inset Formula $\surd$
21604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21607 \begin_layout Plain Layout
21615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21618 \begin_layout Plain Layout
21619 \begin_inset Formula $\checkmark$
21629 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21632 \begin_layout Plain Layout
21640 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21643 \begin_layout Plain Layout
21644 \begin_inset Formula $\yen$
21654 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21657 \begin_layout Plain Layout
21665 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21668 \begin_layout Plain Layout
21669 \begin_inset Formula $\pounds$
21679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21682 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\$$
21702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21705 \begin_layout Plain Layout
21711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21714 \begin_layout Plain Layout
21715 \begin_inset Formula $§$
21729 \begin_inset Tabular
21730 <lyxtabular version="3" rows="10" columns="2">
21732 <column alignment="center" valignment="top" width="0">
21733 <column alignment="center" valignment="top" width="0">
21735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21738 \begin_layout Plain Layout
21744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21747 \begin_layout Plain Layout
21755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21758 \begin_layout Plain Layout
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21769 \begin_layout Plain Layout
21770 \begin_inset Formula $\hbar$
21780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21783 \begin_layout Plain Layout
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21794 \begin_layout Plain Layout
21795 \begin_inset Formula $\hslash$
21805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21808 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $\clubsuit$
21830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21833 \begin_layout Plain Layout
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21844 \begin_layout Plain Layout
21845 \begin_inset Formula $\spadesuit$
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21858 \begin_layout Plain Layout
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21869 \begin_layout Plain Layout
21870 \begin_inset Formula $\bigstar$
21880 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21891 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21894 \begin_layout Plain Layout
21895 \begin_inset Formula $\blacklozenge$
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21908 \begin_layout Plain Layout
21916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21919 \begin_layout Plain Layout
21920 \begin_inset Formula $\blacktriangle$
21930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21933 \begin_layout Plain Layout
21941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21944 \begin_layout Plain Layout
21945 \begin_inset Formula $\blacktriangledown$
21955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21958 \begin_layout Plain Layout
21966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21969 \begin_layout Plain Layout
21970 \begin_inset Formula $\bullet$
21984 \begin_inset Tabular
21985 <lyxtabular version="3" rows="10" columns="2">
21987 <column alignment="center" valignment="top" width="0pt">
21988 <column alignment="center" valignment="top" width="0pt">
21990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21993 \begin_layout Plain Layout
21999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22002 \begin_layout Plain Layout
22010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22013 \begin_layout Plain Layout
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22024 \begin_layout Plain Layout
22025 \begin_inset Formula $\diamondsuit$
22035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22038 \begin_layout Plain Layout
22046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22049 \begin_layout Plain Layout
22050 \begin_inset Formula $\Diamond$
22060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22063 \begin_layout Plain Layout
22071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22074 \begin_layout Plain Layout
22075 \begin_inset Formula $\heartsuit$
22085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22088 \begin_layout Plain Layout
22096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22099 \begin_layout Plain Layout
22100 \begin_inset Formula $\P$
22110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22113 \begin_layout Plain Layout
22121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22124 \begin_layout Plain Layout
22125 \begin_inset Formula $\copyright$
22135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22138 \begin_layout Plain Layout
22146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22149 \begin_layout Plain Layout
22150 \begin_inset Formula $\circledR$
22160 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22163 \begin_layout Plain Layout
22171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22174 \begin_layout Plain Layout
22175 \begin_inset Formula $\maltese$
22185 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22188 \begin_layout Plain Layout
22196 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22199 \begin_layout Plain Layout
22200 \begin_inset Formula $\diagup$
22210 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22213 \begin_layout Plain Layout
22221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22224 \begin_layout Plain Layout
22225 \begin_inset Formula $\diagdown$
22241 \begin_layout Standard
22242 \begin_inset VSpace medskip
22245 More symbols are listed in
22246 \begin_inset CommandInset ref
22248 reference "sub:Miscellaneous-special-Characters"
22255 \begin_layout Standard
22256 Some symbols can be displayed in different sizes, see
22257 \begin_inset CommandInset ref
22259 reference "sub:Font-Sizes"
22266 \begin_layout Subsection
22271 \begin_layout Plain Layout
22272 Symbols ! Euro-symbol
22281 \begin_layout Plain Layout
22288 \begin_layout Plain Layout
22305 \begin_layout Standard
22306 To use the Euro symbol in formulas, the LaTeX-package
22314 \begin_layout Plain Layout
22320 must be installed and loaded with the LaTeX-preamble line
22323 \begin_layout Standard
22328 usepackage[gennarrow]{eurosym}
22331 \begin_layout Standard
22332 The Euro symbol can now be inserted with the command
22342 \begin_layout Plain Layout
22353 \begin_layout Standard
22354 The Euro symbol can directly be inserted with the € key in mathematical
22355 text, without having
22370 can also be inserted in TeX-mode.
22371 The official currency symbol can then be inserted with the command
22381 \begin_layout Plain Layout
22389 , that is only available in TeX-mode.
22392 \begin_layout Standard
22396 \begin_layout Plain Layout
22406 \begin_inset Note Note
22409 \begin_layout Plain Layout
22410 The following table will only be displayed when the LaTeX-package
22422 \begin_layout Standard
22423 An overview about the different Euro symbols:
22426 \begin_layout Standard
22428 \begin_inset Tabular
22429 <lyxtabular version="3" rows="4" columns="3">
22431 <column alignment="center" valignment="top" width="0pt">
22432 <column alignment="center" valignment="top" width="0pt">
22433 <column alignment="center" valignment="top" width="0pt">
22435 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22438 \begin_layout Plain Layout
22444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22447 \begin_layout Plain Layout
22453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22456 \begin_layout Plain Layout
22464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22467 \begin_layout Plain Layout
22473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22476 \begin_layout Plain Layout
22484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22487 \begin_layout Plain Layout
22488 \begin_inset Formula $\euro$
22498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22501 \begin_layout Plain Layout
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22519 \begin_layout Plain Layout
22520 \begin_inset Formula $\mbox{€}$
22530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22533 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22542 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22557 \begin_layout Plain Layout
22579 \begin_layout Standard
22583 \begin_layout Plain Layout
22593 \begin_inset Note Note
22596 \begin_layout Plain Layout
22597 The following will be displayed when the LaTeX-package
22609 \begin_layout Standard
22610 You need to install the LaTeX-package
22614 to see the rest of this subsection in the output.
22617 \begin_layout Standard
22621 \begin_layout Plain Layout
22633 \begin_layout Section
22635 \begin_inset CommandInset label
22637 name "sec:Relations"
22645 \begin_layout Plain Layout
22655 \begin_layout Plain Layout
22660 \begin_layout Plain Layout
22671 \begin_layout Plain Layout
22686 \begin_layout Standard
22687 All relations can also be inserted via the toolbar button
22688 \begin_inset Graphics
22689 filename ../images/math/leq.png
22697 \begin_layout Standard
22698 \begin_inset space \hfill{}
22702 \begin_inset Tabular
22703 <lyxtabular version="3" rows="17" columns="2">
22705 <column alignment="center" valignment="top" width="0pt">
22706 <column alignment="center" valignment="top" width="0pt">
22708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22720 \begin_layout Plain Layout
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22731 \begin_layout Plain Layout
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22740 \begin_layout Plain Layout
22741 \begin_inset Formula $<$
22751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22754 \begin_layout Plain Layout
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22765 \begin_layout Plain Layout
22766 \begin_inset Formula $\le$
22776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22779 \begin_layout Plain Layout
22787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22790 \begin_layout Plain Layout
22791 \begin_inset Formula $\ll$
22801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22804 \begin_layout Plain Layout
22812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22815 \begin_layout Plain Layout
22816 \begin_inset Formula $\prec$
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22829 \begin_layout Plain Layout
22837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22840 \begin_layout Plain Layout
22841 \begin_inset Formula $\preceq$
22851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22854 \begin_layout Plain Layout
22862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22865 \begin_layout Plain Layout
22866 \begin_inset Formula $\subset$
22876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22879 \begin_layout Plain Layout
22887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22890 \begin_layout Plain Layout
22891 \begin_inset Formula $\subseteq$
22901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22904 \begin_layout Plain Layout
22912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22915 \begin_layout Plain Layout
22916 \begin_inset Formula $\sqsubseteq$
22926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22929 \begin_layout Plain Layout
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22940 \begin_layout Plain Layout
22941 \begin_inset Formula $\in$
22951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22954 \begin_layout Plain Layout
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22965 \begin_layout Plain Layout
22966 \begin_inset Formula $\vdash$
22976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22979 \begin_layout Plain Layout
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22990 \begin_layout Plain Layout
22991 \begin_inset Formula $\smile$
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23004 \begin_layout Plain Layout
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23015 \begin_layout Plain Layout
23016 \begin_inset Formula $\lhd$
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23029 \begin_layout Plain Layout
23037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23040 \begin_layout Plain Layout
23041 \begin_inset Formula $\unlhd$
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23054 \begin_layout Plain Layout
23062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23065 \begin_layout Plain Layout
23066 \begin_inset Formula $\gtrless$
23076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23079 \begin_layout Plain Layout
23087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23090 \begin_layout Plain Layout
23091 \begin_inset Formula $\mid$
23101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23104 \begin_layout Plain Layout
23112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23115 \begin_layout Plain Layout
23116 \begin_inset Formula $\nmid$
23130 \begin_inset space \hfill{}
23134 \begin_inset Tabular
23135 <lyxtabular version="3" rows="17" columns="2">
23137 <column alignment="center" valignment="top" width="0pt">
23138 <column alignment="center" valignment="top" width="0pt">
23140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23143 \begin_layout Plain Layout
23149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23152 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23163 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23172 \begin_layout Plain Layout
23173 \begin_inset Formula $=$
23183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23197 \begin_layout Plain Layout
23198 \begin_inset Formula $\not=$
23208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23211 \begin_layout Plain Layout
23219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23222 \begin_layout Plain Layout
23223 \begin_inset Formula $\equiv$
23233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23236 \begin_layout Plain Layout
23244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23247 \begin_layout Plain Layout
23248 \begin_inset Formula $\sim$
23258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23261 \begin_layout Plain Layout
23269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23272 \begin_layout Plain Layout
23273 \begin_inset Formula $\simeq$
23283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23286 \begin_layout Plain Layout
23294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23297 \begin_layout Plain Layout
23298 \begin_inset Formula $\approx$
23308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23311 \begin_layout Plain Layout
23319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23322 \begin_layout Plain Layout
23323 \begin_inset Formula $\cong$
23333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23336 \begin_layout Plain Layout
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23347 \begin_layout Plain Layout
23348 \begin_inset Formula $\bowtie$
23358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23361 \begin_layout Plain Layout
23369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23372 \begin_layout Plain Layout
23373 \begin_inset Formula $\notin$
23383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23386 \begin_layout Plain Layout
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23397 \begin_layout Plain Layout
23398 \begin_inset Formula $\perp$
23408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23411 \begin_layout Plain Layout
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23422 \begin_layout Plain Layout
23423 \begin_inset Formula $\propto$
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23436 \begin_layout Plain Layout
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23447 \begin_layout Plain Layout
23448 \begin_inset Formula $\asymp$
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23461 \begin_layout Plain Layout
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23472 \begin_layout Plain Layout
23473 \begin_inset Formula $\doteq$
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23486 \begin_layout Plain Layout
23494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23497 \begin_layout Plain Layout
23498 \begin_inset Formula $\circeq$
23508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23511 \begin_layout Plain Layout
23519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23522 \begin_layout Plain Layout
23523 \begin_inset Formula $\models$
23533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23536 \begin_layout Plain Layout
23544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23547 \begin_layout Plain Layout
23548 \begin_inset Formula $\widehat{=}$
23562 \begin_inset space \hfill{}
23566 \begin_inset Tabular
23567 <lyxtabular version="3" rows="17" columns="2">
23569 <column alignment="center" valignment="top" width="0pt">
23570 <column alignment="center" valignment="top" width="0pt">
23572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23575 \begin_layout Plain Layout
23581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23595 \begin_layout Plain Layout
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Plain Layout
23605 \begin_inset Formula $>$
23615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23629 \begin_layout Plain Layout
23630 \begin_inset Formula $\ge$
23640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23643 \begin_layout Plain Layout
23651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23654 \begin_layout Plain Layout
23655 \begin_inset Formula $\gg$
23665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23668 \begin_layout Plain Layout
23676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23679 \begin_layout Plain Layout
23680 \begin_inset Formula $\succ$
23690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23693 \begin_layout Plain Layout
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23704 \begin_layout Plain Layout
23705 \begin_inset Formula $\succeq$
23715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23718 \begin_layout Plain Layout
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23729 \begin_layout Plain Layout
23730 \begin_inset Formula $\supset$
23740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23743 \begin_layout Plain Layout
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23754 \begin_layout Plain Layout
23755 \begin_inset Formula $\supseteq$
23765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23768 \begin_layout Plain Layout
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23779 \begin_layout Plain Layout
23780 \begin_inset Formula $\sqsupseteq$
23790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23793 \begin_layout Plain Layout
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23804 \begin_layout Plain Layout
23805 \begin_inset Formula $\ni$
23815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23818 \begin_layout Plain Layout
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23829 \begin_layout Plain Layout
23830 \begin_inset Formula $\dashv$
23840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23843 \begin_layout Plain Layout
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Plain Layout
23855 \begin_inset Formula $\frown$
23865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23868 \begin_layout Plain Layout
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23879 \begin_layout Plain Layout
23880 \begin_inset Formula $\rhd$
23890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23893 \begin_layout Plain Layout
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23904 \begin_layout Plain Layout
23905 \begin_inset Formula $\unrhd$
23915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23918 \begin_layout Plain Layout
23926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23929 \begin_layout Plain Layout
23930 \begin_inset Formula $\lessgtr$
23940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23943 \begin_layout Plain Layout
23951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23954 \begin_layout Plain Layout
23955 \begin_inset Formula $\parallel$
23965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23968 \begin_layout Plain Layout
23976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23979 \begin_layout Plain Layout
23980 \begin_inset Formula $\nparallel$
23994 \begin_inset space \hfill{}
24000 \begin_layout Standard
24001 \begin_inset VSpace medskip
24016 are bigger than the equal looking operators
24031 \begin_layout Standard
24032 Relations are, in contrary to symbols, always surrounded by space.
24035 \begin_layout Standard
24036 Relations with labels can be created with the command
24046 \begin_layout Plain Layout
24057 \begin_layout Standard
24059 \begin_inset Tabular
24060 <lyxtabular version="3" rows="2" columns="2">
24062 <column alignment="center" valignment="top" width="0">
24063 <column alignment="center" valignment="top" width="0">
24065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24068 \begin_layout Plain Layout
24074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24077 \begin_layout Plain Layout
24079 \begin_inset Note Note
24082 \begin_layout Plain Layout
24089 is only used as spacer.
24101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24104 \begin_layout Plain Layout
24111 \begin_layout Plain Layout
24128 \begin_layout Plain Layout
24138 \begin_inset Formula $\downarrow$
24147 \begin_layout Plain Layout
24160 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24177 \begin_layout Plain Layout
24178 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24194 \begin_layout Section
24198 \begin_layout Subsection
24199 Predefined Functions
24200 \begin_inset CommandInset label
24202 name "sub:Predefined-Functions"
24210 \begin_layout Plain Layout
24211 Functions ! predefined
24219 \begin_layout Standard
24220 In general, variables are set
24224 in mathematical expressions, but not function names, because
24225 \begin_inset Formula $sin$
24228 could be misunderstood as
24229 \begin_inset Formula $s\cdot i\cdot n$
24233 Therefore there are predefined functions, that are additionally a bit separated
24235 They are inserted as commands starting with a backslash before their name.
24238 \begin_layout Standard
24240 \begin_inset Tabular
24241 <lyxtabular version="3" rows="2" columns="4">
24243 <column alignment="center" valignment="top" width="0pt">
24244 <column alignment="center" valignment="top" width="0pt">
24245 <column alignment="center" valignment="top" width="0pt">
24246 <column alignment="center" valignment="top" width="0pt">
24248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24251 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24260 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24269 \begin_layout Plain Layout
24275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24278 \begin_layout Plain Layout
24286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24289 \begin_layout Plain Layout
24295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24298 \begin_layout Plain Layout
24299 \begin_inset Formula $Asin(x)+B$
24307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24310 \begin_layout Plain Layout
24318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24321 \begin_layout Plain Layout
24322 \begin_inset Formula $A\sin(x)+B$
24338 \begin_layout Standard
24339 The following functions are predefined:
24342 \begin_layout Standard
24343 \begin_inset VSpace -2mm
24349 \begin_layout Standard
24351 \begin_inset Tabular
24352 <lyxtabular version="3" rows="9" columns="4">
24354 <column alignment="center" valignment="top" width="0pt">
24355 <column alignment="center" valignment="top" width="0pt">
24356 <column alignment="center" valignment="top" width="0pt">
24357 <column alignment="center" valignment="top" width="0pt">
24359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24362 \begin_layout Plain Layout
24368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24371 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24380 \begin_layout Plain Layout
24386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24389 \begin_layout Plain Layout
24397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24400 \begin_layout Plain Layout
24408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24411 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24433 \begin_layout Plain Layout
24443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24446 \begin_layout Plain Layout
24454 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24457 \begin_layout Plain Layout
24465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24468 \begin_layout Plain Layout
24476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24479 \begin_layout Plain Layout
24489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24492 \begin_layout Plain Layout
24500 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24503 \begin_layout Plain Layout
24511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24514 \begin_layout Plain Layout
24522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24525 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24538 \begin_layout Plain Layout
24546 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24549 \begin_layout Plain Layout
24557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24560 \begin_layout Plain Layout
24568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24571 \begin_layout Plain Layout
24581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24584 \begin_layout Plain Layout
24592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24595 \begin_layout Plain Layout
24603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24606 \begin_layout Plain Layout
24614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24617 \begin_layout Plain Layout
24627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24630 \begin_layout Plain Layout
24638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24641 \begin_layout Plain Layout
24649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24652 \begin_layout Plain Layout
24660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24663 \begin_layout Plain Layout
24673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24676 \begin_layout Plain Layout
24684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24687 \begin_layout Plain Layout
24695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24698 \begin_layout Plain Layout
24706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24709 \begin_layout Plain Layout
24719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24722 \begin_layout Plain Layout
24730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24733 \begin_layout Plain Layout
24741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24744 \begin_layout Plain Layout
24752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24755 \begin_layout Plain Layout
24771 \begin_layout Standard
24772 They can also be inserted with the math toolbar button
24773 \begin_inset Graphics
24774 filename ../images/math/functions.png
24782 \begin_layout Subsection
24783 Self-defined Functions
24787 \begin_layout Plain Layout
24788 Functions ! self-defined
24796 \begin_layout Standard
24797 To use a function that is not predefined, like for example the sign function
24798 sgn(x), there are two possibilities:
24801 \begin_layout Itemize
24802 Define the function by inserting the following line to the LaTeX-preamble
24806 \begin_layout Plain Layout
24811 DeclareMathOperator
24814 \begin_inset CommandInset ref
24816 reference "sub:Self-defined-Operators"
24826 \begin_inset Newline newline
24830 \begin_inset VSpace -3mm
24834 \begin_inset Newline newline
24841 DeclareMathOperator{
24849 \begin_layout Plain Layout
24854 DeclareMathOperator
24860 \begin_inset Newline newline
24864 \begin_inset VSpace -2mm
24868 \begin_inset Newline newline
24871 Now the new defined function can be called with the command
24880 \begin_layout Itemize
24881 Write the the formula as usual, mark the formula name, in our example the
24886 , and change it to mathematical text.
24887 At last a space is inserted between prefactor and function.
24890 \begin_layout Standard
24891 The result is the same with both methods as with a predefined function
24895 \begin_layout Plain Layout
24896 In LyX self-defined functions are displayed red, predefined ones black.
24904 \begin_layout Standard
24906 \begin_inset Tabular
24907 <lyxtabular version="3" rows="3" columns="2">
24909 <column alignment="center" valignment="top" width="0pt">
24910 <column alignment="center" valignment="top" width="0pt">
24912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24915 \begin_layout Plain Layout
24921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24924 \begin_layout Plain Layout
24932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24935 \begin_layout Plain Layout
24943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24946 \begin_layout Plain Layout
24947 \begin_inset Formula $A\sgn(x)+B$
24957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24960 \begin_layout Plain Layout
24964 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24975 \begin_layout Plain Layout
24976 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24992 \begin_layout Standard
24993 The first method is more suitable when the self-defined function should
24994 be used several times.
24997 \begin_layout Subsection
25002 \begin_layout Plain Layout
25011 \begin_layout Standard
25012 For limits there are defined besides
25022 \begin_layout Plain Layout
25042 furthermore the following functions:
25045 \begin_layout Standard
25047 \begin_inset Tabular
25048 <lyxtabular version="3" rows="5" columns="2">
25050 <column alignment="center" valignment="top" width="0">
25051 <column alignment="center" valignment="top" width="0">
25053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25056 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25065 \begin_layout Plain Layout
25067 \begin_inset Note Note
25070 \begin_layout Plain Layout
25077 is only used as spacer.
25089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25092 \begin_layout Plain Layout
25100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25103 \begin_layout Plain Layout
25104 \begin_inset Formula $\varliminf$
25114 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25117 \begin_layout Plain Layout
25125 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25128 \begin_layout Plain Layout
25129 \begin_inset Formula $\varlimsup$
25139 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25142 \begin_layout Plain Layout
25150 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25153 \begin_layout Plain Layout
25154 \begin_inset Formula $\varprojlim$
25164 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25167 \begin_layout Plain Layout
25175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25178 \begin_layout Plain Layout
25179 \begin_inset Formula $\varinjlim$
25183 \begin_inset Formula $\raisebox{-2.5mm}{}$
25199 \begin_layout Standard
25200 \begin_inset VSpace medskip
25203 The limit is created by inserting a subscript.
25204 It is set right beside the function in an inline formula:
25207 \begin_layout Standard
25209 \begin_inset Tabular
25210 <lyxtabular version="3" rows="2" columns="2">
25212 <column alignment="center" valignment="top" width="0pt">
25213 <column alignment="center" valignment="top" width="0pt">
25215 <cell alignment="center" valignment="top" usebox="none">
25218 \begin_layout Plain Layout
25224 <cell alignment="center" valignment="top" usebox="none">
25227 \begin_layout Plain Layout
25228 \begin_inset space \hspace{}
25233 \begin_inset Note Note
25236 \begin_layout Plain Layout
25249 are used here as spacer.
25261 <cell alignment="center" valignment="top" usebox="none">
25264 \begin_layout Plain Layout
25273 \begin_layout Plain Layout
25286 \begin_layout Plain Layout
25300 <cell alignment="center" valignment="top" usebox="none">
25303 \begin_layout Plain Layout
25304 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25320 \begin_layout Standard
25321 In a displayed formula the limit is set below the formula, as usual:
25322 \begin_inset Formula \[
25330 \begin_layout Subsection
25335 \begin_layout Plain Layout
25336 Functions ! modulo-
25344 \begin_layout Standard
25345 The modulo-function is special, because it exists in four variants.
25348 \begin_layout Standard
25349 The variants in a displayed formula:
25350 \begin_inset Formula \begin{align*}
25351 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25352 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25353 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25354 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25355 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25362 \begin_layout Standard
25363 In an inline formula less space is set before the function names for all
25367 \begin_layout Section
25372 \begin_layout Plain Layout
25381 \begin_layout Subsection
25382 Special Characters in Mathematical Text
25385 \begin_layout Standard
25386 The following commands can only be used in mathematical text or in TeX-mode:
25389 \begin_layout Standard
25390 \begin_inset space \hfill{}
25394 \begin_inset Tabular
25395 <lyxtabular version="3" rows="8" columns="2">
25397 <column alignment="block" valignment="top" width="0">
25398 <column alignment="block" valignment="top" width="0">
25400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25403 \begin_layout Plain Layout
25409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25412 \begin_layout Plain Layout
25420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25423 \begin_layout Plain Layout
25431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25434 \begin_layout Plain Layout
25435 \begin_inset Formula $\textrm{œ}$
25445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25448 \begin_layout Plain Layout
25456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25459 \begin_layout Plain Layout
25460 \begin_inset Formula $\textrm{Œ}$
25470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25473 \begin_layout Plain Layout
25481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25484 \begin_layout Plain Layout
25485 \begin_inset Formula $\textrm{æ}$
25495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25498 \begin_layout Plain Layout
25506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25509 \begin_layout Plain Layout
25510 \begin_inset Formula $\textrm{Æ}$
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25523 \begin_layout Plain Layout
25531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25534 \begin_layout Plain Layout
25535 \begin_inset Formula $\textrm{\aa}$
25545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25548 \begin_layout Plain Layout
25555 \begin_layout Plain Layout
25562 \begin_layout Plain Layout
25583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25586 \begin_layout Plain Layout
25587 \begin_inset Formula $\textrm{Å}$
25597 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25600 \begin_layout Plain Layout
25608 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25611 \begin_layout Plain Layout
25612 \begin_inset Formula $\textrm{ı}$
25626 \begin_inset space \hfill{}
25630 \begin_inset Tabular
25631 <lyxtabular version="3" rows="8" columns="2">
25633 <column alignment="block" valignment="top" width="0">
25634 <column alignment="center" valignment="top" width="0">
25636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25639 \begin_layout Plain Layout
25641 \begin_inset Note Note
25644 \begin_layout Plain Layout
25651 is used for separation, because otherwise the output will be ¡ and ¿ respective
25662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25665 \begin_layout Plain Layout
25673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25676 \begin_layout Plain Layout
25684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25687 \begin_layout Plain Layout
25688 \begin_inset Formula $\textrm{ø}$
25698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25701 \begin_layout Plain Layout
25709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25712 \begin_layout Plain Layout
25713 \begin_inset Formula $\textrm{Ø}$
25723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25726 \begin_layout Plain Layout
25734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25737 \begin_layout Plain Layout
25738 \begin_inset Formula $\textrm{ł}$
25748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25751 \begin_layout Plain Layout
25759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25762 \begin_layout Plain Layout
25763 \begin_inset Formula $\textrm{Ł}$
25773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25776 \begin_layout Plain Layout
25778 \begin_inset space \hspace{}
25786 \begin_layout Plain Layout
25800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25803 \begin_layout Plain Layout
25804 \begin_inset Formula $\textrm{!`}$
25814 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25817 \begin_layout Plain Layout
25819 \begin_inset space \hspace{}
25827 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25845 \begin_inset Formula $\textrm{?`}$
25855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25858 \begin_layout Plain Layout
25866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25869 \begin_layout Plain Layout
25870 \begin_inset Formula $\textrm{ȷ}$
25884 \begin_inset space \hfill{}
25890 \begin_layout Standard
25892 \begin_inset Formula $\textrm{\textrm{Å}}$
25896 \begin_inset Formula $\textrm{\textrm{Ø}}$
25899 can also be inserted via the math toolbar button
25900 \begin_inset Graphics
25901 filename ../images/math/digamma.png
25909 \begin_layout Standard
25910 An exception are the commands
25913 \begin_inset space \hspace{}
25922 \begin_inset space \hspace{}
25928 , because they can be inserted in LyX directly to text.
25931 \begin_layout Subsection
25933 \begin_inset CommandInset label
25935 name "sub:Accents-in-Text"
25943 \begin_layout Plain Layout
25952 \begin_layout Standard
25953 With the following commands all letters can be accented.
25954 The commands must be inserted in TeX-mode.
25957 \begin_layout Standard
25958 \begin_inset space \hfill{}
25962 \begin_inset Tabular
25963 <lyxtabular version="3" rows="8" columns="2">
25965 <column alignment="block" valignment="top" width="0">
25966 <column alignment="block" valignment="top" width="0">
25968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25971 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25980 \begin_layout Plain Layout
25988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25991 \begin_layout Plain Layout
25995 \begin_inset Quotes grd
26003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26010 \begin_layout Plain Layout
26026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26029 \begin_layout Plain Layout
26037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26040 \begin_layout Plain Layout
26044 \begin_layout Plain Layout
26060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26063 \begin_layout Plain Layout
26070 \begin_layout Plain Layout
26084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26087 \begin_layout Plain Layout
26091 \begin_layout Plain Layout
26107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26110 \begin_layout Plain Layout
26118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26121 \begin_layout Plain Layout
26125 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26144 \begin_layout Plain Layout
26151 \begin_layout Plain Layout
26165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26168 \begin_layout Plain Layout
26172 \begin_layout Plain Layout
26188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26191 \begin_layout Plain Layout
26198 \begin_layout Plain Layout
26212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26215 \begin_layout Plain Layout
26219 \begin_layout Plain Layout
26235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26238 \begin_layout Plain Layout
26245 \begin_layout Plain Layout
26259 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26262 \begin_layout Plain Layout
26266 \begin_layout Plain Layout
26286 \begin_inset space \hfill{}
26290 \begin_inset Tabular
26291 <lyxtabular version="3" rows="8" columns="2">
26293 <column alignment="block" valignment="top" width="0">
26294 <column alignment="center" valignment="top" width="0">
26296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26299 \begin_layout Plain Layout
26305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26308 \begin_layout Plain Layout
26316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26319 \begin_layout Plain Layout
26326 \begin_layout Plain Layout
26340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26343 \begin_layout Plain Layout
26347 \begin_layout Plain Layout
26363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26366 \begin_layout Plain Layout
26374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26377 \begin_layout Plain Layout
26381 \begin_layout Plain Layout
26397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26400 \begin_layout Plain Layout
26407 \begin_layout Plain Layout
26418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26421 \begin_layout Plain Layout
26425 \begin_layout Plain Layout
26441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26444 \begin_layout Plain Layout
26452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26455 \begin_layout Plain Layout
26459 \begin_layout Plain Layout
26475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26478 \begin_layout Plain Layout
26485 \begin_layout Plain Layout
26499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26502 \begin_layout Plain Layout
26506 \begin_layout Plain Layout
26522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26525 \begin_layout Plain Layout
26532 \begin_layout Plain Layout
26546 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26549 \begin_layout Plain Layout
26553 \begin_layout Plain Layout
26569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26572 \begin_layout Plain Layout
26579 \begin_layout Plain Layout
26593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26596 \begin_layout Plain Layout
26600 \begin_layout Plain Layout
26620 \begin_inset space \hfill{}
26626 \begin_layout Standard
26627 \begin_inset VSpace medskip
26636 also two different characters can be accented.
26645 \begin_layout Plain Layout
26660 \begin_layout Plain Layout
26672 \begin_layout Standard
26685 can in combination with vowels directly be inserted with the keyboard without
26687 The same applies for the tilde
26691 \begin_layout Plain Layout
26692 This only applies for keyboards where the tilde is defined as accent.
26701 in combination with
26716 \begin_layout Standard
26759 , and accents inserted directly with the keyboard are also available in
26761 For the other accents there are special math commands to be used in formulas,
26763 \begin_inset CommandInset ref
26765 reference "sub:Accents-for-one"
26772 \begin_layout Standard
26773 \begin_inset VSpace bigskip
26776 Furthermore, with the command
26786 \begin_layout Plain Layout
26794 all numbers and letters can be set into a circle, quasi accented with a
26795 circle, similar to the the copyright symbol.
26798 \begin_layout Standard
26800 \begin_inset Tabular
26801 <lyxtabular version="3" rows="3" columns="2">
26803 <column alignment="center" valignment="top" width="0">
26804 <column alignment="center" valignment="top" width="0">
26806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26809 \begin_layout Plain Layout
26815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26818 \begin_layout Plain Layout
26820 \begin_inset Note Note
26823 \begin_layout Plain Layout
26830 is only used as spacer.
26842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26845 \begin_layout Plain Layout
26853 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26856 \begin_layout Plain Layout
26860 \begin_layout Plain Layout
26876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26879 \begin_layout Plain Layout
26890 raisebox{-1.5pt}{W}}
26895 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26898 \begin_layout Plain Layout
26899 \begin_inset Formula $\raisebox{4.5mm}{}$
26906 \begin_layout Plain Layout
26924 \begin_inset Formula $\raisebox{-2mm}{}$
26940 \begin_layout Standard
26941 One has to take care that the character fits in the circle.
26952 \begin_layout Plain Layout
26954 \begin_inset CommandInset ref
26956 reference "sub:Font-Sizes"
26965 specifies thereby the size of the circle.
26976 \begin_layout Plain Layout
26978 \begin_inset CommandInset ref
26980 reference "sub:Boxes-without-Frame"
26989 the character can be centered.
26992 \begin_layout Subsection
26997 \begin_layout Plain Layout
27006 \begin_layout Standard
27007 Minuscule numbers are created with the command
27017 \begin_layout Plain Layout
27026 The command can be used in formulas and in TeX-mode.
27027 The command scheme is:
27030 \begin_layout Standard
27035 oldstylenums{number}
27038 \begin_layout Standard
27043 oldstylenums{0123456789
27046 \begin_inset Formula $\oldstylenums{0123456789}$
27052 \begin_layout Subsection
27053 Miscellaneous special Characters
27054 \begin_inset CommandInset label
27056 name "sub:Miscellaneous-special-Characters"
27064 \begin_layout Plain Layout
27065 Special characters ! miscellaneous
27073 \begin_layout Standard
27074 The following characters can only be inserted to formulas by using commands:
27077 \begin_layout Standard
27079 \begin_inset Tabular
27080 <lyxtabular version="3" rows="4" columns="2">
27082 <column alignment="center" valignment="top" width="0">
27083 <column alignment="center" valignment="top" width="0">
27085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27088 \begin_layout Plain Layout
27094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27097 \begin_layout Plain Layout
27105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27108 \begin_layout Plain Layout
27115 \begin_layout Plain Layout
27129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27132 \begin_layout Plain Layout
27133 \begin_inset Formula $\mathcircumflex$
27143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27146 \begin_layout Plain Layout
27154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27157 \begin_layout Plain Layout
27158 \begin_inset Formula $\_$
27168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27171 \begin_layout Plain Layout
27176 \begin_layout Plain Layout
27191 \begin_layout Plain Layout
27204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27207 \begin_layout Plain Layout
27208 \begin_inset Formula $^{\circ}$
27224 \begin_layout Standard
27225 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27226 contains the following line
27230 \begin_layout Plain Layout
27231 More about this is described in
27232 \begin_inset CommandInset ref
27234 reference "sub:Text-Characters-in"
27246 \begin_layout Standard
27251 DeclareInputtext{176}{
27264 \begin_layout Section
27266 \begin_inset CommandInset label
27268 name "sec:Formula-Styles"
27276 \begin_layout Plain Layout
27285 \begin_layout Itemize
27286 There are two different alignment styles:
27290 \begin_layout Description
27291 Centered is the predefined standard
27294 \begin_layout Description
27295 Indented for this the option
27299 must be inserted in the menu
27301 Document\SpecialChar \menuseparator
27307 \begin_inset space ~
27313 \begin_layout Standard
27318 is used, the indentation can be adjusted with the length
27328 \begin_layout Plain Layout
27337 Should the distance be 15
27338 \begin_inset space \thinspace{}
27341 mm, the following command line is inserted in the LaTeX-preamble
27344 \begin_layout Standard
27354 \begin_layout Standard
27355 When no length is specified, the predefined value of 30
27356 \begin_inset space \thinspace{}
27363 \begin_layout Itemize
27364 And two different numbering styles:
27368 \begin_layout Description
27369 Right is the predefined standard
27372 \begin_layout Description
27373 Left for this the option
27377 must be inserted in the menu
27379 Document\SpecialChar \menuseparator
27385 \begin_inset space ~
27392 \begin_layout Standard
27401 can also be used together.
27402 In this case both options are inserted, separated by a comma.
27405 \begin_layout Standard
27406 The chosen styles are used for all displayed formulas of the document.
27407 When both, centered and indented formulas should be created in a document,
27413 The indented formulas are then set in a flalign environment, see
27414 \begin_inset CommandInset ref
27416 reference "sub:Flalign-Environment"
27423 \begin_layout Section
27425 \begin_inset CommandInset label
27427 name "sec:Multiline-Formulas"
27435 \begin_layout Plain Layout
27436 Formula ! multiline
27444 \begin_layout Subsection
27448 \begin_layout Standard
27449 In LyX multiline formulas are created by pressing
27454 arg "newline-insert newline"
27460 This creates either an
27462 eqnarray environment
27464 that is described in
27465 \begin_inset CommandInset ref
27467 reference "sub:Eqnarray-Environment"
27471 or, when the option
27473 Use AMS math package
27475 in the document settings is selected, an
27479 that is described in
27480 \begin_inset CommandInset ref
27482 reference "sub:Standard-align-Environment"
27489 \begin_layout Standard
27490 There are other multiline formula environments that can be created via the
27493 Insert\SpecialChar \menuseparator
27497 These environments are described in the following sections.
27500 \begin_layout Standard
27501 In all multiline formula environments a new line is created by pressing
27505 arg "newline-insert newline"
27509 To add or delete lines, the math toolbar buttons
27510 \begin_inset Graphics
27511 filename ../images/tabular-feature_append-row.png
27517 \begin_inset Graphics
27518 filename ../images/tabular-feature_delete-row.png
27523 , respectively, or the menu
27525 Edit\SpecialChar \menuseparator
27531 \begin_layout Subsubsection
27533 \begin_inset CommandInset label
27535 name "sub:Line-Separation"
27543 \begin_layout Plain Layout
27544 Formula ! multiline ! Line separation
27552 \begin_layout Standard
27553 There is sometimes not enough space in multiline formulas between the lines:
27554 \begin_inset Formula \begin{eqnarray*}
27555 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}\\
27556 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*}
27563 \begin_layout Standard
27564 In LaTeX additional line space is specified as optional argument of the
27566 This is not yet possible in LyX
27570 \begin_layout Plain Layout
27572 \begin_inset CommandInset href
27574 name "LyX-bug #1505"
27575 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27584 , therefore the whole formula must be inserted in TeX-mode.
27585 To add in our example space, the command
27593 is inserted at the end of the first line.
27598 \begin_layout Plain Layout
27605 \begin_layout Plain Layout
27607 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27610 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27617 \begin_layout Plain Layout
27621 left(B^{2}+x_{0}^{2}
27629 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27634 \begin_layout Plain Layout
27646 \begin_layout Standard
27647 \begin_inset VSpace bigskip
27650 To set the the line separation for all lines in a formula, the length
27660 \begin_layout Plain Layout
27670 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27681 \begin_inset space \thinspace{}
27686 \begin_inset space \thinspace{}
27689 mm additional line separation as in the previous example, the command
27692 \begin_layout Standard
27702 \begin_layout Standard
27703 is inserted in TeX-mode before the formula.
27704 This requires that the LaTeX-package
27712 \begin_layout Plain Layout
27717 is part of every LaTeX standard installation.
27726 \begin_layout Plain Layout
27732 was loaded in LaTeX-preamble with the line
27735 \begin_layout Standard
27743 \begin_layout Standard
27748 \begin_layout Plain Layout
27760 \begin_inset Formula \begin{eqnarray*}
27761 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}\\
27762 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*}
27769 \begin_layout Standard
27773 \begin_layout Plain Layout
27784 To get back to the predefined distance,
27790 is set to the value 3
27791 \begin_inset space \thinspace{}
27797 \begin_layout Subsubsection
27799 \begin_inset CommandInset label
27801 name "sub:Column-Separation"
27809 \begin_layout Plain Layout
27810 Formula ! multiline ! Column separation
27818 \begin_layout Standard
27819 Multiline formulas form a matrix.
27820 A formula in the eqnarray environment is for example a matrix with three
27822 By changing the column separation in this environment, the space beside
27823 the relation sign can be changed.
27826 \begin_layout Standard
27827 The column separation is specified with the length
27837 \begin_layout Plain Layout
27846 \begin_inset Newline newline
27849 column separation = 2
27850 \begin_inset space \thinspace{}
27860 \begin_inset Newline newline
27866 \begin_layout Standard
27876 \begin_layout Standard
27877 inserted in TeX-mode, sets for all following formulas a column separation
27879 \begin_inset space \thinspace{}
27883 To get back to the predefined distance,
27890 \begin_inset space \thinspace{}
27896 \begin_layout Standard
27898 \begin_inset space \thinspace{}
27901 cm column separation:
27905 \begin_layout Plain Layout
27917 \begin_inset Formula \begin{eqnarray*}
27919 C & \ne & A\end{eqnarray*}
27923 A formula with the predefined column separation for matrices of 10
27924 \begin_inset space \thinspace{}
27931 \begin_layout Plain Layout
27943 \begin_inset Formula \begin{eqnarray*}
27945 C & \ne & A\end{eqnarray*}
27952 \begin_layout Subsubsection
27957 \begin_layout Plain Layout
27966 \begin_layout Standard
27967 Long formulas can be typeset using these methods:
27970 \begin_layout Itemize
27971 When one side of the equation is much shorther than the line width, this
27972 one is chosen for the left side and the right side is typeset over two
27977 \begin_layout Plain Layout
27987 \begin_inset Formula \begin{eqnarray}
27988 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 \\
27989 & & -\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}
27997 \begin_layout Plain Layout
28007 \begin_inset Newline newline
28010 The minus sign at the beginning of the second line does normally not appear
28011 as operator because it is the first character of the line.
28012 Thus it would not be surrounded by space and could not be distinguished
28013 from the fraction bar.
28014 To avoid this, space was inserted behind the minus sign with the command
28025 \begin_layout Plain Layout
28033 \begin_inset CommandInset ref
28035 reference "sub:Variable-Space"
28048 \begin_layout Plain Layout
28059 \begin_layout Itemize
28060 When both sides of the equation are too long, the command
28070 \begin_layout Plain Layout
28079 It is inserted to the first column of the first line and effects that all
28080 further insertions overwrite the following columns:
28084 \begin_layout Plain Layout
28094 \begin_inset Formula \begin{eqnarray}
28095 \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 \\
28096 & & -\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 \\
28097 & & =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}
28105 \begin_layout Plain Layout
28115 \begin_inset Newline newline
28118 After the insertion of
28124 , the cursor is in a purple box that is a bit shifted to the left from the
28126 In this the formula is inserted.
28130 \begin_layout Plain Layout
28140 \begin_inset Newline newline
28143 The content of the further lines is inserted to the second or another formula
28145 The greater the column number where it was inserted, the larger the indentation.
28149 \begin_layout Plain Layout
28159 \begin_inset Newline newline
28163 \begin_inset Note Greyedout
28166 \begin_layout Plain Layout
28167 Note the following when using
28176 \begin_layout Itemize
28177 The formula doesn't use the full page width.
28179 \begin_inset space \thinspace{}
28183 \begin_inset space \space{}
28187 \begin_inset Formula $-B^{2}$
28190 is added to the first line in the above example, it would have been outside
28192 To better use the width, negative space can be inserted at the beginning
28196 \begin_layout Itemize
28197 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28202 \begin_layout Plain Layout
28203 \begin_inset CommandInset href
28205 name "LyX-bug #1429"
28206 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28215 One can only set the cursor at the beginning of the line and move it with
28224 \begin_layout Itemize
28225 Other methods to set long formulas are offered by the environments described
28227 \begin_inset CommandInset ref
28229 reference "sub:Multline-Environment"
28234 \begin_inset CommandInset ref
28236 reference "sub:Multiline-Formula-Parts"
28243 \begin_layout Subsubsection
28245 \begin_inset CommandInset label
28247 name "sub:Multiline-Brackets"
28255 \begin_layout Plain Layout
28256 Brackets ! for multiline expressions
28264 \begin_layout Standard
28265 For brackets spanning multiple lines the following problem occurs:
28266 \begin_inset Formula \begin{eqnarray*}
28267 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28268 & & \left.\cdots+B-D\right]\end{eqnarray*}
28275 \begin_layout Standard
28276 The closing bracket is smaller than the opening bracket because brackets
28277 with variable size may not span multiple lines.
28280 \begin_layout Standard
28281 To set the bracket size for the second line correctly, the first line is
28292 \begin_layout Plain Layout
28300 and the second line with
28308 \begin_layout Plain Layout
28322 \begin_inset CommandInset ref
28324 reference "sub:Automatic-Bracket-Size"
28339 \begin_layout Plain Layout
28365 \begin_layout Plain Layout
28384 \begin_layout Plain Layout
28403 \begin_layout Plain Layout
28415 \begin_inset Formula $\downarrow$
28424 \begin_layout Plain Layout
28432 is inserted, because the multiplication operator with its limits is the
28433 largest symbol in the first line and this should be the size for the bracket
28434 in the second line.
28437 \begin_layout Standard
28438 The result is this:
28439 \begin_inset Formula \begin{eqnarray*}
28440 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28441 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28448 \begin_layout Subsection
28452 \begin_layout Standard
28453 Align environments can be used for every kind of multiline formulas.
28454 They are specially useful to set several formulas side by side.
28457 \begin_layout Standard
28458 Align environments consist of columns.
28459 The odd columns are right aligned, the even ones left aligned.
28460 Every line in an Align environment can be numbered.
28463 \begin_layout Standard
28464 Align environments are created via the menu
28466 Insert\SpecialChar \menuseparator
28472 Edit\SpecialChar \menuseparator
28473 Math\SpecialChar \menuseparator
28474 Change Formula Type
28476 already existing formulas can be converted to Align environments.
28479 \begin_layout Standard
28480 To add or delete columns, the math toolbar buttons
28481 \begin_inset Graphics
28482 filename ../images/tabular-feature_append-column.png
28488 \begin_inset Graphics
28489 filename ../images/tabular-feature_delete-column.png
28494 , respectively, or the menu
28496 Edit\SpecialChar \menuseparator
28502 \begin_layout Subsubsection
28503 Standard align Environment
28504 \begin_inset CommandInset label
28506 name "sub:Standard-align-Environment"
28514 \begin_layout Plain Layout
28515 Formula ! multiline ! align environment
28523 \begin_layout Standard
28524 This Align environment is created by presssing
28527 arg "newline-insert newline"
28530 in a formula or by the menu
28532 Insert\SpecialChar \menuseparator
28533 Math\SpecialChar \menuseparator
28534 AMS align Environment
28539 \begin_layout Standard
28540 An example for two formulas set side by side, that are created with a four
28541 column align environment:
28542 \begin_inset Formula \begin{align*}
28543 A & =\sin(B) & C & =D\\
28544 C & \ne A & B & \ne D\end{align*}
28548 As it can be seen, the formulas in this environment are placed so as if
28557 \begin_layout Plain Layout
28565 \begin_inset CommandInset ref
28567 reference "sub:Variable-Space"
28578 before the first and after every even column.
28579 When the formula style
28585 \begin_layout Plain Layout
28587 \begin_inset CommandInset ref
28589 reference "sec:Formula-Styles"
28600 is used, the formula is set without the
28606 before the first column.
28609 \begin_layout Subsubsection
28610 Alignat Environment
28614 \begin_layout Plain Layout
28615 Formula ! multiline ! alignat environment
28623 \begin_layout Standard
28624 The alignat environment has no predefined column separation.
28625 It can be inserted manually with the spaces that are described
28626 \begin_inset CommandInset ref
28628 reference "sub:Space"
28635 \begin_layout Standard
28636 The above example in the alignat environment where 1
28637 \begin_inset space \thinspace{}
28640 cm space was inserted at the beginning of the second formula:
28641 \begin_inset Formula \begin{alignat*}{2}
28642 A & =\sin(B) & \hspace{1cm}C & =D\\
28643 C & \ne A & B & \ne D\end{alignat*}
28647 Because the column separation can be set separately for every column, this
28648 environment is especially suitable to set three and more formulas side
28652 \begin_layout Subsubsection
28653 Flalign Environment
28654 \begin_inset CommandInset label
28656 name "sub:Flalign-Environment"
28664 \begin_layout Plain Layout
28665 Formula ! multiline ! flalign environment
28673 \begin_layout Standard
28674 In this environment the first two columns are always set as much as possible
28675 to the left and the last two ones to the right.
28677 \begin_inset Formula \begin{flalign*}
28678 A & =1 & B & =2 & C & =3\\
28679 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28686 \begin_layout Standard
28687 By creating a flalign environment with an odd number of columns where an
28688 empty TeX-brace is inserted to the last column, several formulas in a document
28689 can be set to the left, although the formula style
28694 As example the indented formula
28695 \begin_inset CommandInset ref
28697 reference "eq:VolInt"
28702 \begin_inset Formula \begin{flalign}
28703 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28707 The first two columns contain the formula.
28708 To indent it as with the formula style
28713 \begin_inset space \thinspace{}
28716 pt space was inserted at the beginning of the first column.
28719 \begin_layout Subsection
28720 Eqnarray Environment
28721 \begin_inset CommandInset label
28723 name "sub:Eqnarray-Environment"
28731 \begin_layout Plain Layout
28732 Formula ! multiline ! eqnarray environment
28740 \begin_layout Standard
28741 When this environment has been created, three blue boxes appear.
28742 The content of the first box is right aligned, the content of the last
28744 The content of the middle box appears centered and a bit smaller, because
28745 it is designed to insert there only relation characters.
28746 \begin_inset Formula \begin{eqnarray*}
28747 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28749 A & = & A\end{eqnarray*}
28756 \begin_layout Subsection
28761 \begin_layout Plain Layout
28762 Formula ! multiline ! gather environment
28770 \begin_layout Standard
28771 This environment consists of only one centered column.
28772 Every line can be numbered.
28773 \begin_inset Formula \begin{gather}
28775 X=\textrm{-}1\end{gather}
28782 \begin_layout Subsection
28783 Multline Environment
28784 \begin_inset CommandInset label
28786 name "sub:Multline-Environment"
28794 \begin_layout Plain Layout
28795 Formula ! multiline ! multline environment
28803 \begin_layout Standard
28804 The multline environment consists, like the gather environment, of only
28806 But the first line is left aligned, the last one right aligned.
28807 All other lines are centered.
28808 Therefore this environment is suitable for long formulas.
28810 \begin_inset CommandInset ref
28812 reference "eq:lefteqn"
28816 in the multline environment:
28817 \begin_inset Formula \begin{multline}
28818 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}\\
28819 -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}\\
28820 =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}
28827 \begin_layout Standard
28828 In the output only the last (first) line of a multline environment appears
28829 numbered when the document numbering is right (left).
28833 \begin_layout Plain Layout
28834 numbering styles see
28835 \begin_inset CommandInset ref
28837 reference "sec:Formula-Styles"
28849 \begin_layout Standard
28858 \begin_layout Plain Layout
28876 \begin_layout Plain Layout
28886 a centered line can be right or left aligned, respectively.
28887 The commands are used as follows:
28890 \begin_layout Standard
28895 shoveright{line content}
28901 shoveleft{line content}
28904 \begin_layout Standard
28905 \begin_inset VSpace medskip
28916 \begin_layout Plain Layout
28926 specifies the distance of the first line from the left page margin.
28927 Predefined is the length 0
28928 \begin_inset space \thinspace{}
28934 \begin_layout Standard
28935 As example the above formula where the command
28938 \begin_layout Standard
28948 \begin_layout Standard
28949 was inserted in TeX-mode before:
28953 \begin_layout Plain Layout
28965 \begin_inset Formula \begin{multline}
28966 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}\\
28967 \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}}\\
28968 =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}
28976 \begin_layout Plain Layout
28987 The second line was left aligned using
28996 \begin_layout Subsection
28997 Multiline Formula Parts
28998 \begin_inset CommandInset label
29000 name "sub:Multiline-Formula-Parts"
29008 \begin_layout Plain Layout
29009 Formula ! multiline ! formula parts
29017 \begin_layout Standard
29018 To display only parts of a formula with multiple lines, one of the following
29019 environments are used:
29036 They can be inserted via the menu
29038 Insert\SpecialChar \menuseparator
29041 or by using the commands described in this section.
29044 \begin_layout Standard
29045 The first three have the same properties as the corresponding multiline
29046 formula environments, but it is possible to set further formula parts beside
29049 \begin_inset Formula \[
29050 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29051 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29052 \right\} \textrm{Uncertainty relations}\]
29059 \begin_layout Standard
29060 To get this formula, a displayed formula is created where the command
29068 \begin_layout Plain Layout
29079 A purple box appears around the blue formula box where now columns and
29080 lines can be added.
29081 Outside the multiline environment other formula parts can be set, like
29085 \begin_layout Standard
29086 The aligned environment is also suitable for long formulas whose lines are
29087 horizontally aligned.
29088 Using aligned in a displayed formula has the advantage that the formula
29089 number is vertically centered behind the lines.
29091 \begin_inset CommandInset ref
29093 reference "eq:shortlong"
29097 in the aligned environment:
29098 \begin_inset Formula \begin{equation}
29099 \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}|}\\
29100 & -\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}
29108 \begin_layout Standard
29109 To use the environments
29131 \begin_layout Plain Layout
29149 \begin_layout Plain Layout
29167 \begin_layout Plain Layout
29175 are inserted, respectively.
29176 The split environment has the same properties as the aligned environment
29177 but it can only have two columns.
29180 \begin_layout Subsection
29181 Text in multiline Formulas
29182 \begin_inset CommandInset label
29184 name "sub:Text-in-multiline"
29192 \begin_layout Plain Layout
29202 \begin_layout Plain Layout
29203 Formula ! multiline ! text
29211 \begin_layout Standard
29212 In the Align environments, and the multline and gather environment, text
29213 can be inserted that will appear in a separate line and doesn't affect
29214 the column alignment.
29215 To do this, the command
29223 \begin_layout Plain Layout
29233 is used in the following scheme:
29236 \begin_layout Standard
29244 \begin_layout Standard
29245 The text should not be longer than a line because it cannot be hyphenated.
29246 As LyX doesn't yet support
29252 directly, the text is written as mathematical text.
29259 must hereby be at the beginning of a line and appears in the output above
29261 An example where the text was inserted at the beginning of the second line:
29262 \begin_inset Formula \begin{align}
29263 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29264 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29271 \begin_layout Section
29276 \begin_layout Plain Layout
29286 \begin_layout Plain Layout
29287 Formula ! numbering|see
29291 \begin_layout Plain Layout
29302 \begin_layout Plain Layout
29317 \begin_layout Subsection
29321 \begin_layout Standard
29322 Numbered formulas can be created with the menu
29324 Insert\SpecialChar \menuseparator
29325 Math\SpecialChar \menuseparator
29327 \begin_inset space ~
29335 \begin_inset space ~
29341 Existing formulas can be numbered with the menu
29343 Edit\SpecialChar \menuseparator
29344 Math\SpecialChar \menuseparator
29346 \begin_inset space ~
29354 arg "math-number-toggle"
29358 The formula number is displayed in LyX behind the formula as number sign
29360 The number sign is replaced in the output by the formula number.
29363 \begin_layout Standard
29364 When numbering is turned on in multiline formulas, all lines will be numbered.
29365 But the numbering can be controlled with the menu
29367 Edit\SpecialChar \menuseparator
29368 Math\SpecialChar \menuseparator
29370 \begin_inset space ~
29374 \begin_inset space ~
29378 \begin_inset space ~
29386 arg "math-number-line-toggle"
29392 \begin_layout Standard
29393 Except of inline formulas, all formulas can be numbered with two different
29395 \begin_inset CommandInset ref
29397 reference "sec:Formula-Styles"
29404 \begin_layout Subsection
29409 \begin_layout Plain Layout
29410 Cross-references ! to formulas
29418 \begin_layout Standard
29419 All labeled formulas can be cross-referenced.
29420 A label is added by the menu
29422 Insert\SpecialChar \menuseparator
29425 or the toolbar button
29426 \begin_inset Graphics
29427 filename ../images/label-insert.png
29433 The cursor must hereby be inside a displayed formula.
29434 A dialog pops up displaying the prefix
29439 The label is inserted there behind the prefix.
29440 The predefined prefix means
29441 \begin_inset Quotes eld
29445 \begin_inset Quotes erd
29448 and makes it easier to find labels in large documents because it marks
29449 it as formula label to divide it from e.
29450 \begin_inset space \thinspace{}
29454 \begin_inset space \space{}
29458 To change a label, the menu
29460 Insert\SpecialChar \menuseparator
29466 \begin_layout Standard
29467 The name of the label is displayed in LyX within two parentheses behind
29469 A formula with a label is always numbered.
29472 \begin_layout Standard
29473 Cross-references are inserted via the menu
29475 Insert\SpecialChar \menuseparator
29478 or with the toolbar button
29479 \begin_inset Graphics
29480 filename ../images/dialog-show-new-inset_ref.png
29486 A formula cross-reference appears in the output as formula number.
29487 When in the cross-reference dialog window the format
29491 is chosen, the cross-reference appears in the output as formula number
29493 \begin_inset Newline newline
29496 By right-clicking on a cross-reference in LyX, one jumps to the formula
29497 that is referenced.
29500 \begin_layout Standard
29501 Here are as examples cross-references to formulas of the following subsections:
29502 \begin_inset Note Note
29505 \begin_layout Plain Layout
29506 Note the different cross-reference types.
29514 \begin_layout Standard
29516 \begin_inset CommandInset ref
29523 \begin_inset CommandInset ref
29531 \begin_inset CommandInset ref
29537 ) big Latin letters are used for the numbering in contrary to (
29538 \begin_inset CommandInset ref
29547 \begin_layout Standard
29548 \begin_inset VSpace medskip
29551 When the argument of
29559 \begin_layout Plain Layout
29567 \begin_inset CommandInset ref
29569 reference "sub:User-defined-Numbering"
29580 contains a box like in
29581 \begin_inset CommandInset ref
29583 reference "sub:Paragraph-Boxes"
29587 , the formula cannot be referenced.
29590 \begin_layout Subsection
29595 \begin_layout Plain Layout
29596 Formula numbering ! subnumbering
29604 \begin_layout Standard
29605 With the help of the commands
29609 begin{subequations}
29617 formulas can be subnumbered.
29618 Both commands are inserted in TeX-mode.
29621 \begin_layout Standard
29623 \begin_inset Formula \begin{equation}
29624 A=C-B\label{eq:a}\end{equation}
29632 \begin_layout Plain Layout
29636 addtocounter{equation}{-1}
29645 \begin_layout Plain Layout
29649 begin{subequations}
29655 \begin_inset VSpace -5mm
29659 \begin_inset Formula \begin{equation}
29660 B=C-A\label{eq:b}\end{equation}
29665 \begin_inset Formula \begin{equation}
29666 C=A+B\label{eq:c}\end{equation}
29673 \begin_layout Standard
29677 \begin_layout Plain Layout
29689 \begin_layout Standard
29690 To create the example, the following is done:
29693 \begin_layout Enumerate
29694 first formula is inserted
29697 \begin_layout Enumerate
29702 addtocounter{equation}{-1}
29704 begin{subequations}
29708 \begin_layout Plain Layout
29717 \begin_inset Newline newline
29722 is inserted after the first formula
29725 \begin_layout Enumerate
29726 second formula is inserted
29729 \begin_layout Enumerate
29730 third formula is inserted
29733 \begin_layout Enumerate
29740 is inserted after the third formula
29743 \begin_layout Standard
29744 Every formula between the commands
29756 is subnumbered as a, b,
29757 \begin_inset Newline linebreak
29760 c, \SpecialChar \ldots{}
29761 For multiline formulas every line will be subnumbered.
29762 All subnumbered formulas are treated as
29767 But as every numbered formula increases the counter
29771 by one, the command
29777 is needed to decrease it.
29778 Otherwise the formulas
29779 \begin_inset CommandInset ref
29786 \begin_inset CommandInset ref
29793 \begin_inset CommandInset ref
29799 would be numbered as
29800 \begin_inset CommandInset ref
29807 \begin_inset CommandInset ref
29814 \begin_inset CommandInset ref
29823 \begin_layout Standard
29824 By inserting the commands in TeX-mode, a space is created between the first
29827 \begin_inset space \thinspace{}
29830 mm vertical space is inserted after the command
29834 begin{subequations}
29837 When the formula style
29843 \begin_layout Plain Layout
29845 \begin_inset CommandInset ref
29847 reference "sec:Formula-Styles"
29859 \begin_inset space \thinspace{}
29862 mm space is inserted instead.
29865 \begin_layout Standard
29866 Here is an example for a multiline formula where the numbering was turned
29867 off for the second line:
29871 \begin_layout Plain Layout
29875 begin{subequations}
29881 \begin_inset Formula \begin{eqnarray}
29882 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29883 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29884 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29892 \begin_layout Plain Layout
29904 \begin_layout Subsection
29905 User-defined Numbering
29906 \begin_inset CommandInset label
29908 name "sub:User-defined-Numbering"
29916 \begin_layout Plain Layout
29917 Formula numbering ! user-defined
29925 \begin_layout Standard
29929 \begin_layout Plain Layout
29930 Formula numbering ! self-defined delimiters
29935 With the standard numbering parentheses are set around the formula number.
29936 To replace the parentheses for example by vertical bars, the following
29937 line is added to the LaTeX-preamble:
29940 \begin_layout Standard
29952 \begin_inset Note Note
29955 \begin_layout Plain Layout
29956 This macro is already declared in the LaTeX-preamble for testing.
29957 To activate it, remove the percent sign at the beginning.
29965 \begin_layout Standard
29966 To use other characters, the vertical bars besides the
29970 are replaced by one ore more characters.
29971 To get only the formula number the vertical bars are omitted.
29974 \begin_layout Standard
29975 \begin_inset VSpace bigskip
29978 When there should be an expression of your choice instead of the consecutive
29979 formula number in parentheses behind the formula, the command
29989 \begin_layout Plain Layout
29998 \begin_inset Formula \begin{equation}
29999 A+B=C\tag{something}\label{eq:tag}\end{equation}
30003 In this example the command
30011 \begin_layout Plain Layout
30022 was inserted to the formula.
30025 \begin_layout Standard
30034 \begin_layout Plain Layout
30045 is inserted instead, the star prevents the parentheses around the expression:
30046 \begin_inset Formula \[
30047 A+B=C\tag*{something}\]
30054 \begin_layout Standard
30055 \begin_inset VSpace bigskip
30058 To restart the formula numbering with new document parts or sections, the
30059 following command is used:
30062 \begin_layout Standard
30067 @addtoreset{equation}{part}
30073 \begin_layout Plain Layout
30078 \begin_layout Plain Layout
30089 \begin_layout Plain Layout
30102 \begin_layout Plain Layout
30113 \begin_layout Plain Layout
30126 \begin_inset Newline newline
30130 \begin_inset Newline newline
30137 @addtoreset{equation}{section}
30140 \begin_layout Standard
30141 To be able to use these commands in TeX-mode, the
30142 \begin_inset Quotes eld
30146 \begin_inset Quotes erd
30149 character has to be made
30150 \begin_inset Quotes eld
30154 \begin_inset Quotes erd
30157 for LaTeX using the command
30171 So the command sequence in TeX-mode is:
30174 \begin_layout Standard
30180 \begin_inset Newline newline
30185 @addtoreset{equation}{section}
30186 \begin_inset Newline newline
30194 \begin_layout Standard
30195 In the LaTeX-preamble
30207 can be omitted as they are automatically internally inserted by LyX.
30210 \begin_layout Standard
30225 \begin_layout Plain Layout
30230 is part of the LaTeX-package
30238 \begin_layout Plain Layout
30239 Packages ! carlisle
30244 that is part of every LaTeX standard installation.
30253 \begin_layout Plain Layout
30254 Packages ! remreset
30259 has to be loaded in the LaTeX-preamble with the line
30262 \begin_layout Standard
30267 usepackage{remreset}
30270 \begin_layout Standard
30281 \begin_layout Plain Layout
30286 \begin_layout Plain Layout
30297 \begin_layout Plain Layout
30310 \begin_layout Plain Layout
30321 \begin_layout Plain Layout
30333 can be used with the same scheme as
30342 \begin_layout Standard
30343 \begin_inset VSpace bigskip
30346 Sometimes formulas should be numbered in the following form:
30349 \begin_layout Standard
30352 (section number.formula number)
30355 \begin_layout Standard
30356 The formula number should start with every section with
30357 \begin_inset Quotes eld
30361 \begin_inset Quotes erd
30367 \begin_layout Standard
30368 For this case there is the command
30378 \begin_layout Plain Layout
30386 , which is used with the following scheme:
30389 \begin_layout Standard
30394 numberwithin{counter}{sectioning}
30397 \begin_layout Standard
30398 Counter denotes what kind of numbering is affected, sectioning denotes what
30399 number is before the dot.
30402 \begin_layout Standard
30403 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30406 \begin_layout Standard
30411 numberwithin{equation}{section}
30414 \begin_layout Standard
30415 This is the result:
30419 \begin_layout Plain Layout
30423 numberwithin{equation}{section}
30429 \begin_inset Formula \begin{equation}
30430 A+B=C\end{equation}
30437 \begin_layout Standard
30439 \begin_inset space \thinspace{}
30443 \begin_inset space \space{}
30446 tables so that the number of the part is the sectioning,
30447 \begin_inset Newline newline
30454 numberwithin{table}{part}
30459 \begin_layout Standard
30460 To go back to the standard numbering or to prevent this kind of numbering
30461 when it is defined by the document class, the following command is inserted
30462 as TeX-Code or to the LaTeX-preamble:
30465 \begin_layout Standard
30478 \begin_layout Plain Layout
30492 \begin_layout Plain Layout
30508 \begin_inset Newline newline
30516 \begin_inset Newline newline
30528 \begin_layout Standard
30535 uses internally the command
30541 , described above, that also needs to be reverted.
30545 \begin_layout Plain Layout
30552 \begin_layout Plain Layout
30556 @removefromreset{equation}{section}
30559 \begin_layout Plain Layout
30571 \begin_layout Subsection
30572 Numbering with Roman Numbers and Letters
30576 \begin_layout Plain Layout
30577 Formula numbering ! with letters
30586 \begin_layout Plain Layout
30587 Formula numbering ! with Roman numbers
30595 \begin_layout Standard
30596 Formulas can also be numbered with Roman numbers and Latin letters.
30597 To number for example with small Roman numbers, the command
30600 \begin_layout Standard
30612 \begin_layout Standard
30613 is inserted before the formula in TeX-mode.
30624 \begin_layout Plain Layout
30632 redefines the predefined command
30648 \begin_layout Plain Layout
30655 has the same scheme like the command
30661 that is described in
30662 \begin_inset CommandInset ref
30664 reference "sub:The-Command-newcommand"
30677 is the formula counter.
30684 is used as prefix for a counter, the value of the counter is output as
30686 When a formula is numbered, LaTeX sets internally the command
30692 behind the formula.
30701 \begin_layout Plain Layout
30711 outputs the counter as small Roman number.
30714 \begin_layout Standard
30715 All formulas behind the command
30725 are now numbered Roman.
30726 To switch to numbering with big Roman numbers, the command is inserted
30743 \begin_layout Plain Layout
30755 \begin_inset Quotes eld
30759 \begin_inset Quotes erd
30762 with small Latin letters there is the command
30772 \begin_layout Plain Layout
30780 , for big ones there is the command
30790 \begin_layout Plain Layout
30803 \begin_layout Standard
30804 \begin_inset Note Greyedout
30807 \begin_layout Plain Layout
30812 Only maximal 26 formulas can be numbered with Latin letters in one document.
30820 \begin_layout Standard
30824 \begin_layout Plain Layout
30840 \begin_layout Standard
30841 \begin_inset Formula \begin{equation}
30842 A=\textrm{small roman}\label{eq:rom}\end{equation}
30850 \begin_layout Plain Layout
30864 \begin_inset Formula \begin{equation}
30865 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30873 \begin_layout Plain Layout
30887 \begin_inset Formula \begin{equation}
30888 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30896 \begin_layout Plain Layout
30910 \begin_inset Formula \begin{equation}
30911 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30918 \begin_layout Standard
30919 To switch back to the default numbering, insert the command:
30922 \begin_layout Standard
30935 \begin_layout Plain Layout
30946 \begin_layout Standard
30950 \begin_layout Plain Layout
30964 \begin_inset Formula \begin{equation}
30965 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30972 \begin_layout Standard
30973 \begin_inset VSpace medskip
30976 As you see, formulas are numbered serially independent from the numbering
30978 When then numbering should start with
30979 \begin_inset Quotes eld
30983 \begin_inset Quotes erd
30986 when the style is changed, new equation counters have to be defined.
30987 A description about this can be found in the file
30988 \begin_inset CommandInset href
30990 target "Formula-numbering.lyx"
30997 \begin_layout Section
30998 User-defined Commands
31002 \begin_layout Plain Layout
31003 User-defined commands
31011 \begin_layout Standard
31012 \begin_inset Note Greyedout
31015 \begin_layout Plain Layout
31020 The names of user-defined commands and macros may only consist of Latin
31029 \begin_layout Subsection
31033 \begin_inset CommandInset label
31035 name "sub:The-Command-newcommand"
31043 \begin_layout Plain Layout
31044 User-defined commands !
31055 \begin_layout Plain Layout
31066 \begin_layout Standard
31067 Many LaTeX-commands are too long to be used frequently.
31068 But it is possible to define with the command
31074 new shorter commands.
31077 \begin_layout Standard
31078 The command scheme of
31087 \begin_layout Standard
31092 newcommand{new command name}[number of arguments][optional
31097 \begin_inset Newline newline
31104 \begin_layout Plain Layout
31119 \begin_layout Plain Layout
31126 {command definition}
31129 \begin_layout Standard
31130 \begin_inset Note Greyedout
31133 \begin_layout Plain Layout
31138 Assure that the name of the new command is not already used in your document
31139 or by LaTeX-packages that you use.
31140 When you for example define the command
31152 , you get an error message because
31158 is already defined as command for
31159 \begin_inset Quotes eld
31163 \begin_inset Formula $\le$
31167 \begin_inset Quotes erd
31178 \begin_layout Standard
31179 The number of arguments is an integer in the range 0
31180 \begin_inset space \thinspace{}
31184 \begin_inset space \thinspace{}
31187 9 and specifies how many arguments the new command should have.
31188 With the optional value a value for an optional argument can be predefined.
31189 When this is done, the
31197 rgument of the new command is automatically an optional one.
31200 \begin_layout Standard
31201 Here are some examples:
31204 \begin_layout Itemize
31205 To define the command
31217 , the LaTeX-preamble line is:
31221 \begin_layout Plain Layout
31233 \begin_inset Newline newline
31245 \begin_layout Itemize
31246 To define the command
31258 , the argument (that should be underlined) must be taken into account.
31259 For this the preamble line is:
31263 \begin_layout Plain Layout
31275 \begin_inset Newline newline
31290 \begin_layout Plain Layout
31302 \begin_inset Newline newline
31311 acts as argument placeholder, the
31315 behind it denotes that it is the placeholder for the first argument.
31318 \begin_layout Itemize
31326 \begin_inset space \thinspace{}
31330 \begin_inset space \space{}
31343 \begin_layout Plain Layout
31355 \begin_inset Newline newline
31364 framebox#1#2{$#3$}}
31370 \begin_layout Plain Layout
31382 \begin_inset Newline newline
31387 The two Dollar signs creates the extra formula needed for
31394 \begin_inset CommandInset ref
31396 reference "sub:Boxes-with-Frame"
31403 \begin_layout Itemize
31404 To create a new command for
31410 where the color for the box needn't to be specified, the argument for the
31411 color is defined optional:
31415 \begin_layout Plain Layout
31427 \begin_inset Newline newline
31436 fcolorbox{#2}{#1}{$#3$}}
31442 \begin_layout Plain Layout
31452 \begin_inset Newline newline
31455 When the color is not specified when using
31461 , the predefined color
31468 \begin_layout Standard
31469 A test of the new defined commands:
31472 \begin_layout Standard
31474 \begin_inset Tabular
31475 <lyxtabular version="3" rows="6" columns="2">
31477 <column alignment="center" valignment="top" width="0">
31478 <column alignment="center" valignment="top" width="0">
31480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31483 \begin_layout Plain Layout
31489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31492 \begin_layout Plain Layout
31494 \begin_inset Note Note
31497 \begin_layout Plain Layout
31504 is only used as spacer.
31516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31519 \begin_layout Plain Layout
31526 \begin_layout Plain Layout
31540 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31543 \begin_layout Plain Layout
31544 \begin_inset Formula $A\gr B$
31554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31557 \begin_layout Plain Layout
31565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31568 \begin_layout Plain Layout
31569 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31582 \begin_layout Plain Layout
31586 \begin_inset Formula $\to$
31592 \begin_inset Formula $\to$
31603 \begin_layout Plain Layout
31617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31620 \begin_layout Plain Layout
31621 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31634 \begin_layout Plain Layout
31638 \begin_inset Formula $\to$
31649 \begin_layout Plain Layout
31663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31666 \begin_layout Plain Layout
31667 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31680 \begin_layout Plain Layout
31686 \begin_inset Formula $\to$
31697 \begin_layout Plain Layout
31711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31714 \begin_layout Plain Layout
31715 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31731 \begin_layout Subsection
31736 \begin_layout Plain Layout
31737 User-defined commands! Math macros
31746 \begin_layout Plain Layout
31755 \begin_layout Standard
31756 User-defined commands are especially convenient for complex expressions.
31757 When you are for example dealing in a document with quadratic equations,
31758 the same solution type occurs several times.
31759 The general form of a quadratic equation is
31760 \begin_inset Formula \[
31761 0=\lambda^{2}+p\lambda+q\]
31765 The general form of the solution is
31766 \begin_inset Formula \[
31767 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31774 \begin_layout Standard
31775 To define a command for the solution formula where only the three parameters
31777 \begin_inset Formula $\lambda$
31781 \begin_inset Formula $p$
31785 \begin_inset Formula $q$
31788 need to be specified and the index of
31789 \begin_inset Formula $\lambda$
31792 can be given optionally, the LaTeX-preamble line is
31793 \begin_inset Newline newline
31809 \begin_inset Newline newline
31816 \begin_layout Plain Layout
31831 \begin_layout Plain Layout
31842 frac{#3^{2}}{4}-#4}}
31845 \begin_layout Standard
31846 To create with this the solution formula, the command
31847 \begin_inset Newline newline
31857 \begin_inset Formula $\to$
31863 \begin_inset Formula $\to$
31870 is inserted to a formula
31875 \begin_layout Standard
31876 The definition of the new command is unintuitive because one has to know
31877 the schemes of all used LaTeX commands, e.
31878 \begin_inset space \thinspace{}
31882 \begin_inset space \space{}
31885 that a fraction is inserted in LaTeX as
31889 frac{numerator}{denominator}
31892 Furthermore one can easily forget a brace in the definition and cannot
31893 see in LyX what the new command is doing.
31894 To avoid these problems LyX offers the possibility to use math macros instead
31904 \begin_layout Standard
31905 A math macro is created by using the menu
31907 Insert\SpecialChar \menuseparator
31908 Math\SpecialChar \menuseparator
31911 or the toolbar button
31912 \begin_inset Graphics
31913 filename ../images/math-macro_newmacroname_newcommand.png
31919 The math macro toolbar appears together with the following box where the
31921 \begin_inset Newline newline
31925 \begin_inset space \hspace*{\fill}
31929 \begin_inset Graphics
31930 filename clipart/macrobox.png
31937 \begin_inset space \hspace*{\fill}
31941 \begin_inset Newline newline
31945 \begin_inset FormulaMacro
31946 \renewcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31951 newmacroname is the default name of the macro that should be changed to
31952 something sensible.
31953 The wanted formula is inserted in the first blue box.
31954 An argument placeholder is inserted with the command
31961 \begin_inset space \thinspace{}
31965 \begin_inset space \space{}
31974 or by using the macro toolbar button
31975 \begin_inset Graphics
31976 filename ../images/math-macro-add-param.png
31982 Argument placeholders are displayed red.
31983 Maximum 9 arguments are possible.
31984 Optional arguments are created with the toolbar button
31985 \begin_inset Graphics
31986 filename ../images/math-macro-add-optional-param.png
31992 The first non-optional argument can be transformed to an optional one with
31994 \begin_inset Graphics
31995 filename ../images/math-macro-make-optional.png
32001 In the second blue box the appearance of the macro in LyX can be defined.
32002 Normally you want to see it as it is defined, so the box is kept empty.
32003 But when you have created a macro that needs lot of space on the screen,
32004 you can insert in the box for example
32005 \begin_inset Newline newline
32035 \begin_inset Newline newline
32040 For the macro only the arguments with the macro name in front of them will
32041 then be displayed in LyX, leading to a better overview.
32042 The formula appears in the output as defined in the first box.
32043 \begin_inset Newline newline
32046 The appearance of macros in formulas can furthermore be changed for single
32047 macros by setting the cursor in the macro and using the menu
32049 View\SpecialChar \menuseparator
32051 \begin_inset space ~
32055 \begin_inset space ~
32063 \begin_layout Standard
32064 To use a macro, the macro name is inserted as command to a formula, in our
32072 Our macro looks in LyX like this:
32073 \begin_inset Newline newline
32077 \begin_inset space \hspace*{\fill}
32081 \begin_inset Graphics
32082 filename clipart/macrouse.png
32089 \begin_inset space \hspace*{\fill}
32093 \begin_inset Newline newline
32096 Here is our macro example with the arguments
32097 \begin_inset Formula $x$
32101 \begin_inset Formula $\ln(x)$
32105 \begin_inset Formula $B$
32111 \begin_layout Standard
32112 \begin_inset Formula \[
32120 \begin_layout Standard
32121 A math macro is transformed internally to a
32127 command when exporting the document.
32134 command is not placed in the LaTeX-preamble, therefore macros can only
32135 be used in formulas that are in the document below the macro definition
32139 \begin_layout Standard
32140 Math macros can also be directly be created from a
32147 When writing for example the command
32150 \begin_inset Newline newline
32159 xleftarrow[#2]{#1}}
32160 \begin_inset Newline newline
32165 in LyX as normal text, highlighting it completely and using then the shortcut
32170 , the command will be transformed to a math macro.
32171 Using this method you need to be careful that the
32177 command is typed correctly, otherwise you get a faulty macro leading to
32181 \begin_layout Standard
32182 Math macros currently yet have the problem that further formulas in macro
32183 definitions are handled wrongly.
32184 Therefore the example
32191 \begin_inset CommandInset ref
32193 reference "sub:The-Command-newcommand"
32197 cannot be created as macro.
32200 \begin_layout Standard
32201 When the cursor is in a macro definition box, you will see the macro toolbar
32205 \begin_layout Standard
32206 \begin_inset VSpace defskip
32212 \begin_layout Standard
32213 \begin_inset Graphics
32214 filename clipart/MacroToolbar.png
32222 \begin_layout Plain Layout
32231 \begin_layout Standard
32232 \begin_inset VSpace defskip
32238 \begin_layout Standard
32239 The macro toolbar contains from left to right the following buttons:
32242 \begin_layout Standard
32243 \begin_inset VSpace defskip
32249 \begin_layout Standard
32250 \begin_inset Tabular
32251 <lyxtabular version="3" rows="9" columns="2">
32252 <features islongtable="true">
32253 <column alignment="left" valignment="top" width="0">
32254 <column alignment="left" valignment="top" width="85col%">
32255 <row interlinespace="2.5mm">
32256 <cell alignment="center" valignment="top" usebox="none">
32259 \begin_layout Plain Layout
32260 \begin_inset Graphics
32261 filename ../images/math-macro-remove-param.png
32262 BoundingBox 0bp 5bp 20bp 25bp
32263 rotateOrigin center
32272 <cell alignment="center" valignment="top" usebox="none">
32275 \begin_layout Plain Layout
32278 Edit\SpecialChar \menuseparator
32279 Math\SpecialChar \menuseparator
32281 \begin_inset space ~
32284 Definition\SpecialChar \menuseparator
32291 <row interlinespace="2.5mm">
32292 <cell alignment="center" valignment="top" usebox="none">
32295 \begin_layout Plain Layout
32296 \begin_inset Graphics
32297 filename ../images/math-macro-add-param.png
32298 BoundingBox 0bp 5bp 20bp 25bp
32299 rotateOrigin center
32308 <cell alignment="center" valignment="top" usebox="none">
32311 \begin_layout Plain Layout
32314 Edit\SpecialChar \menuseparator
32315 Math\SpecialChar \menuseparator
32317 \begin_inset space ~
32320 Definition\SpecialChar \menuseparator
32321 Append Last Argument
32327 <row interlinespace="2.5mm">
32328 <cell alignment="center" valignment="top" usebox="none">
32331 \begin_layout Plain Layout
32332 \begin_inset Graphics
32333 filename ../images/math-macro-make-optional.png
32334 BoundingBox 0bp 5bp 20bp 25bp
32335 rotateOrigin center
32344 <cell alignment="center" valignment="top" usebox="none">
32347 \begin_layout Plain Layout
32350 Edit\SpecialChar \menuseparator
32351 Math\SpecialChar \menuseparator
32353 \begin_inset space ~
32356 Definition\SpecialChar \menuseparator
32357 Make First Non-Optional into
32358 \begin_inset Newline newline
32365 \begin_layout Plain Layout
32374 Edit\SpecialChar \menuseparator
32375 Math\SpecialChar \menuseparator
32377 \begin_inset space ~
32380 Definition\SpecialChar \menuseparator
32385 \begin_layout Plain Layout
32398 <row interlinespace="2.5mm">
32399 <cell alignment="center" valignment="top" usebox="none">
32402 \begin_layout Plain Layout
32403 \begin_inset Graphics
32404 filename ../images/math-macro-make-nonoptional.png
32405 BoundingBox 0bp 5bp 20bp 25bp
32406 rotateOrigin center
32415 <cell alignment="center" valignment="top" usebox="none">
32418 \begin_layout Plain Layout
32421 Edit\SpecialChar \menuseparator
32422 Math\SpecialChar \menuseparator
32424 \begin_inset space ~
32427 Definition\SpecialChar \menuseparator
32428 Make Last Optional into
32429 \begin_inset Newline newline
32436 \begin_layout Plain Layout
32445 Edit\SpecialChar \menuseparator
32446 Math\SpecialChar \menuseparator
32448 \begin_inset space ~
32451 Definition\SpecialChar \menuseparator
32456 \begin_layout Plain Layout
32463 Non-Optional Argument
32469 <row interlinespace="2.5mm">
32470 <cell alignment="center" valignment="top" usebox="none">
32473 \begin_layout Plain Layout
32474 \begin_inset Graphics
32475 filename ../images/math-macro-remove-optional-param.png
32476 BoundingBox 0bp 5bp 20bp 25bp
32477 rotateOrigin center
32486 <cell alignment="center" valignment="top" usebox="none">
32489 \begin_layout Plain Layout
32492 Edit\SpecialChar \menuseparator
32493 Math\SpecialChar \menuseparator
32495 \begin_inset space ~
32498 Definition\SpecialChar \menuseparator
32499 Remove Optional Argument
32505 <row interlinespace="2.5mm">
32506 <cell alignment="center" valignment="top" usebox="none">
32509 \begin_layout Plain Layout
32510 \begin_inset Graphics
32511 filename ../images/math-macro-add-optional-param.png
32512 BoundingBox 0bp 5bp 20bp 25bp
32513 rotateOrigin center
32522 <cell alignment="center" valignment="top" usebox="none">
32525 \begin_layout Plain Layout
32528 Edit\SpecialChar \menuseparator
32529 Math\SpecialChar \menuseparator
32531 \begin_inset space ~
32534 Definition\SpecialChar \menuseparator
32535 Insert Optional Argument
32541 <row interlinespace="2.5mm">
32542 <cell alignment="center" valignment="top" usebox="none">
32545 \begin_layout Plain Layout
32546 \begin_inset Graphics
32547 filename ../images/math-macro-remove-greedy-param.png
32548 BoundingBox 0bp 5bp 20bp 25bp
32549 rotateOrigin center
32558 <cell alignment="center" valignment="top" usebox="none">
32561 \begin_layout Plain Layout
32564 Edit\SpecialChar \menuseparator
32565 Math\SpecialChar \menuseparator
32567 \begin_inset space ~
32570 Definition\SpecialChar \menuseparator
32571 Remove Last Argument
32572 \begin_inset Newline newline
32579 \begin_layout Plain Layout
32588 Edit\SpecialChar \menuseparator
32589 Math\SpecialChar \menuseparator
32591 \begin_inset space ~
32594 Definition\SpecialChar \menuseparator
32599 \begin_layout Plain Layout
32606 Spitting Out To The Right
32612 <row interlinespace="2.5mm">
32613 <cell alignment="center" valignment="top" usebox="none">
32616 \begin_layout Plain Layout
32617 \begin_inset Graphics
32618 filename ../images/math-macro-append-greedy-param.png
32619 BoundingBox 0bp 5bp 20bp 25bp
32620 rotateOrigin center
32629 <cell alignment="center" valignment="top" usebox="none">
32632 \begin_layout Plain Layout
32635 Edit\SpecialChar \menuseparator
32636 Math\SpecialChar \menuseparator
32638 \begin_inset space ~
32641 Definition\SpecialChar \menuseparator
32643 \begin_inset Newline newline
32650 \begin_layout Plain Layout
32659 Edit\SpecialChar \menuseparator
32660 Math\SpecialChar \menuseparator
32662 \begin_inset space ~
32665 Definition\SpecialChar \menuseparator
32670 \begin_layout Plain Layout
32677 Eating From The Right
32683 <row interlinespace="2.5mm">
32684 <cell alignment="center" valignment="top" usebox="none">
32687 \begin_layout Plain Layout
32688 \begin_inset Graphics
32689 filename ../images/math-macro-add-greedy-optional-param.png
32690 BoundingBox 0bp 5bp 20bp 25bp
32691 rotateOrigin center
32700 <cell alignment="center" valignment="top" usebox="none">
32703 \begin_layout Plain Layout
32706 Edit\SpecialChar \menuseparator
32707 Math\SpecialChar \menuseparator
32709 \begin_inset space ~
32712 Definition\SpecialChar \menuseparator
32713 Append Optional Argument
32714 \begin_inset Newline newline
32721 \begin_layout Plain Layout
32730 Edit\SpecialChar \menuseparator
32731 Math\SpecialChar \menuseparator
32733 \begin_inset space ~
32736 Definition\SpecialChar \menuseparator
32741 \begin_layout Plain Layout
32748 Eating From The Right
32761 \begin_layout Standard
32762 \begin_inset Newpage newpage
32768 \begin_layout Section
32772 \begin_layout Standard
32773 LyX supports two types of commutative diagrams:
32781 that are explained in the following.
32784 \begin_layout Subsection
32789 \begin_layout Plain Layout
32798 \begin_layout Standard
32799 Diagrams of this type visualize relations by vertical and horizontal lines
32801 \begin_inset Formula \[
32802 \begin{CD}A@>>>B@>>>C\\
32804 F@<<<E@<<<D\end{CD}\]
32811 \begin_layout Standard
32812 To get them, the command
32820 \begin_layout Plain Layout
32830 is inserted to a formula.
32831 A blue box appears with two dashed lines where further commands can be
32836 arg "newline-insert newline"
32839 a new line is created.
32840 Horizontal relations are inserted in odd, vertical in even formula lines.
32843 \begin_layout Standard
32844 To create the relations there are the following commands:
32847 \begin_layout Itemize
32852 creates a left arrow,
32863 \begin_layout Itemize
32868 creates an up arrow,
32876 a vertical equal sign
32879 \begin_layout Itemize
32885 is a placeholder for non-existent relations
32888 \begin_layout Standard
32889 All arrows can be labeled as follows:
32892 \begin_layout Itemize
32893 Is text inserted between the first and second < or >, resp., it is placed
32895 When it is inserted between the second and third one, it appears under
32899 \begin_layout Itemize
32900 When text for vertical arrows is inserted between the first and second A
32901 or V, resp., it is placed left beside the arrow.
32902 When it is inserted between the second and third one, it appears right
32904 If the text contains an A or V, these letters must be set into a TeX-brace.
32907 \begin_layout Standard
32908 As example a diagram with all possible relations:
32911 \begin_layout Standard
32912 \begin_inset Formula \[
32913 \begin{CD}A@>j>>B@>>k>C@=F\\
32915 D@<<j<E@>k>>F@=C\end{CD}\]
32922 \begin_layout Standard
32923 The command for this is:
32924 \begin_inset Newline newline
32935 \begin_layout Plain Layout
32944 A@>j>>B@>>k>C@=F Ctrl+Return
32945 \begin_inset Newline newline
32952 \begin_layout Plain Layout
32967 \begin_layout Plain Layout
32980 \begin_layout Plain Layout
32992 \begin_inset Formula $\to$
32998 \begin_inset Newline newline
33005 \begin_layout Plain Layout
33020 \begin_layout Plain Layout
33033 \begin_layout Plain Layout
33043 \begin_layout Subsection
33048 \begin_layout Plain Layout
33049 Diagrams ! xymatrix
33057 \begin_layout Standard
33058 To be able to use xymatrices, the LaTeX-package
33063 A xymatrix is created by inserting the command
33070 Then you are able to add new matrix columns and rows like for normal matrices,
33072 \begin_inset CommandInset ref
33074 reference "sec:Matrices"
33081 \begin_layout Standard
33082 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33084 All possibilities to create commutative diagrams and decorations are explained
33089 that you find in the menu
33091 Help\SpecialChar \menuseparator
33093 \begin_inset space ~
33096 Manuals\SpecialChar \menuseparator
33098 \begin_inset space ~
33106 \begin_layout Standard
33107 \begin_inset Newpage newpage
33113 \begin_layout Section
33118 \begin_layout Plain Layout
33131 \begin_layout Plain Layout
33132 Other useful math tips can be found in
33133 \begin_inset CommandInset citation
33148 \begin_layout Plain Layout
33156 \begin_inset Note Note
33159 \begin_layout Plain Layout
33162 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33165 \begin_layout Plain Layout
33168 texorpdfstring is in section
33169 \begin_inset CommandInset ref
33171 reference "sub:Formulas-in-Section"
33184 \begin_layout Plain Layout
33194 \begin_layout Plain Layout
33199 \begin_layout Plain Layout
33206 Chemical characters
33210 \begin_layout Plain Layout
33225 \begin_layout Subsection
33226 Chemical Symbols and Equations
33227 \begin_inset CommandInset label
33229 name "sub:Chemical-Symbols-and"
33237 \begin_layout Plain Layout
33238 Chemical characters ! Symbols
33247 \begin_layout Plain Layout
33257 \begin_layout Plain Layout
33266 \begin_layout Standard
33267 An example text from chemistry:
33270 \begin_layout Quote
33272 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33275 -ion reacts with two
33276 \begin_inset Formula $\mathrm{Na^{+}}$
33279 -ions to sodium sulfate
33280 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33284 The chemical equation for this is:
33285 \begin_inset Formula \[
33286 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33293 \begin_layout Standard
33294 This chemical equation can directly be created as formula.
33295 To avoid that the symbols appear italic, everything is highlighted and
33296 changed by the shortcut
33302 to the upright font style.
33306 \begin_layout Plain Layout
33312 \begin_inset CommandInset ref
33314 reference "sub:Font-Styles"
33326 \begin_layout Subsection
33331 \begin_layout Plain Layout
33340 \begin_layout Standard
33341 Negative numbers often look ugly in formulas because the minus sign before
33342 the number is set with the same length as the minus operator sign.
33343 When writing the negative number in normal text, the minus sign appears
33347 \begin_layout Standard
33348 Thus, the problem disappears when converting the minus sign to mathematical
33352 \begin_layout Standard
33353 An example to visualize the problem:
33356 \begin_layout Standard
33358 \begin_inset Tabular
33359 <lyxtabular version="3" rows="3" columns="2">
33361 <column alignment="right" valignment="top" width="0">
33362 <column alignment="left" valignment="top" width="0">
33364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33367 \begin_layout Plain Layout
33373 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33376 \begin_layout Plain Layout
33384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33387 \begin_layout Plain Layout
33393 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33396 \begin_layout Plain Layout
33397 \begin_inset Formula $x=-2$
33407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33410 \begin_layout Plain Layout
33416 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33419 \begin_layout Plain Layout
33420 \begin_inset Formula $x=\textrm{-}2$
33436 \begin_layout Subsection
33437 Comma as decimal Separator
33441 \begin_layout Plain Layout
33450 \begin_layout Standard
33451 In LaTeX a comma inside a formula is used, according to the English convention,
33452 as number group separator.
33453 So there will be space added behind all commas in formulas.
33456 \begin_layout Standard
33457 To avoid this, the comma is highlighted and changed to mathematical text
33467 \begin_layout Standard
33468 To use all formula commas in the document as decimal separator, the file
33477 \begin_layout Plain Layout
33482 is part of the LaTeX-package
33490 \begin_layout Plain Layout
33495 \begin_layout Plain Layout
33518 \begin_layout Plain Layout
33524 is loaded with the LaTeX-preamble line
33527 \begin_layout Standard
33535 \begin_layout Subsection
33537 \begin_inset CommandInset label
33539 name "sub:Physical-Vectors"
33547 \begin_layout Plain Layout
33556 \begin_layout Standard
33557 Predefined vectors are offered by the LaTeX-package
33565 \begin_layout Plain Layout
33570 should be part of every LaTeX standard installation.
33579 \begin_layout Plain Layout
33585 that is loaded with the LaTeX-preamble line
33588 \begin_layout Standard
33596 \begin_layout Standard
33600 \begin_layout Plain Layout
33610 \begin_inset Note Note
33613 \begin_layout Plain Layout
33614 The following table will only be displayed when the LaTeX-package
33623 The following commands are defined:
33626 \begin_layout Standard
33628 \begin_inset Tabular
33629 <lyxtabular version="3" rows="4" columns="2">
33631 <column alignment="center" valignment="top" width="0">
33632 <column alignment="center" valignment="top" width="0">
33634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33637 \begin_layout Plain Layout
33643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33646 \begin_layout Plain Layout
33654 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33657 \begin_layout Plain Layout
33667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33670 \begin_layout Plain Layout
33671 \begin_inset Formula $\Bra{\psi}$
33681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33684 \begin_layout Plain Layout
33694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33697 \begin_layout Plain Layout
33698 \begin_inset Formula $\Ket{\psi}$
33708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33711 \begin_layout Plain Layout
33723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33726 \begin_layout Plain Layout
33727 \begin_inset Formula $\Braket{\psi|\phi}$
33743 \begin_layout Standard
33750 assures that all vertical bars are set in the size of the surrounding brackets:
33751 \begin_inset Formula \[
33752 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33760 \begin_layout Plain Layout
33770 \begin_inset Note Note
33773 \begin_layout Plain Layout
33774 The following will be displayed when the LaTeX-package
33786 \begin_layout Standard
33787 You need to install the LaTeX-package
33791 to see the rest of this subsection in the output.
33794 \begin_layout Standard
33798 \begin_layout Plain Layout
33810 \begin_layout Standard
33817 can also be achieved using the command
33823 , that is described in
33824 \begin_inset CommandInset ref
33826 reference "sub:Automatic-Bracket-Size"
33833 \begin_layout Subsection
33834 Self-defined Fractions
33835 \begin_inset CommandInset label
33837 name "sub:Self-defined-Fractions"
33845 \begin_layout Plain Layout
33846 Fractions ! self-defined
33854 \begin_layout Standard
33855 To define custom commands for fractions, the command
33865 \begin_layout Plain Layout
33873 is used in the following scheme:
33876 \begin_layout Standard
33889 bracket}{fraction bar thickness}{style}
33890 \begin_inset Newline newline
33897 \begin_layout Plain Layout
33912 \begin_layout Plain Layout
33919 {numerator}{denominator}
33922 \begin_layout Standard
33923 The style is a number in the range of 0
33924 \begin_inset space \thinspace{}
33928 \begin_inset space \thinspace{}
33934 \begin_layout Standard
33936 \begin_inset Tabular
33937 <lyxtabular version="3" rows="5" columns="2">
33939 <column alignment="center" valignment="top" width="0">
33940 <column alignment="center" valignment="top" width="0">
33942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33945 \begin_layout Plain Layout
33951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33954 \begin_layout Plain Layout
33962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33965 \begin_layout Plain Layout
33971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33974 \begin_layout Plain Layout
33975 display style formula
33982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33985 \begin_layout Plain Layout
33991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33994 \begin_layout Plain Layout
34002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34005 \begin_layout Plain Layout
34011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34014 \begin_layout Plain Layout
34022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34025 \begin_layout Plain Layout
34031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34034 \begin_layout Plain Layout
34048 \begin_layout Standard
34049 When no style is given, the size is adjusted to the surrounding environment
34050 like for the command
34059 \begin_layout Standard
34060 When no fraction bar thickness is given, the predefined value of 0.4
34061 \begin_inset space \thinspace{}
34067 \begin_layout Standard
34068 \begin_inset VSpace medskip
34071 For example, the commands
34084 \begin_inset CommandInset ref
34086 reference "sub:Fractions"
34090 are defined with the commands
34093 \begin_layout Standard
34102 genfrac{}{}{}{0}{#1}{#2}}
34105 \begin_layout Standard
34109 \begin_layout Standard
34118 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34121 \begin_layout Standard
34122 \begin_inset VSpace medskip
34125 To define a fraction where the fraction bar thickness can be given as optional
34126 argument, the following line is inserted to the LaTeX-preamble:
34129 \begin_layout Standard
34138 genfrac{}{}{#1}{}{#2}{#3}}
34141 \begin_layout Standard
34143 \begin_inset Formula \begin{align*}
34144 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34145 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34149 As one can see, the distance of the numerator and the denominator to the
34150 fraction bar is round about three times the bar thickness.
34153 \begin_layout Subsection
34158 \begin_layout Plain Layout
34167 \begin_layout Standard
34168 To cancel formulas or formula parts, the LaTeX-package
34176 \begin_layout Plain Layout
34181 is part of every LaTeX standard installation.
34190 \begin_layout Plain Layout
34196 has to be loaded with the LaTeX-preamble line
34199 \begin_layout Standard
34204 usepackage[samesize]{cancel}
34207 \begin_layout Standard
34208 There are four ways to cancel formulas:
34211 \begin_layout Standard
34213 \begin_inset Tabular
34214 <lyxtabular version="3" rows="5" columns="2">
34216 <column alignment="center" valignment="top" width="0">
34217 <column alignment="center" valignment="top" width="0">
34219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34222 \begin_layout Plain Layout
34228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34231 \begin_layout Plain Layout
34233 \begin_inset Note Note
34236 \begin_layout Plain Layout
34249 are used here as spacer.
34261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34264 \begin_layout Plain Layout
34273 \begin_layout Plain Layout
34287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34290 \begin_layout Plain Layout
34291 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34304 \begin_layout Plain Layout
34313 \begin_layout Plain Layout
34327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34330 \begin_layout Plain Layout
34331 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34344 \begin_layout Plain Layout
34353 \begin_layout Plain Layout
34367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34370 \begin_layout Plain Layout
34371 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34384 \begin_layout Plain Layout
34388 \begin_inset Formula $\to$
34399 \begin_layout Plain Layout
34413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34416 \begin_layout Plain Layout
34417 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34433 \begin_layout Standard
34440 is especially suitable to visualize the reduction of fractions within formulas:
34441 \begin_inset Formula \[
34442 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34449 \begin_layout Subsection
34450 Formulas in Section Headings
34451 \begin_inset CommandInset label
34453 name "sub:Formulas-in-Section"
34461 \begin_layout Plain Layout
34462 Formula ! in section headings
34470 \begin_layout Standard
34471 When formulas are used in section headings, the following has to be taken
34475 \begin_layout Standard
34476 \begin_inset Note Greyedout
34479 \begin_layout Plain Layout
34488 \begin_layout Plain Layout
34489 Packages ! hyperref
34494 support is enabled in the document settings dialog under
34497 \begin_inset space ~
34502 , PDF-bookmarks are created for every section heading in the table of contents.
34503 If a section heading contains formulas, they are incorrectly displayed
34504 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34513 \begin_layout Standard
34514 Both problems can be solved by inserting at the end of the section heading
34515 a short title with the menu
34517 Insert\SpecialChar \menuseparator
34519 \begin_inset space ~
34525 Short titles are used as alternative for multiline section headings to
34526 keep the table of contents clearly arranged.
34527 Only the short title appears in the table of contents and therefore also
34528 in the PDF-bookmark.
34531 \begin_layout Standard
34532 When formulas should be used in the table of contents but
34536 is used, one can use the following command in TeX-mode:
34539 \begin_layout Standard
34544 texorpdfstring{part}{alternative}
34548 \begin_layout Plain Layout
34559 \begin_layout Standard
34560 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34561 This can be characters, formulas, footnotes, but also cross-references.
34562 The alternative is used instead of the part for the bookmark.
34565 \begin_layout Standard
34566 Here are two example headings:
34567 \begin_inset VSpace -3mm
34574 \begin_layout Plain Layout
34586 \begin_layout Subsubsection
34587 Heading without formula in table of contents
34588 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34592 \begin_inset OptArg
34595 \begin_layout Plain Layout
34596 Heading without formula in table of contents
34604 \begin_layout Subsubsection
34605 Heading with formula in table of contents
34609 \begin_layout Plain Layout
34619 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34626 \begin_layout Plain Layout
34636 \begin_layout Standard
34640 \begin_layout Plain Layout
34649 In the first heading a short title was used, in the second one
34658 \begin_layout Standard
34659 To get the same formatting as for the other headings, the complete heading
34668 \begin_layout Plain Layout
34670 \begin_inset CommandInset ref
34672 reference "sub:Bold-Formulas"
34684 \begin_layout Subsection
34685 Formulas in multi-column Text
34689 \begin_layout Plain Layout
34690 Formula ! in multi-column text
34698 \begin_layout Standard
34699 Formulas in multi-column text are often too wide to fit into a column and
34700 thus need to be set over the whole page width.
34701 This is done by using the LaTeX-package
34709 \begin_layout Plain Layout
34714 is part of every LaTeX standard installation.
34723 \begin_layout Plain Layout
34724 Packages ! multicol
34729 , that is loaded with the LaTeX-preamble line
34732 \begin_layout Standard
34737 usepackage{multicol}
34740 \begin_layout Standard
34741 \begin_inset Note Greyedout
34744 \begin_layout Plain Layout
34745 Note herby that the setting
34748 \begin_inset space ~
34755 Document\SpecialChar \menuseparator
34761 \begin_inset space ~
34781 \begin_layout Standard
34782 Before the multi-column text the command
34785 \begin_layout Standard
34790 begin{multicols}{column number}
34793 \begin_layout Standard
34794 is written in TeX-mode.
34795 The column number is a number in the range of 2
34796 \begin_inset space \thinspace{}
34800 \begin_inset space \thinspace{}
34804 Before the formula the multi-column text is ended by inserting the command
34807 \begin_layout Standard
34815 \begin_layout Standard
34819 \begin_layout Standard
34820 Due to the command some space is automatically added before the formula.
34822 \begin_inset space \thinspace{}
34825 mm vertical space is inserted before the formula.
34826 When the formula style
34832 \begin_layout Plain Layout
34834 \begin_inset CommandInset ref
34836 reference "sec:Formula-Styles"
34848 \begin_inset space \thinspace{}
34851 mm space is inserted instead.
34854 \begin_layout Standard
34855 As example a multi-column text with a displayed formula:
34858 \begin_layout Standard
34862 \begin_layout Plain Layout
34866 begin{multicols}{2}
34871 Das Spektrum wird fouriertransformiert.
34872 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34873 , Lösungsmittel) zu trennen.
34874 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34875 nun das Aussehen des Ausgangssignals.
34876 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34877 über alle Phasen integrieren muss.
34879 \begin_inset Formula $S$
34882 unser normiertes Ausgangssignal and
34883 \begin_inset Formula $P$
34886 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34890 \begin_layout Plain Layout
34900 \begin_inset VSpace -6mm
34904 \begin_inset Formula \begin{equation}
34905 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34913 \begin_layout Plain Layout
34917 begin{multicols}{2}
34923 \begin_inset Formula $S_{0}$
34926 das Signal ohne Gradient ist and the Normierungsbedingung
34927 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34931 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34933 \begin_inset Formula $\nicefrac{\pi}{2}$
34937 \begin_inset space \thinspace{}
34940 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34941 das Signal zusätzlich abschwächt.
34942 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34944 \begin_inset Formula $T_{2}$
34950 \begin_layout Standard
34954 \begin_layout Plain Layout
34966 \begin_layout Subsection
34967 Formulas with Description of Variables
34971 \begin_layout Plain Layout
34972 Formula ! with description of variables
34980 \begin_layout Standard
34981 To describe variables within a formula, like in formula
34982 \begin_inset CommandInset ref
34984 reference "eq:within"
34993 \begin_inset Formula $n$
34997 \begin_inset space ~
35000 matrix is used with left aligned columns for the
35001 \begin_inset Formula $n$
35008 \begin_layout Plain Layout
35010 \begin_inset CommandInset ref
35012 reference "sec:Matrices"
35021 To set the description in a smaller size, before the matrix e.
35022 \begin_inset space \thinspace{}
35026 \begin_inset space \space{}
35039 \begin_layout Plain Layout
35041 \begin_inset CommandInset ref
35043 reference "sub:Font-Sizes"
35055 \begin_layout Standard
35056 When the formula style
35062 \begin_layout Plain Layout
35064 \begin_inset CommandInset ref
35066 reference "sec:Formula-Styles"
35087 \begin_layout Plain Layout
35094 only works in formulas with the style
35099 \begin_inset CommandInset ref
35101 reference "sub:Variable-Space"
35110 is inserted before and after the matrix to have the same separation of
35111 the matrix from the equation and the side margin.
35114 \begin_layout Standard
35115 When the formula style
35119 is used, the method described in
35120 \begin_inset CommandInset ref
35122 reference "sub:Flalign-Environment"
35126 is used to indent formulas.
35128 \begin_inset CommandInset ref
35130 reference "eq:within"
35134 consists of five columns whereas in the first two columns contain the equation,
35135 the third the matrix, and the last one an empty TeX-brace.
35136 \begin_inset Formula \begin{flalign}
35137 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35138 \rho & \textrm{density}\\
35139 V & \textrm{volume}\\
35140 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35147 \begin_layout Subsection
35148 Upright small Greek Letters
35149 \begin_inset CommandInset label
35151 name "sub:Upright-small-Greek"
35159 \begin_layout Plain Layout
35160 Greek letters ! upright
35168 \begin_layout Standard
35169 Most of the math fonts only provide italic small Greek letters.
35170 But for symbols of elementary particles like pions and neutrinos, upright
35171 Greek letters are needed.
35180 \begin_layout Plain Layout
35185 is part of the LaTeX-package
35193 \begin_layout Plain Layout
35198 \begin_layout Plain Layout
35221 \begin_layout Plain Layout
35227 that is loaded with the LaTeX-preamble line
35230 \begin_layout Standard
35235 usepackage{upgreek}
35238 \begin_layout Standard
35244 \begin_layout Plain Layout
35254 \begin_inset Note Note
35257 \begin_layout Plain Layout
35258 The following table will only be displayed when the LaTeX-package
35267 They are created when the command for a small Greek letters is started
35273 For example the command
35280 \begin_inset Formula $\uptau$
35286 \begin_layout Standard
35287 With these commands reactions of elementary particles can be typeset:
35288 \begin_inset Formula \[
35289 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35296 \begin_layout Standard
35297 The upright letters are more bold and wider than the italic ones.
35298 They should therefore not be used for units like
35299 \begin_inset Quotes eld
35303 \begin_inset Quotes erd
35309 \begin_layout Standard
35313 \begin_layout Plain Layout
35323 \begin_inset Note Note
35326 \begin_layout Plain Layout
35327 The following will be displayed when the LaTeX-package
35339 \begin_layout Standard
35340 You need to install the LaTeX-package
35344 to see the rest of this subsection in the output.
35347 \begin_layout Standard
35351 \begin_layout Plain Layout
35363 \begin_layout Subsection
35364 Text Characters in Formulas
35365 \begin_inset CommandInset label
35367 name "sub:Text-Characters-in"
35375 \begin_layout Plain Layout
35384 \begin_layout Standard
35385 In some cases you might want to insert text characters directly into formulas.
35386 When for example the centered dot · is often used in formulas like
35387 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35390 , one would have to insert the command
35400 \begin_layout Plain Layout
35402 \begin_inset CommandInset ref
35404 reference "sub:Binary-Operators"
35413 all the time, because this character is defined in all encodings as text
35415 But the encoding can be changed by this LaTeX-preamble line:
35418 \begin_layout Standard
35423 Declare Inputtext{183}{
35433 f\SpecialChar \textcompwordmark{}
35437 \begin_layout Standard
35438 The character encoding (menu
35440 Document\SpecialChar \menuseparator
35441 Settings\SpecialChar \menuseparator
35444 ) specifies what character appears when a keyboard key is pressed.
35445 When the key for the character '·' is pressed, internally the command
35452 But this command is not available in a formula so that you would get LaTeX-erro
35454 With the changed encoding the right command is chosen automatically, depending
35455 on if the character was inserted into a formula or not.
35458 \begin_layout Standard
35459 The encoding of several characters is saved in definition files.
35460 Fore example the encoding
35464 is defined in the file
35468 that is in the installation folder of LaTeX.
35469 Encodings should only be changed via the LaTeX-preamble and not in the
35471 Otherwise own documents could not be edited by other LyX users working
35472 on other computers.
35475 \begin_layout Standard
35476 \begin_inset VSpace medskip
35479 Besides the centered dot, in this document the degree sign ° is defined
35480 with the following LaTeX-preamble line so that it can directly be inserted
35484 \begin_layout Standard
35489 DeclareInputtext{176}{
35499 f\SpecialChar \textcompwordmark{}
35503 \begin_layout Standard
35504 \begin_inset Newpage newpage
35510 \begin_layout Section
35516 \begin_layout Plain Layout
35525 \begin_layout Standard
35526 This section is a summary of the most important typographic rules, listed
35531 \begin_layout Plain Layout
35532 This collection was partly taken from the German semi-official dictionary
35534 \begin_inset Quotes eld
35538 \begin_inset Quotes erd
35542 \begin_inset CommandInset citation
35548 that lists some of the ISO rules.
35556 \begin_layout Itemize
35565 \begin_layout Plain Layout
35566 done with font styles, see
35567 \begin_inset CommandInset ref
35569 reference "sub:Font-Styles"
35579 \begin_inset space \thinspace{}
35583 \begin_inset Newline newline
35586 Between the value and the unit is the smallest space, see
35587 \begin_inset CommandInset ref
35589 reference "sub:Predefined-Space"
35594 \begin_inset Newline newline
35597 This convention is automatically fulfilled when the command
35604 When it is entered to a formula, two boxes appear.
35605 In the first one the value is inserted, in the second one the unit, and
35607 \begin_inset Formula $\unit[30]{km/h}$
35611 \begin_inset space \thinspace{}
35621 is not a real LaTeX command but the command
35627 , therefore you cannot use it in TeX code.
35630 \begin_layout Itemize
35631 Percent and perthousand signs are set like physical units:
35632 \begin_inset Newline newline
35636 \begin_inset space \thinspace{}
35642 \begin_layout Itemize
35643 The degree sign follows directly on the value: 15°, but not when it is used
35645 \begin_inset space \thinspace{}
35651 \begin_layout Itemize
35652 In numbers with more than four digits the smallest space is inserted before
35653 every third digit to group them:
35663 \begin_inset space \thinspace{}
35667 \begin_inset space \thinspace{}
35673 \begin_layout Itemize
35674 For dimensions like 120×90×40
35675 \begin_inset space \thinspace{}
35678 cm the multiplication sign
35679 \begin_inset Quotes eld
35683 \begin_inset Quotes erd
35687 It is available via the menu
35689 Insert\SpecialChar \menuseparator
35690 Special Character\SpecialChar \menuseparator
35694 With some keyboard definitions it can also be inserted directly.
35697 \begin_layout Itemize
35698 Functions with names consisting of several letters are set upright to avoid
35700 \begin_inset CommandInset ref
35702 reference "sub:Predefined-Functions"
35709 \begin_layout Itemize
35710 Indices consisting of several letters, are set upright:
35711 \begin_inset Formula $E_{\mathrm{kin}}$
35715 \begin_inset Newline newline
35718 Components of matrices are set italic:
35719 \begin_inset Formula $\hat{H}_{kl}$
35725 \begin_layout Itemize
35726 The differentiation/integration operator 'd', the Euler's number 'e', and
35727 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35731 \begin_layout Standard
35732 \begin_inset Newpage newpage
35738 \begin_layout Section
35743 \begin_layout Plain Layout
35752 \begin_layout Standard
35753 Some characters and symbols can be created with several commands.
35754 Here is a list of the synonym commands:
35757 \begin_layout Standard
35758 \begin_inset VSpace bigskip
35762 \begin_inset space \hfill{}
35766 \begin_inset Tabular
35767 <lyxtabular version="3" rows="12" columns="2">
35769 <column alignment="center" valignment="top" width="0pt">
35770 <column alignment="center" valignment="top" width="0pt">
35772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35775 \begin_layout Plain Layout
35781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35784 \begin_layout Plain Layout
35786 \begin_inset Note Note
35789 \begin_layout Plain Layout
35796 is only used as spacer.
35808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35811 \begin_layout Plain Layout
35819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35822 \begin_layout Plain Layout
35826 \begin_layout Plain Layout
35839 \begin_layout Plain Layout
35853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35856 \begin_layout Plain Layout
35864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35867 \begin_layout Plain Layout
35877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35880 \begin_layout Plain Layout
35888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35891 \begin_layout Plain Layout
35901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35904 \begin_layout Plain Layout
35912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35915 \begin_layout Plain Layout
35923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35926 \begin_layout Plain Layout
35934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35937 \begin_layout Plain Layout
35945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35948 \begin_layout Plain Layout
35956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35959 \begin_layout Plain Layout
35969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35972 \begin_layout Plain Layout
35980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35983 \begin_layout Plain Layout
35993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35996 \begin_layout Plain Layout
36004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36007 \begin_layout Plain Layout
36017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36020 \begin_layout Plain Layout
36028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36031 \begin_layout Plain Layout
36041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36044 \begin_layout Plain Layout
36052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36055 \begin_layout Plain Layout
36063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36066 \begin_layout Plain Layout
36074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36077 \begin_layout Plain Layout
36089 \begin_inset space \hfill{}
36093 \begin_inset Tabular
36094 <lyxtabular version="3" rows="12" columns="2">
36096 <column alignment="center" valignment="top" width="0pt">
36097 <column alignment="center" valignment="top" width="0pt">
36099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36102 \begin_layout Plain Layout
36108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36111 \begin_layout Plain Layout
36119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36122 \begin_layout Plain Layout
36130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36133 \begin_layout Plain Layout
36145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36148 \begin_layout Plain Layout
36156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36159 \begin_layout Plain Layout
36169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36172 \begin_layout Plain Layout
36180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36183 \begin_layout Plain Layout
36193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36196 \begin_layout Plain Layout
36204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36207 \begin_layout Plain Layout
36215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36218 \begin_layout Plain Layout
36226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36229 \begin_layout Plain Layout
36237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36240 \begin_layout Plain Layout
36248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36251 \begin_layout Plain Layout
36261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36264 \begin_layout Plain Layout
36272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36275 \begin_layout Plain Layout
36285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36288 \begin_layout Plain Layout
36296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36299 \begin_layout Plain Layout
36309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36312 \begin_layout Plain Layout
36320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36323 \begin_layout Plain Layout
36333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36336 \begin_layout Plain Layout
36344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36347 \begin_layout Plain Layout
36357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36360 \begin_layout Plain Layout
36368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36371 \begin_layout Plain Layout
36385 \begin_inset space \hfill{}
36391 \begin_layout Standard
36392 \begin_inset Newpage newpage
36398 \begin_layout Bibliography
36399 \begin_inset CommandInset bibitem
36400 LatexCommand bibitem
36412 The LaTeX Companion
36415 Addison Wesley, 2004
36418 \begin_layout Bibliography
36419 \begin_inset CommandInset bibitem
36420 LatexCommand bibitem
36426 \begin_inset CommandInset href
36429 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36433 of LaTeX's math abilities
36436 \begin_layout Bibliography
36437 \begin_inset CommandInset bibitem
36438 LatexCommand bibitem
36443 LaTeX tips and tricks-
36444 \begin_inset CommandInset href
36447 target "http://tug.org/TeXnik/"
36454 \begin_layout Bibliography
36455 \begin_inset CommandInset bibitem
36456 LatexCommand bibitem
36462 \begin_inset CommandInset href
36465 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36473 \begin_layout Plain Layout
36485 \begin_layout Bibliography
36486 \begin_inset CommandInset bibitem
36487 LatexCommand bibitem
36493 \begin_inset CommandInset href
36496 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36500 of all symbols available with LaTeX-packages
36503 \begin_layout Bibliography
36504 \begin_inset CommandInset bibitem
36505 LatexCommand bibitem
36511 \begin_inset CommandInset href
36513 name "Documentation"
36514 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36518 of the LaTeX-package
36526 \begin_layout Plain Layout
36527 Packages ! hyperref
36535 \begin_layout Bibliography
36536 \begin_inset CommandInset bibitem
36537 LatexCommand bibitem
36543 \begin_inset CommandInset href
36546 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36557 \begin_inset CommandInset ref
36559 reference "sub:Operator-Limits"
36567 \begin_layout Plain Layout
36578 \begin_layout Bibliography
36579 \begin_inset CommandInset bibitem
36580 LatexCommand bibitem
36591 Auflage, Duden 2001
36594 \begin_layout Subsubsection*
36595 \begin_inset CommandInset index_print
36596 LatexCommand printindex