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
10948 \begin_layout Plain Layout
10960 \begin_inset Quotes erd
10963 appears and by pressing
10967 several times one can select one of eight different space sizes.
10968 The spaces can also be inserted using the math toolbar button
10969 \begin_inset Graphics
10970 filename ../images/math/space.png
10975 or special commands.
10976 Independent from the inserted command, one can select the size again by
10984 \begin_layout Standard
10987 \begin_inset VSpace -5mm
10991 \begin_inset Tabular
10992 <lyxtabular version="3" rows="3" columns="7">
10994 <column alignment="center" valignment="middle" width="6.8cm">
10995 <column alignment="center" valignment="top" width="0">
10996 <column alignment="center" valignment="top" width="0">
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">
11002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11005 \begin_layout Plain Layout
11011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11014 \begin_layout Plain Layout
11022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11025 \begin_layout Plain Layout
11033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11036 \begin_layout Plain Layout
11044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11047 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11058 \begin_layout Plain Layout
11066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11069 \begin_layout Plain Layout
11079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11082 \begin_layout Plain Layout
11087 keystrokes after inserting the protected space
11092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11095 \begin_layout Plain Layout
11101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11104 \begin_layout Plain Layout
11110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11113 \begin_layout Plain Layout
11119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11122 \begin_layout Plain Layout
11128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11140 \begin_layout Plain Layout
11148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11151 \begin_layout Plain Layout
11157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11161 \begin_inset Formula $A\, B$
11169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11172 \begin_layout Plain Layout
11173 \begin_inset Formula $A\: B$
11181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11184 \begin_layout Plain Layout
11185 \begin_inset Formula $A\; B$
11193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11196 \begin_layout Plain Layout
11197 \begin_inset Formula $A\quad B$
11205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11208 \begin_layout Plain Layout
11209 \begin_inset Formula $A\qquad B$
11217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11220 \begin_layout Plain Layout
11221 \begin_inset Formula $A\! B$
11237 \begin_layout Standard
11238 The last size seem to produce no space.
11239 It is displayed red in LyX contrary to the other sizes, because it is a
11241 There are two more negative spaces:
11244 \begin_layout Standard
11246 \begin_inset Tabular
11247 <lyxtabular version="3" rows="3" columns="3">
11249 <column alignment="center" valignment="middle" width="6.8cm">
11250 <column alignment="center" valignment="top" width="0pt">
11251 <column alignment="center" valignment="top" width="0pt">
11253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11256 \begin_layout Plain Layout
11262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11265 \begin_layout Plain Layout
11273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11276 \begin_layout Plain Layout
11286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11294 keystrokes after inserting the protected space
11299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11302 \begin_layout Plain Layout
11308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11311 \begin_layout Plain Layout
11319 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11322 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11332 \begin_inset Formula $A\negmedspace B$
11340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11343 \begin_layout Plain Layout
11344 \begin_inset Formula $A\negthickspace B$
11360 \begin_layout Standard
11361 Negative spaces can lead to characters overlapping each other.
11362 Thus they can be used to enforce ligatures, what is e.
11363 \begin_inset space \thinspace{}
11367 \begin_inset space \space{}
11370 useful for summation operators:
11373 \begin_layout Standard
11375 \begin_inset Tabular
11376 <lyxtabular version="3" rows="3" columns="2">
11378 <column alignment="center" valignment="top" width="0">
11379 <column alignment="center" valignment="top" width="0">
11381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11393 \begin_layout Plain Layout
11395 \begin_inset Note Note
11398 \begin_layout Plain Layout
11405 is only used as spacer.
11417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11420 \begin_layout Plain Layout
11429 \begin_layout Plain Layout
11443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11446 \begin_layout Plain Layout
11447 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11460 \begin_layout Plain Layout
11471 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11488 \begin_layout Plain Layout
11489 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11505 \begin_layout Standard
11506 Relations like for example equal signs, are always surrounded by space.
11507 To suppress this, the equal sign is placed into a TeX-brace.
11508 The following example demonstrates this:
11511 \begin_layout Standard
11513 \begin_inset Tabular
11514 <lyxtabular version="3" rows="2" columns="2">
11516 <column alignment="center" valignment="top" width="0pt">
11517 <column alignment="center" valignment="top" width="0pt">
11519 <cell alignment="center" valignment="top" usebox="none">
11522 \begin_layout Plain Layout
11528 <cell alignment="center" valignment="top" usebox="none">
11531 \begin_layout Plain Layout
11532 \begin_inset Formula $A=B$
11542 <cell alignment="center" valignment="top" usebox="none">
11545 \begin_layout Plain Layout
11546 \begin_inset Note Note
11549 \begin_layout Plain Layout
11556 is only used as spacer.
11562 \begin_inset Formula $\raisebox{5mm}{}$
11565 equation without space
11570 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11573 \begin_layout Plain Layout
11574 \begin_inset Formula $A{=}B$
11590 \begin_layout Standard
11592 The command for the last formula is:
11597 \begin_inset Formula $\to$
11603 \begin_layout Standard
11604 \begin_inset VSpace bigskip
11607 Spaces are needed for physical units, because the space between the value
11608 and the unit is the smallest one and not a normal space.
11609 For units in text, the smallest space is inserted via the menu
11611 Insert\SpecialChar \menuseparator
11612 Formatting\SpecialChar \menuseparator
11614 \begin_inset space ~
11622 arg "space-insert thin"
11628 \begin_layout Standard
11629 An example to visualize the difference:
11632 \begin_layout Standard
11633 \begin_inset Tabular
11634 <lyxtabular version="3" rows="2" columns="2">
11636 <column alignment="left" valignment="top" width="0">
11637 <column alignment="left" valignment="top" width="0">
11639 <cell alignment="center" valignment="top" usebox="none">
11642 \begin_layout Plain Layout
11644 \begin_inset Formula $\cdot$
11652 <cell alignment="center" valignment="top" usebox="none">
11655 \begin_layout Plain Layout
11656 space between value and unit
11663 <cell alignment="center" valignment="top" usebox="none">
11666 \begin_layout Plain Layout
11668 \begin_inset space \thinspace{}
11672 \begin_inset Formula $\cdot$
11680 <cell alignment="center" valignment="top" usebox="none">
11683 \begin_layout Plain Layout
11684 smallest space between value and unit
11697 \begin_layout Subsection
11702 \begin_layout Plain Layout
11715 \begin_layout Plain Layout
11716 for vertical space in formulas see
11717 \begin_inset CommandInset ref
11719 reference "sub:Line-Separation"
11732 \begin_layout Plain Layout
11740 \begin_inset Note Note
11743 \begin_layout Plain Layout
11746 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11749 \begin_layout Plain Layout
11752 texorpdfstring is in section
11753 \begin_inset CommandInset ref
11755 reference "sub:Formulas-in-Section"
11765 \begin_inset CommandInset label
11767 name "sub:Variable-Space"
11775 \begin_layout Plain Layout
11776 Space ! horizontal ! variable
11784 \begin_layout Standard
11785 Space with a defined length can be inserted with the command
11795 \begin_layout Plain Layout
11805 \begin_inset Quotes eld
11814 \begin_layout Plain Layout
11826 \begin_inset Quotes erd
11830 The length can be specified by left-clicking on the
11831 \begin_inset Quotes eld
11840 \begin_layout Plain Layout
11852 \begin_inset Quotes erd
11856 The length may also be negative.
11857 To insert so many space that the formula uses all available space, the
11868 \begin_layout Plain Layout
11879 \begin_layout Standard
11880 \begin_inset VSpace -1mm
11886 \begin_layout Standard
11888 \begin_inset Tabular
11889 <lyxtabular version="3" rows="4" columns="2">
11891 <column alignment="center" valignment="top" width="0">
11892 <column alignment="center" valignment="top" width="0">
11894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11897 \begin_layout Plain Layout
11905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11908 \begin_layout Plain Layout
11916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11919 \begin_layout Plain Layout
11926 \begin_layout Plain Layout
11936 \begin_inset Formula $\to$
11942 \begin_inset space \thinspace{}
11950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11953 \begin_layout Plain Layout
11954 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11967 \begin_layout Plain Layout
11974 \begin_layout Plain Layout
11984 \begin_inset Formula $\to$
11990 \begin_inset space \thinspace{}
11998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12001 \begin_layout Plain Layout
12002 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12015 \begin_layout Plain Layout
12022 \begin_layout Plain Layout
12036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12039 \begin_layout Plain Layout
12040 \begin_inset Formula $A=A\hfill B=B$
12056 \begin_layout Standard
12057 In the last example the available space is given by the longest column entry
12059 In an inline formula the space depends on the length of the line in which
12067 Thus, when the line uses the full width, no space will be created.
12074 only has an effect on displayed formulas when the formula style
12079 (Formula styles are explained in
12080 \begin_inset CommandInset ref
12082 reference "sec:Formula-Styles"
12089 \begin_layout Standard
12096 , there are the commands
12108 that fill the space with a pattern, see
12109 \begin_inset CommandInset ref
12111 reference "sub:Ellipses"
12118 \begin_layout Standard
12119 For text, variable space can be inserted via the menu
12121 Insert\SpecialChar \menuseparator
12122 Formatting\SpecialChar \menuseparator
12124 \begin_inset space ~
12132 \begin_layout Standard
12133 This is a line with
12134 \begin_inset space \hspace{}
12139 \begin_inset space \thinspace{}
12145 \begin_layout Standard
12146 This is a line with
12147 \begin_inset space \hfill{}
12153 \begin_layout Subsection
12154 Space besides inline Formulas
12158 \begin_layout Plain Layout
12159 Space ! besides inline formulas
12167 \begin_layout Standard
12168 The space that surrounds inline formulas can be adjusted with the length
12177 \begin_layout Plain Layout
12188 The value of a length is set with the command
12196 \begin_layout Plain Layout
12206 that has the following scheme:
12209 \begin_layout Standard
12214 setlength{length name}{value}
12217 \begin_layout Standard
12225 \begin_inset space \thinspace{}
12231 \begin_layout Standard
12241 \begin_layout Standard
12242 is inserted in TeX-mode.
12244 \begin_inset space \thinspace{}
12247 mm space will now be set around all inline formulas:
12251 \begin_layout Plain Layout
12265 \begin_layout Standard
12266 This is a line with an inline formula
12267 \begin_inset Formula $A=B$
12271 \begin_inset space \thinspace{}
12274 mm surrounding space.
12278 \begin_layout Plain Layout
12292 \begin_layout Standard
12293 To return to the predefined value,
12299 is set to the value 0
12300 \begin_inset space \thinspace{}
12306 \begin_layout Section
12311 \begin_layout Plain Layout
12321 \begin_layout Plain Layout
12326 \begin_layout Plain Layout
12337 \begin_layout Plain Layout
12352 \begin_layout Standard
12353 Boxes for text are described in chapter
12360 \begin_inset space ~
12368 \begin_layout Subsection
12370 \begin_inset CommandInset label
12372 name "sub:Boxes-with-Frame"
12380 \begin_layout Plain Layout
12389 \begin_layout Standard
12390 It is possible to frame formulas or parts of it with the commands
12400 \begin_layout Plain Layout
12418 \begin_layout Plain Layout
12429 \begin_layout Standard
12430 When one of these commands is inserted to a formula, a blue box appears
12431 within a frame to enter formula parts.
12438 an additional formula has to be created by
12446 \begin_layout Plain Layout
12447 Due to a bug in LyX it is not possible to create a new formula with
12452 \begin_inset CommandInset href
12454 name "LyX-bug #1435"
12455 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12464 , because the box content will otherwise be treated as mathematical text.
12471 is used, a new formula is automatically created inside the frame.
12474 \begin_layout Standard
12481 is not suitable to frame displayed formulas, because the formula will always
12482 be set in the size of the text.
12489 is in contrary not suitable to frame inline formulas, because the formula
12490 will always be set in the size of a displayed formula.
12493 \begin_layout Standard
12500 there is the command
12510 \begin_layout Plain Layout
12518 where additionally the frame width and the alignment can be specified.
12525 is used in the following scheme:
12528 \begin_layout Standard
12533 framebox[frame width][position]{box content}
12536 \begin_layout Standard
12537 The position can either be
12554 right aligns the formula in the box.
12555 When no position is given, the formula will be centered.
12556 \begin_inset Newline newline
12559 Is no width given, also no position can be given.
12560 In this case the frame width is adjusted to the box content like for
12569 \begin_layout Standard
12576 is inserted, a box appears containing three blue boxes.
12577 The first two boxes are surrounded by brackets and denote the two optional
12579 The third box is for formula parts like for
12588 \begin_layout Standard
12590 \begin_inset Note Note
12593 \begin_layout Plain Layout
12594 The table has been set into a minipage to make the footnote appearing.
12595 Otherwise the footnote text would not be displayed.
12601 \begin_inset Box Frameless
12610 height_special "totalheight"
12613 \begin_layout Plain Layout
12615 \begin_inset Tabular
12616 <lyxtabular version="3" rows="5" columns="2">
12618 <column alignment="center" valignment="top" width="0">
12619 <column alignment="center" valignment="top" width="0">
12621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12624 \begin_layout Plain Layout
12629 \begin_layout Plain Layout
12630 Due to a bug in LyX it is not possible to create a new formula with
12635 \begin_inset CommandInset href
12637 name "LyX-bug #1435"
12638 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12655 \begin_layout Plain Layout
12657 \begin_inset Note Note
12660 \begin_layout Plain Layout
12667 is only used as spacer.
12679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12682 \begin_layout Plain Layout
12689 \begin_layout Plain Layout
12708 \begin_layout Plain Layout
12722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12725 \begin_layout Plain Layout
12726 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12739 \begin_layout Plain Layout
12746 \begin_layout Plain Layout
12761 \begin_layout Plain Layout
12775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12778 \begin_layout Plain Layout
12779 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12792 \begin_layout Plain Layout
12799 \begin_layout Plain Layout
12813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12816 \begin_layout Plain Layout
12817 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12830 \begin_layout Plain Layout
12837 \begin_layout Plain Layout
12847 \begin_inset Formula $\to$
12851 \begin_inset Formula $\to$
12864 \begin_layout Plain Layout
12874 \begin_inset Formula $\downarrow$
12882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12885 \begin_layout Plain Layout
12886 \begin_inset Formula $\raisebox{6mm}{}$
12890 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12894 \begin_inset Formula $\raisebox{-4mm}{}$
12915 \begin_layout Standard
12916 The frame thickness can also be adjusted.
12917 To do this the following commands have to be inserted in TeX-mode before
12921 \begin_layout Standard
12931 \begin_inset Quotes eld
12935 \begin_inset Quotes erd
12949 \begin_inset Quotes eld
12953 \begin_inset Quotes erd
12959 \begin_layout Standard
12960 \begin_inset Quotes eld
12964 \begin_inset Quotes erd
12967 specifies the minimal distance between the frame and the first character
12969 An example for this is the following framed formula:
12973 \begin_layout Plain Layout
12985 \begin_inset Formula \[
12990 Before this formula the commands
12993 \begin_layout Standard
13015 \begin_layout Standard
13016 were inserted in TeX-mode.
13017 The given values are used for all following boxes.
13020 \begin_layout Standard
13021 To return to the standard frame size, the command
13024 \begin_layout Standard
13049 \begin_layout Plain Layout
13063 \begin_layout Standard
13064 is inserted in TeX-mode before the next formula.
13067 \begin_layout Subsection
13068 Boxes without Frame
13069 \begin_inset CommandInset label
13071 name "sub:Boxes-without-Frame"
13079 \begin_layout Plain Layout
13080 Boxes ! without frame
13088 \begin_layout Standard
13089 For boxes without a frame there are the following box commands:
13099 \begin_layout Plain Layout
13117 \begin_layout Plain Layout
13135 \begin_layout Plain Layout
13146 \begin_layout Standard
13153 a box can be super- or subscripted.
13154 But in contrary to normal super- and subscripting, the characters in the
13155 box keep their font size.
13162 is used in the following scheme:
13165 \begin_layout Standard
13170 raisebox{height}{box content}
13173 \begin_layout Standard
13174 When the box should contain a formula, an extra formula is needed like for
13184 \begin_layout Standard
13186 \begin_inset Tabular
13187 <lyxtabular version="3" rows="4" columns="2">
13189 <column alignment="center" valignment="top" width="0">
13190 <column alignment="center" valignment="top" width="0">
13192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13195 \begin_layout Plain Layout
13201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13204 \begin_layout Plain Layout
13212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13215 \begin_layout Plain Layout
13219 \begin_inset Formula $\to$
13225 \begin_inset Formula $\to$
13233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13236 \begin_layout Plain Layout
13237 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13250 \begin_layout Plain Layout
13254 \begin_inset Formula $\to$
13260 \begin_inset Formula $\to$
13268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13271 \begin_layout Plain Layout
13272 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13285 \begin_layout Plain Layout
13289 \begin_inset Formula $\to$
13304 \begin_layout Plain Layout
13318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13321 \begin_layout Plain Layout
13325 \begin_layout Plain Layout
13349 \begin_layout Standard
13350 The last formula can currently only be created using TeX-mode because LyX
13351 inserts a box instead of the needed extra formula.
13355 \begin_layout Plain Layout
13357 \begin_inset CommandInset href
13359 name "LyX-bug #1435"
13360 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13372 \begin_layout Standard
13397 , with the difference that there is no frame.
13400 \begin_layout Subsection
13402 \begin_inset CommandInset label
13404 name "sub:Colored-Boxes"
13412 \begin_layout Plain Layout
13421 \begin_layout Standard
13422 To be able to use all commands explained in this section, the LaTeX-package
13431 \begin_layout Plain Layout
13436 is part of every LaTeX standard installation.
13445 \begin_layout Plain Layout
13451 has to be loaded in the LaTeX-preamble with the line
13455 \begin_layout Plain Layout
13456 When text is colored somewhere in the document with a predefined color,
13457 LyX loads the LaTeX-package
13462 Thus it is possible that the package is loaded twice, but this doesn't
13469 \begin_inset Note Note
13472 \begin_layout Plain Layout
13473 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13482 \begin_layout Standard
13490 \begin_layout Standard
13491 \begin_inset VSpace medskip
13494 To color boxes, the command
13504 \begin_layout Plain Layout
13512 is used in the following scheme:
13515 \begin_layout Standard
13520 colorbox{color}{box content}
13523 \begin_layout Standard
13524 The box content can also be a box and a
13530 can also be part of another box (see the 2nd and 3rd example).
13531 When the box should contain a formula, an extra formula has to be created,
13542 \begin_layout Plain Layout
13543 This also applies for the command
13551 \begin_inset CommandInset href
13553 name "LyX-bug #1435"
13554 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13566 \begin_layout Standard
13567 One of the following predefined colors can be chosen:
13570 \begin_layout Standard
13604 \begin_layout Standard
13606 \begin_inset Tabular
13607 <lyxtabular version="3" rows="4" columns="2">
13609 <column alignment="center" valignment="top" width="0">
13610 <column alignment="center" valignment="top" width="0">
13612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13615 \begin_layout Plain Layout
13621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13624 \begin_layout Plain Layout
13626 \begin_inset Note Note
13629 \begin_layout Plain Layout
13636 is only used as spacer.
13648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13651 \begin_layout Plain Layout
13655 \begin_inset Formula $\to$
13665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13668 \begin_layout Plain Layout
13669 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13682 \begin_layout Plain Layout
13686 \begin_inset Formula $\to$
13697 \begin_layout Plain Layout
13711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13714 \begin_layout Plain Layout
13715 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13728 \begin_layout Plain Layout
13735 \begin_layout Plain Layout
13747 \begin_inset Formula $\to$
13757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13760 \begin_layout Plain Layout
13761 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13777 \begin_layout Standard
13784 only colors the box but not the characters in the box.
13785 To color all characters, the whole formula is highlighted and the wanted
13786 color is chosen in the
13789 \begin_inset space ~
13795 The dialog can be called with the toolbar button
13796 \begin_inset Graphics
13797 filename ../images/dialog-show_character.png
13804 Edit\SpecialChar \menuseparator
13806 \begin_inset space ~
13809 Style\SpecialChar \menuseparator
13813 The formula number has then the same color as the formula.
13814 When the formula number should get another color than the formula characters,
13815 the color must be changed within the formula.
13818 \begin_layout Standard
13822 \begin_layout Standard
13825 \begin_inset Formula \begin{equation}
13826 \int A=B\label{eq:red}\end{equation}
13833 \begin_inset Formula \begin{equation}
13834 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13841 \begin_layout Standard
13843 \begin_inset CommandInset ref
13849 is completely colored red.
13850 \begin_inset Newline newline
13854 \begin_inset CommandInset ref
13856 reference "eq:redgreen"
13860 was first completely colored green to set the color for the formula number.
13861 Subsequently the formula characters were colored red.
13864 \begin_layout Standard
13865 \begin_inset VSpace bigskip
13868 To color the frame different than the rest of the box, the command
13878 \begin_layout Plain Layout
13886 is used in the following scheme:
13889 \begin_layout Standard
13894 fcolorbox{frame color}{color}{box content}
13897 \begin_layout Standard
13904 is an extension of the command
13911 The frame width is set, like for
13934 \begin_layout Plain Layout
13946 \begin_inset Formula \[
13947 \fcolorbox{cyan}{magenta}{A=B}\]
13955 \begin_layout Plain Layout
13969 \begin_layout Standard
13970 This formula was created with the command
13971 \begin_inset Newline newline
13979 \begin_inset Formula $\to$
13985 \begin_inset Formula $\to$
13995 \begin_layout Standard
13996 \begin_inset VSpace bigskip
13999 To use other colors than the predefined ones, they have to be defined first.
14002 \begin_layout Standard
14003 One can for example define the color
14004 \begin_inset Quotes eld
14012 \begin_inset Quotes erd
14015 with the LaTeX-preamble line:
14018 \begin_layout Standard
14023 definecolor{darkgreen}{cmyk}{0.5,
14041 \begin_layout Plain Layout
14052 \begin_layout Standard
14057 is the color space that denotes the colors
14074 The four comma separated numbers are the portion factor for the corresponding
14075 colors of the color space.
14076 The factors can be in the range of 0
14077 \begin_inset space \thinspace{}
14081 \begin_inset space \thinspace{}
14089 also the color space
14093 can be used for definitions.
14110 , so that there are in this case three portion factors for the corresponding
14112 Furthermore there is the color space
14116 with one portion factor for the gray value.
14119 \begin_layout Standard
14120 As example a framed box with the new defined color
14124 where the characters have been colored
14129 \begin_inset Formula \begin{equation}
14130 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14137 \begin_layout Standard
14138 Self-defined colors can also be used for text with the help of the command
14149 \begin_layout Plain Layout
14158 \begin_layout Standard
14162 \begin_layout Plain Layout
14166 textcolor{darkgreen}{
14172 \begin_inset Quotes eld
14176 \begin_inset Quotes erd
14183 \begin_layout Plain Layout
14193 \begin_layout Standard
14204 \begin_layout Plain Layout
14212 is used in the scheme
14216 textcolor{color}{characters to color}
14221 \begin_layout Subsection
14223 \begin_inset CommandInset label
14225 name "sub:Paragraph-Boxes"
14233 \begin_layout Plain Layout
14234 Boxes ! as paragraph
14242 \begin_layout Standard
14243 A box that can contain several lines and paragraphs, a so called paragraph
14244 box (parbox), can be created with the menu
14246 Insert\SpecialChar \menuseparator
14249 or the toolbar button
14250 \begin_inset Graphics
14251 filename ../images/box-insert.png
14259 \begin_layout Standard
14260 The following example shows a framed parbox in a line:
14263 \begin_layout Standard
14264 \begin_inset VSpace medskip
14268 \begin_inset Box Boxed
14277 height_special "totalheight"
14280 \begin_layout Plain Layout
14281 This is a paragraph box.
14283 \begin_inset space \thinspace{}
14286 cm long and can also contain formulas:
14287 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14298 \begin_layout Standard
14299 \begin_inset VSpace medskip
14305 \begin_layout Standard
14306 Such a box is created by right-clicking on the gray box inset.
14307 A dialog pops up showing the box properties.
14321 \begin_inset space \thinspace{}
14326 Vertical Box Alignment
14331 \begin_layout Standard
14332 \begin_inset VSpace medskip
14335 In LaTeX a parbox is created with the command
14345 \begin_layout Plain Layout
14353 that has the following scheme:
14356 \begin_layout Standard
14361 parbox[position]{width}{box content}
14364 \begin_layout Standard
14378 for bottom means that the box is aligned within the surrounding text with
14384 for top this is done with the first line.
14385 When no position is given, the box will be vertically centered, see section
14393 \begin_inset space ~
14398 manual for examples.
14401 \begin_layout Standard
14402 \begin_inset VSpace bigskip
14405 To frame formulas completely, including the formula number, the formula
14406 must be set into a parbox.
14407 To do this, the command
14421 is inserted in TeX-mode before the formula.
14430 \begin_layout Plain Layout
14440 is hereby the line width set for the document.
14441 Because the frame is outside the parbox, 2
14442 \begin_inset space \thinspace{}
14445 times the frame separation and the frame thickness must be subtracted from
14447 As this is not automatically done by LyX due to a bug
14451 \begin_layout Plain Layout
14452 \begin_inset CommandInset href
14454 name "LyX-bug #4483"
14455 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14464 , TeX-mode has to be used.
14465 To be able to multiply and subtract in arguments, the LaTeX-package
14473 \begin_layout Plain Layout
14478 is part of every LaTeX standard installation.
14487 \begin_layout Plain Layout
14493 must be loaded in the LaTeX-preamble with the line
14496 \begin_layout Standard
14504 \begin_layout Standard
14505 Behind the formula both boxes are closed by entering
14510 Here is an example:
14514 \begin_layout Plain Layout
14528 \begin_layout Standard
14532 \begin_layout Plain Layout
14550 \begin_inset Formula \begin{equation}
14551 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14559 \begin_layout Plain Layout
14570 \begin_layout Plain Layout
14584 \begin_layout Standard
14585 \begin_inset VSpace medskip
14588 As a parbox is used as argument of
14594 , there is in this case no difference between
14609 \begin_layout Standard
14610 \begin_inset VSpace bigskip
14613 Paragraph boxes are very useful to comment formulas directly.
14620 is used in combination with the command
14634 \begin_inset CommandInset ref
14636 reference "sub:User-defined-Numbering"
14643 \begin_layout Standard
14644 An example of a formula commented with
14653 \begin_layout Standard
14657 \begin_layout Plain Layout
14670 This is a description.
14671 It is distinctly separated from the formula and multiline.
14675 \begin_layout Plain Layout
14687 \begin_layout Standard
14688 Such a formula must be inserted completely in TeX-mode because LyX does
14689 not yet support the command
14696 The formula is created with the following command sequence:
14699 \begin_layout Standard
14712 is inserted in TeX-mode.
14716 \begin_layout Plain Layout
14717 When the formula style
14729 can also be replaced by
14736 (formula styles see
14737 \begin_inset CommandInset ref
14739 reference "sec:Formula-Styles"
14748 Then the description follows as normal text, and finally
14754 is inserted in TeX-mode.
14767 hereby create a displayed formula.
14770 \begin_layout Standard
14777 can be seen in this example that was
14778 \begin_inset Quotes eld
14782 \begin_inset Quotes erd
14785 using the mathematical textmode:
14786 \begin_inset Formula \[
14787 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14794 \begin_layout Section
14799 \begin_layout Plain Layout
14808 \begin_layout Subsection
14810 \begin_inset CommandInset label
14812 name "sub:Big-Operators"
14820 \begin_layout Plain Layout
14830 \begin_layout Plain Layout
14840 \begin_layout Plain Layout
14849 \begin_layout Standard
14850 To be able to use all integral operators listed here, the option
14852 Use esint package automatically
14854 must be set in the document settings under
14857 \begin_inset space ~
14865 \begin_layout Standard
14866 \begin_inset space \hfill{}
14870 \begin_inset Tabular
14871 <lyxtabular version="3" rows="11" columns="2">
14873 <column alignment="center" valignment="top" width="0pt">
14874 <column alignment="center" valignment="top" width="0pt">
14876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14879 \begin_layout Plain Layout
14885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14888 \begin_layout Plain Layout
14896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14899 \begin_layout Plain Layout
14906 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14923 \begin_inset Formula $\sum$
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14943 \begin_layout Plain Layout
14956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14959 \begin_layout Plain Layout
14960 \begin_inset Formula $\int$
14970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14973 \begin_layout Plain Layout
14981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14984 \begin_layout Plain Layout
14985 \begin_inset Formula $\intop$
14995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14998 \begin_layout Plain Layout
15006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15009 \begin_layout Plain Layout
15010 \begin_inset Formula $\oint$
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15023 \begin_layout Plain Layout
15031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15034 \begin_layout Plain Layout
15035 \begin_inset Formula $\ointop$
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15048 \begin_layout Plain Layout
15056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15059 \begin_layout Plain Layout
15060 \begin_inset Formula $\ointctrclockwise$
15070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15073 \begin_layout Plain Layout
15081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15084 \begin_layout Plain Layout
15085 \begin_inset Formula $\ointclockwise$
15095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15098 \begin_layout Plain Layout
15106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15109 \begin_layout Plain Layout
15110 \begin_inset Formula $\sqint$
15120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15123 \begin_layout Plain Layout
15131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15134 \begin_layout Plain Layout
15135 \begin_inset Formula $\bigcap$
15145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15148 \begin_layout Plain Layout
15156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15159 \begin_layout Plain Layout
15160 \begin_inset Formula $\bigcup$
15174 \begin_inset space \hfill{}
15178 \begin_inset Tabular
15179 <lyxtabular version="3" rows="10" columns="2">
15181 <column alignment="center" valignment="top" width="0pt">
15182 <column alignment="center" valignment="top" width="0pt">
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15187 \begin_layout Plain Layout
15193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15196 \begin_layout Plain Layout
15204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15207 \begin_layout Plain Layout
15214 \begin_layout Plain Layout
15227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15230 \begin_layout Plain Layout
15231 \begin_inset Formula $\prod$
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15244 \begin_layout Plain Layout
15252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15255 \begin_layout Plain Layout
15256 \begin_inset Formula $\coprod$
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15269 \begin_layout Plain Layout
15277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15280 \begin_layout Plain Layout
15281 \begin_inset Formula $\bigodot$
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15294 \begin_layout Plain Layout
15302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15305 \begin_layout Plain Layout
15306 \begin_inset Formula $\bigotimes$
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15319 \begin_layout Plain Layout
15327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15330 \begin_layout Plain Layout
15331 \begin_inset Formula $\bigoplus$
15341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15344 \begin_layout Plain Layout
15352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15355 \begin_layout Plain Layout
15356 \begin_inset Formula $\bigwedge$
15366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15369 \begin_layout Plain Layout
15377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15380 \begin_layout Plain Layout
15381 \begin_inset Formula $\bigvee$
15391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15394 \begin_layout Plain Layout
15402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15405 \begin_layout Plain Layout
15406 \begin_inset Formula $\bigsqcup$
15416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15419 \begin_layout Plain Layout
15427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15430 \begin_layout Plain Layout
15431 \begin_inset Formula $\biguplus$
15445 \begin_inset space \hfill{}
15451 \begin_layout Standard
15452 All big operators can also be inserted via the math toolbar button
15453 \begin_inset Graphics
15454 filename ../images/math/intop.png
15462 \begin_layout Standard
15463 The operators are called big because they are bigger than the sometimes
15464 equal looking binary operators.
15465 All big operators can have limits as described in the next subsection.
15468 \begin_layout Standard
15494 \begin_inset space ~
15497 in the style the operator limits are displayed, see
15498 \begin_inset CommandInset ref
15500 reference "sub:Operator-Limits"
15508 \begin_layout Subsubsection*
15509 Advices for Integrals
15512 \begin_layout Standard
15517 in an integral is an operator, that therefore has to be set upright.
15518 This is done by highlighting the
15522 and using the keyboard shortcut
15532 \begin_layout Plain Layout
15538 \begin_inset CommandInset ref
15540 reference "sub:Font-Styles"
15550 Finally the smallest space is inserted before the
15554 , as this is usual for operators.
15558 \begin_layout Standard
15560 \begin_inset Formula $\int A(x)dx$
15564 \begin_inset Newline newline
15571 \begin_layout Plain Layout
15581 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15587 \begin_layout Standard
15588 For multiple integrals there are the following commands:
15589 \begin_inset VSpace medskip
15595 \begin_layout Standard
15596 \begin_inset space \hfill{}
15600 \begin_inset Tabular
15601 <lyxtabular version="3" rows="4" columns="2">
15603 <column alignment="center" valignment="top" width="0">
15604 <column alignment="center" valignment="top" width="0">
15606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15609 \begin_layout Plain Layout
15615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15618 \begin_layout Plain Layout
15620 \begin_inset Note Note
15623 \begin_layout Plain Layout
15630 is only used as spacer.
15642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15645 \begin_layout Plain Layout
15653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15656 \begin_layout Plain Layout
15657 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15670 \begin_layout Plain Layout
15678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15681 \begin_layout Plain Layout
15682 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15695 \begin_layout Plain Layout
15703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15706 \begin_layout Plain Layout
15707 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15721 \begin_inset space \hfill{}
15725 \begin_inset Tabular
15726 <lyxtabular version="3" rows="4" columns="2">
15728 <column alignment="center" valignment="top" width="0">
15729 <column alignment="center" valignment="top" width="0">
15731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15734 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15743 \begin_layout Plain Layout
15751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15754 \begin_layout Plain Layout
15762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15765 \begin_layout Plain Layout
15766 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15779 \begin_layout Plain Layout
15787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15790 \begin_layout Plain Layout
15791 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15804 \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
15816 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15830 \begin_inset space \hfill{}
15836 \begin_layout Subsection
15838 \begin_inset CommandInset label
15840 name "sub:Operator-Limits"
15848 \begin_layout Plain Layout
15857 \begin_layout Standard
15858 Limits are created by super- and subscripts:
15861 \begin_layout Standard
15863 \begin_inset Tabular
15864 <lyxtabular version="3" rows="2" columns="2">
15866 <column alignment="center" valignment="top" width="0pt">
15867 <column alignment="center" valignment="top" width="0pt">
15869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15872 \begin_layout Plain Layout
15878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15881 \begin_layout Plain Layout
15883 \begin_inset Note Note
15886 \begin_layout Plain Layout
15893 is only used as spacer.
15905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15908 \begin_layout Plain Layout
15917 \begin_layout Plain Layout
15927 \begin_inset Formula $\to$
15931 \begin_inset Formula $\to$
15939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15942 \begin_layout Plain Layout
15943 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15959 \begin_layout Standard
15960 Limits of inline formulas are set right beside the operator.
15961 Limits in displayed formulas are set above or below the operator, except
15962 of integral limits.
15965 \begin_layout Standard
15966 To force that the limits are set beside the operator, the cursor is set
15967 directly behind the operator and the limits type is changed with the menu
15970 Edit\SpecialChar \menuseparator
15971 Math\SpecialChar \menuseparator
15990 \begin_layout Standard
15991 The default limits type is this:
15992 \begin_inset Formula \[
15993 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15997 This is how it looks when the limits type was changed to
16004 \begin_inset Formula \[
16005 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16009 For integrals, except of
16021 , the limits are by default set beside the operator.
16022 But for multiple integrals the limits are often set below the operator.
16023 In the following example the limits type was therefore set to
16027 and so set below the integrals:
16028 \begin_inset Formula \begin{equation}
16029 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16036 \begin_layout Standard
16037 \begin_inset VSpace medskip
16040 To specify conditions for limits, the commands
16050 \begin_layout Plain Layout
16068 \begin_layout Plain Layout
16077 To create for example this expression
16078 \begin_inset Formula \begin{equation}
16079 \sum_{\begin{subarray}{c}
16081 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16088 \begin_layout Standard
16089 the following has to be done:
16090 \begin_inset Newline newline
16105 \begin_layout Plain Layout
16117 One is now in a blue box under the summation operator and insert there
16126 \begin_layout Plain Layout
16138 The blue box is now within a purple box and now several lines can be written
16140 A new line is created by inserting a line break (
16143 arg "newline-insert newline"
16148 \begin_inset Newline newline
16153 0<k<1000 Ctrl+Return
16154 \begin_inset Newline newline
16159 is typed in, a new box appears below for the new line.
16162 \begin_layout Standard
16163 The alignment of the lines can be changed to left aligned with the
16173 Edit\SpecialChar \menuseparator
16177 To get right alignment,
16185 \begin_layout Plain Layout
16196 is inserted at the beginning of the line.
16199 \begin_layout Standard
16212 with the difference that the lines are always centered.
16215 \begin_layout Standard
16216 \begin_inset VSpace bigskip
16220 \begin_inset CommandInset ref
16222 reference "eq:substack"
16226 there can be too much space beside an operator, because the characters
16227 following the operator are set beside the limits.
16230 \begin_layout Standard
16231 To avoid this, the following macro can be used in the LaTeX-preamble:
16234 \begin_layout Standard
16248 \begin_inset Newline newline
16260 \begin_inset Newline newline
16267 mathclapinternal #1#2{
16271 mathsurround =0pt #1{#2}$}}
16274 \begin_layout Standard
16275 This defines the command
16285 \begin_layout Plain Layout
16293 that sets the width of the limit to 0
16294 \begin_inset space \thinspace{}
16298 The command scheme is
16301 \begin_layout Standard
16309 \begin_layout Standard
16310 where the limit can consist of several conditions.
16313 \begin_layout Standard
16315 \begin_inset CommandInset ref
16317 reference "eq:substack"
16321 , one uses the command
16324 \begin_layout Standard
16337 \begin_layout Plain Layout
16346 0<k<1000 Ctrl+Return
16349 \begin_layout Standard
16350 to create the lower limit.
16351 The summand is now directly behind the summation operator:
16352 \begin_inset Formula \[
16353 \sum_{\mathclap{\substack{0<k<1000\\
16354 \\k\,\in\,\mathbb{N}}
16362 \begin_layout Standard
16363 \begin_inset VSpace bigskip
16366 How to use one limit for several operators is described in
16367 \begin_inset CommandInset ref
16369 reference "sub:Self-defined-Operators"
16376 \begin_layout Standard
16377 \begin_inset Newpage newpage
16383 \begin_layout Subsection
16385 \begin_inset CommandInset label
16387 name "sub:Binary-Operators"
16395 \begin_layout Plain Layout
16404 \begin_layout Standard
16405 Binary operators are surrounded by space when there is a character before
16407 \begin_inset VSpace medskip
16413 \begin_layout Standard
16414 \begin_inset space \hfill{}
16418 \begin_inset Tabular
16419 <lyxtabular version="3" rows="13" columns="2">
16421 <column alignment="center" valignment="top" width="0pt">
16422 <column alignment="center" valignment="top" width="0pt">
16424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16427 \begin_layout Plain Layout
16429 \begin_inset Note Note
16432 \begin_layout Plain Layout
16439 is only used as spacer.
16449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16452 \begin_layout Plain Layout
16460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16463 \begin_layout Plain Layout
16469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16472 \begin_layout Plain Layout
16473 \begin_inset Formula $+$
16483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16486 \begin_layout Plain Layout
16492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16495 \begin_layout Plain Layout
16496 \begin_inset Formula $-$
16506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16509 \begin_layout Plain Layout
16517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16520 \begin_layout Plain Layout
16521 \begin_inset Formula $\pm$
16531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16534 \begin_layout Plain Layout
16542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16545 \begin_layout Plain Layout
16546 \begin_inset Formula $\mp$
16556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16559 \begin_layout Plain Layout
16567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16570 \begin_layout Plain Layout
16571 \begin_inset Formula $\cdot$
16581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16584 \begin_layout Plain Layout
16592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16595 \begin_layout Plain Layout
16596 \begin_inset Formula $\times$
16606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16609 \begin_layout Plain Layout
16617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16620 \begin_layout Plain Layout
16621 \begin_inset Formula $\div$
16631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16634 \begin_layout Plain Layout
16638 \begin_layout Plain Layout
16651 \begin_layout Plain Layout
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16666 \begin_layout Plain Layout
16667 \begin_inset Formula $*$
16677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16680 \begin_layout Plain Layout
16688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16691 \begin_layout Plain Layout
16692 \begin_inset Formula $\star$
16702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16705 \begin_layout Plain Layout
16713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16716 \begin_layout Plain Layout
16717 \begin_inset Formula $\circ$
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16730 \begin_layout Plain Layout
16738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16741 \begin_layout Plain Layout
16742 \begin_inset Formula $\diamond$
16752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16755 \begin_layout Plain Layout
16763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16767 \begin_inset Formula $\bullet$
16781 \begin_inset space \hfill{}
16785 \begin_inset Tabular
16786 <lyxtabular version="3" rows="13" columns="2">
16788 <column alignment="center" valignment="top" width="0pt">
16789 <column alignment="center" valignment="top" width="0pt">
16791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16794 \begin_layout Plain Layout
16800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16803 \begin_layout Plain Layout
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16814 \begin_layout Plain Layout
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16825 \begin_layout Plain Layout
16826 \begin_inset Formula $\nabla$
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16839 \begin_layout Plain Layout
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16850 \begin_layout Plain Layout
16851 \begin_inset Formula $\bigtriangledown$
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16864 \begin_layout Plain Layout
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16875 \begin_layout Plain Layout
16876 \begin_inset Formula $\bigtriangleup$
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16889 \begin_layout Plain Layout
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16900 \begin_layout Plain Layout
16901 \begin_inset Formula $\Box$
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16914 \begin_layout Plain Layout
16922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16925 \begin_layout Plain Layout
16926 \begin_inset Formula $\cap$
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16939 \begin_layout Plain Layout
16947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16950 \begin_layout Plain Layout
16951 \begin_inset Formula $\cup$
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16964 \begin_layout Plain Layout
16972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16975 \begin_layout Plain Layout
16976 \begin_inset Formula $\dagger$
16986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16989 \begin_layout Plain Layout
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17000 \begin_layout Plain Layout
17001 \begin_inset Formula $\ddagger$
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17014 \begin_layout Plain Layout
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17025 \begin_layout Plain Layout
17026 \begin_inset Formula $\wr$
17036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17039 \begin_layout Plain Layout
17047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17050 \begin_layout Plain Layout
17051 \begin_inset Formula $\bigcirc$
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17064 \begin_layout Plain Layout
17072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17075 \begin_layout Plain Layout
17076 \begin_inset Formula $\wedge$
17086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17089 \begin_layout Plain Layout
17097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17100 \begin_layout Plain Layout
17101 \begin_inset Formula $\vee$
17115 \begin_inset space \hfill{}
17119 \begin_inset Tabular
17120 <lyxtabular version="3" rows="13" columns="2">
17122 <column alignment="center" valignment="top" width="0pt">
17123 <column alignment="center" valignment="top" width="0pt">
17125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17137 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17148 \begin_layout Plain Layout
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17159 \begin_layout Plain Layout
17160 \begin_inset Formula $\oplus$
17170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17173 \begin_layout Plain Layout
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17184 \begin_layout Plain Layout
17185 \begin_inset Formula $\ominus$
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17198 \begin_layout Plain Layout
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17209 \begin_layout Plain Layout
17210 \begin_inset Formula $\otimes$
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17223 \begin_layout Plain Layout
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17234 \begin_layout Plain Layout
17235 \begin_inset Formula $\oslash$
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17248 \begin_layout Plain Layout
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17259 \begin_layout Plain Layout
17260 \begin_inset Formula $\odot$
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17273 \begin_layout Plain Layout
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17284 \begin_layout Plain Layout
17285 \begin_inset Formula $\amalg$
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17298 \begin_layout Plain Layout
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17309 \begin_layout Plain Layout
17310 \begin_inset Formula $\uplus$
17320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17323 \begin_layout Plain Layout
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17334 \begin_layout Plain Layout
17335 \begin_inset Formula $\setminus$
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17348 \begin_layout Plain Layout
17356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17359 \begin_layout Plain Layout
17360 \begin_inset Formula $\sqcap$
17370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17373 \begin_layout Plain Layout
17381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17384 \begin_layout Plain Layout
17385 \begin_inset Formula $\sqcup$
17395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17398 \begin_layout Plain Layout
17406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17409 \begin_layout Plain Layout
17410 \begin_inset Formula $\triangleleft$
17420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17423 \begin_layout Plain Layout
17431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17434 \begin_layout Plain Layout
17435 \begin_inset Formula $\triangleright$
17449 \begin_inset space \hfill{}
17455 \begin_layout Standard
17456 All binary operators can also be inserted via the math toolbar button
17457 \begin_inset Graphics
17458 filename ../images/math/pm.png
17466 \begin_layout Standard
17467 To typeset the Laplace operator also
17484 \begin_inset Formula $\nabla^{2}$
17487 ) can be used instead of
17496 \begin_layout Standard
17503 Insert\SpecialChar \menuseparator
17515 \begin_layout Subsection
17516 Self-defined Operators
17517 \begin_inset CommandInset label
17519 name "sub:Self-defined-Operators"
17527 \begin_layout Plain Layout
17528 Operators ! self-defined
17536 \begin_layout Standard
17537 With the help of the command
17541 DeclareMathOperator
17547 \begin_layout Plain Layout
17552 DeclareMathOperator
17557 custom operators can be defined in the LaTeX-preamble.
17558 Its command scheme is:
17561 \begin_layout Standard
17566 DeclareMathOperator{new command}{display}
17569 \begin_layout Standard
17570 Display can be characters or symbols that define how the operator looks
17572 To define a big operator a * is set behind the command.
17573 All self-defined big operators can have limits as described in
17574 \begin_inset CommandInset ref
17576 reference "sub:Operator-Limits"
17583 \begin_layout Standard
17584 For example the LaTeX-preamble line
17587 \begin_layout Standard
17592 DeclareMathOperator*{
17599 \begin_layout Standard
17600 defines the command
17606 , that inserts a big operator consisting of the lozenge symbol from
17607 \begin_inset CommandInset ref
17609 reference "sub:Miscellaneous-Symbols"
17614 \begin_inset Formula \[
17615 \Lozenge_{n=1}^{\infty}\]
17619 The command for this formula is:
17630 \begin_inset Formula $\to$
17636 \begin_layout Standard
17637 \begin_inset VSpace bigskip
17640 When self-defined operators are not used several times in the document,
17641 they can also be defined with the commands
17651 \begin_layout Plain Layout
17669 \begin_layout Plain Layout
17677 , which have the following scheme:
17680 \begin_layout Standard
17694 \begin_layout Standard
17701 defines big operators,
17710 \begin_layout Standard
17718 \begin_inset space \thinspace{}
17722 \begin_inset space \space{}
17725 be used to use one limit for several operators:
17728 \begin_layout Standard
17729 \begin_inset Formula \[
17730 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17737 \begin_layout Standard
17738 The command for the formula above is:
17739 \begin_inset Newline newline
17758 \begin_layout Plain Layout
17770 \begin_inset Formula $\to$
17779 \begin_layout Plain Layout
17793 \begin_layout Section
17798 \begin_layout Plain Layout
17807 \begin_layout Subsection
17809 \begin_inset CommandInset label
17811 name "sub:Font-Styles"
17819 \begin_layout Plain Layout
17828 \begin_layout Standard
17829 Latin letters in formulas can be set in one of the following font styles:
17830 \begin_inset VSpace -2mm
17836 \begin_layout Standard
17838 \begin_inset Tabular
17839 <lyxtabular version="3" rows="6" columns="3">
17841 <column alignment="center" valignment="top" width="0">
17842 <column alignment="center" valignment="top" width="0">
17843 <column alignment="center" valignment="top" width="0">
17845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17848 \begin_layout Plain Layout
17854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17857 \begin_layout Plain Layout
17863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17866 \begin_layout Plain Layout
17874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17877 \begin_layout Plain Layout
17886 \begin_layout Plain Layout
17902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17905 \begin_layout Plain Layout
17906 \begin_inset Formula $\mathbb{ABC}$
17914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17917 \begin_layout Plain Layout
17930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17933 \begin_layout Plain Layout
17942 \begin_layout Plain Layout
17958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17961 \begin_layout Plain Layout
17962 \begin_inset Formula $\mathbf{AbC}$
17970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17973 \begin_layout Plain Layout
17986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17989 \begin_layout Plain Layout
17998 \begin_layout Plain Layout
18014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18017 \begin_layout Plain Layout
18018 \begin_inset Formula $\boldsymbol{AbC}$
18026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18029 \begin_layout Plain Layout
18032 arg "font-boldsymbol"
18042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18045 \begin_layout Plain Layout
18054 \begin_layout Plain Layout
18070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18073 \begin_layout Plain Layout
18074 \begin_inset Formula $\mathcal{ABC}$
18082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18085 \begin_layout Plain Layout
18098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18101 \begin_layout Plain Layout
18110 \begin_layout Plain Layout
18126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18129 \begin_layout Plain Layout
18130 \begin_inset Formula $\mathfrak{AbC}$
18138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18141 \begin_layout Plain Layout
18155 \begin_layout Standard
18157 \begin_inset Tabular
18158 <lyxtabular version="3" rows="5" columns="3">
18160 <column alignment="center" valignment="top" width="0">
18161 <column alignment="center" valignment="top" width="0">
18162 <column alignment="center" valignment="top" width="0">
18164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18167 \begin_layout Plain Layout
18173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18176 \begin_layout Plain Layout
18182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18185 \begin_layout Plain Layout
18193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18196 \begin_layout Plain Layout
18205 \begin_layout Plain Layout
18221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18224 \begin_layout Plain Layout
18225 \begin_inset Formula $\mathit{AbC}$
18233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18247 \begin_layout Plain Layout
18256 \begin_layout Plain Layout
18272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18275 \begin_layout Plain Layout
18276 \begin_inset Formula $\mathrm{AbC}$
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18287 \begin_layout Plain Layout
18300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18303 \begin_layout Plain Layout
18312 \begin_layout Plain Layout
18328 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18331 \begin_layout Plain Layout
18332 \begin_inset Formula $\mathsf{AbC}$
18340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18343 \begin_layout Plain Layout
18356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18359 \begin_layout Plain Layout
18368 \begin_layout Plain Layout
18384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18387 \begin_layout Plain Layout
18388 \begin_inset Formula $\mathtt{AbC}$
18396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18399 \begin_layout Plain Layout
18402 arg "font-typewriter"
18418 \begin_layout Standard
18419 \begin_inset Note Greyedout
18422 \begin_layout Plain Layout
18439 can only be used for big letters.
18447 \begin_layout Standard
18448 Predefined is the style
18457 \begin_layout Standard
18458 The style commands work also for letters in mathematical constructs:
18459 \begin_inset Formula \[
18460 \mathfrak{A=\frac{b}{C}}\]
18467 \begin_layout Standard
18468 Characters in mathematical text don't appear in a math font style but in
18469 the text font style
18476 That their style can't be set correctly via the text style dialog is a
18481 \begin_layout Plain Layout
18482 \begin_inset CommandInset href
18484 name "LyX-bug #4091"
18485 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18497 \begin_layout Standard
18498 Instead of the style commands the dialog
18500 Edit\SpecialChar \menuseparator
18501 Math\SpecialChar \menuseparator
18504 or the toolbar button
18505 \begin_inset Graphics
18506 filename ../images/math/font.png
18514 \begin_layout Subsection
18516 \begin_inset CommandInset label
18518 name "sub:Bold-Formulas"
18526 \begin_layout Plain Layout
18535 \begin_layout Standard
18536 To make a complete formula bold, the command
18542 from the previous subsection cannot be used, because it doesn't work for
18543 small Greek letters.
18544 Furthermore it prints Latin letters always upright, like in the following
18548 \begin_layout Standard
18549 \begin_inset Formula \[
18550 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18557 \begin_layout Standard
18558 To display the formula correctly, the command
18565 \begin_inset Formula \[
18566 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18570 It is also possible to set the formula in a
18572 boldmath environment
18575 This environment is created by inserting the command
18583 \begin_layout Plain Layout
18594 To end the environment, the command
18602 \begin_layout Plain Layout
18612 is inserted in TeX-mode.
18616 \begin_layout Plain Layout
18626 \begin_inset Formula \[
18627 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18635 \begin_layout Plain Layout
18647 \begin_layout Subsection
18652 \begin_layout Plain Layout
18661 \begin_layout Standard
18662 Formulas can be colored like normal text: Highlight a formula or a formula
18668 Here is a formula in magenta:
18669 \begin_inset Formula \[
18670 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18677 \begin_layout Standard
18678 You can also define your own colors as described in
18679 \begin_inset CommandInset ref
18681 reference "sub:Colored-Boxes"
18686 They can be used with the TeX code command
18696 \begin_layout Plain Layout
18707 \begin_layout Standard
18712 textcolor{color}{characters or formula}
18715 \begin_layout Standard
18716 The following example was colored completely dark green and partly red:
18719 \begin_layout Standard
18723 \begin_layout Plain Layout
18727 textcolor{darkgreen}{
18733 \begin_inset Formula \[
18734 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18742 \begin_layout Plain Layout
18752 \begin_layout Standard
18753 Due to a bug in LyX only complete formulas can be colored with self-defined
18758 \begin_layout Plain Layout
18759 \begin_inset CommandInset href
18761 name "LyX-bug #5269"
18762 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18774 \begin_layout Subsection
18776 \begin_inset CommandInset label
18778 name "sub:Font-Sizes"
18786 \begin_layout Plain Layout
18795 \begin_layout Standard
18796 For characters in formulas there are, analog to characters in text, the
18797 following size commands:
18800 \begin_layout Standard
18844 \begin_inset Newline newline
18866 \begin_layout Standard
18867 The size produced by the commands depends on the document font size, that
18868 corresponds with the command
18875 The other commands produce smaller or larger sizes than
18882 The font size can however not exceed a certain value.
18883 Is for example the document font size 12
18884 \begin_inset space \thinspace{}
18893 switches to the same size as
18903 \begin_layout Standard
18904 A size command is inserted in TeX-mode before the formula and sets the size
18905 for all following formula and text characters.
18906 To switch back to the initial size, the command
18912 is inserted behind the formula in TeX-mode.
18915 \begin_layout Standard
18916 Within a formula the size can only be changed for symbols or letters in
18918 To do this, the size command is inserted in mathematical text.
18919 All following characters until the end of the mathematical text or until
18920 another size command will have the selected size.
18922 \begin_inset VSpace -2mm
18928 \begin_layout Standard
18932 \begin_layout Plain Layout
18942 \begin_inset Formula \[
18943 A=\frac{B}{c}\cdot\maltese\]
18948 \begin_inset Formula \[
18949 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18957 \begin_layout Plain Layout
18969 \begin_layout Standard
18970 \begin_inset VSpace medskip
18973 Before both formulas the command
18980 The command for the second formula is:
18981 \begin_inset Newline newline
18992 \begin_layout Plain Layout
19007 \begin_layout Plain Layout
19022 \begin_layout Plain Layout
19037 \begin_layout Plain Layout
19047 \begin_inset Formula $\to$
19051 \begin_inset Formula $\to$
19055 \begin_inset Newline newline
19059 \begin_inset space \hspace*{}
19073 \begin_layout Plain Layout
19088 \begin_layout Plain Layout
19103 \begin_layout Plain Layout
19115 \begin_layout Standard
19116 If a symbol cannot be displayed in different sizes, it will always be displayed
19117 in the default size.
19120 \begin_layout Section
19125 \begin_layout Plain Layout
19134 \begin_layout Standard
19135 All Greek letters can also be inserted via the toolbar button
19136 \begin_inset Graphics
19137 filename ../images/math/alpha.png
19145 \begin_layout Subsection
19150 \begin_layout Plain Layout
19151 Greek letters ! small
19159 \begin_layout Standard
19160 \begin_inset space \hfill{}
19164 \begin_inset Tabular
19165 <lyxtabular version="3" rows="11" columns="2">
19167 <column alignment="center" valignment="top" width="0pt">
19168 <column alignment="center" valignment="top" width="0pt">
19170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19173 \begin_layout Plain Layout
19179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19182 \begin_layout Plain Layout
19190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19193 \begin_layout Plain Layout
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19204 \begin_layout Plain Layout
19205 \begin_inset Formula $\alpha$
19215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19218 \begin_layout Plain Layout
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19229 \begin_layout Plain Layout
19230 \begin_inset Formula $\beta$
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19243 \begin_layout Plain Layout
19251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19254 \begin_layout Plain Layout
19255 \begin_inset Formula $\gamma$
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19268 \begin_layout Plain Layout
19276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19279 \begin_layout Plain Layout
19280 \begin_inset Formula $\delta$
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19293 \begin_layout Plain Layout
19301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19304 \begin_layout Plain Layout
19305 \begin_inset Formula $\epsilon$
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19329 \begin_layout Plain Layout
19330 \begin_inset Formula $\varepsilon$
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19343 \begin_layout Plain Layout
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19354 \begin_layout Plain Layout
19355 \begin_inset Formula $\zeta$
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19368 \begin_layout Plain Layout
19376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19379 \begin_layout Plain Layout
19380 \begin_inset Formula $\eta$
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19393 \begin_layout Plain Layout
19401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19404 \begin_layout Plain Layout
19405 \begin_inset Formula $\theta$
19415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19418 \begin_layout Plain Layout
19426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19429 \begin_layout Plain Layout
19430 \begin_inset Formula $\vartheta$
19444 \begin_inset space \hfill{}
19448 \begin_inset Tabular
19449 <lyxtabular version="3" rows="12" columns="2">
19451 <column alignment="center" valignment="top" width="0pt">
19452 <column alignment="center" valignment="top" width="0pt">
19454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19457 \begin_layout Plain Layout
19463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19466 \begin_layout Plain Layout
19474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19477 \begin_layout Plain Layout
19485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19488 \begin_layout Plain Layout
19489 \begin_inset Formula $\iota$
19499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19502 \begin_layout Plain Layout
19510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19513 \begin_layout Plain Layout
19514 \begin_inset Formula $\kappa$
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19527 \begin_layout Plain Layout
19535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19538 \begin_layout Plain Layout
19539 \begin_inset Formula $\varkappa$
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19552 \begin_layout Plain Layout
19560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19563 \begin_layout Plain Layout
19564 \begin_inset Formula $\lambda$
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19577 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19589 \begin_inset Formula $\mu$
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19602 \begin_layout Plain Layout
19610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19613 \begin_layout Plain Layout
19614 \begin_inset Formula $\nu$
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19627 \begin_layout Plain Layout
19635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19638 \begin_layout Plain Layout
19639 \begin_inset Formula $\xi$
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19652 \begin_layout Plain Layout
19658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19661 \begin_layout Plain Layout
19662 \begin_inset Formula $o$
19672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19675 \begin_layout Plain Layout
19683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19686 \begin_layout Plain Layout
19687 \begin_inset Formula $\pi$
19697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19700 \begin_layout Plain Layout
19708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19711 \begin_layout Plain Layout
19712 \begin_inset Formula $\varpi$
19722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19725 \begin_layout Plain Layout
19733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19736 \begin_layout Plain Layout
19737 \begin_inset Formula $\rho$
19751 \begin_inset space \hfill{}
19755 \begin_inset Tabular
19756 <lyxtabular version="3" rows="11" columns="2">
19758 <column alignment="center" valignment="top" width="0pt">
19759 <column alignment="center" valignment="top" width="0pt">
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19764 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\varrho$
19806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Plain Layout
19821 \begin_inset Formula $\sigma$
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19834 \begin_layout Plain Layout
19842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19845 \begin_layout Plain Layout
19846 \begin_inset Formula $\varsigma$
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19859 \begin_layout Plain Layout
19867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19870 \begin_layout Plain Layout
19871 \begin_inset Formula $\tau$
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19884 \begin_layout Plain Layout
19892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19895 \begin_layout Plain Layout
19896 \begin_inset Formula $\upsilon$
19906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19909 \begin_layout Plain Layout
19917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19920 \begin_layout Plain Layout
19921 \begin_inset Formula $\phi$
19931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19934 \begin_layout Plain Layout
19942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19945 \begin_layout Plain Layout
19946 \begin_inset Formula $\varphi$
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19959 \begin_layout Plain Layout
19967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19970 \begin_layout Plain Layout
19971 \begin_inset Formula $\chi$
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19984 \begin_layout Plain Layout
19992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19995 \begin_layout Plain Layout
19996 \begin_inset Formula $\psi$
20006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20009 \begin_layout Plain Layout
20017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20020 \begin_layout Plain Layout
20021 \begin_inset Formula $\omega$
20035 \begin_inset space \hfill{}
20041 \begin_layout Standard
20042 \begin_inset VSpace medskip
20048 \begin_layout Standard
20049 How to create upright Greek letters is explained in
20050 \begin_inset CommandInset ref
20052 reference "sub:Upright-small-Greek"
20059 \begin_layout Subsection
20064 \begin_layout Plain Layout
20065 Greek letters ! big
20073 \begin_layout Standard
20074 \begin_inset space \hfill{}
20078 \begin_inset Tabular
20079 <lyxtabular version="3" rows="7" columns="2">
20081 <column alignment="center" valignment="top" width="0pt">
20082 <column alignment="center" valignment="top" width="0pt">
20084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20087 \begin_layout Plain Layout
20093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20096 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20107 \begin_layout Plain Layout
20115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20118 \begin_layout Plain Layout
20119 \begin_inset Formula $\Gamma$
20129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20132 \begin_layout Plain Layout
20140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20143 \begin_layout Plain Layout
20144 \begin_inset Formula $\Delta$
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20157 \begin_layout Plain Layout
20165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20168 \begin_layout Plain Layout
20169 \begin_inset Formula $\Theta$
20179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20182 \begin_layout Plain Layout
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20193 \begin_layout Plain Layout
20194 \begin_inset Formula $\Lambda$
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20207 \begin_layout Plain Layout
20215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20218 \begin_layout Plain Layout
20219 \begin_inset Formula $\Xi$
20229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20232 \begin_layout Plain Layout
20240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20243 \begin_layout Plain Layout
20244 \begin_inset Formula $\Pi$
20258 \begin_inset space \hfill{}
20262 \begin_inset Tabular
20263 <lyxtabular version="3" rows="6" columns="2">
20265 <column alignment="center" valignment="top" width="0pt">
20266 <column alignment="center" valignment="top" width="0pt">
20268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20271 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20291 \begin_layout Plain Layout
20299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20302 \begin_layout Plain Layout
20303 \begin_inset Formula $\Sigma$
20313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20316 \begin_layout Plain Layout
20324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20327 \begin_layout Plain Layout
20328 \begin_inset Formula $\Upsilon$
20338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20341 \begin_layout Plain Layout
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20352 \begin_layout Plain Layout
20353 \begin_inset Formula $\Phi$
20363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20366 \begin_layout Plain Layout
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20377 \begin_layout Plain Layout
20378 \begin_inset Formula $\Psi$
20388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20391 \begin_layout Plain Layout
20399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20402 \begin_layout Plain Layout
20403 \begin_inset Formula $\Omega$
20417 \begin_inset space \hfill{}
20423 \begin_layout Standard
20424 \begin_inset VSpace medskip
20427 That the big Greek letters appear upright is caused by a design bug when
20429 To get correct italic big letters, begin every command with
20434 For example the command
20441 \begin_inset Formula $\varGamma$
20447 \begin_layout Subsection
20452 \begin_layout Plain Layout
20453 Greek letters ! bold
20461 \begin_layout Standard
20462 Greek letters cannot be set with different font styles like Latin letters.
20463 They can only be made bold with the command
20473 \begin_layout Plain Layout
20484 \begin_layout Standard
20486 \begin_inset Tabular
20487 <lyxtabular version="3" rows="3" columns="2">
20489 <column alignment="center" valignment="top" width="0">
20490 <column alignment="center" valignment="top" width="0">
20492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20495 \begin_layout Plain Layout
20501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20504 \begin_layout Plain Layout
20512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20515 \begin_layout Plain Layout
20527 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20530 \begin_layout Plain Layout
20531 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20544 \begin_layout Plain Layout
20556 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20559 \begin_layout Plain Layout
20560 \begin_inset Formula $\theta\boldsymbol{\theta}$
20576 \begin_layout Section
20581 \begin_layout Plain Layout
20594 \begin_layout Plain Layout
20595 A list with all symbols of most of the LaTeX-packages can be found in
20596 \begin_inset CommandInset citation
20611 \begin_layout Plain Layout
20619 \begin_inset Note Note
20622 \begin_layout Plain Layout
20625 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20628 \begin_layout Plain Layout
20631 texorpdfstring is in section
20632 \begin_inset CommandInset ref
20634 reference "sub:Formulas-in-Section"
20647 \begin_layout Plain Layout
20656 \begin_layout Standard
20657 Many of the symbols listed in this section can also be inserted via the
20659 \begin_inset Graphics
20660 filename ../images/math/nabla.png
20666 \begin_inset Graphics
20667 filename ../images/math/digamma.png
20675 \begin_layout Subsection
20676 Mathematical Symbols
20677 \begin_inset CommandInset label
20679 name "sub:Mathematical-Symbols"
20687 \begin_layout Plain Layout
20688 Symbols ! mathematical
20696 \begin_layout Standard
20697 \begin_inset space \hfill{}
20701 \begin_inset Tabular
20702 <lyxtabular version="3" rows="10" columns="2">
20704 <column alignment="center" valignment="top" width="0pt">
20705 <column alignment="center" valignment="top" width="0pt">
20707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20710 \begin_layout Plain Layout
20716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20719 \begin_layout Plain Layout
20727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20730 \begin_layout Plain Layout
20738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20741 \begin_layout Plain Layout
20742 \begin_inset Formula $\neg$
20752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20755 \begin_layout Plain Layout
20763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20766 \begin_layout Plain Layout
20767 \begin_inset Formula $\Im$
20777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20780 \begin_layout Plain Layout
20788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20791 \begin_layout Plain Layout
20792 \begin_inset Formula $\Re$
20802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20805 \begin_layout Plain Layout
20813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20816 \begin_layout Plain Layout
20817 \begin_inset Formula $\aleph$
20827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20830 \begin_layout Plain Layout
20838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20841 \begin_layout Plain Layout
20842 \begin_inset Formula $\partial$
20852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20855 \begin_layout Plain Layout
20863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20866 \begin_layout Plain Layout
20867 \begin_inset Formula $\infty$
20877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20880 \begin_layout Plain Layout
20888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20891 \begin_layout Plain Layout
20892 \begin_inset Formula $\wp$
20902 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20905 \begin_layout Plain Layout
20913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20916 \begin_layout Plain Layout
20917 \begin_inset Formula $\imath$
20927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20930 \begin_layout Plain Layout
20938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20941 \begin_layout Plain Layout
20942 \begin_inset Formula $\jmath$
20956 \begin_inset space \hfill{}
20960 \begin_inset Tabular
20961 <lyxtabular version="3" rows="10" columns="2">
20963 <column alignment="center" valignment="top" width="0pt">
20964 <column alignment="center" valignment="top" width="0pt">
20966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20969 \begin_layout Plain Layout
20975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20978 \begin_layout Plain Layout
20980 \begin_inset Note Note
20983 \begin_layout Plain Layout
20990 is only used as spacer.
21002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21005 \begin_layout Plain Layout
21013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21016 \begin_layout Plain Layout
21017 \begin_inset Formula $\forall$
21027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21030 \begin_layout Plain Layout
21038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21041 \begin_layout Plain Layout
21042 \begin_inset Formula $\exists$
21052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21055 \begin_layout Plain Layout
21063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21066 \begin_layout Plain Layout
21067 \begin_inset Formula $\nexists$
21077 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21080 \begin_layout Plain Layout
21088 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21091 \begin_layout Plain Layout
21092 \begin_inset Formula $\emptyset$
21102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21117 \begin_inset Formula $\varnothing$
21127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21130 \begin_layout Plain Layout
21138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21141 \begin_layout Plain Layout
21142 \begin_inset Formula $\dag$
21152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21155 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21166 \begin_layout Plain Layout
21167 \begin_inset Formula $\ddag$
21177 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21180 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21191 \begin_layout Plain Layout
21195 \begin_layout Plain Layout
21205 \begin_inset Formula $\complement$
21212 \begin_layout Plain Layout
21226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21229 \begin_layout Plain Layout
21237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21240 \begin_layout Plain Layout
21241 \begin_inset Formula $\Bbbk$
21255 \begin_inset space \hfill{}
21259 \begin_inset Tabular
21260 <lyxtabular version="3" rows="10" columns="2">
21262 <column alignment="center" valignment="top" width="0pt">
21263 <column alignment="center" valignment="top" width="0pt">
21265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21268 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21288 \begin_layout Plain Layout
21296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21299 \begin_layout Plain Layout
21300 \begin_inset Formula $\prime$
21310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21313 \begin_layout Plain Layout
21321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21324 \begin_layout Plain Layout
21325 \begin_inset Formula $\backprime$
21335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21338 \begin_layout Plain Layout
21346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21349 \begin_layout Plain Layout
21350 \begin_inset Formula $\mho$
21360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21363 \begin_layout Plain Layout
21371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21374 \begin_layout Plain Layout
21375 \begin_inset Formula $\triangle$
21385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21388 \begin_layout Plain Layout
21396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21399 \begin_layout Plain Layout
21400 \begin_inset Formula $\angle$
21410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21413 \begin_layout Plain Layout
21421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21424 \begin_layout Plain Layout
21425 \begin_inset Formula $\measuredangle$
21435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21438 \begin_layout Plain Layout
21446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21449 \begin_layout Plain Layout
21450 \begin_inset Formula $\sphericalangle$
21460 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21463 \begin_layout Plain Layout
21471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21474 \begin_layout Plain Layout
21475 \begin_inset Formula $\top$
21485 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21488 \begin_layout Plain Layout
21496 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21499 \begin_layout Plain Layout
21500 \begin_inset Formula $\bot$
21514 \begin_inset space \hfill{}
21520 \begin_layout Subsection
21521 Miscellaneous Symbols
21522 \begin_inset CommandInset label
21524 name "sub:Miscellaneous-Symbols"
21532 \begin_layout Plain Layout
21533 Symbols ! miscellaneous
21541 \begin_layout Standard
21544 \begin_inset Tabular
21545 <lyxtabular version="3" rows="10" columns="2">
21547 <column alignment="center" valignment="top" width="0pt">
21548 <column alignment="center" valignment="top" width="0pt">
21550 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21553 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21573 \begin_layout Plain Layout
21581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21584 \begin_layout Plain Layout
21585 \begin_inset Formula $\flat$
21595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21598 \begin_layout Plain Layout
21606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21609 \begin_layout Plain Layout
21610 \begin_inset Formula $\natural$
21620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21623 \begin_layout Plain Layout
21631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21634 \begin_layout Plain Layout
21635 \begin_inset Formula $\sharp$
21645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21648 \begin_layout Plain Layout
21656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21659 \begin_layout Plain Layout
21660 \begin_inset Formula $\surd$
21670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21673 \begin_layout Plain Layout
21681 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21684 \begin_layout Plain Layout
21685 \begin_inset Formula $\checkmark$
21695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21698 \begin_layout Plain Layout
21706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21709 \begin_layout Plain Layout
21710 \begin_inset Formula $\yen$
21720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21723 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21734 \begin_layout Plain Layout
21735 \begin_inset Formula $\pounds$
21745 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21748 \begin_layout Plain Layout
21754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21757 \begin_layout Plain Layout
21758 \begin_inset Formula $\$$
21768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21771 \begin_layout Plain Layout
21777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21780 \begin_layout Plain Layout
21781 \begin_inset Formula $§$
21795 \begin_inset Tabular
21796 <lyxtabular version="3" rows="10" columns="2">
21798 <column alignment="center" valignment="top" width="0">
21799 <column alignment="center" valignment="top" width="0">
21801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21804 \begin_layout Plain Layout
21810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21813 \begin_layout Plain Layout
21821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21824 \begin_layout Plain Layout
21832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21835 \begin_layout Plain Layout
21836 \begin_inset Formula $\hbar$
21846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21849 \begin_layout Plain Layout
21857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21860 \begin_layout Plain Layout
21861 \begin_inset Formula $\hslash$
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21874 \begin_layout Plain Layout
21882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21885 \begin_layout Plain Layout
21886 \begin_inset Formula $\clubsuit$
21896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21899 \begin_layout Plain Layout
21907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21910 \begin_layout Plain Layout
21911 \begin_inset Formula $\spadesuit$
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\bigstar$
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\blacklozenge$
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\blacktriangle$
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\blacktriangledown$
22021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\bullet$
22050 \begin_inset Tabular
22051 <lyxtabular version="3" rows="10" columns="2">
22053 <column alignment="center" valignment="top" width="0pt">
22054 <column alignment="center" valignment="top" width="0pt">
22056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22059 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22079 \begin_layout Plain Layout
22087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22090 \begin_layout Plain Layout
22091 \begin_inset Formula $\diamondsuit$
22101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22104 \begin_layout Plain Layout
22112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22115 \begin_layout Plain Layout
22116 \begin_inset Formula $\Diamond$
22126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22129 \begin_layout Plain Layout
22137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22140 \begin_layout Plain Layout
22141 \begin_inset Formula $\heartsuit$
22151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22154 \begin_layout Plain Layout
22162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22165 \begin_layout Plain Layout
22166 \begin_inset Formula $\P$
22176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22179 \begin_layout Plain Layout
22187 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22190 \begin_layout Plain Layout
22191 \begin_inset Formula $\copyright$
22201 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22204 \begin_layout Plain Layout
22212 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22215 \begin_layout Plain Layout
22216 \begin_inset Formula $\circledR$
22226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22229 \begin_layout Plain Layout
22237 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22240 \begin_layout Plain Layout
22241 \begin_inset Formula $\maltese$
22251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22254 \begin_layout Plain Layout
22262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22265 \begin_layout Plain Layout
22266 \begin_inset Formula $\diagup$
22276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22279 \begin_layout Plain Layout
22287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22290 \begin_layout Plain Layout
22291 \begin_inset Formula $\diagdown$
22307 \begin_layout Standard
22308 \begin_inset VSpace medskip
22311 More symbols are listed in
22312 \begin_inset CommandInset ref
22314 reference "sub:Miscellaneous-special-Characters"
22321 \begin_layout Standard
22322 Some symbols can be displayed in different sizes, see
22323 \begin_inset CommandInset ref
22325 reference "sub:Font-Sizes"
22332 \begin_layout Subsection
22337 \begin_layout Plain Layout
22338 Symbols ! Euro-symbol
22347 \begin_layout Plain Layout
22354 \begin_layout Plain Layout
22371 \begin_layout Standard
22372 To use the Euro symbol in formulas, the LaTeX-package
22380 \begin_layout Plain Layout
22386 must be installed and loaded with the LaTeX-preamble line
22389 \begin_layout Standard
22394 usepackage[gennarrow]{eurosym}
22397 \begin_layout Standard
22398 The Euro symbol can now be inserted with the command
22408 \begin_layout Plain Layout
22419 \begin_layout Standard
22420 The Euro symbol can directly be inserted with the € key in mathematical
22421 text, without having
22436 can also be inserted in TeX-mode.
22437 The official currency symbol can then be inserted with the command
22447 \begin_layout Plain Layout
22455 , that is only available in TeX-mode.
22458 \begin_layout Standard
22462 \begin_layout Plain Layout
22472 \begin_inset Note Note
22475 \begin_layout Plain Layout
22476 The following table will only be displayed when the LaTeX-package
22488 \begin_layout Standard
22489 An overview about the different Euro symbols:
22492 \begin_layout Standard
22494 \begin_inset Tabular
22495 <lyxtabular version="3" rows="4" columns="3">
22497 <column alignment="center" valignment="top" width="0pt">
22498 <column alignment="center" valignment="top" width="0pt">
22499 <column alignment="center" valignment="top" width="0pt">
22501 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22504 \begin_layout Plain Layout
22510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22513 \begin_layout Plain Layout
22519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22522 \begin_layout Plain Layout
22530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22533 \begin_layout Plain Layout
22539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22542 \begin_layout Plain Layout
22550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22553 \begin_layout Plain Layout
22554 \begin_inset Formula $\euro$
22564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22567 \begin_layout Plain Layout
22573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22576 \begin_layout Plain Layout
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22585 \begin_layout Plain Layout
22586 \begin_inset Formula $\mbox{€}$
22596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22619 \begin_layout Plain Layout
22623 \begin_layout Plain Layout
22645 \begin_layout Standard
22649 \begin_layout Plain Layout
22659 \begin_inset Note Note
22662 \begin_layout Plain Layout
22663 The following will be displayed when the LaTeX-package
22675 \begin_layout Standard
22676 You need to install the LaTeX-package
22680 to see the rest of this subsection in the output.
22683 \begin_layout Standard
22687 \begin_layout Plain Layout
22699 \begin_layout Section
22701 \begin_inset CommandInset label
22703 name "sec:Relations"
22711 \begin_layout Plain Layout
22721 \begin_layout Plain Layout
22726 \begin_layout Plain Layout
22737 \begin_layout Plain Layout
22752 \begin_layout Standard
22753 All relations can also be inserted via the toolbar button
22754 \begin_inset Graphics
22755 filename ../images/math/leq.png
22763 \begin_layout Standard
22764 \begin_inset space \hfill{}
22768 \begin_inset Tabular
22769 <lyxtabular version="3" rows="17" columns="2">
22771 <column alignment="center" valignment="top" width="0pt">
22772 <column alignment="center" valignment="top" width="0pt">
22774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22777 \begin_layout Plain Layout
22783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22786 \begin_layout Plain Layout
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22797 \begin_layout Plain Layout
22803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22806 \begin_layout Plain Layout
22807 \begin_inset Formula $<$
22817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22820 \begin_layout Plain Layout
22828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22831 \begin_layout Plain Layout
22832 \begin_inset Formula $\le$
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22845 \begin_layout Plain Layout
22853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22856 \begin_layout Plain Layout
22857 \begin_inset Formula $\ll$
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22870 \begin_layout Plain Layout
22878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22881 \begin_layout Plain Layout
22882 \begin_inset Formula $\prec$
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22895 \begin_layout Plain Layout
22903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22906 \begin_layout Plain Layout
22907 \begin_inset Formula $\preceq$
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22920 \begin_layout Plain Layout
22928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22931 \begin_layout Plain Layout
22932 \begin_inset Formula $\subset$
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22945 \begin_layout Plain Layout
22953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22956 \begin_layout Plain Layout
22957 \begin_inset Formula $\subseteq$
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22970 \begin_layout Plain Layout
22978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22981 \begin_layout Plain Layout
22982 \begin_inset Formula $\sqsubseteq$
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $\in$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\vdash$
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\smile$
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23082 \begin_inset Formula $\lhd$
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\unlhd$
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23132 \begin_inset Formula $\gtrless$
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23156 \begin_layout Plain Layout
23157 \begin_inset Formula $\mid$
23167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23182 \begin_inset Formula $\nmid$
23196 \begin_inset space \hfill{}
23200 \begin_inset Tabular
23201 <lyxtabular version="3" rows="17" columns="2">
23203 <column alignment="center" valignment="top" width="0pt">
23204 <column alignment="center" valignment="top" width="0pt">
23206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23218 \begin_layout Plain Layout
23226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23229 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23239 \begin_inset Formula $=$
23249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23252 \begin_layout Plain Layout
23260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23263 \begin_layout Plain Layout
23264 \begin_inset Formula $\not=$
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23277 \begin_layout Plain Layout
23285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23288 \begin_layout Plain Layout
23289 \begin_inset Formula $\equiv$
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23302 \begin_layout Plain Layout
23310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23313 \begin_layout Plain Layout
23314 \begin_inset Formula $\sim$
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23327 \begin_layout Plain Layout
23335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23338 \begin_layout Plain Layout
23339 \begin_inset Formula $\simeq$
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23352 \begin_layout Plain Layout
23360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23363 \begin_layout Plain Layout
23364 \begin_inset Formula $\approx$
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23377 \begin_layout Plain Layout
23385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23388 \begin_layout Plain Layout
23389 \begin_inset Formula $\cong$
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23402 \begin_layout Plain Layout
23410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23413 \begin_layout Plain Layout
23414 \begin_inset Formula $\bowtie$
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $\notin$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\perp$
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\propto$
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\asymp$
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\doteq$
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\circeq$
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\models$
23599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\widehat{=}$
23628 \begin_inset space \hfill{}
23632 \begin_inset Tabular
23633 <lyxtabular version="3" rows="17" columns="2">
23635 <column alignment="center" valignment="top" width="0pt">
23636 <column alignment="center" valignment="top" width="0pt">
23638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23650 \begin_layout Plain Layout
23658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23661 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23671 \begin_inset Formula $>$
23681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23684 \begin_layout Plain Layout
23692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23695 \begin_layout Plain Layout
23696 \begin_inset Formula $\ge$
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23709 \begin_layout Plain Layout
23717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23720 \begin_layout Plain Layout
23721 \begin_inset Formula $\gg$
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23734 \begin_layout Plain Layout
23742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23745 \begin_layout Plain Layout
23746 \begin_inset Formula $\succ$
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23770 \begin_layout Plain Layout
23771 \begin_inset Formula $\succeq$
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23784 \begin_layout Plain Layout
23792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23795 \begin_layout Plain Layout
23796 \begin_inset Formula $\supset$
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23809 \begin_layout Plain Layout
23817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23820 \begin_layout Plain Layout
23821 \begin_inset Formula $\supseteq$
23831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23834 \begin_layout Plain Layout
23842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23845 \begin_layout Plain Layout
23846 \begin_inset Formula $\sqsupseteq$
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23859 \begin_layout Plain Layout
23867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23870 \begin_layout Plain Layout
23871 \begin_inset Formula $\ni$
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23884 \begin_layout Plain Layout
23892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23895 \begin_layout Plain Layout
23896 \begin_inset Formula $\dashv$
23906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23909 \begin_layout Plain Layout
23917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23920 \begin_layout Plain Layout
23921 \begin_inset Formula $\frown$
23931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23934 \begin_layout Plain Layout
23942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23945 \begin_layout Plain Layout
23946 \begin_inset Formula $\rhd$
23956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23959 \begin_layout Plain Layout
23967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23970 \begin_layout Plain Layout
23971 \begin_inset Formula $\unrhd$
23981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23984 \begin_layout Plain Layout
23992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23995 \begin_layout Plain Layout
23996 \begin_inset Formula $\lessgtr$
24006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24009 \begin_layout Plain Layout
24017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24020 \begin_layout Plain Layout
24021 \begin_inset Formula $\parallel$
24031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24042 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24045 \begin_layout Plain Layout
24046 \begin_inset Formula $\nparallel$
24060 \begin_inset space \hfill{}
24066 \begin_layout Standard
24067 \begin_inset VSpace medskip
24082 are bigger than the equal looking operators
24097 \begin_layout Standard
24098 Relations are, in contrary to symbols, always surrounded by space.
24101 \begin_layout Standard
24102 Relations with labels can be created with the command
24112 \begin_layout Plain Layout
24123 \begin_layout Standard
24125 \begin_inset Tabular
24126 <lyxtabular version="3" rows="2" columns="2">
24128 <column alignment="center" valignment="top" width="0">
24129 <column alignment="center" valignment="top" width="0">
24131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24134 \begin_layout Plain Layout
24140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24143 \begin_layout Plain Layout
24145 \begin_inset Note Note
24148 \begin_layout Plain Layout
24155 is only used as spacer.
24167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24170 \begin_layout Plain Layout
24177 \begin_layout Plain Layout
24194 \begin_layout Plain Layout
24204 \begin_inset Formula $\downarrow$
24213 \begin_layout Plain Layout
24226 \begin_layout Plain Layout
24240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24243 \begin_layout Plain Layout
24244 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24260 \begin_layout Section
24264 \begin_layout Subsection
24265 Predefined Functions
24266 \begin_inset CommandInset label
24268 name "sub:Predefined-Functions"
24276 \begin_layout Plain Layout
24277 Functions ! predefined
24285 \begin_layout Standard
24286 In general, variables are set
24290 in mathematical expressions, but not function names, because
24291 \begin_inset Formula $sin$
24294 could be misunderstood as
24295 \begin_inset Formula $s\cdot i\cdot n$
24299 Therefore there are predefined functions, that are additionally a bit separated
24301 They are inserted as commands starting with a backslash before their name.
24304 \begin_layout Standard
24306 \begin_inset Tabular
24307 <lyxtabular version="3" rows="2" columns="4">
24309 <column alignment="center" valignment="top" width="0pt">
24310 <column alignment="center" valignment="top" width="0pt">
24311 <column alignment="center" valignment="top" width="0pt">
24312 <column alignment="center" valignment="top" width="0pt">
24314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24317 \begin_layout Plain Layout
24323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24326 \begin_layout Plain Layout
24332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24335 \begin_layout Plain Layout
24341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24344 \begin_layout Plain Layout
24352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24355 \begin_layout Plain Layout
24361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24364 \begin_layout Plain Layout
24365 \begin_inset Formula $Asin(x)+B$
24373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24387 \begin_layout Plain Layout
24388 \begin_inset Formula $A\sin(x)+B$
24404 \begin_layout Standard
24405 The following functions are predefined:
24408 \begin_layout Standard
24409 \begin_inset VSpace -2mm
24415 \begin_layout Standard
24417 \begin_inset Tabular
24418 <lyxtabular version="3" rows="9" columns="4">
24420 <column alignment="center" valignment="top" width="0pt">
24421 <column alignment="center" valignment="top" width="0pt">
24422 <column alignment="center" valignment="top" width="0pt">
24423 <column alignment="center" valignment="top" width="0pt">
24425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24437 \begin_layout Plain Layout
24443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24446 \begin_layout Plain Layout
24452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24455 \begin_layout Plain Layout
24463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24488 \begin_layout Plain Layout
24496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24499 \begin_layout Plain Layout
24509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24512 \begin_layout Plain Layout
24520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24523 \begin_layout Plain Layout
24531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24534 \begin_layout Plain Layout
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24545 \begin_layout Plain Layout
24555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24558 \begin_layout Plain Layout
24566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24569 \begin_layout Plain Layout
24577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24580 \begin_layout Plain Layout
24588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24591 \begin_layout Plain Layout
24601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24604 \begin_layout Plain Layout
24612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24615 \begin_layout Plain Layout
24623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24626 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24637 \begin_layout Plain Layout
24647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24650 \begin_layout Plain Layout
24658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24661 \begin_layout Plain Layout
24669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24672 \begin_layout Plain Layout
24680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24683 \begin_layout Plain Layout
24693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24696 \begin_layout Plain Layout
24704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24707 \begin_layout Plain Layout
24715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24718 \begin_layout Plain Layout
24726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24729 \begin_layout Plain Layout
24739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24742 \begin_layout Plain Layout
24750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24753 \begin_layout Plain Layout
24761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24764 \begin_layout Plain Layout
24772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24775 \begin_layout Plain Layout
24785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24788 \begin_layout Plain Layout
24796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24799 \begin_layout Plain Layout
24807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24810 \begin_layout Plain Layout
24818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24821 \begin_layout Plain Layout
24837 \begin_layout Standard
24838 They can also be inserted with the math toolbar button
24839 \begin_inset Graphics
24840 filename ../images/math/functions.png
24848 \begin_layout Subsection
24849 Self-defined Functions
24853 \begin_layout Plain Layout
24854 Functions ! self-defined
24862 \begin_layout Standard
24863 To use a function that is not predefined, like for example the sign function
24864 sgn(x), there are two possibilities:
24867 \begin_layout Itemize
24868 Define the function by inserting the following line to the LaTeX-preamble
24872 \begin_layout Plain Layout
24877 DeclareMathOperator
24880 \begin_inset CommandInset ref
24882 reference "sub:Self-defined-Operators"
24892 \begin_inset Newline newline
24896 \begin_inset VSpace -3mm
24900 \begin_inset Newline newline
24907 DeclareMathOperator{
24915 \begin_layout Plain Layout
24920 DeclareMathOperator
24926 \begin_inset Newline newline
24930 \begin_inset VSpace -2mm
24934 \begin_inset Newline newline
24937 Now the new defined function can be called with the command
24946 \begin_layout Itemize
24947 Write the the formula as usual, mark the formula name, in our example the
24952 , and change it to mathematical text.
24953 At last a space is inserted between prefactor and function.
24956 \begin_layout Standard
24957 The result is the same with both methods as with a predefined function
24961 \begin_layout Plain Layout
24962 In LyX self-defined functions are displayed red, predefined ones black.
24970 \begin_layout Standard
24972 \begin_inset Tabular
24973 <lyxtabular version="3" rows="3" columns="2">
24975 <column alignment="center" valignment="top" width="0pt">
24976 <column alignment="center" valignment="top" width="0pt">
24978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24981 \begin_layout Plain Layout
24987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24990 \begin_layout Plain Layout
24998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25001 \begin_layout Plain Layout
25009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25012 \begin_layout Plain Layout
25013 \begin_inset Formula $A\sgn(x)+B$
25023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25026 \begin_layout Plain Layout
25030 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
25038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25041 \begin_layout Plain Layout
25042 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25058 \begin_layout Standard
25059 The first method is more suitable when the self-defined function should
25060 be used several times.
25063 \begin_layout Subsection
25068 \begin_layout Plain Layout
25077 \begin_layout Standard
25078 For limits there are defined besides
25088 \begin_layout Plain Layout
25108 furthermore the following functions:
25111 \begin_layout Standard
25113 \begin_inset Tabular
25114 <lyxtabular version="3" rows="5" columns="2">
25116 <column alignment="center" valignment="top" width="0">
25117 <column alignment="center" valignment="top" width="0">
25119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25122 \begin_layout Plain Layout
25128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25131 \begin_layout Plain Layout
25133 \begin_inset Note Note
25136 \begin_layout Plain Layout
25143 is only used as spacer.
25155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25158 \begin_layout Plain Layout
25166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25169 \begin_layout Plain Layout
25170 \begin_inset Formula $\varliminf$
25180 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25183 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25194 \begin_layout Plain Layout
25195 \begin_inset Formula $\varlimsup$
25205 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25208 \begin_layout Plain Layout
25216 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25219 \begin_layout Plain Layout
25220 \begin_inset Formula $\varprojlim$
25230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25233 \begin_layout Plain Layout
25241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25244 \begin_layout Plain Layout
25245 \begin_inset Formula $\varinjlim$
25249 \begin_inset Formula $\raisebox{-2.5mm}{}$
25265 \begin_layout Standard
25266 \begin_inset VSpace medskip
25269 The limit is created by inserting a subscript.
25270 It is set right beside the function in an inline formula:
25273 \begin_layout Standard
25275 \begin_inset Tabular
25276 <lyxtabular version="3" rows="2" columns="2">
25278 <column alignment="center" valignment="top" width="0pt">
25279 <column alignment="center" valignment="top" width="0pt">
25281 <cell alignment="center" valignment="top" usebox="none">
25284 \begin_layout Plain Layout
25290 <cell alignment="center" valignment="top" usebox="none">
25293 \begin_layout Plain Layout
25294 \begin_inset space \hspace{}
25299 \begin_inset Note Note
25302 \begin_layout Plain Layout
25315 are used here as spacer.
25327 <cell alignment="center" valignment="top" usebox="none">
25330 \begin_layout Plain Layout
25339 \begin_layout Plain Layout
25352 \begin_layout Plain Layout
25366 <cell alignment="center" valignment="top" usebox="none">
25369 \begin_layout Plain Layout
25370 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25386 \begin_layout Standard
25387 In a displayed formula the limit is set below the formula, as usual:
25388 \begin_inset Formula \[
25396 \begin_layout Subsection
25401 \begin_layout Plain Layout
25402 Functions ! modulo-
25410 \begin_layout Standard
25411 The modulo-function is special, because it exists in four variants.
25414 \begin_layout Standard
25415 The variants in a displayed formula:
25416 \begin_inset Formula \begin{align*}
25417 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25418 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25419 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25420 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25421 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25428 \begin_layout Standard
25429 In an inline formula less space is set before the function names for all
25433 \begin_layout Section
25438 \begin_layout Plain Layout
25447 \begin_layout Subsection
25448 Special Characters in Mathematical Text
25451 \begin_layout Standard
25452 The following commands can only be used in mathematical text or in TeX-mode:
25455 \begin_layout Standard
25456 \begin_inset space \hfill{}
25460 \begin_inset Tabular
25461 <lyxtabular version="3" rows="8" columns="2">
25463 <column alignment="block" valignment="top" width="0">
25464 <column alignment="block" valignment="top" width="0">
25466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25469 \begin_layout Plain Layout
25475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25478 \begin_layout Plain Layout
25486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25489 \begin_layout Plain Layout
25497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25500 \begin_layout Plain Layout
25501 \begin_inset Formula $\textrm{œ}$
25511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25514 \begin_layout Plain Layout
25522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25525 \begin_layout Plain Layout
25526 \begin_inset Formula $\textrm{Œ}$
25536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25539 \begin_layout Plain Layout
25547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25550 \begin_layout Plain Layout
25551 \begin_inset Formula $\textrm{æ}$
25561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25564 \begin_layout Plain Layout
25572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25575 \begin_layout Plain Layout
25576 \begin_inset Formula $\textrm{Æ}$
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25600 \begin_layout Plain Layout
25601 \begin_inset Formula $\textrm{\aa}$
25611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25621 \begin_layout Plain Layout
25628 \begin_layout Plain Layout
25649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25652 \begin_layout Plain Layout
25653 \begin_inset Formula $\textrm{Å}$
25663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25666 \begin_layout Plain Layout
25674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25677 \begin_layout Plain Layout
25678 \begin_inset Formula $\textrm{ı}$
25692 \begin_inset space \hfill{}
25696 \begin_inset Tabular
25697 <lyxtabular version="3" rows="8" columns="2">
25699 <column alignment="block" valignment="top" width="0">
25700 <column alignment="center" valignment="top" width="0">
25702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25705 \begin_layout Plain Layout
25707 \begin_inset Note Note
25710 \begin_layout Plain Layout
25717 is used for separation, because otherwise the output will be ¡ and ¿ respective
25728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25731 \begin_layout Plain Layout
25739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25742 \begin_layout Plain Layout
25750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25753 \begin_layout Plain Layout
25754 \begin_inset Formula $\textrm{ø}$
25764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25767 \begin_layout Plain Layout
25775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25778 \begin_layout Plain Layout
25779 \begin_inset Formula $\textrm{Ø}$
25789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25792 \begin_layout Plain Layout
25800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25803 \begin_layout Plain Layout
25804 \begin_inset Formula $\textrm{ł}$
25814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25817 \begin_layout Plain Layout
25825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25828 \begin_layout Plain Layout
25829 \begin_inset Formula $\textrm{Ł}$
25839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25842 \begin_layout Plain Layout
25844 \begin_inset space \hspace{}
25852 \begin_layout Plain Layout
25866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25869 \begin_layout Plain Layout
25870 \begin_inset Formula $\textrm{!`}$
25880 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25883 \begin_layout Plain Layout
25885 \begin_inset space \hspace{}
25893 \begin_layout Plain Layout
25907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25910 \begin_layout Plain Layout
25911 \begin_inset Formula $\textrm{?`}$
25921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25924 \begin_layout Plain Layout
25932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25935 \begin_layout Plain Layout
25936 \begin_inset Formula $\textrm{ȷ}$
25950 \begin_inset space \hfill{}
25956 \begin_layout Standard
25958 \begin_inset Formula $\textrm{\textrm{Å}}$
25962 \begin_inset Formula $\textrm{\textrm{Ø}}$
25965 can also be inserted via the math toolbar button
25966 \begin_inset Graphics
25967 filename ../images/math/digamma.png
25975 \begin_layout Standard
25976 An exception are the commands
25979 \begin_inset space \hspace{}
25988 \begin_inset space \hspace{}
25994 , because they can be inserted in LyX directly to text.
25997 \begin_layout Subsection
25999 \begin_inset CommandInset label
26001 name "sub:Accents-in-Text"
26009 \begin_layout Plain Layout
26018 \begin_layout Standard
26019 With the following commands all letters can be accented.
26020 The commands must be inserted in TeX-mode.
26023 \begin_layout Standard
26024 \begin_inset space \hfill{}
26028 \begin_inset Tabular
26029 <lyxtabular version="3" rows="8" columns="2">
26031 <column alignment="block" valignment="top" width="0">
26032 <column alignment="block" valignment="top" width="0">
26034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26037 \begin_layout Plain Layout
26043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26046 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26057 \begin_layout Plain Layout
26061 \begin_inset Quotes grd
26069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26072 \begin_layout Plain Layout
26076 \begin_layout Plain Layout
26092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26095 \begin_layout Plain Layout
26103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26106 \begin_layout Plain Layout
26110 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26129 \begin_layout Plain Layout
26136 \begin_layout Plain Layout
26150 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26153 \begin_layout Plain Layout
26157 \begin_layout Plain Layout
26173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26176 \begin_layout Plain Layout
26184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26187 \begin_layout Plain Layout
26191 \begin_layout Plain Layout
26207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26210 \begin_layout Plain Layout
26217 \begin_layout Plain Layout
26231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26234 \begin_layout Plain Layout
26238 \begin_layout Plain Layout
26254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26257 \begin_layout Plain Layout
26264 \begin_layout Plain Layout
26278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26281 \begin_layout Plain Layout
26285 \begin_layout Plain Layout
26301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26304 \begin_layout Plain Layout
26311 \begin_layout Plain Layout
26325 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26328 \begin_layout Plain Layout
26332 \begin_layout Plain Layout
26352 \begin_inset space \hfill{}
26356 \begin_inset Tabular
26357 <lyxtabular version="3" rows="8" columns="2">
26359 <column alignment="block" valignment="top" width="0">
26360 <column alignment="center" valignment="top" width="0">
26362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26365 \begin_layout Plain Layout
26371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26374 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26385 \begin_layout Plain Layout
26392 \begin_layout Plain Layout
26406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26409 \begin_layout Plain Layout
26413 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26432 \begin_layout Plain Layout
26440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26443 \begin_layout Plain Layout
26447 \begin_layout Plain Layout
26463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26466 \begin_layout Plain Layout
26473 \begin_layout Plain Layout
26484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26487 \begin_layout Plain Layout
26491 \begin_layout Plain Layout
26507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26510 \begin_layout Plain Layout
26518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26521 \begin_layout Plain Layout
26525 \begin_layout Plain Layout
26541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26544 \begin_layout Plain Layout
26551 \begin_layout Plain Layout
26565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26568 \begin_layout Plain Layout
26572 \begin_layout Plain Layout
26588 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26591 \begin_layout Plain Layout
26598 \begin_layout Plain Layout
26612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26615 \begin_layout Plain Layout
26619 \begin_layout Plain Layout
26635 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26638 \begin_layout Plain Layout
26645 \begin_layout Plain Layout
26659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26662 \begin_layout Plain Layout
26666 \begin_layout Plain Layout
26686 \begin_inset space \hfill{}
26692 \begin_layout Standard
26693 \begin_inset VSpace medskip
26702 also two different characters can be accented.
26711 \begin_layout Plain Layout
26726 \begin_layout Plain Layout
26738 \begin_layout Standard
26751 can in combination with vowels directly be inserted with the keyboard without
26753 The same applies for the tilde
26757 \begin_layout Plain Layout
26758 This only applies for keyboards where the tilde is defined as accent.
26767 in combination with
26782 \begin_layout Standard
26825 , and accents inserted directly with the keyboard are also available in
26827 For the other accents there are special math commands to be used in formulas,
26829 \begin_inset CommandInset ref
26831 reference "sub:Accents-for-one"
26838 \begin_layout Standard
26839 \begin_inset VSpace bigskip
26842 Furthermore, with the command
26852 \begin_layout Plain Layout
26860 all numbers and letters can be set into a circle, quasi accented with a
26861 circle, similar to the the copyright symbol.
26864 \begin_layout Standard
26866 \begin_inset Tabular
26867 <lyxtabular version="3" rows="3" columns="2">
26869 <column alignment="center" valignment="top" width="0">
26870 <column alignment="center" valignment="top" width="0">
26872 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26875 \begin_layout Plain Layout
26881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26884 \begin_layout Plain Layout
26886 \begin_inset Note Note
26889 \begin_layout Plain Layout
26896 is only used as spacer.
26908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26911 \begin_layout Plain Layout
26919 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26926 \begin_layout Plain Layout
26942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26945 \begin_layout Plain Layout
26956 raisebox{-1.5pt}{W}}
26961 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26964 \begin_layout Plain Layout
26965 \begin_inset Formula $\raisebox{4.5mm}{}$
26972 \begin_layout Plain Layout
26990 \begin_inset Formula $\raisebox{-2mm}{}$
27006 \begin_layout Standard
27007 One has to take care that the character fits in the circle.
27018 \begin_layout Plain Layout
27020 \begin_inset CommandInset ref
27022 reference "sub:Font-Sizes"
27031 specifies thereby the size of the circle.
27042 \begin_layout Plain Layout
27044 \begin_inset CommandInset ref
27046 reference "sub:Boxes-without-Frame"
27055 the character can be centered.
27058 \begin_layout Subsection
27063 \begin_layout Plain Layout
27072 \begin_layout Standard
27073 Minuscule numbers are created with the command
27083 \begin_layout Plain Layout
27092 The command can be used in formulas and in TeX-mode.
27093 The command scheme is:
27096 \begin_layout Standard
27101 oldstylenums{number}
27104 \begin_layout Standard
27109 oldstylenums{0123456789
27112 \begin_inset Formula $\oldstylenums{0123456789}$
27118 \begin_layout Subsection
27119 Miscellaneous special Characters
27120 \begin_inset CommandInset label
27122 name "sub:Miscellaneous-special-Characters"
27130 \begin_layout Plain Layout
27131 Special characters ! miscellaneous
27139 \begin_layout Standard
27140 The following characters can only be inserted to formulas by using commands:
27143 \begin_layout Standard
27145 \begin_inset Tabular
27146 <lyxtabular version="3" rows="4" columns="2">
27148 <column alignment="center" valignment="top" width="0">
27149 <column alignment="center" valignment="top" width="0">
27151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27154 \begin_layout Plain Layout
27160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27163 \begin_layout Plain Layout
27171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27174 \begin_layout Plain Layout
27181 \begin_layout Plain Layout
27195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27198 \begin_layout Plain Layout
27199 \begin_inset Formula $\mathcircumflex$
27209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27212 \begin_layout Plain Layout
27220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27223 \begin_layout Plain Layout
27224 \begin_inset Formula $\_$
27234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27237 \begin_layout Plain Layout
27242 \begin_layout Plain Layout
27257 \begin_layout Plain Layout
27270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27273 \begin_layout Plain Layout
27274 \begin_inset Formula $^{\circ}$
27290 \begin_layout Standard
27291 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27292 contains the following line
27296 \begin_layout Plain Layout
27297 More about this is described in
27298 \begin_inset CommandInset ref
27300 reference "sub:Text-Characters-in"
27312 \begin_layout Standard
27317 DeclareInputtext{176}{
27330 \begin_layout Section
27332 \begin_inset CommandInset label
27334 name "sec:Formula-Styles"
27342 \begin_layout Plain Layout
27351 \begin_layout Itemize
27352 There are two different alignment styles:
27356 \begin_layout Description
27357 Centered is the predefined standard
27360 \begin_layout Description
27361 Indented for this the option
27365 must be inserted in the menu
27367 Document\SpecialChar \menuseparator
27373 \begin_inset space ~
27379 \begin_layout Standard
27384 is used, the indentation can be adjusted with the length
27394 \begin_layout Plain Layout
27403 Should the distance be 15
27404 \begin_inset space \thinspace{}
27407 mm, the following command line is inserted in the LaTeX-preamble
27410 \begin_layout Standard
27420 \begin_layout Standard
27421 When no length is specified, the predefined value of 30
27422 \begin_inset space \thinspace{}
27429 \begin_layout Itemize
27430 And two different numbering styles:
27434 \begin_layout Description
27435 Right is the predefined standard
27438 \begin_layout Description
27439 Left for this the option
27443 must be inserted in the menu
27445 Document\SpecialChar \menuseparator
27451 \begin_inset space ~
27458 \begin_layout Standard
27467 can also be used together.
27468 In this case both options are inserted, separated by a comma.
27471 \begin_layout Standard
27472 The chosen styles are used for all displayed formulas of the document.
27473 When both, centered and indented formulas should be created in a document,
27479 The indented formulas are then set in a flalign environment, see
27480 \begin_inset CommandInset ref
27482 reference "sub:Flalign-Environment"
27489 \begin_layout Section
27491 \begin_inset CommandInset label
27493 name "sec:Multiline-Formulas"
27501 \begin_layout Plain Layout
27502 Formula ! multiline
27510 \begin_layout Subsection
27514 \begin_layout Standard
27515 In LyX multiline formulas are created by pressing
27520 arg "newline-insert newline"
27526 This creates either an
27528 eqnarray environment
27530 that is described in
27531 \begin_inset CommandInset ref
27533 reference "sub:Eqnarray-Environment"
27537 or, when the option
27539 Use AMS math package
27541 in the document settings is selected, an
27545 that is described in
27546 \begin_inset CommandInset ref
27548 reference "sub:Standard-align-Environment"
27555 \begin_layout Standard
27556 There are other multiline formula environments that can be created via the
27559 Insert\SpecialChar \menuseparator
27563 These environments are described in the following sections.
27566 \begin_layout Standard
27567 In all multiline formula environments a new line is created by pressing
27571 arg "newline-insert newline"
27575 To add or delete lines, the math toolbar buttons
27576 \begin_inset Graphics
27577 filename ../images/tabular-feature_append-row.png
27583 \begin_inset Graphics
27584 filename ../images/tabular-feature_delete-row.png
27589 , respectively, or the menu
27591 Edit\SpecialChar \menuseparator
27597 \begin_layout Subsubsection
27599 \begin_inset CommandInset label
27601 name "sub:Line-Separation"
27609 \begin_layout Plain Layout
27610 Formula ! multiline ! Line separation
27618 \begin_layout Standard
27619 There is sometimes not enough space in multiline formulas between the lines:
27620 \begin_inset Formula \begin{eqnarray*}
27621 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}\\
27622 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*}
27629 \begin_layout Standard
27630 In LaTeX additional line space is specified as optional argument of the
27632 This is not yet possible in LyX
27636 \begin_layout Plain Layout
27638 \begin_inset CommandInset href
27640 name "LyX-bug #1505"
27641 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27650 , therefore the whole formula must be inserted in TeX-mode.
27651 To add in our example space, the command
27659 is inserted at the end of the first line.
27664 \begin_layout Plain Layout
27671 \begin_layout Plain Layout
27673 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27676 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27683 \begin_layout Plain Layout
27687 left(B^{2}+x_{0}^{2}
27695 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27700 \begin_layout Plain Layout
27712 \begin_layout Standard
27713 \begin_inset VSpace bigskip
27716 To set the the line separation for all lines in a formula, the length
27726 \begin_layout Plain Layout
27736 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27747 \begin_inset space \thinspace{}
27752 \begin_inset space \thinspace{}
27755 mm additional line separation as in the previous example, the command
27758 \begin_layout Standard
27768 \begin_layout Standard
27769 is inserted in TeX-mode before the formula.
27770 This requires that the LaTeX-package
27778 \begin_layout Plain Layout
27783 is part of every LaTeX standard installation.
27792 \begin_layout Plain Layout
27798 was loaded in LaTeX-preamble with the line
27801 \begin_layout Standard
27809 \begin_layout Standard
27814 \begin_layout Plain Layout
27826 \begin_inset Formula \begin{eqnarray*}
27827 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}\\
27828 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*}
27835 \begin_layout Standard
27839 \begin_layout Plain Layout
27850 To get back to the predefined distance,
27856 is set to the value 3
27857 \begin_inset space \thinspace{}
27863 \begin_layout Subsubsection
27865 \begin_inset CommandInset label
27867 name "sub:Column-Separation"
27875 \begin_layout Plain Layout
27876 Formula ! multiline ! Column separation
27884 \begin_layout Standard
27885 Multiline formulas form a matrix.
27886 A formula in the eqnarray environment is for example a matrix with three
27888 By changing the column separation in this environment, the space beside
27889 the relation sign can be changed.
27892 \begin_layout Standard
27893 The column separation is specified with the length
27903 \begin_layout Plain Layout
27912 \begin_inset Newline newline
27915 column separation = 2
27916 \begin_inset space \thinspace{}
27926 \begin_inset Newline newline
27932 \begin_layout Standard
27942 \begin_layout Standard
27943 inserted in TeX-mode, sets for all following formulas a column separation
27945 \begin_inset space \thinspace{}
27949 To get back to the predefined distance,
27956 \begin_inset space \thinspace{}
27962 \begin_layout Standard
27964 \begin_inset space \thinspace{}
27967 cm column separation:
27971 \begin_layout Plain Layout
27983 \begin_inset Formula \begin{eqnarray*}
27985 C & \ne & A\end{eqnarray*}
27989 A formula with the predefined column separation for matrices of 10
27990 \begin_inset space \thinspace{}
27997 \begin_layout Plain Layout
28009 \begin_inset Formula \begin{eqnarray*}
28011 C & \ne & A\end{eqnarray*}
28018 \begin_layout Subsubsection
28023 \begin_layout Plain Layout
28032 \begin_layout Standard
28033 Long formulas can be typeset using these methods:
28036 \begin_layout Itemize
28037 When one side of the equation is much shorther than the line width, this
28038 one is chosen for the left side and the right side is typeset over two
28043 \begin_layout Plain Layout
28053 \begin_inset Formula \begin{eqnarray}
28054 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 \\
28055 & & -\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}
28063 \begin_layout Plain Layout
28073 \begin_inset Newline newline
28076 The minus sign at the beginning of the second line does normally not appear
28077 as operator because it is the first character of the line.
28078 Thus it would not be surrounded by space and could not be distinguished
28079 from the fraction bar.
28080 To avoid this, space was inserted behind the minus sign with the command
28091 \begin_layout Plain Layout
28099 \begin_inset CommandInset ref
28101 reference "sub:Variable-Space"
28114 \begin_layout Plain Layout
28125 \begin_layout Itemize
28126 When both sides of the equation are too long, the command
28136 \begin_layout Plain Layout
28145 It is inserted to the first column of the first line and effects that all
28146 further insertions overwrite the following columns:
28150 \begin_layout Plain Layout
28160 \begin_inset Formula \begin{eqnarray}
28161 \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 \\
28162 & & -\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 \\
28163 & & =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}
28171 \begin_layout Plain Layout
28181 \begin_inset Newline newline
28184 After the insertion of
28190 , the cursor is in a purple box that is a bit shifted to the left from the
28192 In this the formula is inserted.
28196 \begin_layout Plain Layout
28206 \begin_inset Newline newline
28209 The content of the further lines is inserted to the second or another formula
28211 The greater the column number where it was inserted, the larger the indentation.
28215 \begin_layout Plain Layout
28225 \begin_inset Newline newline
28229 \begin_inset Note Greyedout
28232 \begin_layout Plain Layout
28233 Note the following when using
28242 \begin_layout Itemize
28243 The formula doesn't use the full page width.
28245 \begin_inset space \thinspace{}
28249 \begin_inset space \space{}
28253 \begin_inset Formula $-B^{2}$
28256 is added to the first line in the above example, it would have been outside
28258 To better use the width, negative space can be inserted at the beginning
28262 \begin_layout Itemize
28263 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28268 \begin_layout Plain Layout
28269 \begin_inset CommandInset href
28271 name "LyX-bug #1429"
28272 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28281 One can only set the cursor at the beginning of the line and move it with
28290 \begin_layout Itemize
28291 Other methods to set long formulas are offered by the environments described
28293 \begin_inset CommandInset ref
28295 reference "sub:Multline-Environment"
28300 \begin_inset CommandInset ref
28302 reference "sub:Multiline-Formula-Parts"
28309 \begin_layout Subsubsection
28311 \begin_inset CommandInset label
28313 name "sub:Multiline-Brackets"
28321 \begin_layout Plain Layout
28322 Brackets ! for multiline expressions
28330 \begin_layout Standard
28331 For brackets spanning multiple lines the following problem occurs:
28332 \begin_inset Formula \begin{eqnarray*}
28333 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28334 & & \left.\cdots+B-D\right]\end{eqnarray*}
28341 \begin_layout Standard
28342 The closing bracket is smaller than the opening bracket because brackets
28343 with variable size may not span multiple lines.
28346 \begin_layout Standard
28347 To set the bracket size for the second line correctly, the first line is
28358 \begin_layout Plain Layout
28366 and the second line with
28374 \begin_layout Plain Layout
28388 \begin_inset CommandInset ref
28390 reference "sub:Automatic-Bracket-Size"
28405 \begin_layout Plain Layout
28431 \begin_layout Plain Layout
28450 \begin_layout Plain Layout
28469 \begin_layout Plain Layout
28481 \begin_inset Formula $\downarrow$
28490 \begin_layout Plain Layout
28498 is inserted, because the multiplication operator with its limits is the
28499 largest symbol in the first line and this should be the size for the bracket
28500 in the second line.
28503 \begin_layout Standard
28504 The result is this:
28505 \begin_inset Formula \begin{eqnarray*}
28506 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28507 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28514 \begin_layout Subsection
28518 \begin_layout Standard
28519 Align environments can be used for every kind of multiline formulas.
28520 They are specially useful to set several formulas side by side.
28523 \begin_layout Standard
28524 Align environments consist of columns.
28525 The odd columns are right aligned, the even ones left aligned.
28526 Every line in an Align environment can be numbered.
28529 \begin_layout Standard
28530 Align environments are created via the menu
28532 Insert\SpecialChar \menuseparator
28538 Edit\SpecialChar \menuseparator
28539 Math\SpecialChar \menuseparator
28540 Change Formula Type
28542 already existing formulas can be converted to Align environments.
28545 \begin_layout Standard
28546 To add or delete columns, the math toolbar buttons
28547 \begin_inset Graphics
28548 filename ../images/tabular-feature_append-column.png
28554 \begin_inset Graphics
28555 filename ../images/tabular-feature_delete-column.png
28560 , respectively, or the menu
28562 Edit\SpecialChar \menuseparator
28568 \begin_layout Subsubsection
28569 Standard align Environment
28570 \begin_inset CommandInset label
28572 name "sub:Standard-align-Environment"
28580 \begin_layout Plain Layout
28581 Formula ! multiline ! align environment
28589 \begin_layout Standard
28590 This Align environment is created by presssing
28593 arg "newline-insert newline"
28596 in a formula or by the menu
28598 Insert\SpecialChar \menuseparator
28599 Math\SpecialChar \menuseparator
28600 AMS align Environment
28605 \begin_layout Standard
28606 An example for two formulas set side by side, that are created with a four
28607 column align environment:
28608 \begin_inset Formula \begin{align*}
28609 A & =\sin(B) & C & =D\\
28610 C & \ne A & B & \ne D\end{align*}
28614 As it can be seen, the formulas in this environment are placed so as if
28623 \begin_layout Plain Layout
28631 \begin_inset CommandInset ref
28633 reference "sub:Variable-Space"
28644 before the first and after every even column.
28645 When the formula style
28651 \begin_layout Plain Layout
28653 \begin_inset CommandInset ref
28655 reference "sec:Formula-Styles"
28666 is used, the formula is set without the
28672 before the first column.
28675 \begin_layout Subsubsection
28676 Alignat Environment
28680 \begin_layout Plain Layout
28681 Formula ! multiline ! alignat environment
28689 \begin_layout Standard
28690 The alignat environment has no predefined column separation.
28691 It can be inserted manually with the spaces that are described
28692 \begin_inset CommandInset ref
28694 reference "sub:Space"
28701 \begin_layout Standard
28702 The above example in the alignat environment where 1
28703 \begin_inset space \thinspace{}
28706 cm space was inserted at the beginning of the second formula:
28707 \begin_inset Formula \begin{alignat*}{2}
28708 A & =\sin(B) & \hspace{1cm}C & =D\\
28709 C & \ne A & B & \ne D\end{alignat*}
28713 Because the column separation can be set separately for every column, this
28714 environment is especially suitable to set three and more formulas side
28718 \begin_layout Subsubsection
28719 Flalign Environment
28720 \begin_inset CommandInset label
28722 name "sub:Flalign-Environment"
28730 \begin_layout Plain Layout
28731 Formula ! multiline ! flalign environment
28739 \begin_layout Standard
28740 In this environment the first two columns are always set as much as possible
28741 to the left and the last two ones to the right.
28743 \begin_inset Formula \begin{flalign*}
28744 A & =1 & B & =2 & C & =3\\
28745 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28752 \begin_layout Standard
28753 By creating a flalign environment with an odd number of columns where an
28754 empty TeX-brace is inserted to the last column, several formulas in a document
28755 can be set to the left, although the formula style
28760 As example the indented formula
28761 \begin_inset CommandInset ref
28763 reference "eq:VolInt"
28768 \begin_inset Formula \begin{flalign}
28769 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28773 The first two columns contain the formula.
28774 To indent it as with the formula style
28779 \begin_inset space \thinspace{}
28782 pt space was inserted at the beginning of the first column.
28785 \begin_layout Subsection
28786 Eqnarray Environment
28787 \begin_inset CommandInset label
28789 name "sub:Eqnarray-Environment"
28797 \begin_layout Plain Layout
28798 Formula ! multiline ! eqnarray environment
28806 \begin_layout Standard
28807 When this environment has been created, three blue boxes appear.
28808 The content of the first box is right aligned, the content of the last
28810 The content of the middle box appears centered and a bit smaller, because
28811 it is designed to insert there only relation characters.
28812 \begin_inset Formula \begin{eqnarray*}
28813 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28815 A & = & A\end{eqnarray*}
28822 \begin_layout Subsection
28827 \begin_layout Plain Layout
28828 Formula ! multiline ! gather environment
28836 \begin_layout Standard
28837 This environment consists of only one centered column.
28838 Every line can be numbered.
28839 \begin_inset Formula \begin{gather}
28841 X=\textrm{-}1\end{gather}
28848 \begin_layout Subsection
28849 Multline Environment
28850 \begin_inset CommandInset label
28852 name "sub:Multline-Environment"
28860 \begin_layout Plain Layout
28861 Formula ! multiline ! multline environment
28869 \begin_layout Standard
28870 The multline environment consists, like the gather environment, of only
28872 But the first line is left aligned, the last one right aligned.
28873 All other lines are centered.
28874 Therefore this environment is suitable for long formulas.
28876 \begin_inset CommandInset ref
28878 reference "eq:lefteqn"
28882 in the multline environment:
28883 \begin_inset Formula \begin{multline}
28884 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}\\
28885 -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}\\
28886 =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}
28893 \begin_layout Standard
28894 In the output only the last (first) line of a multline environment appears
28895 numbered when the document numbering is right (left).
28899 \begin_layout Plain Layout
28900 numbering styles see
28901 \begin_inset CommandInset ref
28903 reference "sec:Formula-Styles"
28915 \begin_layout Standard
28924 \begin_layout Plain Layout
28942 \begin_layout Plain Layout
28952 a centered line can be right or left aligned, respectively.
28953 The commands are used as follows:
28956 \begin_layout Standard
28961 shoveright{line content}
28967 shoveleft{line content}
28970 \begin_layout Standard
28971 \begin_inset VSpace medskip
28982 \begin_layout Plain Layout
28992 specifies the distance of the first line from the left page margin.
28993 Predefined is the length 0
28994 \begin_inset space \thinspace{}
29000 \begin_layout Standard
29001 As example the above formula where the command
29004 \begin_layout Standard
29014 \begin_layout Standard
29015 was inserted in TeX-mode before:
29019 \begin_layout Plain Layout
29031 \begin_inset Formula \begin{multline}
29032 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}\\
29033 \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}}\\
29034 =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}
29042 \begin_layout Plain Layout
29053 The second line was left aligned using
29062 \begin_layout Subsection
29063 Multiline Formula Parts
29064 \begin_inset CommandInset label
29066 name "sub:Multiline-Formula-Parts"
29074 \begin_layout Plain Layout
29075 Formula ! multiline ! formula parts
29083 \begin_layout Standard
29084 To display only parts of a formula with multiple lines, one of the following
29085 environments are used:
29102 They can be inserted via the menu
29104 Insert\SpecialChar \menuseparator
29107 or by using the commands described in this section.
29110 \begin_layout Standard
29111 The first three have the same properties as the corresponding multiline
29112 formula environments, but it is possible to set further formula parts beside
29115 \begin_inset Formula \[
29116 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29117 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29118 \right\} \textrm{Uncertainty relations}\]
29125 \begin_layout Standard
29126 To get this formula, a displayed formula is created where the command
29134 \begin_layout Plain Layout
29145 A purple box appears around the blue formula box where now columns and
29146 lines can be added.
29147 Outside the multiline environment other formula parts can be set, like
29151 \begin_layout Standard
29152 The aligned environment is also suitable for long formulas whose lines are
29153 horizontally aligned.
29154 Using aligned in a displayed formula has the advantage that the formula
29155 number is vertically centered behind the lines.
29157 \begin_inset CommandInset ref
29159 reference "eq:shortlong"
29163 in the aligned environment:
29164 \begin_inset Formula \begin{equation}
29165 \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}|}\\
29166 & -\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}
29174 \begin_layout Standard
29175 To use the environments
29197 \begin_layout Plain Layout
29215 \begin_layout Plain Layout
29233 \begin_layout Plain Layout
29241 are inserted, respectively.
29242 The split environment has the same properties as the aligned environment
29243 but it can only have two columns.
29246 \begin_layout Subsection
29247 Text in multiline Formulas
29248 \begin_inset CommandInset label
29250 name "sub:Text-in-multiline"
29258 \begin_layout Plain Layout
29268 \begin_layout Plain Layout
29269 Formula ! multiline ! text
29277 \begin_layout Standard
29278 In the Align environments, and the multline and gather environment, text
29279 can be inserted that will appear in a separate line and doesn't affect
29280 the column alignment.
29281 To do this, the command
29289 \begin_layout Plain Layout
29299 is used in the following scheme:
29302 \begin_layout Standard
29310 \begin_layout Standard
29311 The text should not be longer than a line because it cannot be hyphenated.
29312 As LyX doesn't yet support
29318 directly, the text is written as mathematical text.
29325 must hereby be at the beginning of a line and appears in the output above
29327 An example where the text was inserted at the beginning of the second line:
29328 \begin_inset Formula \begin{align}
29329 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29330 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29337 \begin_layout Section
29342 \begin_layout Plain Layout
29352 \begin_layout Plain Layout
29353 Formula ! numbering|see
29357 \begin_layout Plain Layout
29368 \begin_layout Plain Layout
29383 \begin_layout Subsection
29387 \begin_layout Standard
29388 Numbered formulas can be created with the menu
29390 Insert\SpecialChar \menuseparator
29391 Math\SpecialChar \menuseparator
29393 \begin_inset space ~
29401 \begin_inset space ~
29407 Existing formulas can be numbered with the menu
29409 Edit\SpecialChar \menuseparator
29410 Math\SpecialChar \menuseparator
29412 \begin_inset space ~
29420 arg "math-number-toggle"
29424 The formula number is displayed in LyX behind the formula as number sign
29426 The number sign is replaced in the output by the formula number.
29429 \begin_layout Standard
29430 When numbering is turned on in multiline formulas, all lines will be numbered.
29431 But the numbering can be controlled with the menu
29433 Edit\SpecialChar \menuseparator
29434 Math\SpecialChar \menuseparator
29436 \begin_inset space ~
29440 \begin_inset space ~
29444 \begin_inset space ~
29452 arg "math-number-line-toggle"
29458 \begin_layout Standard
29459 Except of inline formulas, all formulas can be numbered with two different
29461 \begin_inset CommandInset ref
29463 reference "sec:Formula-Styles"
29470 \begin_layout Subsection
29475 \begin_layout Plain Layout
29476 Cross-references ! to formulas
29484 \begin_layout Standard
29485 All labeled formulas can be cross-referenced.
29486 A label is added by the menu
29488 Insert\SpecialChar \menuseparator
29491 or the toolbar button
29492 \begin_inset Graphics
29493 filename ../images/label-insert.png
29499 The cursor must hereby be inside a displayed formula.
29500 A dialog pops up displaying the prefix
29505 The label is inserted there behind the prefix.
29506 The predefined prefix means
29507 \begin_inset Quotes eld
29511 \begin_inset Quotes erd
29514 and makes it easier to find labels in large documents because it marks
29515 it as formula label to divide it from e.
29516 \begin_inset space \thinspace{}
29520 \begin_inset space \space{}
29524 To change a label, the menu
29526 Insert\SpecialChar \menuseparator
29532 \begin_layout Standard
29533 The name of the label is displayed in LyX within two parentheses behind
29535 A formula with a label is always numbered.
29538 \begin_layout Standard
29539 Cross-references are inserted via the menu
29541 Insert\SpecialChar \menuseparator
29544 or with the toolbar button
29545 \begin_inset Graphics
29546 filename ../images/dialog-show-new-inset_ref.png
29552 A formula cross-reference appears in the output as formula number.
29553 When in the cross-reference dialog window the format
29557 is chosen, the cross-reference appears in the output as formula number
29559 \begin_inset Newline newline
29562 By right-clicking on a cross-reference in LyX, one jumps to the formula
29563 that is referenced.
29566 \begin_layout Standard
29567 Here are as examples cross-references to formulas of the following subsections:
29568 \begin_inset Note Note
29571 \begin_layout Plain Layout
29572 Note the different cross-reference types.
29580 \begin_layout Standard
29582 \begin_inset CommandInset ref
29589 \begin_inset CommandInset ref
29597 \begin_inset CommandInset ref
29603 ) big Latin letters are used for the numbering in contrary to (
29604 \begin_inset CommandInset ref
29613 \begin_layout Standard
29614 \begin_inset VSpace medskip
29617 When the argument of
29625 \begin_layout Plain Layout
29633 \begin_inset CommandInset ref
29635 reference "sub:User-defined-Numbering"
29646 contains a box like in
29647 \begin_inset CommandInset ref
29649 reference "sub:Paragraph-Boxes"
29653 , the formula cannot be referenced.
29656 \begin_layout Subsection
29661 \begin_layout Plain Layout
29662 Formula numbering ! subnumbering
29670 \begin_layout Standard
29671 With the help of the commands
29675 begin{subequations}
29683 formulas can be subnumbered.
29684 Both commands are inserted in TeX-mode.
29687 \begin_layout Standard
29689 \begin_inset Formula \begin{equation}
29690 A=C-B\label{eq:a}\end{equation}
29698 \begin_layout Plain Layout
29702 addtocounter{equation}{-1}
29711 \begin_layout Plain Layout
29715 begin{subequations}
29721 \begin_inset VSpace -5mm
29725 \begin_inset Formula \begin{equation}
29726 B=C-A\label{eq:b}\end{equation}
29731 \begin_inset Formula \begin{equation}
29732 C=A+B\label{eq:c}\end{equation}
29739 \begin_layout Standard
29743 \begin_layout Plain Layout
29755 \begin_layout Standard
29756 To create the example, the following is done:
29759 \begin_layout Enumerate
29760 first formula is inserted
29763 \begin_layout Enumerate
29768 addtocounter{equation}{-1}
29770 begin{subequations}
29774 \begin_layout Plain Layout
29783 \begin_inset Newline newline
29788 is inserted after the first formula
29791 \begin_layout Enumerate
29792 second formula is inserted
29795 \begin_layout Enumerate
29796 third formula is inserted
29799 \begin_layout Enumerate
29806 is inserted after the third formula
29809 \begin_layout Standard
29810 Every formula between the commands
29822 is subnumbered as a, b,
29823 \begin_inset Newline linebreak
29826 c, \SpecialChar \ldots{}
29827 For multiline formulas every line will be subnumbered.
29828 All subnumbered formulas are treated as
29833 But as every numbered formula increases the counter
29837 by one, the command
29843 is needed to decrease it.
29844 Otherwise the formulas
29845 \begin_inset CommandInset ref
29852 \begin_inset CommandInset ref
29859 \begin_inset CommandInset ref
29865 would be numbered as
29866 \begin_inset CommandInset ref
29873 \begin_inset CommandInset ref
29880 \begin_inset CommandInset ref
29889 \begin_layout Standard
29890 By inserting the commands in TeX-mode, a space is created between the first
29893 \begin_inset space \thinspace{}
29896 mm vertical space is inserted after the command
29900 begin{subequations}
29903 When the formula style
29909 \begin_layout Plain Layout
29911 \begin_inset CommandInset ref
29913 reference "sec:Formula-Styles"
29925 \begin_inset space \thinspace{}
29928 mm space is inserted instead.
29931 \begin_layout Standard
29932 Here is an example for a multiline formula where the numbering was turned
29933 off for the second line:
29937 \begin_layout Plain Layout
29941 begin{subequations}
29947 \begin_inset Formula \begin{eqnarray}
29948 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29949 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29950 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29958 \begin_layout Plain Layout
29970 \begin_layout Subsection
29971 User-defined Numbering
29972 \begin_inset CommandInset label
29974 name "sub:User-defined-Numbering"
29982 \begin_layout Plain Layout
29983 Formula numbering ! user-defined
29991 \begin_layout Standard
29995 \begin_layout Plain Layout
29996 Formula numbering ! self-defined delimiters
30001 With the standard numbering parentheses are set around the formula number.
30002 To replace the parentheses for example by vertical bars, the following
30003 line is added to the LaTeX-preamble:
30006 \begin_layout Standard
30018 \begin_inset Note Note
30021 \begin_layout Plain Layout
30022 This macro is already declared in the LaTeX-preamble for testing.
30023 To activate it, remove the percent sign at the beginning.
30031 \begin_layout Standard
30032 To use other characters, the vertical bars besides the
30036 are replaced by one ore more characters.
30037 To get only the formula number the vertical bars are omitted.
30040 \begin_layout Standard
30041 \begin_inset VSpace bigskip
30044 When there should be an expression of your choice instead of the consecutive
30045 formula number in parentheses behind the formula, the command
30055 \begin_layout Plain Layout
30064 \begin_inset Formula \begin{equation}
30065 A+B=C\tag{something}\label{eq:tag}\end{equation}
30069 In this example the command
30077 \begin_layout Plain Layout
30088 was inserted to the formula.
30091 \begin_layout Standard
30100 \begin_layout Plain Layout
30111 is inserted instead, the star prevents the parentheses around the expression:
30112 \begin_inset Formula \[
30113 A+B=C\tag*{something}\]
30120 \begin_layout Standard
30121 \begin_inset VSpace bigskip
30124 To restart the formula numbering with new document parts or sections, the
30125 following command is used:
30128 \begin_layout Standard
30133 @addtoreset{equation}{part}
30139 \begin_layout Plain Layout
30144 \begin_layout Plain Layout
30155 \begin_layout Plain Layout
30168 \begin_layout Plain Layout
30179 \begin_layout Plain Layout
30192 \begin_inset Newline newline
30196 \begin_inset Newline newline
30203 @addtoreset{equation}{section}
30206 \begin_layout Standard
30207 To be able to use these commands in TeX-mode, the
30208 \begin_inset Quotes eld
30212 \begin_inset Quotes erd
30215 character has to be made
30216 \begin_inset Quotes eld
30220 \begin_inset Quotes erd
30223 for LaTeX using the command
30237 So the command sequence in TeX-mode is:
30240 \begin_layout Standard
30246 \begin_inset Newline newline
30251 @addtoreset{equation}{section}
30252 \begin_inset Newline newline
30260 \begin_layout Standard
30261 In the LaTeX-preamble
30273 can be omitted as they are automatically internally inserted by LyX.
30276 \begin_layout Standard
30291 \begin_layout Plain Layout
30296 is part of the LaTeX-package
30304 \begin_layout Plain Layout
30305 Packages ! carlisle
30310 that is part of every LaTeX standard installation.
30319 \begin_layout Plain Layout
30320 Packages ! remreset
30325 has to be loaded in the LaTeX-preamble with the line
30328 \begin_layout Standard
30333 usepackage{remreset}
30336 \begin_layout Standard
30347 \begin_layout Plain Layout
30352 \begin_layout Plain Layout
30363 \begin_layout Plain Layout
30376 \begin_layout Plain Layout
30387 \begin_layout Plain Layout
30399 can be used with the same scheme as
30408 \begin_layout Standard
30409 \begin_inset VSpace bigskip
30412 Sometimes formulas should be numbered in the following form:
30415 \begin_layout Standard
30418 (section number.formula number)
30421 \begin_layout Standard
30422 The formula number should start with every section with
30423 \begin_inset Quotes eld
30427 \begin_inset Quotes erd
30433 \begin_layout Standard
30434 For this case there is the command
30444 \begin_layout Plain Layout
30452 , which is used with the following scheme:
30455 \begin_layout Standard
30460 numberwithin{counter}{sectioning}
30463 \begin_layout Standard
30464 Counter denotes what kind of numbering is affected, sectioning denotes what
30465 number is before the dot.
30468 \begin_layout Standard
30469 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30472 \begin_layout Standard
30477 numberwithin{equation}{section}
30480 \begin_layout Standard
30481 This is the result:
30485 \begin_layout Plain Layout
30489 numberwithin{equation}{section}
30495 \begin_inset Formula \begin{equation}
30496 A+B=C\end{equation}
30503 \begin_layout Standard
30505 \begin_inset space \thinspace{}
30509 \begin_inset space \space{}
30512 tables so that the number of the part is the sectioning,
30513 \begin_inset Newline newline
30520 numberwithin{table}{part}
30525 \begin_layout Standard
30526 To go back to the standard numbering or to prevent this kind of numbering
30527 when it is defined by the document class, the following command is inserted
30528 as TeX-Code or to the LaTeX-preamble:
30531 \begin_layout Standard
30544 \begin_layout Plain Layout
30558 \begin_layout Plain Layout
30574 \begin_inset Newline newline
30582 \begin_inset Newline newline
30594 \begin_layout Standard
30601 uses internally the command
30607 , described above, that also needs to be reverted.
30611 \begin_layout Plain Layout
30618 \begin_layout Plain Layout
30622 @removefromreset{equation}{section}
30625 \begin_layout Plain Layout
30637 \begin_layout Subsection
30638 Numbering with Roman Numbers and Letters
30642 \begin_layout Plain Layout
30643 Formula numbering ! with letters
30652 \begin_layout Plain Layout
30653 Formula numbering ! with Roman numbers
30661 \begin_layout Standard
30662 Formulas can also be numbered with Roman numbers and Latin letters.
30663 To number for example with small Roman numbers, the command
30666 \begin_layout Standard
30678 \begin_layout Standard
30679 is inserted before the formula in TeX-mode.
30690 \begin_layout Plain Layout
30698 redefines the predefined command
30714 \begin_layout Plain Layout
30721 has the same scheme like the command
30727 that is described in
30728 \begin_inset CommandInset ref
30730 reference "sub:The-Command-newcommand"
30743 is the formula counter.
30750 is used as prefix for a counter, the value of the counter is output as
30752 When a formula is numbered, LaTeX sets internally the command
30758 behind the formula.
30767 \begin_layout Plain Layout
30777 outputs the counter as small Roman number.
30780 \begin_layout Standard
30781 All formulas behind the command
30791 are now numbered Roman.
30792 To switch to numbering with big Roman numbers, the command is inserted
30809 \begin_layout Plain Layout
30821 \begin_inset Quotes eld
30825 \begin_inset Quotes erd
30828 with small Latin letters there is the command
30838 \begin_layout Plain Layout
30846 , for big ones there is the command
30856 \begin_layout Plain Layout
30869 \begin_layout Standard
30870 \begin_inset Note Greyedout
30873 \begin_layout Plain Layout
30878 Only maximal 26 formulas can be numbered with Latin letters in one document.
30886 \begin_layout Standard
30890 \begin_layout Plain Layout
30906 \begin_layout Standard
30907 \begin_inset Formula \begin{equation}
30908 A=\textrm{small roman}\label{eq:rom}\end{equation}
30916 \begin_layout Plain Layout
30930 \begin_inset Formula \begin{equation}
30931 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30939 \begin_layout Plain Layout
30953 \begin_inset Formula \begin{equation}
30954 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30962 \begin_layout Plain Layout
30976 \begin_inset Formula \begin{equation}
30977 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30984 \begin_layout Standard
30985 To switch back to the default numbering, insert the command:
30988 \begin_layout Standard
31001 \begin_layout Plain Layout
31012 \begin_layout Standard
31016 \begin_layout Plain Layout
31030 \begin_inset Formula \begin{equation}
31031 E=\textrm{Arabic}\label{eq:arab}\end{equation}
31038 \begin_layout Standard
31039 \begin_inset VSpace medskip
31042 As you see, formulas are numbered serially independent from the numbering
31044 When then numbering should start with
31045 \begin_inset Quotes eld
31049 \begin_inset Quotes erd
31052 when the style is changed, new equation counters have to be defined.
31053 A description about this can be found in the file
31054 \begin_inset CommandInset href
31056 target "Formula-numbering.lyx"
31063 \begin_layout Section
31064 User-defined Commands
31068 \begin_layout Plain Layout
31069 User-defined commands
31077 \begin_layout Standard
31078 \begin_inset Note Greyedout
31081 \begin_layout Plain Layout
31086 The names of user-defined commands and macros may only consist of Latin
31095 \begin_layout Subsection
31099 \begin_inset CommandInset label
31101 name "sub:The-Command-newcommand"
31109 \begin_layout Plain Layout
31110 User-defined commands !
31121 \begin_layout Plain Layout
31132 \begin_layout Standard
31133 Many LaTeX-commands are too long to be used frequently.
31134 But it is possible to define with the command
31140 new shorter commands.
31143 \begin_layout Standard
31144 The command scheme of
31153 \begin_layout Standard
31158 newcommand{new command name}[number of arguments][optional
31163 \begin_inset Newline newline
31170 \begin_layout Plain Layout
31185 \begin_layout Plain Layout
31192 {command definition}
31195 \begin_layout Standard
31196 \begin_inset Note Greyedout
31199 \begin_layout Plain Layout
31204 Assure that the name of the new command is not already used in your document
31205 or by LaTeX-packages that you use.
31206 When you for example define the command
31218 , you get an error message because
31224 is already defined as command for
31225 \begin_inset Quotes eld
31229 \begin_inset Formula $\le$
31233 \begin_inset Quotes erd
31244 \begin_layout Standard
31245 The number of arguments is an integer in the range 0
31246 \begin_inset space \thinspace{}
31250 \begin_inset space \thinspace{}
31253 9 and specifies how many arguments the new command should have.
31254 With the optional value a value for an optional argument can be predefined.
31255 When this is done, the
31263 rgument of the new command is automatically an optional one.
31266 \begin_layout Standard
31267 Here are some examples:
31270 \begin_layout Itemize
31271 To define the command
31283 , the LaTeX-preamble line is:
31287 \begin_layout Plain Layout
31299 \begin_inset Newline newline
31311 \begin_layout Itemize
31312 To define the command
31324 , the argument (that should be underlined) must be taken into account.
31325 For this the preamble line is:
31329 \begin_layout Plain Layout
31341 \begin_inset Newline newline
31356 \begin_layout Plain Layout
31368 \begin_inset Newline newline
31377 acts as argument placeholder, the
31381 behind it denotes that it is the placeholder for the first argument.
31384 \begin_layout Itemize
31392 \begin_inset space \thinspace{}
31396 \begin_inset space \space{}
31409 \begin_layout Plain Layout
31421 \begin_inset Newline newline
31430 framebox#1#2{$#3$}}
31436 \begin_layout Plain Layout
31448 \begin_inset Newline newline
31453 The two Dollar signs creates the extra formula needed for
31460 \begin_inset CommandInset ref
31462 reference "sub:Boxes-with-Frame"
31469 \begin_layout Itemize
31470 To create a new command for
31476 where the color for the box needn't to be specified, the argument for the
31477 color is defined optional:
31481 \begin_layout Plain Layout
31493 \begin_inset Newline newline
31502 fcolorbox{#2}{#1}{$#3$}}
31508 \begin_layout Plain Layout
31518 \begin_inset Newline newline
31521 When the color is not specified when using
31527 , the predefined color
31534 \begin_layout Standard
31535 A test of the new defined commands:
31538 \begin_layout Standard
31540 \begin_inset Tabular
31541 <lyxtabular version="3" rows="6" columns="2">
31543 <column alignment="center" valignment="top" width="0">
31544 <column alignment="center" valignment="top" width="0">
31546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31549 \begin_layout Plain Layout
31555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31558 \begin_layout Plain Layout
31560 \begin_inset Note Note
31563 \begin_layout Plain Layout
31570 is only used as spacer.
31582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31585 \begin_layout Plain Layout
31592 \begin_layout Plain Layout
31606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31609 \begin_layout Plain Layout
31610 \begin_inset Formula $A\gr B$
31620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31623 \begin_layout Plain Layout
31631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31634 \begin_layout Plain Layout
31635 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31648 \begin_layout Plain Layout
31652 \begin_inset Formula $\to$
31658 \begin_inset Formula $\to$
31669 \begin_layout Plain Layout
31683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31686 \begin_layout Plain Layout
31687 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31700 \begin_layout Plain Layout
31704 \begin_inset Formula $\to$
31715 \begin_layout Plain Layout
31729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31732 \begin_layout Plain Layout
31733 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31746 \begin_layout Plain Layout
31752 \begin_inset Formula $\to$
31763 \begin_layout Plain Layout
31777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31780 \begin_layout Plain Layout
31781 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31797 \begin_layout Subsection
31802 \begin_layout Plain Layout
31803 User-defined commands! Math macros
31812 \begin_layout Plain Layout
31821 \begin_layout Standard
31822 User-defined commands are especially convenient for complex expressions.
31823 When you are for example dealing in a document with quadratic equations,
31824 the same solution type occurs several times.
31825 The general form of a quadratic equation is
31826 \begin_inset Formula \[
31827 0=\lambda^{2}+p\lambda+q\]
31831 The general form of the solution is
31832 \begin_inset Formula \[
31833 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31840 \begin_layout Standard
31841 To define a command for the solution formula where only the three parameters
31843 \begin_inset Formula $\lambda$
31847 \begin_inset Formula $p$
31851 \begin_inset Formula $q$
31854 need to be specified and the index of
31855 \begin_inset Formula $\lambda$
31858 can be given optionally, the LaTeX-preamble line is
31859 \begin_inset Newline newline
31875 \begin_inset Newline newline
31882 \begin_layout Plain Layout
31897 \begin_layout Plain Layout
31908 frac{#3^{2}}{4}-#4}}
31911 \begin_layout Standard
31912 To create with this the solution formula, the command
31913 \begin_inset Newline newline
31923 \begin_inset Formula $\to$
31929 \begin_inset Formula $\to$
31936 is inserted to a formula
31941 \begin_layout Standard
31942 The definition of the new command is unintuitive because one has to know
31943 the schemes of all used LaTeX commands, e.
31944 \begin_inset space \thinspace{}
31948 \begin_inset space \space{}
31951 that a fraction is inserted in LaTeX as
31955 frac{numerator}{denominator}
31958 Furthermore one can easily forget a brace in the definition and cannot
31959 see in LyX what the new command is doing.
31960 To avoid these problems LyX offers the possibility to use math macros instead
31970 \begin_layout Standard
31971 A math macro is created by using the menu
31973 Insert\SpecialChar \menuseparator
31974 Math\SpecialChar \menuseparator
31977 or the toolbar button
31978 \begin_inset Graphics
31979 filename ../images/math-macro_newmacroname_newcommand.png
31985 The math macro toolbar appears together with the following box where the
31987 \begin_inset Newline newline
31991 \begin_inset space \hspace*{\fill}
31995 \begin_inset Graphics
31996 filename clipart/macrobox.png
32003 \begin_inset space \hspace*{\fill}
32007 \begin_inset Newline newline
32011 \begin_inset FormulaMacro
32012 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
32017 newmacroname is the default name of the macro that should be changed to
32018 something sensible.
32019 The wanted formula is inserted in the first blue box.
32020 An argument placeholder is inserted with the command
32027 \begin_inset space \thinspace{}
32031 \begin_inset space \space{}
32040 or by using the macro toolbar button
32041 \begin_inset Graphics
32042 filename ../images/math-macro-add-param.png
32048 Argument placeholders are displayed red.
32049 Maximum 9 arguments are possible.
32050 Optional arguments are created with the toolbar button
32051 \begin_inset Graphics
32052 filename ../images/math-macro-add-optional-param.png
32058 The first non-optional argument can be transformed to an optional one with
32060 \begin_inset Graphics
32061 filename ../images/math-macro-make-optional.png
32067 In the second blue box the appearance of the macro in LyX can be defined.
32068 Normally you want to see it as it is defined, so the box is kept empty.
32069 But when you have created a macro that needs lot of space on the screen,
32070 you can insert in the box for example
32071 \begin_inset Newline newline
32101 \begin_inset Newline newline
32106 For the macro only the arguments with the macro name in front of them will
32107 then be displayed in LyX, leading to a better overview.
32108 The formula appears in the output as defined in the first box.
32109 \begin_inset Newline newline
32112 The appearance of macros in formulas can furthermore be changed for single
32113 macros by setting the cursor in the macro and using the menu
32115 View\SpecialChar \menuseparator
32117 \begin_inset space ~
32121 \begin_inset space ~
32129 \begin_layout Standard
32130 To use a macro, the macro name is inserted as command to a formula, in our
32138 Our macro looks in LyX like this:
32139 \begin_inset Newline newline
32143 \begin_inset space \hspace*{\fill}
32147 \begin_inset Graphics
32148 filename clipart/macrouse.png
32155 \begin_inset space \hspace*{\fill}
32159 \begin_inset Newline newline
32162 Here is our macro example with the arguments
32163 \begin_inset Formula $x$
32167 \begin_inset Formula $\ln(x)$
32171 \begin_inset Formula $B$
32177 \begin_layout Standard
32178 \begin_inset Formula \[
32186 \begin_layout Standard
32187 A math macro is transformed internally to a
32193 command when exporting the document.
32200 command is not placed in the LaTeX-preamble, therefore macros can only
32201 be used in formulas that are in the document below the macro definition
32205 \begin_layout Standard
32206 Math macros can also be directly be created from a
32213 When writing for example the command
32216 \begin_inset Newline newline
32225 xleftarrow[#2]{#1}}
32226 \begin_inset Newline newline
32231 in LyX as normal text, highlighting it completely and using then the shortcut
32236 , the command will be transformed to a math macro.
32237 Using this method you need to be careful that the
32243 command is typed correctly, otherwise you get a faulty macro leading to
32247 \begin_layout Standard
32248 Math macros currently yet have the problem that further formulas in macro
32249 definitions are handled wrongly.
32250 Therefore the example
32257 \begin_inset CommandInset ref
32259 reference "sub:The-Command-newcommand"
32263 cannot be created as macro.
32266 \begin_layout Standard
32267 When the cursor is in a macro definition box, you will see the macro toolbar
32271 \begin_layout Standard
32272 \begin_inset VSpace defskip
32278 \begin_layout Standard
32279 \begin_inset Graphics
32280 filename clipart/MacroToolbar.png
32288 \begin_layout Plain Layout
32297 \begin_layout Standard
32298 \begin_inset VSpace defskip
32304 \begin_layout Standard
32305 The macro toolbar contains from left to right the following buttons:
32308 \begin_layout Standard
32309 \begin_inset VSpace defskip
32315 \begin_layout Standard
32316 \begin_inset Tabular
32317 <lyxtabular version="3" rows="9" columns="2">
32318 <features islongtable="true">
32319 <column alignment="left" valignment="top" width="0">
32320 <column alignment="left" valignment="top" width="85col%">
32321 <row interlinespace="2.5mm">
32322 <cell alignment="center" valignment="top" usebox="none">
32325 \begin_layout Plain Layout
32326 \begin_inset Graphics
32327 filename ../images/math-macro-remove-param.png
32328 BoundingBox 0bp 5bp 20bp 25bp
32329 rotateOrigin center
32338 <cell alignment="center" valignment="top" usebox="none">
32341 \begin_layout Plain Layout
32344 Edit\SpecialChar \menuseparator
32345 Math\SpecialChar \menuseparator
32347 \begin_inset space ~
32350 Definition\SpecialChar \menuseparator
32357 <row interlinespace="2.5mm">
32358 <cell alignment="center" valignment="top" usebox="none">
32361 \begin_layout Plain Layout
32362 \begin_inset Graphics
32363 filename ../images/math-macro-add-param.png
32364 BoundingBox 0bp 5bp 20bp 25bp
32365 rotateOrigin center
32374 <cell alignment="center" valignment="top" usebox="none">
32377 \begin_layout Plain Layout
32380 Edit\SpecialChar \menuseparator
32381 Math\SpecialChar \menuseparator
32383 \begin_inset space ~
32386 Definition\SpecialChar \menuseparator
32387 Append Last Argument
32393 <row interlinespace="2.5mm">
32394 <cell alignment="center" valignment="top" usebox="none">
32397 \begin_layout Plain Layout
32398 \begin_inset Graphics
32399 filename ../images/math-macro-make-optional.png
32400 BoundingBox 0bp 5bp 20bp 25bp
32401 rotateOrigin center
32410 <cell alignment="center" valignment="top" usebox="none">
32413 \begin_layout Plain Layout
32416 Edit\SpecialChar \menuseparator
32417 Math\SpecialChar \menuseparator
32419 \begin_inset space ~
32422 Definition\SpecialChar \menuseparator
32423 Make First Non-Optional into
32424 \begin_inset Newline newline
32431 \begin_layout Plain Layout
32440 Edit\SpecialChar \menuseparator
32441 Math\SpecialChar \menuseparator
32443 \begin_inset space ~
32446 Definition\SpecialChar \menuseparator
32451 \begin_layout Plain Layout
32464 <row interlinespace="2.5mm">
32465 <cell alignment="center" valignment="top" usebox="none">
32468 \begin_layout Plain Layout
32469 \begin_inset Graphics
32470 filename ../images/math-macro-make-nonoptional.png
32471 BoundingBox 0bp 5bp 20bp 25bp
32472 rotateOrigin center
32481 <cell alignment="center" valignment="top" usebox="none">
32484 \begin_layout Plain Layout
32487 Edit\SpecialChar \menuseparator
32488 Math\SpecialChar \menuseparator
32490 \begin_inset space ~
32493 Definition\SpecialChar \menuseparator
32494 Make Last Optional into
32495 \begin_inset Newline newline
32502 \begin_layout Plain Layout
32511 Edit\SpecialChar \menuseparator
32512 Math\SpecialChar \menuseparator
32514 \begin_inset space ~
32517 Definition\SpecialChar \menuseparator
32522 \begin_layout Plain Layout
32529 Non-Optional Argument
32535 <row interlinespace="2.5mm">
32536 <cell alignment="center" valignment="top" usebox="none">
32539 \begin_layout Plain Layout
32540 \begin_inset Graphics
32541 filename ../images/math-macro-remove-optional-param.png
32542 BoundingBox 0bp 5bp 20bp 25bp
32543 rotateOrigin center
32552 <cell alignment="center" valignment="top" usebox="none">
32555 \begin_layout Plain Layout
32558 Edit\SpecialChar \menuseparator
32559 Math\SpecialChar \menuseparator
32561 \begin_inset space ~
32564 Definition\SpecialChar \menuseparator
32565 Remove Optional Argument
32571 <row interlinespace="2.5mm">
32572 <cell alignment="center" valignment="top" usebox="none">
32575 \begin_layout Plain Layout
32576 \begin_inset Graphics
32577 filename ../images/math-macro-add-optional-param.png
32578 BoundingBox 0bp 5bp 20bp 25bp
32579 rotateOrigin center
32588 <cell alignment="center" valignment="top" usebox="none">
32591 \begin_layout Plain Layout
32594 Edit\SpecialChar \menuseparator
32595 Math\SpecialChar \menuseparator
32597 \begin_inset space ~
32600 Definition\SpecialChar \menuseparator
32601 Insert Optional Argument
32607 <row interlinespace="2.5mm">
32608 <cell alignment="center" valignment="top" usebox="none">
32611 \begin_layout Plain Layout
32612 \begin_inset Graphics
32613 filename ../images/math-macro-remove-greedy-param.png
32614 BoundingBox 0bp 5bp 20bp 25bp
32615 rotateOrigin center
32624 <cell alignment="center" valignment="top" usebox="none">
32627 \begin_layout Plain Layout
32630 Edit\SpecialChar \menuseparator
32631 Math\SpecialChar \menuseparator
32633 \begin_inset space ~
32636 Definition\SpecialChar \menuseparator
32637 Remove Last Argument
32638 \begin_inset Newline newline
32645 \begin_layout Plain Layout
32654 Edit\SpecialChar \menuseparator
32655 Math\SpecialChar \menuseparator
32657 \begin_inset space ~
32660 Definition\SpecialChar \menuseparator
32665 \begin_layout Plain Layout
32672 Spitting Out To The Right
32678 <row interlinespace="2.5mm">
32679 <cell alignment="center" valignment="top" usebox="none">
32682 \begin_layout Plain Layout
32683 \begin_inset Graphics
32684 filename ../images/math-macro-append-greedy-param.png
32685 BoundingBox 0bp 5bp 20bp 25bp
32686 rotateOrigin center
32695 <cell alignment="center" valignment="top" usebox="none">
32698 \begin_layout Plain Layout
32701 Edit\SpecialChar \menuseparator
32702 Math\SpecialChar \menuseparator
32704 \begin_inset space ~
32707 Definition\SpecialChar \menuseparator
32709 \begin_inset Newline newline
32716 \begin_layout Plain Layout
32725 Edit\SpecialChar \menuseparator
32726 Math\SpecialChar \menuseparator
32728 \begin_inset space ~
32731 Definition\SpecialChar \menuseparator
32736 \begin_layout Plain Layout
32743 Eating From The Right
32749 <row interlinespace="2.5mm">
32750 <cell alignment="center" valignment="top" usebox="none">
32753 \begin_layout Plain Layout
32754 \begin_inset Graphics
32755 filename ../images/math-macro-add-greedy-optional-param.png
32756 BoundingBox 0bp 5bp 20bp 25bp
32757 rotateOrigin center
32766 <cell alignment="center" valignment="top" usebox="none">
32769 \begin_layout Plain Layout
32772 Edit\SpecialChar \menuseparator
32773 Math\SpecialChar \menuseparator
32775 \begin_inset space ~
32778 Definition\SpecialChar \menuseparator
32779 Append Optional Argument
32780 \begin_inset Newline newline
32787 \begin_layout Plain Layout
32796 Edit\SpecialChar \menuseparator
32797 Math\SpecialChar \menuseparator
32799 \begin_inset space ~
32802 Definition\SpecialChar \menuseparator
32807 \begin_layout Plain Layout
32814 Eating From The Right
32827 \begin_layout Standard
32828 \begin_inset Newpage newpage
32834 \begin_layout Section
32838 \begin_layout Standard
32839 LyX supports two types of commutative diagrams:
32847 that are explained in the following.
32850 \begin_layout Subsection
32855 \begin_layout Plain Layout
32864 \begin_layout Standard
32865 Diagrams of this type visualize relations by vertical and horizontal lines
32867 \begin_inset Formula \[
32868 \begin{CD}A@>>>B@>>>C\\
32870 F@<<<E@<<<D\end{CD}\]
32877 \begin_layout Standard
32878 To get them, the command
32886 \begin_layout Plain Layout
32896 is inserted to a formula.
32897 A blue box appears with two dashed lines where further commands can be
32902 arg "newline-insert newline"
32905 a new line is created.
32906 Horizontal relations are inserted in odd, vertical in even formula lines.
32909 \begin_layout Standard
32910 To create the relations there are the following commands:
32913 \begin_layout Itemize
32918 creates a left arrow,
32929 \begin_layout Itemize
32934 creates an up arrow,
32942 a vertical equal sign
32945 \begin_layout Itemize
32951 is a placeholder for non-existent relations
32954 \begin_layout Standard
32955 All arrows can be labeled as follows:
32958 \begin_layout Itemize
32959 Is text inserted between the first and second < or >, resp., it is placed
32961 When it is inserted between the second and third one, it appears under
32965 \begin_layout Itemize
32966 When text for vertical arrows is inserted between the first and second A
32967 or V, resp., it is placed left beside the arrow.
32968 When it is inserted between the second and third one, it appears right
32970 If the text contains an A or V, these letters must be set into a TeX-brace.
32973 \begin_layout Standard
32974 As example a diagram with all possible relations:
32977 \begin_layout Standard
32978 \begin_inset Formula \[
32979 \begin{CD}A@>j>>B@>>k>C@=F\\
32981 D@<<j<E@>k>>F@=C\end{CD}\]
32988 \begin_layout Standard
32989 The command for this is:
32990 \begin_inset Newline newline
33001 \begin_layout Plain Layout
33010 A@>j>>B@>>k>C@=F Ctrl+Return
33011 \begin_inset Newline newline
33018 \begin_layout Plain Layout
33033 \begin_layout Plain Layout
33046 \begin_layout Plain Layout
33058 \begin_inset Formula $\to$
33064 \begin_inset Newline newline
33071 \begin_layout Plain Layout
33086 \begin_layout Plain Layout
33099 \begin_layout Plain Layout
33109 \begin_layout Subsection
33114 \begin_layout Plain Layout
33115 Diagrams ! xymatrix
33123 \begin_layout Standard
33124 To be able to use xymatrices, the LaTeX-package
33129 A xymatrix is created by inserting the command
33136 Then you are able to add new matrix columns and rows like for normal matrices,
33138 \begin_inset CommandInset ref
33140 reference "sec:Matrices"
33147 \begin_layout Standard
33148 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33150 All possibilities to create commutative diagrams and decorations are explained
33155 that you find in the menu
33157 Help\SpecialChar \menuseparator
33159 \begin_inset space ~
33162 Manuals\SpecialChar \menuseparator
33164 \begin_inset space ~
33172 \begin_layout Standard
33173 \begin_inset Newpage newpage
33179 \begin_layout Section
33184 \begin_layout Plain Layout
33197 \begin_layout Plain Layout
33198 Other useful math tips can be found in
33199 \begin_inset CommandInset citation
33214 \begin_layout Plain Layout
33222 \begin_inset Note Note
33225 \begin_layout Plain Layout
33228 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33231 \begin_layout Plain Layout
33234 texorpdfstring is in section
33235 \begin_inset CommandInset ref
33237 reference "sub:Formulas-in-Section"
33250 \begin_layout Plain Layout
33260 \begin_layout Plain Layout
33265 \begin_layout Plain Layout
33272 Chemical characters
33276 \begin_layout Plain Layout
33291 \begin_layout Subsection
33292 Chemical Symbols and Equations
33293 \begin_inset CommandInset label
33295 name "sub:Chemical-Symbols-and"
33303 \begin_layout Plain Layout
33304 Chemical characters ! Symbols
33313 \begin_layout Plain Layout
33323 \begin_layout Plain Layout
33332 \begin_layout Standard
33333 An example text from chemistry:
33336 \begin_layout Quote
33338 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33341 -ion reacts with two
33342 \begin_inset Formula $\mathrm{Na^{+}}$
33345 -ions to sodium sulfate
33346 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33350 The chemical equation for this is:
33351 \begin_inset Formula \[
33352 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33359 \begin_layout Standard
33360 This chemical equation can directly be created as formula.
33361 To avoid that the symbols appear italic, everything is highlighted and
33362 changed by the shortcut
33368 to the upright font style.
33372 \begin_layout Plain Layout
33378 \begin_inset CommandInset ref
33380 reference "sub:Font-Styles"
33392 \begin_layout Subsection
33397 \begin_layout Plain Layout
33406 \begin_layout Standard
33407 Negative numbers often look ugly in formulas because the minus sign before
33408 the number is set with the same length as the minus operator sign.
33409 When writing the negative number in normal text, the minus sign appears
33413 \begin_layout Standard
33414 Thus, the problem disappears when converting the minus sign to mathematical
33418 \begin_layout Standard
33419 An example to visualize the problem:
33422 \begin_layout Standard
33424 \begin_inset Tabular
33425 <lyxtabular version="3" rows="3" columns="2">
33427 <column alignment="right" valignment="top" width="0">
33428 <column alignment="left" valignment="top" width="0">
33430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33433 \begin_layout Plain Layout
33439 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33442 \begin_layout Plain Layout
33450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33453 \begin_layout Plain Layout
33459 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33462 \begin_layout Plain Layout
33463 \begin_inset Formula $x=-2$
33473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33476 \begin_layout Plain Layout
33482 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33485 \begin_layout Plain Layout
33486 \begin_inset Formula $x=\textrm{-}2$
33502 \begin_layout Subsection
33503 Comma as decimal Separator
33507 \begin_layout Plain Layout
33516 \begin_layout Standard
33517 In LaTeX a comma inside a formula is used, according to the English convention,
33518 as number group separator.
33519 So there will be space added behind all commas in formulas.
33522 \begin_layout Standard
33523 To avoid this, the comma is highlighted and changed to mathematical text
33533 \begin_layout Standard
33534 To use all formula commas in the document as decimal separator, the file
33543 \begin_layout Plain Layout
33548 is part of the LaTeX-package
33556 \begin_layout Plain Layout
33561 \begin_layout Plain Layout
33584 \begin_layout Plain Layout
33590 is loaded with the LaTeX-preamble line
33593 \begin_layout Standard
33601 \begin_layout Subsection
33603 \begin_inset CommandInset label
33605 name "sub:Physical-Vectors"
33613 \begin_layout Plain Layout
33622 \begin_layout Standard
33623 Predefined vectors are offered by the LaTeX-package
33631 \begin_layout Plain Layout
33636 should be part of every LaTeX standard installation.
33645 \begin_layout Plain Layout
33651 that is loaded with the LaTeX-preamble line
33654 \begin_layout Standard
33662 \begin_layout Standard
33666 \begin_layout Plain Layout
33676 \begin_inset Note Note
33679 \begin_layout Plain Layout
33680 The following table will only be displayed when the LaTeX-package
33689 The following commands are defined:
33692 \begin_layout Standard
33694 \begin_inset Tabular
33695 <lyxtabular version="3" rows="4" columns="2">
33697 <column alignment="center" valignment="top" width="0">
33698 <column alignment="center" valignment="top" width="0">
33700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33703 \begin_layout Plain Layout
33709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33712 \begin_layout Plain Layout
33720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33723 \begin_layout Plain Layout
33733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33736 \begin_layout Plain Layout
33737 \begin_inset Formula $\Bra{\psi}$
33747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33750 \begin_layout Plain Layout
33760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33763 \begin_layout Plain Layout
33764 \begin_inset Formula $\Ket{\psi}$
33774 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33777 \begin_layout Plain Layout
33789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33792 \begin_layout Plain Layout
33793 \begin_inset Formula $\Braket{\psi|\phi}$
33809 \begin_layout Standard
33816 assures that all vertical bars are set in the size of the surrounding brackets:
33817 \begin_inset Formula \[
33818 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33826 \begin_layout Plain Layout
33836 \begin_inset Note Note
33839 \begin_layout Plain Layout
33840 The following will be displayed when the LaTeX-package
33852 \begin_layout Standard
33853 You need to install the LaTeX-package
33857 to see the rest of this subsection in the output.
33860 \begin_layout Standard
33864 \begin_layout Plain Layout
33876 \begin_layout Standard
33883 can also be achieved using the command
33889 , that is described in
33890 \begin_inset CommandInset ref
33892 reference "sub:Automatic-Bracket-Size"
33899 \begin_layout Subsection
33900 Self-defined Fractions
33901 \begin_inset CommandInset label
33903 name "sub:Self-defined-Fractions"
33911 \begin_layout Plain Layout
33912 Fractions ! self-defined
33920 \begin_layout Standard
33921 To define custom commands for fractions, the command
33931 \begin_layout Plain Layout
33939 is used in the following scheme:
33942 \begin_layout Standard
33955 bracket}{fraction bar thickness}{style}
33956 \begin_inset Newline newline
33963 \begin_layout Plain Layout
33978 \begin_layout Plain Layout
33985 {numerator}{denominator}
33988 \begin_layout Standard
33989 The style is a number in the range of 0
33990 \begin_inset space \thinspace{}
33994 \begin_inset space \thinspace{}
34000 \begin_layout Standard
34002 \begin_inset Tabular
34003 <lyxtabular version="3" rows="5" columns="2">
34005 <column alignment="center" valignment="top" width="0">
34006 <column alignment="center" valignment="top" width="0">
34008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34011 \begin_layout Plain Layout
34017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34020 \begin_layout Plain Layout
34028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34031 \begin_layout Plain Layout
34037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34040 \begin_layout Plain Layout
34041 display style formula
34048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34051 \begin_layout Plain Layout
34057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34060 \begin_layout Plain Layout
34068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34071 \begin_layout Plain Layout
34077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34080 \begin_layout Plain Layout
34088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34091 \begin_layout Plain Layout
34097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34100 \begin_layout Plain Layout
34114 \begin_layout Standard
34115 When no style is given, the size is adjusted to the surrounding environment
34116 like for the command
34125 \begin_layout Standard
34126 When no fraction bar thickness is given, the predefined value of 0.4
34127 \begin_inset space \thinspace{}
34133 \begin_layout Standard
34134 \begin_inset VSpace medskip
34137 For example, the commands
34150 \begin_inset CommandInset ref
34152 reference "sub:Fractions"
34156 are defined with the commands
34159 \begin_layout Standard
34168 genfrac{}{}{}{0}{#1}{#2}}
34171 \begin_layout Standard
34175 \begin_layout Standard
34184 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34187 \begin_layout Standard
34188 \begin_inset VSpace medskip
34191 To define a fraction where the fraction bar thickness can be given as optional
34192 argument, the following line is inserted to the LaTeX-preamble:
34195 \begin_layout Standard
34204 genfrac{}{}{#1}{}{#2}{#3}}
34207 \begin_layout Standard
34209 \begin_inset Formula \begin{align*}
34210 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34211 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34215 As one can see, the distance of the numerator and the denominator to the
34216 fraction bar is round about three times the bar thickness.
34219 \begin_layout Subsection
34224 \begin_layout Plain Layout
34233 \begin_layout Standard
34234 To cancel formulas or formula parts, the LaTeX-package
34242 \begin_layout Plain Layout
34247 is part of every LaTeX standard installation.
34256 \begin_layout Plain Layout
34262 has to be loaded with the LaTeX-preamble line
34265 \begin_layout Standard
34270 usepackage[samesize]{cancel}
34273 \begin_layout Standard
34274 There are four ways to cancel formulas:
34277 \begin_layout Standard
34279 \begin_inset Tabular
34280 <lyxtabular version="3" rows="5" columns="2">
34282 <column alignment="center" valignment="top" width="0">
34283 <column alignment="center" valignment="top" width="0">
34285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34288 \begin_layout Plain Layout
34294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34297 \begin_layout Plain Layout
34299 \begin_inset Note Note
34302 \begin_layout Plain Layout
34315 are used here as spacer.
34327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34330 \begin_layout Plain Layout
34339 \begin_layout Plain Layout
34353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34356 \begin_layout Plain Layout
34357 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34370 \begin_layout Plain Layout
34379 \begin_layout Plain Layout
34393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34396 \begin_layout Plain Layout
34397 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34410 \begin_layout Plain Layout
34419 \begin_layout Plain Layout
34433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34436 \begin_layout Plain Layout
34437 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34450 \begin_layout Plain Layout
34454 \begin_inset Formula $\to$
34465 \begin_layout Plain Layout
34479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34482 \begin_layout Plain Layout
34483 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34499 \begin_layout Standard
34506 is especially suitable to visualize the reduction of fractions within formulas:
34507 \begin_inset Formula \[
34508 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34515 \begin_layout Subsection
34516 Formulas in Section Headings
34517 \begin_inset CommandInset label
34519 name "sub:Formulas-in-Section"
34527 \begin_layout Plain Layout
34528 Formula ! in section headings
34536 \begin_layout Standard
34537 When formulas are used in section headings, the following has to be taken
34541 \begin_layout Standard
34542 \begin_inset Note Greyedout
34545 \begin_layout Plain Layout
34554 \begin_layout Plain Layout
34555 Packages ! hyperref
34560 support is enabled in the document settings dialog under
34563 \begin_inset space ~
34568 , PDF-bookmarks are created for every section heading in the table of contents.
34569 If a section heading contains formulas, they are incorrectly displayed
34570 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34579 \begin_layout Standard
34580 Both problems can be solved by inserting at the end of the section heading
34581 a short title with the menu
34583 Insert\SpecialChar \menuseparator
34585 \begin_inset space ~
34591 Short titles are used as alternative for multiline section headings to
34592 keep the table of contents clearly arranged.
34593 Only the short title appears in the table of contents and therefore also
34594 in the PDF-bookmark.
34597 \begin_layout Standard
34598 When formulas should be used in the table of contents but
34602 is used, one can use the following command in TeX-mode:
34605 \begin_layout Standard
34610 texorpdfstring{part}{alternative}
34614 \begin_layout Plain Layout
34625 \begin_layout Standard
34626 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34627 This can be characters, formulas, footnotes, but also cross-references.
34628 The alternative is used instead of the part for the bookmark.
34631 \begin_layout Standard
34632 Here are two example headings:
34633 \begin_inset VSpace -3mm
34640 \begin_layout Plain Layout
34652 \begin_layout Subsubsection
34653 Heading without formula in table of contents
34654 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34658 \begin_inset OptArg
34661 \begin_layout Plain Layout
34662 Heading without formula in table of contents
34670 \begin_layout Subsubsection
34671 Heading with formula in table of contents
34675 \begin_layout Plain Layout
34685 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34692 \begin_layout Plain Layout
34702 \begin_layout Standard
34706 \begin_layout Plain Layout
34715 In the first heading a short title was used, in the second one
34724 \begin_layout Standard
34725 To get the same formatting as for the other headings, the complete heading
34734 \begin_layout Plain Layout
34736 \begin_inset CommandInset ref
34738 reference "sub:Bold-Formulas"
34750 \begin_layout Subsection
34751 Formulas in multi-column Text
34755 \begin_layout Plain Layout
34756 Formula ! in multi-column text
34764 \begin_layout Standard
34765 Formulas in multi-column text are often too wide to fit into a column and
34766 thus need to be set over the whole page width.
34767 This is done by using the LaTeX-package
34775 \begin_layout Plain Layout
34780 is part of every LaTeX standard installation.
34789 \begin_layout Plain Layout
34790 Packages ! multicol
34795 , that is loaded with the LaTeX-preamble line
34798 \begin_layout Standard
34803 usepackage{multicol}
34806 \begin_layout Standard
34807 \begin_inset Note Greyedout
34810 \begin_layout Plain Layout
34811 Note herby that the setting
34814 \begin_inset space ~
34821 Document\SpecialChar \menuseparator
34827 \begin_inset space ~
34847 \begin_layout Standard
34848 Before the multi-column text the command
34851 \begin_layout Standard
34856 begin{multicols}{column number}
34859 \begin_layout Standard
34860 is written in TeX-mode.
34861 The column number is a number in the range of 2
34862 \begin_inset space \thinspace{}
34866 \begin_inset space \thinspace{}
34870 Before the formula the multi-column text is ended by inserting the command
34873 \begin_layout Standard
34881 \begin_layout Standard
34885 \begin_layout Standard
34886 Due to the command some space is automatically added before the formula.
34888 \begin_inset space \thinspace{}
34891 mm vertical space is inserted before the formula.
34892 When the formula style
34898 \begin_layout Plain Layout
34900 \begin_inset CommandInset ref
34902 reference "sec:Formula-Styles"
34914 \begin_inset space \thinspace{}
34917 mm space is inserted instead.
34920 \begin_layout Standard
34921 As example a multi-column text with a displayed formula:
34924 \begin_layout Standard
34928 \begin_layout Plain Layout
34932 begin{multicols}{2}
34937 Das Spektrum wird fouriertransformiert.
34938 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34939 , Lösungsmittel) zu trennen.
34940 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34941 nun das Aussehen des Ausgangssignals.
34942 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34943 über alle Phasen integrieren muss.
34945 \begin_inset Formula $S$
34948 unser normiertes Ausgangssignal and
34949 \begin_inset Formula $P$
34952 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34956 \begin_layout Plain Layout
34966 \begin_inset VSpace -6mm
34970 \begin_inset Formula \begin{equation}
34971 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34979 \begin_layout Plain Layout
34983 begin{multicols}{2}
34989 \begin_inset Formula $S_{0}$
34992 das Signal ohne Gradient ist and the Normierungsbedingung
34993 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34997 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34999 \begin_inset Formula $\nicefrac{\pi}{2}$
35003 \begin_inset space \thinspace{}
35006 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
35007 das Signal zusätzlich abschwächt.
35008 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
35010 \begin_inset Formula $T_{2}$
35016 \begin_layout Standard
35020 \begin_layout Plain Layout
35032 \begin_layout Subsection
35033 Formulas with Description of Variables
35037 \begin_layout Plain Layout
35038 Formula ! with description of variables
35046 \begin_layout Standard
35047 To describe variables within a formula, like in formula
35048 \begin_inset CommandInset ref
35050 reference "eq:within"
35059 \begin_inset Formula $n$
35063 \begin_inset space ~
35066 matrix is used with left aligned columns for the
35067 \begin_inset Formula $n$
35074 \begin_layout Plain Layout
35076 \begin_inset CommandInset ref
35078 reference "sec:Matrices"
35087 To set the description in a smaller size, before the matrix e.
35088 \begin_inset space \thinspace{}
35092 \begin_inset space \space{}
35105 \begin_layout Plain Layout
35107 \begin_inset CommandInset ref
35109 reference "sub:Font-Sizes"
35121 \begin_layout Standard
35122 When the formula style
35128 \begin_layout Plain Layout
35130 \begin_inset CommandInset ref
35132 reference "sec:Formula-Styles"
35153 \begin_layout Plain Layout
35160 only works in formulas with the style
35165 \begin_inset CommandInset ref
35167 reference "sub:Variable-Space"
35176 is inserted before and after the matrix to have the same separation of
35177 the matrix from the equation and the side margin.
35180 \begin_layout Standard
35181 When the formula style
35185 is used, the method described in
35186 \begin_inset CommandInset ref
35188 reference "sub:Flalign-Environment"
35192 is used to indent formulas.
35194 \begin_inset CommandInset ref
35196 reference "eq:within"
35200 consists of five columns whereas in the first two columns contain the equation,
35201 the third the matrix, and the last one an empty TeX-brace.
35202 \begin_inset Formula \begin{flalign}
35203 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35204 \rho & \textrm{density}\\
35205 V & \textrm{volume}\\
35206 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35213 \begin_layout Subsection
35214 Upright small Greek Letters
35215 \begin_inset CommandInset label
35217 name "sub:Upright-small-Greek"
35225 \begin_layout Plain Layout
35226 Greek letters ! upright
35234 \begin_layout Standard
35235 Most of the math fonts only provide italic small Greek letters.
35236 But for symbols of elementary particles like pions and neutrinos, upright
35237 Greek letters are needed.
35246 \begin_layout Plain Layout
35251 is part of the LaTeX-package
35259 \begin_layout Plain Layout
35264 \begin_layout Plain Layout
35287 \begin_layout Plain Layout
35293 that is loaded with the LaTeX-preamble line
35296 \begin_layout Standard
35301 usepackage{upgreek}
35304 \begin_layout Standard
35310 \begin_layout Plain Layout
35320 \begin_inset Note Note
35323 \begin_layout Plain Layout
35324 The following table will only be displayed when the LaTeX-package
35333 They are created when the command for a small Greek letters is started
35339 For example the command
35346 \begin_inset Formula $\uptau$
35352 \begin_layout Standard
35353 With these commands reactions of elementary particles can be typeset:
35354 \begin_inset Formula \[
35355 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35362 \begin_layout Standard
35363 The upright letters are more bold and wider than the italic ones.
35364 They should therefore not be used for units like
35365 \begin_inset Quotes eld
35369 \begin_inset Quotes erd
35375 \begin_layout Standard
35379 \begin_layout Plain Layout
35389 \begin_inset Note Note
35392 \begin_layout Plain Layout
35393 The following will be displayed when the LaTeX-package
35405 \begin_layout Standard
35406 You need to install the LaTeX-package
35410 to see the rest of this subsection in the output.
35413 \begin_layout Standard
35417 \begin_layout Plain Layout
35429 \begin_layout Subsection
35430 Text Characters in Formulas
35431 \begin_inset CommandInset label
35433 name "sub:Text-Characters-in"
35441 \begin_layout Plain Layout
35450 \begin_layout Standard
35451 In some cases you might want to insert text characters directly into formulas.
35452 When for example the centered dot · is often used in formulas like
35453 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35456 , one would have to insert the command
35466 \begin_layout Plain Layout
35468 \begin_inset CommandInset ref
35470 reference "sub:Binary-Operators"
35479 all the time, because this character is defined in all encodings as text
35481 But the encoding can be changed by this LaTeX-preamble line:
35484 \begin_layout Standard
35489 Declare Inputtext{183}{
35499 f\SpecialChar \textcompwordmark{}
35503 \begin_layout Standard
35504 The character encoding (menu
35506 Document\SpecialChar \menuseparator
35507 Settings\SpecialChar \menuseparator
35510 ) specifies what character appears when a keyboard key is pressed.
35511 When the key for the character '·' is pressed, internally the command
35518 But this command is not available in a formula so that you would get LaTeX-erro
35520 With the changed encoding the right command is chosen automatically, depending
35521 on if the character was inserted into a formula or not.
35524 \begin_layout Standard
35525 The encoding of several characters is saved in definition files.
35526 Fore example the encoding
35530 is defined in the file
35534 that is in the installation folder of LaTeX.
35535 Encodings should only be changed via the LaTeX-preamble and not in the
35537 Otherwise own documents could not be edited by other LyX users working
35538 on other computers.
35541 \begin_layout Standard
35542 \begin_inset VSpace medskip
35545 Besides the centered dot, in this document the degree sign ° is defined
35546 with the following LaTeX-preamble line so that it can directly be inserted
35550 \begin_layout Standard
35555 DeclareInputtext{176}{
35565 f\SpecialChar \textcompwordmark{}
35569 \begin_layout Standard
35570 \begin_inset Newpage newpage
35576 \begin_layout Section
35582 \begin_layout Plain Layout
35591 \begin_layout Standard
35592 This section is a summary of the most important typographic rules, listed
35597 \begin_layout Plain Layout
35598 This collection was partly taken from the German semi-official dictionary
35600 \begin_inset Quotes eld
35604 \begin_inset Quotes erd
35608 \begin_inset CommandInset citation
35614 that lists some of the ISO rules.
35622 \begin_layout Itemize
35631 \begin_layout Plain Layout
35632 done with font styles, see
35633 \begin_inset CommandInset ref
35635 reference "sub:Font-Styles"
35645 \begin_inset space \thinspace{}
35649 \begin_inset Newline newline
35652 Between the value and the unit is the smallest space, see
35653 \begin_inset CommandInset ref
35655 reference "sub:Predefined-Space"
35660 \begin_inset Newline newline
35663 This convention is automatically fulfilled when the command
35670 When it is entered to a formula, two boxes appear.
35671 In the first one the value is inserted, in the second one the unit, and
35673 \begin_inset Formula $\unit[30]{km/h}$
35677 \begin_inset space \thinspace{}
35687 is not a real LaTeX command but the command
35693 , therefore you cannot use it in TeX code.
35696 \begin_layout Itemize
35697 Percent and perthousand signs are set like physical units:
35698 \begin_inset Newline newline
35702 \begin_inset space \thinspace{}
35708 \begin_layout Itemize
35709 The degree sign follows directly on the value: 15°, but not when it is used
35711 \begin_inset space \thinspace{}
35717 \begin_layout Itemize
35718 In numbers with more than four digits the smallest space is inserted before
35719 every third digit to group them:
35729 \begin_inset space \thinspace{}
35733 \begin_inset space \thinspace{}
35739 \begin_layout Itemize
35740 For dimensions like 120×90×40
35741 \begin_inset space \thinspace{}
35744 cm the multiplication sign
35745 \begin_inset Quotes eld
35749 \begin_inset Quotes erd
35753 It is available via the menu
35755 Insert\SpecialChar \menuseparator
35756 Special Character\SpecialChar \menuseparator
35760 With some keyboard definitions it can also be inserted directly.
35763 \begin_layout Itemize
35764 Functions with names consisting of several letters are set upright to avoid
35766 \begin_inset CommandInset ref
35768 reference "sub:Predefined-Functions"
35775 \begin_layout Itemize
35776 Indices consisting of several letters, are set upright:
35777 \begin_inset Formula $E_{\mathrm{kin}}$
35781 \begin_inset Newline newline
35784 Components of matrices are set italic:
35785 \begin_inset Formula $\hat{H}_{kl}$
35791 \begin_layout Itemize
35792 The differentiation/integration operator 'd', the Euler's number 'e', and
35793 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35797 \begin_layout Standard
35798 \begin_inset Newpage newpage
35804 \begin_layout Section
35809 \begin_layout Plain Layout
35818 \begin_layout Standard
35819 Some characters and symbols can be created with several commands.
35820 Here is a list of the synonym commands:
35823 \begin_layout Standard
35824 \begin_inset VSpace bigskip
35828 \begin_inset space \hfill{}
35832 \begin_inset Tabular
35833 <lyxtabular version="3" rows="12" columns="2">
35835 <column alignment="center" valignment="top" width="0pt">
35836 <column alignment="center" valignment="top" width="0pt">
35838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35841 \begin_layout Plain Layout
35847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35850 \begin_layout Plain Layout
35852 \begin_inset Note Note
35855 \begin_layout Plain Layout
35862 is only used as spacer.
35874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35877 \begin_layout Plain Layout
35885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35888 \begin_layout Plain Layout
35892 \begin_layout Plain Layout
35905 \begin_layout Plain Layout
35919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35922 \begin_layout Plain Layout
35930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35933 \begin_layout Plain Layout
35943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35946 \begin_layout Plain Layout
35954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35957 \begin_layout Plain Layout
35967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35970 \begin_layout Plain Layout
35978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35981 \begin_layout Plain Layout
35989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35992 \begin_layout Plain Layout
36000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36003 \begin_layout Plain Layout
36011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36014 \begin_layout Plain Layout
36022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36025 \begin_layout Plain Layout
36035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36038 \begin_layout Plain Layout
36046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36049 \begin_layout Plain Layout
36059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36062 \begin_layout Plain Layout
36070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36073 \begin_layout Plain Layout
36083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36086 \begin_layout Plain Layout
36094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36097 \begin_layout Plain Layout
36107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36110 \begin_layout Plain Layout
36118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36121 \begin_layout Plain Layout
36129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36132 \begin_layout Plain Layout
36140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36143 \begin_layout Plain Layout
36155 \begin_inset space \hfill{}
36159 \begin_inset Tabular
36160 <lyxtabular version="3" rows="12" columns="2">
36162 <column alignment="center" valignment="top" width="0pt">
36163 <column alignment="center" valignment="top" width="0pt">
36165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36168 \begin_layout Plain Layout
36174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36177 \begin_layout Plain Layout
36185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36188 \begin_layout Plain Layout
36196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36199 \begin_layout Plain Layout
36211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36214 \begin_layout Plain Layout
36222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36225 \begin_layout Plain Layout
36235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36238 \begin_layout Plain Layout
36246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36249 \begin_layout Plain Layout
36259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36262 \begin_layout Plain Layout
36270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36273 \begin_layout Plain Layout
36281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36284 \begin_layout Plain Layout
36292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36295 \begin_layout Plain Layout
36303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36306 \begin_layout Plain Layout
36314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36317 \begin_layout Plain Layout
36327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36330 \begin_layout Plain Layout
36338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36341 \begin_layout Plain Layout
36351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36354 \begin_layout Plain Layout
36362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36365 \begin_layout Plain Layout
36375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36378 \begin_layout Plain Layout
36386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36389 \begin_layout Plain Layout
36399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36402 \begin_layout Plain Layout
36410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36413 \begin_layout Plain Layout
36423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36426 \begin_layout Plain Layout
36434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36437 \begin_layout Plain Layout
36451 \begin_inset space \hfill{}
36457 \begin_layout Standard
36458 \begin_inset Newpage newpage
36464 \begin_layout Bibliography
36465 \begin_inset CommandInset bibitem
36466 LatexCommand bibitem
36478 The LaTeX Companion
36481 Addison Wesley, 2004
36484 \begin_layout Bibliography
36485 \begin_inset CommandInset bibitem
36486 LatexCommand bibitem
36492 \begin_inset CommandInset href
36495 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36499 of LaTeX's math abilities
36502 \begin_layout Bibliography
36503 \begin_inset CommandInset bibitem
36504 LatexCommand bibitem
36509 LaTeX tips and tricks-
36510 \begin_inset CommandInset href
36513 target "http://tug.org/TeXnik/"
36520 \begin_layout Bibliography
36521 \begin_inset CommandInset bibitem
36522 LatexCommand bibitem
36528 \begin_inset CommandInset href
36531 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36539 \begin_layout Plain Layout
36551 \begin_layout Bibliography
36552 \begin_inset CommandInset bibitem
36553 LatexCommand bibitem
36559 \begin_inset CommandInset href
36562 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36566 of all symbols available with LaTeX-packages
36569 \begin_layout Bibliography
36570 \begin_inset CommandInset bibitem
36571 LatexCommand bibitem
36577 \begin_inset CommandInset href
36579 name "Documentation"
36580 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36584 of the LaTeX-package
36592 \begin_layout Plain Layout
36593 Packages ! hyperref
36601 \begin_layout Bibliography
36602 \begin_inset CommandInset bibitem
36603 LatexCommand bibitem
36609 \begin_inset CommandInset href
36612 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36623 \begin_inset CommandInset ref
36625 reference "sub:Operator-Limits"
36633 \begin_layout Plain Layout
36644 \begin_layout Bibliography
36645 \begin_inset CommandInset bibitem
36646 LatexCommand bibitem
36657 Auflage, Duden 2001
36660 \begin_layout Subsubsection*
36661 \begin_inset CommandInset index_print
36662 LatexCommand printindex