1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
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">
1017 <features tabularvalignment="middle">
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">
1525 <features tabularvalignment="middle">
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">
1809 <features tabularvalignment="middle">
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">
2357 <features tabularvalignment="middle">
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">
2753 <features tabularvalignment="middle">
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">
3027 <features tabularvalignment="middle">
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">
3245 <features tabularvalignment="middle">
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">
3469 <features tabularvalignment="middle">
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">
3607 <features tabularvalignment="middle">
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">
4025 <features tabularvalignment="middle">
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">
4445 <features tabularvalignment="middle">
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">
5203 <features tabularvalignment="middle">
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">
5397 <features tabularvalignment="middle">
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">
5785 <features tabularvalignment="middle">
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">
6009 <features tabularvalignment="middle">
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">
6385 <features tabularvalignment="middle">
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">
6640 <features tabularvalignment="middle">
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">
7241 <features tabularvalignment="middle">
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">
7903 <features tabularvalignment="middle">
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">
8112 <features tabularvalignment="middle">
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">
8328 <features tabularvalignment="middle">
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">
8492 <features tabularvalignment="middle">
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">
8721 <features tabularvalignment="middle">
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">
8890 <features tabularvalignment="middle">
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">
9074 <features tabularvalignment="middle">
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">
9363 <features tabularvalignment="middle">
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">
9676 <features tabularvalignment="middle">
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">
9992 <features tabularvalignment="middle">
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">
10401 <features tabularvalignment="middle">
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">
10603 <features tabularvalignment="middle">
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">
10993 <features tabularvalignment="middle">
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">
11248 <features tabularvalignment="middle">
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">
11377 <features tabularvalignment="middle">
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">
11515 <features tabularvalignment="middle">
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">
11635 <features tabularvalignment="middle">
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">
11890 <features tabularvalignment="middle">
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">
12617 <features tabularvalignment="middle">
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">
13188 <features tabularvalignment="middle">
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">
13608 <features tabularvalignment="middle">
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">
14872 <features tabularvalignment="middle">
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 $\int$
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14947 \begin_layout Plain Layout
14948 \begin_inset Formula $\oint$
14958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14961 \begin_layout Plain Layout
14969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14972 \begin_layout Plain Layout
14973 \begin_inset Formula $\ointctrclockwise$
14983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14986 \begin_layout Plain Layout
14994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14997 \begin_layout Plain Layout
14998 \begin_inset Formula $\ointclockwise$
15008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15011 \begin_layout Plain Layout
15019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15022 \begin_layout Plain Layout
15023 \begin_inset Formula $\sqint$
15033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15036 \begin_layout Plain Layout
15044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15047 \begin_layout Plain Layout
15049 \begin_inset Formula $\fint$
15059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15075 \begin_inset Formula $\landupint$
15085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15088 \begin_layout Plain Layout
15096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15099 \begin_layout Plain Layout
15101 \begin_inset Formula $\landdownint$
15111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15114 \begin_layout Plain Layout
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15125 \begin_layout Plain Layout
15126 \begin_inset Formula $\bigcap$
15136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15139 \begin_layout Plain Layout
15147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15150 \begin_layout Plain Layout
15151 \begin_inset Formula $\bigcup$
15165 \begin_inset space \hfill{}
15169 \begin_inset Tabular
15170 <lyxtabular version="3" rows="11" columns="2">
15171 <features tabularvalignment="middle">
15172 <column alignment="center" valignment="top" width="0pt">
15173 <column alignment="center" valignment="top" width="0pt">
15175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15178 \begin_layout Plain Layout
15184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15187 \begin_layout Plain Layout
15195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15205 \begin_layout Plain Layout
15218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15221 \begin_layout Plain Layout
15222 \begin_inset Formula $\sum$
15232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15235 \begin_layout Plain Layout
15242 \begin_layout Plain Layout
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15258 \begin_layout Plain Layout
15259 \begin_inset Formula $\prod$
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15272 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15284 \begin_inset Formula $\coprod$
15294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15297 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15309 \begin_inset Formula $\bigodot$
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15333 \begin_layout Plain Layout
15334 \begin_inset Formula $\bigotimes$
15344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15347 \begin_layout Plain Layout
15355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15358 \begin_layout Plain Layout
15359 \begin_inset Formula $\bigoplus$
15369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15372 \begin_layout Plain Layout
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15383 \begin_layout Plain Layout
15384 \begin_inset Formula $\bigwedge$
15394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15397 \begin_layout Plain Layout
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15408 \begin_layout Plain Layout
15409 \begin_inset Formula $\bigvee$
15419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15422 \begin_layout Plain Layout
15430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15433 \begin_layout Plain Layout
15434 \begin_inset Formula $\bigsqcup$
15444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15447 \begin_layout Plain Layout
15455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15458 \begin_layout Plain Layout
15459 \begin_inset Formula $\biguplus$
15473 \begin_inset space \hfill{}
15479 \begin_layout Standard
15480 All big operators can also be inserted via the math toolbar button
15481 \begin_inset Graphics
15482 filename ../images/math/intop.png
15490 \begin_layout Standard
15491 The operators are called big because they are bigger than the sometimes
15492 equal looking binary operators.
15493 All big operators can have limits as described in the next subsection.
15496 \begin_layout Standard
15497 For all integral operators there is a second version available, ending on
15515 These operators are different from
15522 \begin_inset space \space{}
15525 in the style the operator limits are displayed, see
15526 \begin_inset CommandInset ref
15528 reference "sub:Operator-Limits"
15536 \begin_layout Subsubsection*
15537 Advices for Integrals
15540 \begin_layout Standard
15545 in an integral is an operator, that therefore has to be set upright.
15546 This is done by highlighting the
15550 and using the keyboard shortcut
15560 \begin_layout Plain Layout
15566 \begin_inset CommandInset ref
15568 reference "sub:Font-Styles"
15578 Finally the smallest space is inserted before the
15582 , as this is usual for operators.
15586 \begin_layout Standard
15588 \begin_inset Formula $\int A(x)dx$
15592 \begin_inset Newline newline
15599 \begin_layout Plain Layout
15609 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15615 \begin_layout Standard
15616 For multiple integrals there are the following commands:
15617 \begin_inset VSpace medskip
15623 \begin_layout Standard
15624 \begin_inset space \hfill{}
15628 \begin_inset Tabular
15629 <lyxtabular version="3" rows="4" columns="2">
15630 <features tabularvalignment="middle">
15631 <column alignment="center" valignment="top" width="0">
15632 <column alignment="center" valignment="top" width="0">
15634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15637 \begin_layout Plain Layout
15643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15646 \begin_layout Plain Layout
15648 \begin_inset Note Note
15651 \begin_layout Plain Layout
15658 is only used as spacer.
15670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15673 \begin_layout Plain Layout
15681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15684 \begin_layout Plain Layout
15685 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15698 \begin_layout Plain Layout
15706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15709 \begin_layout Plain Layout
15710 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15723 \begin_layout Plain Layout
15731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15734 \begin_layout Plain Layout
15735 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15749 \begin_inset space \hfill{}
15753 \begin_inset Tabular
15754 <lyxtabular version="3" rows="4" columns="2">
15755 <features tabularvalignment="middle">
15756 <column alignment="center" valignment="top" width="0">
15757 <column alignment="center" valignment="top" width="0">
15759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15762 \begin_layout Plain Layout
15768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15771 \begin_layout Plain Layout
15779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15782 \begin_layout Plain Layout
15790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15793 \begin_layout Plain Layout
15794 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15807 \begin_layout Plain Layout
15815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15818 \begin_layout Plain Layout
15819 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15832 \begin_layout Plain Layout
15840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15843 \begin_layout Plain Layout
15844 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15858 \begin_inset space \hfill{}
15864 \begin_layout Subsection
15866 \begin_inset CommandInset label
15868 name "sub:Operator-Limits"
15876 \begin_layout Plain Layout
15885 \begin_layout Standard
15886 Limits are created by super- and subscripts:
15889 \begin_layout Standard
15891 \begin_inset Tabular
15892 <lyxtabular version="3" rows="2" columns="2">
15893 <features tabularvalignment="middle">
15894 <column alignment="center" valignment="top" width="0pt">
15895 <column alignment="center" valignment="top" width="0pt">
15897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15900 \begin_layout Plain Layout
15906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15909 \begin_layout Plain Layout
15911 \begin_inset Note Note
15914 \begin_layout Plain Layout
15921 is only used as spacer.
15933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15936 \begin_layout Plain Layout
15945 \begin_layout Plain Layout
15955 \begin_inset Formula $\to$
15959 \begin_inset Formula $\to$
15967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15970 \begin_layout Plain Layout
15971 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15987 \begin_layout Standard
15988 Limits of inline formulas are set right beside the operator.
15989 Limits in displayed formulas are set above or below the operator, except
15990 of integral limits.
15993 \begin_layout Standard
15994 To force that the limits are set beside the operator, the cursor is set
15995 directly behind the operator and the limits type is changed with the menu
15998 Edit\SpecialChar \menuseparator
15999 Math\SpecialChar \menuseparator
16018 \begin_layout Standard
16019 The default limits type is this:
16020 \begin_inset Formula \[
16021 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16025 This is how it looks when the limits type was changed to
16032 \begin_inset Formula \[
16033 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16037 For integrals, except those ending with
16053 etc., the limits are by default set beside the operator.
16054 But for multiple integrals the limits are often set below the operator.
16055 In the following example the limits type was therefore set to
16059 and so set below the integrals:
16060 \begin_inset Formula \begin{equation}
16061 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16068 \begin_layout Standard
16069 \begin_inset VSpace medskip
16072 To specify conditions for limits, the commands
16082 \begin_layout Plain Layout
16100 \begin_layout Plain Layout
16109 To create for example this expression
16110 \begin_inset Formula \begin{equation}
16111 \sum_{\begin{subarray}{c}
16113 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16120 \begin_layout Standard
16121 the following has to be done:
16122 \begin_inset Newline newline
16137 \begin_layout Plain Layout
16149 One is now in a blue box under the summation operator and insert there
16158 \begin_layout Plain Layout
16170 The blue box is now within a purple box and now several lines can be written
16172 A new line is created by inserting a line break (
16175 arg "newline-insert newline"
16180 \begin_inset Newline newline
16185 0<k<1000 Ctrl+Return
16186 \begin_inset Newline newline
16191 is typed in, a new box appears below for the new line.
16194 \begin_layout Standard
16195 The alignment of the lines can be changed to left aligned with the
16205 Edit\SpecialChar \menuseparator
16209 To get right alignment,
16217 \begin_layout Plain Layout
16228 is inserted at the beginning of the line.
16231 \begin_layout Standard
16244 with the difference that the lines are always centered.
16247 \begin_layout Standard
16248 \begin_inset VSpace bigskip
16252 \begin_inset CommandInset ref
16254 reference "eq:substack"
16258 there can be too much space beside an operator, because the characters
16259 following the operator are set beside the limits.
16262 \begin_layout Standard
16263 To avoid this, the following macro can be used in the LaTeX-preamble:
16266 \begin_layout Standard
16280 \begin_inset Newline newline
16292 \begin_inset Newline newline
16299 mathclapinternal #1#2{
16303 mathsurround =0pt #1{#2}$}}
16306 \begin_layout Standard
16307 This defines the command
16317 \begin_layout Plain Layout
16325 that sets the width of the limit to 0
16326 \begin_inset space \thinspace{}
16330 The command scheme is
16333 \begin_layout Standard
16341 \begin_layout Standard
16342 where the limit can consist of several conditions.
16345 \begin_layout Standard
16347 \begin_inset CommandInset ref
16349 reference "eq:substack"
16353 , one uses the command
16356 \begin_layout Standard
16369 \begin_layout Plain Layout
16378 0<k<1000 Ctrl+Return
16381 \begin_layout Standard
16382 to create the lower limit.
16383 The summand is now directly behind the summation operator:
16384 \begin_inset Formula \[
16385 \sum_{\mathclap{\substack{0<k<1000\\
16386 \\k\,\in\,\mathbb{N}}
16394 \begin_layout Standard
16395 \begin_inset VSpace bigskip
16398 How to use one limit for several operators is described in
16399 \begin_inset CommandInset ref
16401 reference "sub:Self-defined-Operators"
16408 \begin_layout Standard
16409 \begin_inset Newpage newpage
16415 \begin_layout Subsection
16417 \begin_inset CommandInset label
16419 name "sub:Binary-Operators"
16427 \begin_layout Plain Layout
16436 \begin_layout Standard
16437 Binary operators are surrounded by space when there is a character before
16439 \begin_inset VSpace medskip
16445 \begin_layout Standard
16446 \begin_inset space \hfill{}
16450 \begin_inset Tabular
16451 <lyxtabular version="3" rows="13" columns="2">
16452 <features tabularvalignment="middle">
16453 <column alignment="center" valignment="top" width="0pt">
16454 <column alignment="center" valignment="top" width="0pt">
16456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16459 \begin_layout Plain Layout
16461 \begin_inset Note Note
16464 \begin_layout Plain Layout
16471 is only used as spacer.
16481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16484 \begin_layout Plain Layout
16492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16495 \begin_layout Plain Layout
16501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16504 \begin_layout Plain Layout
16505 \begin_inset Formula $+$
16515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16518 \begin_layout Plain Layout
16524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16527 \begin_layout Plain Layout
16528 \begin_inset Formula $-$
16538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16541 \begin_layout Plain Layout
16549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16552 \begin_layout Plain Layout
16553 \begin_inset Formula $\pm$
16563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16566 \begin_layout Plain Layout
16574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16577 \begin_layout Plain Layout
16578 \begin_inset Formula $\mp$
16588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16591 \begin_layout Plain Layout
16599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16602 \begin_layout Plain Layout
16603 \begin_inset Formula $\cdot$
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16616 \begin_layout Plain Layout
16624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16627 \begin_layout Plain Layout
16628 \begin_inset Formula $\times$
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16641 \begin_layout Plain Layout
16649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16652 \begin_layout Plain Layout
16653 \begin_inset Formula $\div$
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16666 \begin_layout Plain Layout
16670 \begin_layout Plain Layout
16683 \begin_layout Plain Layout
16695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16698 \begin_layout Plain Layout
16699 \begin_inset Formula $*$
16709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16712 \begin_layout Plain Layout
16720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16723 \begin_layout Plain Layout
16724 \begin_inset Formula $\star$
16734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16737 \begin_layout Plain Layout
16745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16748 \begin_layout Plain Layout
16749 \begin_inset Formula $\circ$
16759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16762 \begin_layout Plain Layout
16770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16773 \begin_layout Plain Layout
16774 \begin_inset Formula $\diamond$
16784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16787 \begin_layout Plain Layout
16795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16798 \begin_layout Plain Layout
16799 \begin_inset Formula $\bullet$
16813 \begin_inset space \hfill{}
16817 \begin_inset Tabular
16818 <lyxtabular version="3" rows="13" columns="2">
16819 <features tabularvalignment="middle">
16820 <column alignment="center" valignment="top" width="0pt">
16821 <column alignment="center" valignment="top" width="0pt">
16823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16826 \begin_layout Plain Layout
16832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16835 \begin_layout Plain Layout
16843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16846 \begin_layout Plain Layout
16854 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16857 \begin_layout Plain Layout
16858 \begin_inset Formula $\nabla$
16868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16871 \begin_layout Plain Layout
16879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16882 \begin_layout Plain Layout
16883 \begin_inset Formula $\bigtriangledown$
16893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16896 \begin_layout Plain Layout
16904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16907 \begin_layout Plain Layout
16908 \begin_inset Formula $\bigtriangleup$
16918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16921 \begin_layout Plain Layout
16929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16932 \begin_layout Plain Layout
16933 \begin_inset Formula $\Box$
16943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16946 \begin_layout Plain Layout
16954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16957 \begin_layout Plain Layout
16958 \begin_inset Formula $\cap$
16968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16971 \begin_layout Plain Layout
16979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16982 \begin_layout Plain Layout
16983 \begin_inset Formula $\cup$
16993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16996 \begin_layout Plain Layout
17004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17007 \begin_layout Plain Layout
17008 \begin_inset Formula $\dagger$
17018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17021 \begin_layout Plain Layout
17029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17032 \begin_layout Plain Layout
17033 \begin_inset Formula $\ddagger$
17043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17046 \begin_layout Plain Layout
17054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17057 \begin_layout Plain Layout
17058 \begin_inset Formula $\wr$
17068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17071 \begin_layout Plain Layout
17079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17082 \begin_layout Plain Layout
17083 \begin_inset Formula $\bigcirc$
17093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17096 \begin_layout Plain Layout
17104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17107 \begin_layout Plain Layout
17108 \begin_inset Formula $\wedge$
17118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17121 \begin_layout Plain Layout
17129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17132 \begin_layout Plain Layout
17133 \begin_inset Formula $\vee$
17147 \begin_inset space \hfill{}
17151 \begin_inset Tabular
17152 <lyxtabular version="3" rows="13" columns="2">
17153 <features tabularvalignment="middle">
17154 <column alignment="center" valignment="top" width="0pt">
17155 <column alignment="center" valignment="top" width="0pt">
17157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17160 \begin_layout Plain Layout
17166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17169 \begin_layout Plain Layout
17177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17180 \begin_layout Plain Layout
17188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17191 \begin_layout Plain Layout
17192 \begin_inset Formula $\oplus$
17202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17205 \begin_layout Plain Layout
17213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17216 \begin_layout Plain Layout
17217 \begin_inset Formula $\ominus$
17227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17230 \begin_layout Plain Layout
17238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17241 \begin_layout Plain Layout
17242 \begin_inset Formula $\otimes$
17252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17255 \begin_layout Plain Layout
17263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17266 \begin_layout Plain Layout
17267 \begin_inset Formula $\oslash$
17277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17280 \begin_layout Plain Layout
17288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17291 \begin_layout Plain Layout
17292 \begin_inset Formula $\odot$
17302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17305 \begin_layout Plain Layout
17313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17316 \begin_layout Plain Layout
17317 \begin_inset Formula $\amalg$
17327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17330 \begin_layout Plain Layout
17338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17341 \begin_layout Plain Layout
17342 \begin_inset Formula $\uplus$
17352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17355 \begin_layout Plain Layout
17363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17366 \begin_layout Plain Layout
17367 \begin_inset Formula $\setminus$
17377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17380 \begin_layout Plain Layout
17388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17391 \begin_layout Plain Layout
17392 \begin_inset Formula $\sqcap$
17402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17405 \begin_layout Plain Layout
17413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17416 \begin_layout Plain Layout
17417 \begin_inset Formula $\sqcup$
17427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17430 \begin_layout Plain Layout
17438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17441 \begin_layout Plain Layout
17442 \begin_inset Formula $\triangleleft$
17452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17455 \begin_layout Plain Layout
17463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17466 \begin_layout Plain Layout
17467 \begin_inset Formula $\triangleright$
17481 \begin_inset space \hfill{}
17487 \begin_layout Standard
17488 All binary operators can also be inserted via the math toolbar button
17489 \begin_inset Graphics
17490 filename ../images/math/pm.png
17498 \begin_layout Standard
17499 To typeset the Laplace operator also
17516 \begin_inset Formula $\nabla^{2}$
17519 ) can be used instead of
17528 \begin_layout Standard
17535 Insert\SpecialChar \menuseparator
17547 \begin_layout Subsection
17548 Self-defined Operators
17549 \begin_inset CommandInset label
17551 name "sub:Self-defined-Operators"
17559 \begin_layout Plain Layout
17560 Operators ! self-defined
17568 \begin_layout Standard
17569 With the help of the command
17573 DeclareMathOperator
17579 \begin_layout Plain Layout
17584 DeclareMathOperator
17589 custom operators can be defined in the LaTeX-preamble.
17590 Its command scheme is:
17593 \begin_layout Standard
17598 DeclareMathOperator{new command}{display}
17601 \begin_layout Standard
17602 Display can be characters or symbols that define how the operator looks
17604 To define a big operator a * is set behind the command.
17605 All self-defined big operators can have limits as described in
17606 \begin_inset CommandInset ref
17608 reference "sub:Operator-Limits"
17615 \begin_layout Standard
17616 For example the LaTeX-preamble line
17619 \begin_layout Standard
17624 DeclareMathOperator*{
17631 \begin_layout Standard
17632 defines the command
17638 , that inserts a big operator consisting of the lozenge symbol from
17639 \begin_inset CommandInset ref
17641 reference "sub:Miscellaneous-Symbols"
17646 \begin_inset Formula \[
17647 \Lozenge_{n=1}^{\infty}\]
17651 The command for this formula is:
17662 \begin_inset Formula $\to$
17668 \begin_layout Standard
17669 \begin_inset VSpace bigskip
17672 When self-defined operators are not used several times in the document,
17673 they can also be defined with the commands
17683 \begin_layout Plain Layout
17701 \begin_layout Plain Layout
17709 , which have the following scheme:
17712 \begin_layout Standard
17726 \begin_layout Standard
17733 defines big operators,
17742 \begin_layout Standard
17750 \begin_inset space \thinspace{}
17754 \begin_inset space \space{}
17757 be used to use one limit for several operators:
17760 \begin_layout Standard
17761 \begin_inset Formula \[
17762 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17769 \begin_layout Standard
17770 The command for the formula above is:
17771 \begin_inset Newline newline
17790 \begin_layout Plain Layout
17802 \begin_inset Formula $\to$
17811 \begin_layout Plain Layout
17825 \begin_layout Section
17830 \begin_layout Plain Layout
17839 \begin_layout Subsection
17841 \begin_inset CommandInset label
17843 name "sub:Font-Styles"
17851 \begin_layout Plain Layout
17860 \begin_layout Standard
17861 Latin letters in formulas can be set in one of the following font styles:
17862 \begin_inset VSpace -2mm
17868 \begin_layout Standard
17870 \begin_inset Tabular
17871 <lyxtabular version="3" rows="6" columns="3">
17872 <features tabularvalignment="middle">
17873 <column alignment="center" valignment="top" width="0">
17874 <column alignment="center" valignment="top" width="0">
17875 <column alignment="center" valignment="top" width="0">
17877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17880 \begin_layout Plain Layout
17886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17889 \begin_layout Plain Layout
17895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17898 \begin_layout Plain Layout
17906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17909 \begin_layout Plain Layout
17918 \begin_layout Plain Layout
17934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17937 \begin_layout Plain Layout
17938 \begin_inset Formula $\mathbb{ABC}$
17946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17949 \begin_layout Plain Layout
17962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17965 \begin_layout Plain Layout
17974 \begin_layout Plain Layout
17990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17993 \begin_layout Plain Layout
17994 \begin_inset Formula $\mathbf{AbC}$
18002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18005 \begin_layout Plain Layout
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18021 \begin_layout Plain Layout
18030 \begin_layout Plain Layout
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18049 \begin_layout Plain Layout
18050 \begin_inset Formula $\boldsymbol{AbC}$
18058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18061 \begin_layout Plain Layout
18064 arg "font-boldsymbol"
18074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18077 \begin_layout Plain Layout
18086 \begin_layout Plain Layout
18102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18105 \begin_layout Plain Layout
18106 \begin_inset Formula $\mathcal{ABC}$
18114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18117 \begin_layout Plain Layout
18130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18133 \begin_layout Plain Layout
18142 \begin_layout Plain Layout
18158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18161 \begin_layout Plain Layout
18162 \begin_inset Formula $\mathfrak{AbC}$
18170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18173 \begin_layout Plain Layout
18187 \begin_layout Standard
18189 \begin_inset Tabular
18190 <lyxtabular version="3" rows="5" columns="3">
18191 <features tabularvalignment="middle">
18192 <column alignment="center" valignment="top" width="0">
18193 <column alignment="center" valignment="top" width="0">
18194 <column alignment="center" valignment="top" width="0">
18196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18199 \begin_layout Plain Layout
18205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18208 \begin_layout Plain Layout
18214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18217 \begin_layout Plain Layout
18225 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18228 \begin_layout Plain Layout
18237 \begin_layout Plain Layout
18253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18256 \begin_layout Plain Layout
18257 \begin_inset Formula $\mathit{AbC}$
18265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18268 \begin_layout Plain Layout
18276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18279 \begin_layout Plain Layout
18288 \begin_layout Plain Layout
18304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18307 \begin_layout Plain Layout
18308 \begin_inset Formula $\mathrm{AbC}$
18316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18319 \begin_layout Plain Layout
18332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18335 \begin_layout Plain Layout
18344 \begin_layout Plain Layout
18360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18363 \begin_layout Plain Layout
18364 \begin_inset Formula $\mathsf{AbC}$
18372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18375 \begin_layout Plain Layout
18388 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18391 \begin_layout Plain Layout
18400 \begin_layout Plain Layout
18416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18419 \begin_layout Plain Layout
18420 \begin_inset Formula $\mathtt{AbC}$
18428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18431 \begin_layout Plain Layout
18434 arg "font-typewriter"
18450 \begin_layout Standard
18451 \begin_inset Note Greyedout
18454 \begin_layout Plain Layout
18471 can only be used for big letters.
18479 \begin_layout Standard
18480 Predefined is the style
18489 \begin_layout Standard
18490 The style commands work also for letters in mathematical constructs:
18491 \begin_inset Formula \[
18492 \mathfrak{A=\frac{b}{C}}\]
18499 \begin_layout Standard
18500 Characters in mathematical text don't appear in a math font style but in
18501 the text font style
18508 That their style can't be set correctly via the text style dialog is a
18513 \begin_layout Plain Layout
18514 \begin_inset CommandInset href
18516 name "LyX-bug #4091"
18517 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18529 \begin_layout Standard
18530 Instead of the style commands the dialog
18532 Edit\SpecialChar \menuseparator
18533 Math\SpecialChar \menuseparator
18536 or the toolbar button
18537 \begin_inset Graphics
18538 filename ../images/math/font.png
18546 \begin_layout Subsection
18548 \begin_inset CommandInset label
18550 name "sub:Bold-Formulas"
18558 \begin_layout Plain Layout
18567 \begin_layout Standard
18568 To make a complete formula bold, the command
18574 from the previous subsection cannot be used, because it doesn't work for
18575 small Greek letters.
18576 Furthermore it prints Latin letters always upright, like in the following
18580 \begin_layout Standard
18581 \begin_inset Formula \[
18582 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18589 \begin_layout Standard
18590 To display the formula correctly, the command
18597 \begin_inset Formula \[
18598 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18602 It is also possible to set the formula in a
18604 boldmath environment
18607 This environment is created by inserting the command
18615 \begin_layout Plain Layout
18626 To end the environment, the command
18634 \begin_layout Plain Layout
18644 is inserted in TeX-mode.
18648 \begin_layout Plain Layout
18658 \begin_inset Formula \[
18659 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18667 \begin_layout Plain Layout
18679 \begin_layout Subsection
18684 \begin_layout Plain Layout
18693 \begin_layout Standard
18694 Formulas can be colored like normal text: Highlight a formula or a formula
18700 Here is a formula in magenta:
18701 \begin_inset Formula \[
18702 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18709 \begin_layout Standard
18710 You can also define your own colors as described in
18711 \begin_inset CommandInset ref
18713 reference "sub:Colored-Boxes"
18718 They can be used with the TeX code command
18728 \begin_layout Plain Layout
18739 \begin_layout Standard
18744 textcolor{color}{characters or formula}
18747 \begin_layout Standard
18748 The following example was colored completely dark green and partly red:
18751 \begin_layout Standard
18755 \begin_layout Plain Layout
18759 textcolor{darkgreen}{
18765 \begin_inset Formula \[
18766 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18774 \begin_layout Plain Layout
18784 \begin_layout Standard
18785 Due to a bug in LyX only complete formulas can be colored with self-defined
18790 \begin_layout Plain Layout
18791 \begin_inset CommandInset href
18793 name "LyX-bug #5269"
18794 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18806 \begin_layout Subsection
18808 \begin_inset CommandInset label
18810 name "sub:Font-Sizes"
18818 \begin_layout Plain Layout
18827 \begin_layout Standard
18828 For characters in formulas there are, analog to characters in text, the
18829 following size commands:
18832 \begin_layout Standard
18876 \begin_inset Newline newline
18898 \begin_layout Standard
18899 The size produced by the commands depends on the document font size, that
18900 corresponds with the command
18907 The other commands produce smaller or larger sizes than
18914 The font size can however not exceed a certain value.
18915 Is for example the document font size 12
18916 \begin_inset space \thinspace{}
18925 switches to the same size as
18935 \begin_layout Standard
18936 A size command is inserted in TeX-mode before the formula and sets the size
18937 for all following formula and text characters.
18938 To switch back to the initial size, the command
18944 is inserted behind the formula in TeX-mode.
18947 \begin_layout Standard
18948 Within a formula the size can only be changed for symbols or letters in
18950 To do this, the size command is inserted in mathematical text.
18951 All following characters until the end of the mathematical text or until
18952 another size command will have the selected size.
18954 \begin_inset VSpace -2mm
18960 \begin_layout Standard
18964 \begin_layout Plain Layout
18974 \begin_inset Formula \[
18975 A=\frac{B}{c}\cdot\maltese\]
18980 \begin_inset Formula \[
18981 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18989 \begin_layout Plain Layout
19001 \begin_layout Standard
19002 \begin_inset VSpace medskip
19005 Before both formulas the command
19012 The command for the second formula is:
19013 \begin_inset Newline newline
19024 \begin_layout Plain Layout
19039 \begin_layout Plain Layout
19054 \begin_layout Plain Layout
19069 \begin_layout Plain Layout
19079 \begin_inset Formula $\to$
19083 \begin_inset Formula $\to$
19087 \begin_inset Newline newline
19091 \begin_inset space \hspace*{}
19105 \begin_layout Plain Layout
19120 \begin_layout Plain Layout
19135 \begin_layout Plain Layout
19147 \begin_layout Standard
19148 If a symbol cannot be displayed in different sizes, it will always be displayed
19149 in the default size.
19152 \begin_layout Section
19157 \begin_layout Plain Layout
19166 \begin_layout Standard
19167 All Greek letters can also be inserted via the toolbar button
19168 \begin_inset Graphics
19169 filename ../images/math/alpha.png
19177 \begin_layout Subsection
19182 \begin_layout Plain Layout
19183 Greek letters ! small
19191 \begin_layout Standard
19192 \begin_inset space \hfill{}
19196 \begin_inset Tabular
19197 <lyxtabular version="3" rows="11" columns="2">
19198 <features tabularvalignment="middle">
19199 <column alignment="center" valignment="top" width="0pt">
19200 <column alignment="center" valignment="top" width="0pt">
19202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19205 \begin_layout Plain Layout
19211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19214 \begin_layout Plain Layout
19222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19225 \begin_layout Plain Layout
19233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19236 \begin_layout Plain Layout
19237 \begin_inset Formula $\alpha$
19247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19250 \begin_layout Plain Layout
19258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19261 \begin_layout Plain Layout
19262 \begin_inset Formula $\beta$
19272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19275 \begin_layout Plain Layout
19283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19286 \begin_layout Plain Layout
19287 \begin_inset Formula $\gamma$
19297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19300 \begin_layout Plain Layout
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19311 \begin_layout Plain Layout
19312 \begin_inset Formula $\delta$
19322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19325 \begin_layout Plain Layout
19333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19336 \begin_layout Plain Layout
19337 \begin_inset Formula $\epsilon$
19347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19350 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19362 \begin_inset Formula $\varepsilon$
19372 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19375 \begin_layout Plain Layout
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19386 \begin_layout Plain Layout
19387 \begin_inset Formula $\zeta$
19397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19400 \begin_layout Plain Layout
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19411 \begin_layout Plain Layout
19412 \begin_inset Formula $\eta$
19422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19425 \begin_layout Plain Layout
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19436 \begin_layout Plain Layout
19437 \begin_inset Formula $\theta$
19447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19450 \begin_layout Plain Layout
19458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19461 \begin_layout Plain Layout
19462 \begin_inset Formula $\vartheta$
19476 \begin_inset space \hfill{}
19480 \begin_inset Tabular
19481 <lyxtabular version="3" rows="12" columns="2">
19482 <features tabularvalignment="middle">
19483 <column alignment="center" valignment="top" width="0pt">
19484 <column alignment="center" valignment="top" width="0pt">
19486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19489 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19509 \begin_layout Plain Layout
19517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19520 \begin_layout Plain Layout
19521 \begin_inset Formula $\iota$
19531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19534 \begin_layout Plain Layout
19542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19545 \begin_layout Plain Layout
19546 \begin_inset Formula $\kappa$
19556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19559 \begin_layout Plain Layout
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19570 \begin_layout Plain Layout
19571 \begin_inset Formula $\varkappa$
19581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19584 \begin_layout Plain Layout
19592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19595 \begin_layout Plain Layout
19596 \begin_inset Formula $\lambda$
19606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19609 \begin_layout Plain Layout
19617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19620 \begin_layout Plain Layout
19621 \begin_inset Formula $\mu$
19631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19634 \begin_layout Plain Layout
19642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19645 \begin_layout Plain Layout
19646 \begin_inset Formula $\nu$
19656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19659 \begin_layout Plain Layout
19667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19670 \begin_layout Plain Layout
19671 \begin_inset Formula $\xi$
19681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19684 \begin_layout Plain Layout
19690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19693 \begin_layout Plain Layout
19694 \begin_inset Formula $o$
19704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19707 \begin_layout Plain Layout
19715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19718 \begin_layout Plain Layout
19719 \begin_inset Formula $\pi$
19729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19732 \begin_layout Plain Layout
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19743 \begin_layout Plain Layout
19744 \begin_inset Formula $\varpi$
19754 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19757 \begin_layout Plain Layout
19765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19768 \begin_layout Plain Layout
19769 \begin_inset Formula $\rho$
19783 \begin_inset space \hfill{}
19787 \begin_inset Tabular
19788 <lyxtabular version="3" rows="11" columns="2">
19789 <features tabularvalignment="middle">
19790 <column alignment="center" valignment="top" width="0pt">
19791 <column alignment="center" valignment="top" width="0pt">
19793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19796 \begin_layout Plain Layout
19802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19805 \begin_layout Plain Layout
19813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19816 \begin_layout Plain Layout
19824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19827 \begin_layout Plain Layout
19828 \begin_inset Formula $\varrho$
19838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19841 \begin_layout Plain Layout
19849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19852 \begin_layout Plain Layout
19853 \begin_inset Formula $\sigma$
19863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19866 \begin_layout Plain Layout
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19877 \begin_layout Plain Layout
19878 \begin_inset Formula $\varsigma$
19888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19891 \begin_layout Plain Layout
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19902 \begin_layout Plain Layout
19903 \begin_inset Formula $\tau$
19913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19916 \begin_layout Plain Layout
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19927 \begin_layout Plain Layout
19928 \begin_inset Formula $\upsilon$
19938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19941 \begin_layout Plain Layout
19949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19952 \begin_layout Plain Layout
19953 \begin_inset Formula $\phi$
19963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19966 \begin_layout Plain Layout
19974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19977 \begin_layout Plain Layout
19978 \begin_inset Formula $\varphi$
19988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20002 \begin_layout Plain Layout
20003 \begin_inset Formula $\chi$
20013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20016 \begin_layout Plain Layout
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20027 \begin_layout Plain Layout
20028 \begin_inset Formula $\psi$
20038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20041 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20052 \begin_layout Plain Layout
20053 \begin_inset Formula $\omega$
20067 \begin_inset space \hfill{}
20073 \begin_layout Standard
20074 \begin_inset VSpace medskip
20080 \begin_layout Standard
20081 How to create upright Greek letters is explained in
20082 \begin_inset CommandInset ref
20084 reference "sub:Upright-small-Greek"
20091 \begin_layout Subsection
20096 \begin_layout Plain Layout
20097 Greek letters ! big
20105 \begin_layout Standard
20106 \begin_inset space \hfill{}
20110 \begin_inset Tabular
20111 <lyxtabular version="3" rows="7" columns="2">
20112 <features tabularvalignment="middle">
20113 <column alignment="center" valignment="top" width="0pt">
20114 <column alignment="center" valignment="top" width="0pt">
20116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20119 \begin_layout Plain Layout
20125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20128 \begin_layout Plain Layout
20136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20139 \begin_layout Plain Layout
20147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20150 \begin_layout Plain Layout
20151 \begin_inset Formula $\Gamma$
20161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20164 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20175 \begin_layout Plain Layout
20176 \begin_inset Formula $\Delta$
20186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20189 \begin_layout Plain Layout
20197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20200 \begin_layout Plain Layout
20201 \begin_inset Formula $\Theta$
20211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20214 \begin_layout Plain Layout
20222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20225 \begin_layout Plain Layout
20226 \begin_inset Formula $\Lambda$
20236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20239 \begin_layout Plain Layout
20247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20250 \begin_layout Plain Layout
20251 \begin_inset Formula $\Xi$
20261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20264 \begin_layout Plain Layout
20272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20275 \begin_layout Plain Layout
20276 \begin_inset Formula $\Pi$
20290 \begin_inset space \hfill{}
20294 \begin_inset Tabular
20295 <lyxtabular version="3" rows="6" columns="2">
20296 <features tabularvalignment="middle">
20297 <column alignment="center" valignment="top" width="0pt">
20298 <column alignment="center" valignment="top" width="0pt">
20300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20303 \begin_layout Plain Layout
20309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20312 \begin_layout Plain Layout
20320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20323 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20335 \begin_inset Formula $\Sigma$
20345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20348 \begin_layout Plain Layout
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20359 \begin_layout Plain Layout
20360 \begin_inset Formula $\Upsilon$
20370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20373 \begin_layout Plain Layout
20381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20384 \begin_layout Plain Layout
20385 \begin_inset Formula $\Phi$
20395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20398 \begin_layout Plain Layout
20406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20409 \begin_layout Plain Layout
20410 \begin_inset Formula $\Psi$
20420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20434 \begin_layout Plain Layout
20435 \begin_inset Formula $\Omega$
20449 \begin_inset space \hfill{}
20455 \begin_layout Standard
20456 \begin_inset VSpace medskip
20459 That the big Greek letters appear upright is caused by a design bug when
20461 To get correct italic big letters, begin every command with
20466 For example the command
20473 \begin_inset Formula $\varGamma$
20479 \begin_layout Subsection
20484 \begin_layout Plain Layout
20485 Greek letters ! bold
20493 \begin_layout Standard
20494 Greek letters cannot be set with different font styles like Latin letters.
20495 They can only be made bold with the command
20505 \begin_layout Plain Layout
20516 \begin_layout Standard
20518 \begin_inset Tabular
20519 <lyxtabular version="3" rows="3" columns="2">
20520 <features tabularvalignment="middle">
20521 <column alignment="center" valignment="top" width="0">
20522 <column alignment="center" valignment="top" width="0">
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Plain Layout
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20562 \begin_layout Plain Layout
20563 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20576 \begin_layout Plain Layout
20588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20591 \begin_layout Plain Layout
20592 \begin_inset Formula $\theta\boldsymbol{\theta}$
20608 \begin_layout Section
20613 \begin_layout Plain Layout
20626 \begin_layout Plain Layout
20627 A list with all symbols of most of the LaTeX-packages can be found in
20628 \begin_inset CommandInset citation
20643 \begin_layout Plain Layout
20651 \begin_inset Note Note
20654 \begin_layout Plain Layout
20657 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20660 \begin_layout Plain Layout
20663 texorpdfstring is in section
20664 \begin_inset CommandInset ref
20666 reference "sub:Formulas-in-Section"
20679 \begin_layout Plain Layout
20688 \begin_layout Standard
20689 Many of the symbols listed in this section can also be inserted via the
20691 \begin_inset Graphics
20692 filename ../images/math/nabla.png
20698 \begin_inset Graphics
20699 filename ../images/math/digamma.png
20707 \begin_layout Subsection
20708 Mathematical Symbols
20709 \begin_inset CommandInset label
20711 name "sub:Mathematical-Symbols"
20719 \begin_layout Plain Layout
20720 Symbols ! mathematical
20728 \begin_layout Standard
20729 \begin_inset space \hfill{}
20733 \begin_inset Tabular
20734 <lyxtabular version="3" rows="10" columns="2">
20735 <features tabularvalignment="middle">
20736 <column alignment="center" valignment="top" width="0pt">
20737 <column alignment="center" valignment="top" width="0pt">
20739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20742 \begin_layout Plain Layout
20748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20751 \begin_layout Plain Layout
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20762 \begin_layout Plain Layout
20770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20773 \begin_layout Plain Layout
20774 \begin_inset Formula $\neg$
20784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20787 \begin_layout Plain Layout
20795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20798 \begin_layout Plain Layout
20799 \begin_inset Formula $\Im$
20809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20812 \begin_layout Plain Layout
20820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20823 \begin_layout Plain Layout
20824 \begin_inset Formula $\Re$
20834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20837 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20849 \begin_inset Formula $\aleph$
20859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20862 \begin_layout Plain Layout
20870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20873 \begin_layout Plain Layout
20874 \begin_inset Formula $\partial$
20884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20887 \begin_layout Plain Layout
20895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20898 \begin_layout Plain Layout
20899 \begin_inset Formula $\infty$
20909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20912 \begin_layout Plain Layout
20920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20923 \begin_layout Plain Layout
20924 \begin_inset Formula $\wp$
20934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20937 \begin_layout Plain Layout
20945 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20948 \begin_layout Plain Layout
20949 \begin_inset Formula $\imath$
20959 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20962 \begin_layout Plain Layout
20970 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20973 \begin_layout Plain Layout
20974 \begin_inset Formula $\jmath$
20988 \begin_inset space \hfill{}
20992 \begin_inset Tabular
20993 <lyxtabular version="3" rows="10" columns="2">
20994 <features tabularvalignment="middle">
20995 <column alignment="center" valignment="top" width="0pt">
20996 <column alignment="center" valignment="top" width="0pt">
20998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21001 \begin_layout Plain Layout
21007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21010 \begin_layout Plain Layout
21012 \begin_inset Note Note
21015 \begin_layout Plain Layout
21022 is only used as spacer.
21034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21037 \begin_layout Plain Layout
21045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21048 \begin_layout Plain Layout
21049 \begin_inset Formula $\forall$
21059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21062 \begin_layout Plain Layout
21070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21073 \begin_layout Plain Layout
21074 \begin_inset Formula $\exists$
21084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21087 \begin_layout Plain Layout
21095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21098 \begin_layout Plain Layout
21099 \begin_inset Formula $\nexists$
21109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21112 \begin_layout Plain Layout
21120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21123 \begin_layout Plain Layout
21124 \begin_inset Formula $\emptyset$
21134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21137 \begin_layout Plain Layout
21145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21148 \begin_layout Plain Layout
21149 \begin_inset Formula $\varnothing$
21159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21162 \begin_layout Plain Layout
21170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21173 \begin_layout Plain Layout
21174 \begin_inset Formula $\dag$
21184 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21187 \begin_layout Plain Layout
21195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21198 \begin_layout Plain Layout
21199 \begin_inset Formula $\ddag$
21209 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21212 \begin_layout Plain Layout
21220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21223 \begin_layout Plain Layout
21227 \begin_layout Plain Layout
21237 \begin_inset Formula $\complement$
21244 \begin_layout Plain Layout
21258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21261 \begin_layout Plain Layout
21269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21272 \begin_layout Plain Layout
21273 \begin_inset Formula $\Bbbk$
21287 \begin_inset space \hfill{}
21291 \begin_inset Tabular
21292 <lyxtabular version="3" rows="10" columns="2">
21293 <features tabularvalignment="middle">
21294 <column alignment="center" valignment="top" width="0pt">
21295 <column alignment="center" valignment="top" width="0pt">
21297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21300 \begin_layout Plain Layout
21306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21309 \begin_layout Plain Layout
21317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21320 \begin_layout Plain Layout
21328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21331 \begin_layout Plain Layout
21332 \begin_inset Formula $\prime$
21342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21345 \begin_layout Plain Layout
21353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21356 \begin_layout Plain Layout
21357 \begin_inset Formula $\backprime$
21367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21370 \begin_layout Plain Layout
21378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21381 \begin_layout Plain Layout
21382 \begin_inset Formula $\mho$
21392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21395 \begin_layout Plain Layout
21403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21406 \begin_layout Plain Layout
21407 \begin_inset Formula $\triangle$
21417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21420 \begin_layout Plain Layout
21428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21431 \begin_layout Plain Layout
21432 \begin_inset Formula $\angle$
21442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21445 \begin_layout Plain Layout
21453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21456 \begin_layout Plain Layout
21457 \begin_inset Formula $\measuredangle$
21467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21470 \begin_layout Plain Layout
21478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21481 \begin_layout Plain Layout
21482 \begin_inset Formula $\sphericalangle$
21492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21495 \begin_layout Plain Layout
21503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21506 \begin_layout Plain Layout
21507 \begin_inset Formula $\top$
21517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21520 \begin_layout Plain Layout
21528 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21531 \begin_layout Plain Layout
21532 \begin_inset Formula $\bot$
21546 \begin_inset space \hfill{}
21552 \begin_layout Subsection
21553 Miscellaneous Symbols
21554 \begin_inset CommandInset label
21556 name "sub:Miscellaneous-Symbols"
21564 \begin_layout Plain Layout
21565 Symbols ! miscellaneous
21573 \begin_layout Standard
21576 \begin_inset Tabular
21577 <lyxtabular version="3" rows="10" columns="2">
21578 <features tabularvalignment="middle">
21579 <column alignment="center" valignment="top" width="0pt">
21580 <column alignment="center" valignment="top" width="0pt">
21582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21585 \begin_layout Plain Layout
21591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21594 \begin_layout Plain Layout
21602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21605 \begin_layout Plain Layout
21613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21616 \begin_layout Plain Layout
21617 \begin_inset Formula $\flat$
21627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21630 \begin_layout Plain Layout
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21641 \begin_layout Plain Layout
21642 \begin_inset Formula $\natural$
21652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21655 \begin_layout Plain Layout
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21666 \begin_layout Plain Layout
21667 \begin_inset Formula $\sharp$
21677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21680 \begin_layout Plain Layout
21688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21691 \begin_layout Plain Layout
21692 \begin_inset Formula $\surd$
21702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21705 \begin_layout Plain Layout
21713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21716 \begin_layout Plain Layout
21717 \begin_inset Formula $\checkmark$
21727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21730 \begin_layout Plain Layout
21738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21741 \begin_layout Plain Layout
21742 \begin_inset Formula $\yen$
21752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21755 \begin_layout Plain Layout
21763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21766 \begin_layout Plain Layout
21767 \begin_inset Formula $\pounds$
21777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21780 \begin_layout Plain Layout
21786 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21789 \begin_layout Plain Layout
21790 \begin_inset Formula $\$$
21800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21803 \begin_layout Plain Layout
21809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21812 \begin_layout Plain Layout
21813 \begin_inset Formula $§$
21827 \begin_inset Tabular
21828 <lyxtabular version="3" rows="10" columns="2">
21829 <features tabularvalignment="middle">
21830 <column alignment="center" valignment="top" width="0">
21831 <column alignment="center" valignment="top" width="0">
21833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21836 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21845 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21856 \begin_layout Plain Layout
21864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21867 \begin_layout Plain Layout
21868 \begin_inset Formula $\hbar$
21878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21881 \begin_layout Plain Layout
21889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21892 \begin_layout Plain Layout
21893 \begin_inset Formula $\hslash$
21903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21906 \begin_layout Plain Layout
21914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21917 \begin_layout Plain Layout
21918 \begin_inset Formula $\clubsuit$
21928 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21931 \begin_layout Plain Layout
21939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21942 \begin_layout Plain Layout
21943 \begin_inset Formula $\spadesuit$
21953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21956 \begin_layout Plain Layout
21964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21967 \begin_layout Plain Layout
21968 \begin_inset Formula $\bigstar$
21978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21981 \begin_layout Plain Layout
21989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21992 \begin_layout Plain Layout
21993 \begin_inset Formula $\blacklozenge$
22003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22006 \begin_layout Plain Layout
22014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22017 \begin_layout Plain Layout
22018 \begin_inset Formula $\blacktriangle$
22028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22031 \begin_layout Plain Layout
22039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22042 \begin_layout Plain Layout
22043 \begin_inset Formula $\blacktriangledown$
22053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22056 \begin_layout Plain Layout
22064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22067 \begin_layout Plain Layout
22068 \begin_inset Formula $\bullet$
22082 \begin_inset Tabular
22083 <lyxtabular version="3" rows="10" columns="2">
22084 <features tabularvalignment="middle">
22085 <column alignment="center" valignment="top" width="0pt">
22086 <column alignment="center" valignment="top" width="0pt">
22088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22091 \begin_layout Plain Layout
22097 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22100 \begin_layout Plain Layout
22108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22111 \begin_layout Plain Layout
22119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22122 \begin_layout Plain Layout
22123 \begin_inset Formula $\diamondsuit$
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22136 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22148 \begin_inset Formula $\Diamond$
22158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22161 \begin_layout Plain Layout
22169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22172 \begin_layout Plain Layout
22173 \begin_inset Formula $\heartsuit$
22183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22186 \begin_layout Plain Layout
22194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22197 \begin_layout Plain Layout
22198 \begin_inset Formula $\P$
22208 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22211 \begin_layout Plain Layout
22219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22222 \begin_layout Plain Layout
22223 \begin_inset Formula $\copyright$
22233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22236 \begin_layout Plain Layout
22244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22247 \begin_layout Plain Layout
22248 \begin_inset Formula $\circledR$
22258 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22261 \begin_layout Plain Layout
22269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22272 \begin_layout Plain Layout
22273 \begin_inset Formula $\maltese$
22283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22286 \begin_layout Plain Layout
22294 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22297 \begin_layout Plain Layout
22298 \begin_inset Formula $\diagup$
22308 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22311 \begin_layout Plain Layout
22319 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22322 \begin_layout Plain Layout
22323 \begin_inset Formula $\diagdown$
22339 \begin_layout Standard
22340 \begin_inset VSpace medskip
22343 More symbols are listed in
22344 \begin_inset CommandInset ref
22346 reference "sub:Miscellaneous-special-Characters"
22353 \begin_layout Standard
22354 Some symbols can be displayed in different sizes, see
22355 \begin_inset CommandInset ref
22357 reference "sub:Font-Sizes"
22364 \begin_layout Subsection
22369 \begin_layout Plain Layout
22370 Symbols ! Euro-symbol
22379 \begin_layout Plain Layout
22386 \begin_layout Plain Layout
22403 \begin_layout Standard
22404 To use the Euro symbol in formulas, the LaTeX-package
22412 \begin_layout Plain Layout
22418 must be installed and loaded with the LaTeX-preamble line
22421 \begin_layout Standard
22426 usepackage[gennarrow]{eurosym}
22429 \begin_layout Standard
22430 The Euro symbol can now be inserted with the command
22440 \begin_layout Plain Layout
22451 \begin_layout Standard
22452 The Euro symbol can directly be inserted with the € key in mathematical
22453 text, without having
22468 can also be inserted in TeX-mode.
22469 The official currency symbol can then be inserted with the command
22479 \begin_layout Plain Layout
22487 , that is only available in TeX-mode.
22490 \begin_layout Standard
22494 \begin_layout Plain Layout
22504 \begin_inset Note Note
22507 \begin_layout Plain Layout
22508 The following table will only be displayed when the LaTeX-package
22520 \begin_layout Standard
22521 An overview about the different Euro symbols:
22524 \begin_layout Standard
22526 \begin_inset Tabular
22527 <lyxtabular version="3" rows="4" columns="3">
22528 <features tabularvalignment="middle">
22529 <column alignment="center" valignment="top" width="0pt">
22530 <column alignment="center" valignment="top" width="0pt">
22531 <column alignment="center" valignment="top" width="0pt">
22533 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22536 \begin_layout Plain Layout
22542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22565 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22574 \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 $\euro$
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22608 \begin_layout Plain Layout
22614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22617 \begin_layout Plain Layout
22618 \begin_inset Formula $\mbox{€}$
22628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22631 \begin_layout Plain Layout
22637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22640 \begin_layout Plain Layout
22648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22651 \begin_layout Plain Layout
22655 \begin_layout Plain Layout
22677 \begin_layout Standard
22681 \begin_layout Plain Layout
22691 \begin_inset Note Note
22694 \begin_layout Plain Layout
22695 The following will be displayed when the LaTeX-package
22707 \begin_layout Standard
22708 You need to install the LaTeX-package
22712 to see the rest of this subsection in the output.
22715 \begin_layout Standard
22719 \begin_layout Plain Layout
22731 \begin_layout Section
22733 \begin_inset CommandInset label
22735 name "sec:Relations"
22743 \begin_layout Plain Layout
22753 \begin_layout Plain Layout
22758 \begin_layout Plain Layout
22769 \begin_layout Plain Layout
22784 \begin_layout Standard
22785 All relations can also be inserted via the toolbar button
22786 \begin_inset Graphics
22787 filename ../images/math/leq.png
22795 \begin_layout Standard
22796 \begin_inset space \hfill{}
22800 \begin_inset Tabular
22801 <lyxtabular version="3" rows="17" columns="2">
22802 <features tabularvalignment="middle">
22803 <column alignment="center" valignment="top" width="0pt">
22804 <column alignment="center" valignment="top" width="0pt">
22806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22809 \begin_layout Plain Layout
22815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22818 \begin_layout Plain Layout
22826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22829 \begin_layout Plain Layout
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22838 \begin_layout Plain Layout
22839 \begin_inset Formula $<$
22849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22852 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22864 \begin_inset Formula $\le$
22874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22877 \begin_layout Plain Layout
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22888 \begin_layout Plain Layout
22889 \begin_inset Formula $\ll$
22899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22902 \begin_layout Plain Layout
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22913 \begin_layout Plain Layout
22914 \begin_inset Formula $\prec$
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Plain Layout
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22938 \begin_layout Plain Layout
22939 \begin_inset Formula $\preceq$
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22963 \begin_layout Plain Layout
22964 \begin_inset Formula $\subset$
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22989 \begin_inset Formula $\subseteq$
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23002 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23013 \begin_layout Plain Layout
23014 \begin_inset Formula $\sqsubseteq$
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23027 \begin_layout Plain Layout
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23038 \begin_layout Plain Layout
23039 \begin_inset Formula $\in$
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23052 \begin_layout Plain Layout
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23063 \begin_layout Plain Layout
23064 \begin_inset Formula $\vdash$
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23077 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23088 \begin_layout Plain Layout
23089 \begin_inset Formula $\smile$
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23102 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23114 \begin_inset Formula $\lhd$
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Plain Layout
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23138 \begin_layout Plain Layout
23139 \begin_inset Formula $\unlhd$
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23163 \begin_layout Plain Layout
23164 \begin_inset Formula $\gtrless$
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23177 \begin_layout Plain Layout
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23188 \begin_layout Plain Layout
23189 \begin_inset Formula $\mid$
23199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23202 \begin_layout Plain Layout
23210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23213 \begin_layout Plain Layout
23214 \begin_inset Formula $\nmid$
23228 \begin_inset space \hfill{}
23232 \begin_inset Tabular
23233 <lyxtabular version="3" rows="17" columns="2">
23234 <features tabularvalignment="middle">
23235 <column alignment="center" valignment="top" width="0pt">
23236 <column alignment="center" valignment="top" width="0pt">
23238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23241 \begin_layout Plain Layout
23247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23250 \begin_layout Plain Layout
23258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23261 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23270 \begin_layout Plain Layout
23271 \begin_inset Formula $=$
23281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23284 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $\not=$
23306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23309 \begin_layout Plain Layout
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23320 \begin_layout Plain Layout
23321 \begin_inset Formula $\equiv$
23331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23345 \begin_layout Plain Layout
23346 \begin_inset Formula $\sim$
23356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23359 \begin_layout Plain Layout
23367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23370 \begin_layout Plain Layout
23371 \begin_inset Formula $\simeq$
23381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $\approx$
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\cong$
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\bowtie$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\notin$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\perp$
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\propto$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\asymp$
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\doteq$
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Plain Layout
23596 \begin_inset Formula $\circeq$
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23620 \begin_layout Plain Layout
23621 \begin_inset Formula $\models$
23631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23634 \begin_layout Plain Layout
23642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23645 \begin_layout Plain Layout
23646 \begin_inset Formula $\widehat{=}$
23660 \begin_inset space \hfill{}
23664 \begin_inset Tabular
23665 <lyxtabular version="3" rows="17" columns="2">
23666 <features tabularvalignment="middle">
23667 <column alignment="center" valignment="top" width="0pt">
23668 <column alignment="center" valignment="top" width="0pt">
23670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23673 \begin_layout Plain Layout
23679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23682 \begin_layout Plain Layout
23690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23693 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23702 \begin_layout Plain Layout
23703 \begin_inset Formula $>$
23713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23716 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23728 \begin_inset Formula $\ge$
23738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23741 \begin_layout Plain Layout
23749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23752 \begin_layout Plain Layout
23753 \begin_inset Formula $\gg$
23763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23766 \begin_layout Plain Layout
23774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23777 \begin_layout Plain Layout
23778 \begin_inset Formula $\succ$
23788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23791 \begin_layout Plain Layout
23799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23802 \begin_layout Plain Layout
23803 \begin_inset Formula $\succeq$
23813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23816 \begin_layout Plain Layout
23824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23827 \begin_layout Plain Layout
23828 \begin_inset Formula $\supset$
23838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23841 \begin_layout Plain Layout
23849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23852 \begin_layout Plain Layout
23853 \begin_inset Formula $\supseteq$
23863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23866 \begin_layout Plain Layout
23874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23877 \begin_layout Plain Layout
23878 \begin_inset Formula $\sqsupseteq$
23888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23891 \begin_layout Plain Layout
23899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23902 \begin_layout Plain Layout
23903 \begin_inset Formula $\ni$
23913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23916 \begin_layout Plain Layout
23924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23927 \begin_layout Plain Layout
23928 \begin_inset Formula $\dashv$
23938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23941 \begin_layout Plain Layout
23949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23952 \begin_layout Plain Layout
23953 \begin_inset Formula $\frown$
23963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23966 \begin_layout Plain Layout
23974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23977 \begin_layout Plain Layout
23978 \begin_inset Formula $\rhd$
23988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23991 \begin_layout Plain Layout
23999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24002 \begin_layout Plain Layout
24003 \begin_inset Formula $\unrhd$
24013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24027 \begin_layout Plain Layout
24028 \begin_inset Formula $\lessgtr$
24038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24041 \begin_layout Plain Layout
24049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24052 \begin_layout Plain Layout
24053 \begin_inset Formula $\parallel$
24063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24077 \begin_layout Plain Layout
24078 \begin_inset Formula $\nparallel$
24092 \begin_inset space \hfill{}
24098 \begin_layout Standard
24099 \begin_inset VSpace medskip
24114 are bigger than the equal looking operators
24129 \begin_layout Standard
24130 Relations are, in contrary to symbols, always surrounded by space.
24133 \begin_layout Standard
24134 Relations with labels can be created with the command
24144 \begin_layout Plain Layout
24155 \begin_layout Standard
24157 \begin_inset Tabular
24158 <lyxtabular version="3" rows="2" columns="2">
24159 <features tabularvalignment="middle">
24160 <column alignment="center" valignment="top" width="0">
24161 <column alignment="center" valignment="top" width="0">
24163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24166 \begin_layout Plain Layout
24172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24175 \begin_layout Plain Layout
24177 \begin_inset Note Note
24180 \begin_layout Plain Layout
24187 is only used as spacer.
24199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24202 \begin_layout Plain Layout
24209 \begin_layout Plain Layout
24226 \begin_layout Plain Layout
24236 \begin_inset Formula $\downarrow$
24245 \begin_layout Plain Layout
24258 \begin_layout Plain Layout
24272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24275 \begin_layout Plain Layout
24276 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24292 \begin_layout Section
24296 \begin_layout Subsection
24297 Predefined Functions
24298 \begin_inset CommandInset label
24300 name "sub:Predefined-Functions"
24308 \begin_layout Plain Layout
24309 Functions ! predefined
24317 \begin_layout Standard
24318 In general, variables are set
24322 in mathematical expressions, but not function names, because
24323 \begin_inset Formula $sin$
24326 could be misunderstood as
24327 \begin_inset Formula $s\cdot i\cdot n$
24331 Therefore there are predefined functions, that are additionally a bit separated
24333 They are inserted as commands starting with a backslash before their name.
24336 \begin_layout Standard
24338 \begin_inset Tabular
24339 <lyxtabular version="3" rows="2" columns="4">
24340 <features tabularvalignment="middle">
24341 <column alignment="center" valignment="top" width="0pt">
24342 <column alignment="center" valignment="top" width="0pt">
24343 <column alignment="center" valignment="top" width="0pt">
24344 <column alignment="center" valignment="top" width="0pt">
24346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24349 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24367 \begin_layout Plain Layout
24373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24387 \begin_layout Plain Layout
24393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24396 \begin_layout Plain Layout
24397 \begin_inset Formula $Asin(x)+B$
24405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24419 \begin_layout Plain Layout
24420 \begin_inset Formula $A\sin(x)+B$
24436 \begin_layout Standard
24437 The following functions are predefined:
24440 \begin_layout Standard
24441 \begin_inset VSpace -2mm
24447 \begin_layout Standard
24449 \begin_inset Tabular
24450 <lyxtabular version="3" rows="9" columns="4">
24451 <features tabularvalignment="middle">
24452 <column alignment="center" valignment="top" width="0pt">
24453 <column alignment="center" valignment="top" width="0pt">
24454 <column alignment="center" valignment="top" width="0pt">
24455 <column alignment="center" valignment="top" width="0pt">
24457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24460 \begin_layout Plain Layout
24466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24469 \begin_layout Plain Layout
24475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24478 \begin_layout Plain Layout
24484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24487 \begin_layout Plain Layout
24495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24498 \begin_layout Plain Layout
24506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24509 \begin_layout Plain Layout
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24544 \begin_layout Plain Layout
24552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24555 \begin_layout Plain Layout
24563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24566 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24577 \begin_layout Plain Layout
24587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24590 \begin_layout Plain Layout
24598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24601 \begin_layout Plain Layout
24609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24612 \begin_layout Plain Layout
24620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24623 \begin_layout Plain Layout
24633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24636 \begin_layout Plain Layout
24644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24647 \begin_layout Plain Layout
24655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24658 \begin_layout Plain Layout
24666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24669 \begin_layout Plain Layout
24679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24682 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24693 \begin_layout Plain Layout
24701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24704 \begin_layout Plain Layout
24712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24715 \begin_layout Plain Layout
24725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24728 \begin_layout Plain Layout
24736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24739 \begin_layout Plain Layout
24747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24750 \begin_layout Plain Layout
24758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24761 \begin_layout Plain Layout
24771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24774 \begin_layout Plain Layout
24782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24785 \begin_layout Plain Layout
24793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24796 \begin_layout Plain Layout
24804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24807 \begin_layout Plain Layout
24817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24820 \begin_layout Plain Layout
24828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24831 \begin_layout Plain Layout
24839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24842 \begin_layout Plain Layout
24850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24853 \begin_layout Plain Layout
24869 \begin_layout Standard
24870 They can also be inserted with the math toolbar button
24871 \begin_inset Graphics
24872 filename ../images/math/functions.png
24880 \begin_layout Subsection
24881 Self-defined Functions
24885 \begin_layout Plain Layout
24886 Functions ! self-defined
24894 \begin_layout Standard
24895 To use a function that is not predefined, like for example the sign function
24896 sgn(x), there are two possibilities:
24899 \begin_layout Itemize
24900 Define the function by inserting the following line to the LaTeX-preamble
24904 \begin_layout Plain Layout
24909 DeclareMathOperator
24912 \begin_inset CommandInset ref
24914 reference "sub:Self-defined-Operators"
24924 \begin_inset Newline newline
24928 \begin_inset VSpace -3mm
24932 \begin_inset Newline newline
24939 DeclareMathOperator{
24947 \begin_layout Plain Layout
24952 DeclareMathOperator
24958 \begin_inset Newline newline
24962 \begin_inset VSpace -2mm
24966 \begin_inset Newline newline
24969 Now the new defined function can be called with the command
24978 \begin_layout Itemize
24979 Write the the formula as usual, mark the formula name, in our example the
24984 , and change it to mathematical text.
24985 At last a space is inserted between prefactor and function.
24988 \begin_layout Standard
24989 The result is the same with both methods as with a predefined function
24993 \begin_layout Plain Layout
24994 In LyX self-defined functions are displayed red, predefined ones black.
25002 \begin_layout Standard
25004 \begin_inset Tabular
25005 <lyxtabular version="3" rows="3" columns="2">
25006 <features tabularvalignment="middle">
25007 <column alignment="center" valignment="top" width="0pt">
25008 <column alignment="center" valignment="top" width="0pt">
25010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25013 \begin_layout Plain Layout
25019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25022 \begin_layout Plain Layout
25030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25033 \begin_layout Plain Layout
25041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25044 \begin_layout Plain Layout
25045 \begin_inset Formula $A\sgn(x)+B$
25055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25058 \begin_layout Plain Layout
25062 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25073 \begin_layout Plain Layout
25074 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25090 \begin_layout Standard
25091 The first method is more suitable when the self-defined function should
25092 be used several times.
25095 \begin_layout Subsection
25100 \begin_layout Plain Layout
25109 \begin_layout Standard
25110 For limits there are defined besides
25120 \begin_layout Plain Layout
25140 furthermore the following functions:
25143 \begin_layout Standard
25145 \begin_inset Tabular
25146 <lyxtabular version="3" rows="5" columns="2">
25147 <features tabularvalignment="middle">
25148 <column alignment="center" valignment="top" width="0">
25149 <column alignment="center" valignment="top" width="0">
25151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25154 \begin_layout Plain Layout
25160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25163 \begin_layout Plain Layout
25165 \begin_inset Note Note
25168 \begin_layout Plain Layout
25175 is only used as spacer.
25187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25190 \begin_layout Plain Layout
25198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25201 \begin_layout Plain Layout
25202 \begin_inset Formula $\varliminf$
25212 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25215 \begin_layout Plain Layout
25223 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25226 \begin_layout Plain Layout
25227 \begin_inset Formula $\varlimsup$
25237 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25251 \begin_layout Plain Layout
25252 \begin_inset Formula $\varprojlim$
25262 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25265 \begin_layout Plain Layout
25273 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25276 \begin_layout Plain Layout
25277 \begin_inset Formula $\varinjlim$
25281 \begin_inset Formula $\raisebox{-2.5mm}{}$
25297 \begin_layout Standard
25298 \begin_inset VSpace medskip
25301 The limit is created by inserting a subscript.
25302 It is set right beside the function in an inline formula:
25305 \begin_layout Standard
25307 \begin_inset Tabular
25308 <lyxtabular version="3" rows="2" columns="2">
25309 <features tabularvalignment="middle">
25310 <column alignment="center" valignment="top" width="0pt">
25311 <column alignment="center" valignment="top" width="0pt">
25313 <cell alignment="center" valignment="top" usebox="none">
25316 \begin_layout Plain Layout
25322 <cell alignment="center" valignment="top" usebox="none">
25325 \begin_layout Plain Layout
25326 \begin_inset space \hspace{}
25331 \begin_inset Note Note
25334 \begin_layout Plain Layout
25347 are used here as spacer.
25359 <cell alignment="center" valignment="top" usebox="none">
25362 \begin_layout Plain Layout
25371 \begin_layout Plain Layout
25384 \begin_layout Plain Layout
25398 <cell alignment="center" valignment="top" usebox="none">
25401 \begin_layout Plain Layout
25402 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25418 \begin_layout Standard
25419 In a displayed formula the limit is set below the formula, as usual:
25420 \begin_inset Formula \[
25428 \begin_layout Subsection
25433 \begin_layout Plain Layout
25434 Functions ! modulo-
25442 \begin_layout Standard
25443 The modulo-function is special, because it exists in four variants.
25446 \begin_layout Standard
25447 The variants in a displayed formula:
25448 \begin_inset Formula \begin{align*}
25449 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25450 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25451 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25452 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25453 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25460 \begin_layout Standard
25461 In an inline formula less space is set before the function names for all
25465 \begin_layout Section
25470 \begin_layout Plain Layout
25479 \begin_layout Subsection
25480 Special Characters in Mathematical Text
25483 \begin_layout Standard
25484 The following commands can only be used in mathematical text or in TeX-mode:
25487 \begin_layout Standard
25488 \begin_inset space \hfill{}
25492 \begin_inset Tabular
25493 <lyxtabular version="3" rows="8" columns="2">
25494 <features tabularvalignment="middle">
25495 <column alignment="block" valignment="top" width="0">
25496 <column alignment="block" valignment="top" width="0">
25498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25501 \begin_layout Plain Layout
25507 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25510 \begin_layout Plain Layout
25518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25521 \begin_layout Plain Layout
25529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25532 \begin_layout Plain Layout
25533 \begin_inset Formula $\textrm{œ}$
25543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25546 \begin_layout Plain Layout
25554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25557 \begin_layout Plain Layout
25558 \begin_inset Formula $\textrm{Œ}$
25568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25571 \begin_layout Plain Layout
25579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25582 \begin_layout Plain Layout
25583 \begin_inset Formula $\textrm{æ}$
25593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25596 \begin_layout Plain Layout
25604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25608 \begin_inset Formula $\textrm{Æ}$
25618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25621 \begin_layout Plain Layout
25629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25632 \begin_layout Plain Layout
25633 \begin_inset Formula $\textrm{\aa}$
25643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25646 \begin_layout Plain Layout
25653 \begin_layout Plain Layout
25660 \begin_layout Plain Layout
25681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25684 \begin_layout Plain Layout
25685 \begin_inset Formula $\textrm{Å}$
25695 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25698 \begin_layout Plain Layout
25706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25709 \begin_layout Plain Layout
25710 \begin_inset Formula $\textrm{ı}$
25724 \begin_inset space \hfill{}
25728 \begin_inset Tabular
25729 <lyxtabular version="3" rows="8" columns="2">
25730 <features tabularvalignment="middle">
25731 <column alignment="block" valignment="top" width="0">
25732 <column alignment="center" valignment="top" width="0">
25734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25737 \begin_layout Plain Layout
25739 \begin_inset Note Note
25742 \begin_layout Plain Layout
25749 is used for separation, because otherwise the output will be ¡ and ¿ respective
25760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25763 \begin_layout Plain Layout
25771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25774 \begin_layout Plain Layout
25782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25785 \begin_layout Plain Layout
25786 \begin_inset Formula $\textrm{ø}$
25796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25799 \begin_layout Plain Layout
25807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25810 \begin_layout Plain Layout
25811 \begin_inset Formula $\textrm{Ø}$
25821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25824 \begin_layout Plain Layout
25832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25835 \begin_layout Plain Layout
25836 \begin_inset Formula $\textrm{ł}$
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25860 \begin_layout Plain Layout
25861 \begin_inset Formula $\textrm{Ł}$
25871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25876 \begin_inset space \hspace{}
25884 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25901 \begin_layout Plain Layout
25902 \begin_inset Formula $\textrm{!`}$
25912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25915 \begin_layout Plain Layout
25917 \begin_inset space \hspace{}
25925 \begin_layout Plain Layout
25939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25942 \begin_layout Plain Layout
25943 \begin_inset Formula $\textrm{?`}$
25953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25956 \begin_layout Plain Layout
25964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25968 \begin_inset Formula $\textrm{ȷ}$
25982 \begin_inset space \hfill{}
25988 \begin_layout Standard
25990 \begin_inset Formula $\textrm{\textrm{Å}}$
25994 \begin_inset Formula $\textrm{\textrm{Ø}}$
25997 can also be inserted via the math toolbar button
25998 \begin_inset Graphics
25999 filename ../images/math/digamma.png
26007 \begin_layout Standard
26008 An exception are the commands
26011 \begin_inset space \hspace{}
26020 \begin_inset space \hspace{}
26026 , because they can be inserted in LyX directly to text.
26029 \begin_layout Subsection
26031 \begin_inset CommandInset label
26033 name "sub:Accents-in-Text"
26041 \begin_layout Plain Layout
26050 \begin_layout Standard
26051 With the following commands all letters can be accented.
26052 The commands must be inserted in TeX-mode.
26055 \begin_layout Standard
26056 \begin_inset space \hfill{}
26060 \begin_inset Tabular
26061 <lyxtabular version="3" rows="8" columns="2">
26062 <features tabularvalignment="middle">
26063 <column alignment="block" valignment="top" width="0">
26064 <column alignment="block" valignment="top" width="0">
26066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26069 \begin_layout Plain Layout
26075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26078 \begin_layout Plain Layout
26086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26089 \begin_layout Plain Layout
26093 \begin_inset Quotes grd
26101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26104 \begin_layout Plain Layout
26108 \begin_layout Plain Layout
26124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26127 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26138 \begin_layout Plain Layout
26142 \begin_layout Plain Layout
26158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26161 \begin_layout Plain Layout
26168 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26185 \begin_layout Plain Layout
26189 \begin_layout Plain Layout
26205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26219 \begin_layout Plain Layout
26223 \begin_layout Plain Layout
26239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26242 \begin_layout Plain Layout
26249 \begin_layout Plain Layout
26263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26266 \begin_layout Plain Layout
26270 \begin_layout Plain Layout
26286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26289 \begin_layout Plain Layout
26296 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26313 \begin_layout Plain Layout
26317 \begin_layout Plain Layout
26333 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26336 \begin_layout Plain Layout
26343 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26364 \begin_layout Plain Layout
26384 \begin_inset space \hfill{}
26388 \begin_inset Tabular
26389 <lyxtabular version="3" rows="8" columns="2">
26390 <features tabularvalignment="middle">
26391 <column alignment="block" valignment="top" width="0">
26392 <column alignment="center" valignment="top" width="0">
26394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26406 \begin_layout Plain Layout
26414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26417 \begin_layout Plain Layout
26424 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26441 \begin_layout Plain Layout
26445 \begin_layout Plain Layout
26461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26464 \begin_layout Plain Layout
26472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26475 \begin_layout Plain Layout
26479 \begin_layout Plain Layout
26495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26498 \begin_layout Plain Layout
26505 \begin_layout Plain Layout
26516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26519 \begin_layout Plain Layout
26523 \begin_layout Plain Layout
26539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26542 \begin_layout Plain Layout
26550 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26553 \begin_layout Plain Layout
26557 \begin_layout Plain Layout
26573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26576 \begin_layout Plain Layout
26583 \begin_layout Plain Layout
26597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26600 \begin_layout Plain Layout
26604 \begin_layout Plain Layout
26620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26623 \begin_layout Plain Layout
26630 \begin_layout Plain Layout
26644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26647 \begin_layout Plain Layout
26651 \begin_layout Plain Layout
26667 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26670 \begin_layout Plain Layout
26677 \begin_layout Plain Layout
26691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26694 \begin_layout Plain Layout
26698 \begin_layout Plain Layout
26718 \begin_inset space \hfill{}
26724 \begin_layout Standard
26725 \begin_inset VSpace medskip
26734 also two different characters can be accented.
26743 \begin_layout Plain Layout
26758 \begin_layout Plain Layout
26770 \begin_layout Standard
26783 can in combination with vowels directly be inserted with the keyboard without
26785 The same applies for the tilde
26789 \begin_layout Plain Layout
26790 This only applies for keyboards where the tilde is defined as accent.
26799 in combination with
26814 \begin_layout Standard
26857 , and accents inserted directly with the keyboard are also available in
26859 For the other accents there are special math commands to be used in formulas,
26861 \begin_inset CommandInset ref
26863 reference "sub:Accents-for-one"
26870 \begin_layout Standard
26871 \begin_inset VSpace bigskip
26874 Furthermore, with the command
26884 \begin_layout Plain Layout
26892 all numbers and letters can be set into a circle, quasi accented with a
26893 circle, similar to the the copyright symbol.
26896 \begin_layout Standard
26898 \begin_inset Tabular
26899 <lyxtabular version="3" rows="3" columns="2">
26900 <features tabularvalignment="middle">
26901 <column alignment="center" valignment="top" width="0">
26902 <column alignment="center" valignment="top" width="0">
26904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26907 \begin_layout Plain Layout
26913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26916 \begin_layout Plain Layout
26918 \begin_inset Note Note
26921 \begin_layout Plain Layout
26928 is only used as spacer.
26940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26943 \begin_layout Plain Layout
26951 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26954 \begin_layout Plain Layout
26958 \begin_layout Plain Layout
26974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26977 \begin_layout Plain Layout
26988 raisebox{-1.5pt}{W}}
26993 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26996 \begin_layout Plain Layout
26997 \begin_inset Formula $\raisebox{4.5mm}{}$
27004 \begin_layout Plain Layout
27022 \begin_inset Formula $\raisebox{-2mm}{}$
27038 \begin_layout Standard
27039 One has to take care that the character fits in the circle.
27050 \begin_layout Plain Layout
27052 \begin_inset CommandInset ref
27054 reference "sub:Font-Sizes"
27063 specifies thereby the size of the circle.
27074 \begin_layout Plain Layout
27076 \begin_inset CommandInset ref
27078 reference "sub:Boxes-without-Frame"
27087 the character can be centered.
27090 \begin_layout Subsection
27095 \begin_layout Plain Layout
27104 \begin_layout Standard
27105 Minuscule numbers are created with the command
27115 \begin_layout Plain Layout
27124 The command can be used in formulas and in TeX-mode.
27125 The command scheme is:
27128 \begin_layout Standard
27133 oldstylenums{number}
27136 \begin_layout Standard
27141 oldstylenums{0123456789
27144 \begin_inset Formula $\oldstylenums{0123456789}$
27150 \begin_layout Subsection
27151 Miscellaneous special Characters
27152 \begin_inset CommandInset label
27154 name "sub:Miscellaneous-special-Characters"
27162 \begin_layout Plain Layout
27163 Special characters ! miscellaneous
27171 \begin_layout Standard
27172 The following characters can only be inserted to formulas by using commands:
27175 \begin_layout Standard
27177 \begin_inset Tabular
27178 <lyxtabular version="3" rows="4" columns="2">
27179 <features tabularvalignment="middle">
27180 <column alignment="center" valignment="top" width="0">
27181 <column alignment="center" valignment="top" width="0">
27183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27186 \begin_layout Plain Layout
27192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27195 \begin_layout Plain Layout
27203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27206 \begin_layout Plain Layout
27213 \begin_layout Plain Layout
27227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27230 \begin_layout Plain Layout
27231 \begin_inset Formula $\mathcircumflex$
27241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27244 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27255 \begin_layout Plain Layout
27256 \begin_inset Formula $\_$
27266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27269 \begin_layout Plain Layout
27274 \begin_layout Plain Layout
27289 \begin_layout Plain Layout
27302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27305 \begin_layout Plain Layout
27306 \begin_inset Formula $^{\circ}$
27322 \begin_layout Standard
27323 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27324 contains the following line
27328 \begin_layout Plain Layout
27329 More about this is described in
27330 \begin_inset CommandInset ref
27332 reference "sub:Text-Characters-in"
27344 \begin_layout Standard
27349 DeclareInputtext{176}{
27362 \begin_layout Section
27364 \begin_inset CommandInset label
27366 name "sec:Formula-Styles"
27374 \begin_layout Plain Layout
27383 \begin_layout Itemize
27384 There are two different alignment styles:
27388 \begin_layout Description
27389 Centered is the predefined standard
27392 \begin_layout Description
27393 Indented for this the option
27397 must be inserted in the menu
27399 Document\SpecialChar \menuseparator
27405 \begin_inset space ~
27411 \begin_layout Standard
27416 is used, the indentation can be adjusted with the length
27426 \begin_layout Plain Layout
27435 Should the distance be 15
27436 \begin_inset space \thinspace{}
27439 mm, the following command line is inserted in the LaTeX-preamble
27442 \begin_layout Standard
27452 \begin_layout Standard
27453 When no length is specified, the predefined value of 30
27454 \begin_inset space \thinspace{}
27461 \begin_layout Itemize
27462 And two different numbering styles:
27466 \begin_layout Description
27467 Right is the predefined standard
27470 \begin_layout Description
27471 Left for this the option
27475 must be inserted in the menu
27477 Document\SpecialChar \menuseparator
27483 \begin_inset space ~
27490 \begin_layout Standard
27499 can also be used together.
27500 In this case both options are inserted, separated by a comma.
27503 \begin_layout Standard
27504 The chosen styles are used for all displayed formulas of the document.
27505 When both, centered and indented formulas should be created in a document,
27511 The indented formulas are then set in a flalign environment, see
27512 \begin_inset CommandInset ref
27514 reference "sub:Flalign-Environment"
27521 \begin_layout Section
27523 \begin_inset CommandInset label
27525 name "sec:Multiline-Formulas"
27533 \begin_layout Plain Layout
27534 Formula ! multiline
27542 \begin_layout Subsection
27546 \begin_layout Standard
27547 In LyX multiline formulas are created by pressing
27552 arg "newline-insert newline"
27558 This creates either an
27560 eqnarray environment
27562 that is described in
27563 \begin_inset CommandInset ref
27565 reference "sub:Eqnarray-Environment"
27569 or, when the option
27571 Use AMS math package
27573 in the document settings is selected, an
27577 that is described in
27578 \begin_inset CommandInset ref
27580 reference "sub:Standard-align-Environment"
27587 \begin_layout Standard
27588 There are other multiline formula environments that can be created via the
27591 Insert\SpecialChar \menuseparator
27595 These environments are described in the following sections.
27598 \begin_layout Standard
27599 In all multiline formula environments a new line is created by pressing
27603 arg "newline-insert newline"
27607 To add or delete lines, the math toolbar buttons
27608 \begin_inset Graphics
27609 filename ../images/tabular-feature_append-row.png
27615 \begin_inset Graphics
27616 filename ../images/tabular-feature_delete-row.png
27621 , respectively, or the menu
27623 Edit\SpecialChar \menuseparator
27629 \begin_layout Subsubsection
27631 \begin_inset CommandInset label
27633 name "sub:Line-Separation"
27641 \begin_layout Plain Layout
27642 Formula ! multiline ! Line separation
27650 \begin_layout Standard
27651 There is sometimes not enough space in multiline formulas between the lines:
27652 \begin_inset Formula \begin{eqnarray*}
27653 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}\\
27654 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*}
27661 \begin_layout Standard
27662 In LaTeX additional line space is specified as optional argument of the
27664 This is not yet possible in LyX
27668 \begin_layout Plain Layout
27670 \begin_inset CommandInset href
27672 name "LyX-bug #1505"
27673 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27682 , therefore the whole formula must be inserted in TeX-mode.
27683 To add in our example space, the command
27691 is inserted at the end of the first line.
27696 \begin_layout Plain Layout
27703 \begin_layout Plain Layout
27705 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27708 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27715 \begin_layout Plain Layout
27719 left(B^{2}+x_{0}^{2}
27727 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27732 \begin_layout Plain Layout
27744 \begin_layout Standard
27745 \begin_inset VSpace bigskip
27748 To set the the line separation for all lines in a formula, the length
27758 \begin_layout Plain Layout
27768 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27779 \begin_inset space \thinspace{}
27784 \begin_inset space \thinspace{}
27787 mm additional line separation as in the previous example, the command
27790 \begin_layout Standard
27800 \begin_layout Standard
27801 is inserted in TeX-mode before the formula.
27802 This requires that the LaTeX-package
27810 \begin_layout Plain Layout
27815 is part of every LaTeX standard installation.
27824 \begin_layout Plain Layout
27830 was loaded in LaTeX-preamble with the line
27833 \begin_layout Standard
27841 \begin_layout Standard
27846 \begin_layout Plain Layout
27858 \begin_inset Formula \begin{eqnarray*}
27859 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}\\
27860 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*}
27867 \begin_layout Standard
27871 \begin_layout Plain Layout
27882 To get back to the predefined distance,
27888 is set to the value 3
27889 \begin_inset space \thinspace{}
27895 \begin_layout Subsubsection
27897 \begin_inset CommandInset label
27899 name "sub:Column-Separation"
27907 \begin_layout Plain Layout
27908 Formula ! multiline ! Column separation
27916 \begin_layout Standard
27917 Multiline formulas form a matrix.
27918 A formula in the eqnarray environment is for example a matrix with three
27920 By changing the column separation in this environment, the space beside
27921 the relation sign can be changed.
27924 \begin_layout Standard
27925 The column separation is specified with the length
27935 \begin_layout Plain Layout
27944 \begin_inset Newline newline
27947 column separation = 2
27948 \begin_inset space \thinspace{}
27958 \begin_inset Newline newline
27964 \begin_layout Standard
27974 \begin_layout Standard
27975 inserted in TeX-mode, sets for all following formulas a column separation
27977 \begin_inset space \thinspace{}
27981 To get back to the predefined distance,
27988 \begin_inset space \thinspace{}
27994 \begin_layout Standard
27996 \begin_inset space \thinspace{}
27999 cm column separation:
28003 \begin_layout Plain Layout
28015 \begin_inset Formula \begin{eqnarray*}
28017 C & \ne & A\end{eqnarray*}
28021 A formula with the predefined column separation for matrices of 10
28022 \begin_inset space \thinspace{}
28029 \begin_layout Plain Layout
28041 \begin_inset Formula \begin{eqnarray*}
28043 C & \ne & A\end{eqnarray*}
28050 \begin_layout Subsubsection
28055 \begin_layout Plain Layout
28064 \begin_layout Standard
28065 Long formulas can be typeset using these methods:
28068 \begin_layout Itemize
28069 When one side of the equation is much shorther than the line width, this
28070 one is chosen for the left side and the right side is typeset over two
28072 \begin_inset Formula \begin{eqnarray}
28073 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 \\
28074 & & -\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}
28078 The minus sign at the beginning of the second line does normally not appear
28079 as operator because it is the first character of the line.
28080 Thus it would not be surrounded by space and could not be distinguished
28081 from the fraction bar.
28082 To avoid this, space was inserted behind the minus sign with the command
28093 \begin_layout Plain Layout
28101 \begin_inset CommandInset ref
28103 reference "sub:Variable-Space"
28116 \begin_layout Plain Layout
28127 \begin_layout Itemize
28128 When both sides of the equation are too long, the command
28138 \begin_layout Plain Layout
28147 It is inserted to the first column of the first line and effects that all
28148 further insertions overwrite the following columns:
28149 \begin_inset Formula \begin{eqnarray}
28150 \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 \\
28151 & & -\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 \\
28152 & & =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}
28156 After the insertion of
28162 , the cursor is in a purple box that is a bit shifted to the left from the
28164 In this the formula is inserted.
28165 \begin_inset Newline newline
28168 The content of the further lines is inserted to the second or another formula
28170 The greater the column number where it was inserted, the larger the indentation.
28171 \begin_inset VSpace medskip
28175 \begin_inset Newline newline
28179 \begin_inset Note Greyedout
28182 \begin_layout Plain Layout
28183 Note the following when using
28192 \begin_layout Itemize
28193 The formula doesn't use the full page width.
28195 \begin_inset space \thinspace{}
28199 \begin_inset space \space{}
28203 \begin_inset Formula $-B^{2}$
28206 is added to the first line in the above example, it would have been outside
28208 To better use the width, negative space can be inserted at the beginning
28212 \begin_layout Itemize
28213 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28218 \begin_layout Plain Layout
28219 \begin_inset CommandInset href
28221 name "LyX-bug #1429"
28222 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28231 One can only set the cursor at the beginning of the line and move it with
28240 \begin_layout Itemize
28241 Other methods to set long formulas are offered by the environments described
28243 \begin_inset CommandInset ref
28245 reference "sub:Multline-Environment"
28250 \begin_inset CommandInset ref
28252 reference "sub:Multiline-Formula-Parts"
28259 \begin_layout Subsubsection
28261 \begin_inset CommandInset label
28263 name "sub:Multiline-Brackets"
28271 \begin_layout Plain Layout
28272 Brackets ! for multiline expressions
28280 \begin_layout Standard
28281 For brackets spanning multiple lines the following problem occurs:
28282 \begin_inset Formula \begin{eqnarray*}
28283 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28284 & & \left.\cdots+B-D\right]\end{eqnarray*}
28291 \begin_layout Standard
28292 The closing bracket is smaller than the opening bracket because brackets
28293 with variable size may not span multiple lines.
28296 \begin_layout Standard
28297 To set the bracket size for the second line correctly, the first line is
28308 \begin_layout Plain Layout
28316 and the second line with
28324 \begin_layout Plain Layout
28338 \begin_inset CommandInset ref
28340 reference "sub:Automatic-Bracket-Size"
28355 \begin_layout Plain Layout
28381 \begin_layout Plain Layout
28400 \begin_layout Plain Layout
28419 \begin_layout Plain Layout
28431 \begin_inset Formula $\downarrow$
28440 \begin_layout Plain Layout
28448 is inserted, because the multiplication operator with its limits is the
28449 largest symbol in the first line and this should be the size for the bracket
28450 in the second line.
28453 \begin_layout Standard
28454 The result is this:
28455 \begin_inset Formula \begin{eqnarray*}
28456 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28457 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28464 \begin_layout Subsection
28468 \begin_layout Standard
28469 Align environments can be used for every kind of multiline formulas.
28470 They are specially useful to set several formulas side by side.
28473 \begin_layout Standard
28474 Align environments consist of columns.
28475 The odd columns are right aligned, the even ones left aligned.
28476 Every line in an Align environment can be numbered.
28479 \begin_layout Standard
28480 Align environments are created via the menu
28482 Insert\SpecialChar \menuseparator
28488 Edit\SpecialChar \menuseparator
28489 Math\SpecialChar \menuseparator
28490 Change Formula Type
28492 already existing formulas can be converted to Align environments.
28495 \begin_layout Standard
28496 To add or delete columns, the math toolbar buttons
28497 \begin_inset Graphics
28498 filename ../images/tabular-feature_append-column.png
28504 \begin_inset Graphics
28505 filename ../images/tabular-feature_delete-column.png
28510 , respectively, or the menu
28512 Edit\SpecialChar \menuseparator
28518 \begin_layout Subsubsection
28519 Standard align Environment
28520 \begin_inset CommandInset label
28522 name "sub:Standard-align-Environment"
28530 \begin_layout Plain Layout
28531 Formula ! multiline ! align environment
28539 \begin_layout Standard
28540 This Align environment is created by presssing
28543 arg "newline-insert newline"
28546 in a formula or by the menu
28548 Insert\SpecialChar \menuseparator
28549 Math\SpecialChar \menuseparator
28550 AMS align Environment
28555 \begin_layout Standard
28556 An example for two formulas set side by side, that are created with a four
28557 column align environment:
28558 \begin_inset Formula \begin{align*}
28559 A & =\sin(B) & C & =D\\
28560 C & \ne A & B & \ne D\end{align*}
28564 As it can be seen, the formulas in this environment are placed so as if
28573 \begin_layout Plain Layout
28581 \begin_inset CommandInset ref
28583 reference "sub:Variable-Space"
28594 before the first and after every even column.
28595 When the formula style
28601 \begin_layout Plain Layout
28603 \begin_inset CommandInset ref
28605 reference "sec:Formula-Styles"
28616 is used, the formula is set without the
28622 before the first column.
28625 \begin_layout Subsubsection
28626 Alignat Environment
28630 \begin_layout Plain Layout
28631 Formula ! multiline ! alignat environment
28639 \begin_layout Standard
28640 The alignat environment has no predefined column separation.
28641 It can be inserted manually with the spaces that are described
28642 \begin_inset CommandInset ref
28644 reference "sub:Space"
28651 \begin_layout Standard
28652 The above example in the alignat environment where 1
28653 \begin_inset space \thinspace{}
28656 cm space was inserted at the beginning of the second formula:
28657 \begin_inset Formula \begin{alignat*}{2}
28658 A & =\sin(B) & \hspace{1cm}C & =D\\
28659 C & \ne A & B & \ne D\end{alignat*}
28663 Because the column separation can be set separately for every column, this
28664 environment is especially suitable to set three and more formulas side
28668 \begin_layout Subsubsection
28669 Flalign Environment
28670 \begin_inset CommandInset label
28672 name "sub:Flalign-Environment"
28680 \begin_layout Plain Layout
28681 Formula ! multiline ! flalign environment
28689 \begin_layout Standard
28690 In this environment the first two columns are always set as much as possible
28691 to the left and the last two ones to the right.
28693 \begin_inset Formula \begin{flalign*}
28694 A & =1 & B & =2 & C & =3\\
28695 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28702 \begin_layout Standard
28703 By creating a flalign environment with an odd number of columns where an
28704 empty TeX-brace is inserted to the last column, several formulas in a document
28705 can be set to the left, although the formula style
28710 As example the indented formula
28711 \begin_inset CommandInset ref
28713 reference "eq:VolInt"
28718 \begin_inset Formula \begin{flalign}
28719 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28723 The first two columns contain the formula.
28724 To indent it as with the formula style
28729 \begin_inset space \thinspace{}
28732 pt space was inserted at the beginning of the first column.
28735 \begin_layout Subsection
28736 Eqnarray Environment
28737 \begin_inset CommandInset label
28739 name "sub:Eqnarray-Environment"
28747 \begin_layout Plain Layout
28748 Formula ! multiline ! eqnarray environment
28756 \begin_layout Standard
28757 When this environment has been created, three blue boxes appear.
28758 The content of the first box is right aligned, the content of the last
28760 The content of the middle box appears centered and a bit smaller, because
28761 it is designed to insert there only relation characters.
28762 \begin_inset Formula \begin{eqnarray*}
28763 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28765 A & = & A\end{eqnarray*}
28772 \begin_layout Subsection
28777 \begin_layout Plain Layout
28778 Formula ! multiline ! gather environment
28786 \begin_layout Standard
28787 This environment consists of only one centered column.
28788 Every line can be numbered.
28789 \begin_inset Formula \begin{gather}
28791 X=\textrm{-}1\end{gather}
28798 \begin_layout Subsection
28799 Multline Environment
28800 \begin_inset CommandInset label
28802 name "sub:Multline-Environment"
28810 \begin_layout Plain Layout
28811 Formula ! multiline ! multline environment
28819 \begin_layout Standard
28820 The multline environment consists, like the gather environment, of only
28822 But the first line is left aligned, the last one right aligned.
28823 All other lines are centered.
28824 Therefore this environment is suitable for long formulas.
28826 \begin_inset CommandInset ref
28828 reference "eq:lefteqn"
28832 in the multline environment:
28833 \begin_inset Formula \begin{multline}
28834 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}\\
28835 -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}\\
28836 =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}
28843 \begin_layout Standard
28844 In the output only the last (first) line of a multline environment appears
28845 numbered when the document numbering is right (left).
28849 \begin_layout Plain Layout
28850 numbering styles see
28851 \begin_inset CommandInset ref
28853 reference "sec:Formula-Styles"
28865 \begin_layout Standard
28874 \begin_layout Plain Layout
28892 \begin_layout Plain Layout
28902 a centered line can be right or left aligned, respectively.
28903 The commands are used as follows:
28906 \begin_layout Standard
28911 shoveright{line content}
28917 shoveleft{line content}
28920 \begin_layout Standard
28921 \begin_inset VSpace medskip
28932 \begin_layout Plain Layout
28942 specifies the distance of the first line from the left page margin.
28943 Predefined is the length 0
28944 \begin_inset space \thinspace{}
28950 \begin_layout Standard
28951 As example the above formula where the command
28954 \begin_layout Standard
28964 \begin_layout Standard
28965 was inserted in TeX-mode before:
28969 \begin_layout Plain Layout
28981 \begin_inset Formula \begin{multline}
28982 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}\\
28983 \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}}\\
28984 =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}
28992 \begin_layout Plain Layout
29003 The second line was left aligned using
29012 \begin_layout Subsection
29013 Multiline Formula Parts
29014 \begin_inset CommandInset label
29016 name "sub:Multiline-Formula-Parts"
29024 \begin_layout Plain Layout
29025 Formula ! multiline ! formula parts
29033 \begin_layout Standard
29034 To display only parts of a formula with multiple lines, one of the following
29035 environments are used:
29052 They can be inserted via the menu
29054 Insert\SpecialChar \menuseparator
29057 or by using the commands described in this section.
29060 \begin_layout Standard
29061 The first three have the same properties as the corresponding multiline
29062 formula environments, but it is possible to set further formula parts beside
29065 \begin_inset Formula \[
29066 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29067 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29068 \right\} \textrm{Uncertainty relations}\]
29075 \begin_layout Standard
29076 To get this formula, a displayed formula is created where the command
29084 \begin_layout Plain Layout
29095 A purple box appears around the blue formula box where now columns and
29096 lines can be added.
29097 Outside the multiline environment other formula parts can be set, like
29101 \begin_layout Standard
29102 The aligned environment is also suitable for long formulas whose lines are
29103 horizontally aligned.
29104 Using aligned in a displayed formula has the advantage that the formula
29105 number is vertically centered behind the lines.
29107 \begin_inset CommandInset ref
29109 reference "eq:shortlong"
29113 in the aligned environment:
29114 \begin_inset Formula \begin{equation}
29115 \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}|}\\
29116 & -\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}
29124 \begin_layout Standard
29125 To use the environments
29147 \begin_layout Plain Layout
29165 \begin_layout Plain Layout
29183 \begin_layout Plain Layout
29191 are inserted, respectively.
29192 The split environment has the same properties as the aligned environment
29193 but it can only have two columns.
29196 \begin_layout Subsection
29197 Text in multiline Formulas
29198 \begin_inset CommandInset label
29200 name "sub:Text-in-multiline"
29208 \begin_layout Plain Layout
29218 \begin_layout Plain Layout
29219 Formula ! multiline ! text
29227 \begin_layout Standard
29228 In the Align environments, and the multline and gather environment, text
29229 can be inserted that will appear in a separate line and doesn't affect
29230 the column alignment.
29231 To do this, the command
29239 \begin_layout Plain Layout
29249 is used in the following scheme:
29252 \begin_layout Standard
29260 \begin_layout Standard
29261 The text should not be longer than a line because it cannot be hyphenated.
29262 As LyX doesn't yet support
29268 directly, the text is written as mathematical text.
29275 must hereby be at the beginning of a line and appears in the output above
29277 An example where the text was inserted at the beginning of the second line:
29278 \begin_inset Formula \begin{align}
29279 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29280 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29287 \begin_layout Section
29292 \begin_layout Plain Layout
29302 \begin_layout Plain Layout
29303 Formula ! numbering|see
29307 \begin_layout Plain Layout
29318 \begin_layout Plain Layout
29333 \begin_layout Subsection
29337 \begin_layout Standard
29338 Numbered formulas can be created with the menu
29340 Insert\SpecialChar \menuseparator
29341 Math\SpecialChar \menuseparator
29343 \begin_inset space ~
29351 \begin_inset space ~
29357 Existing formulas can be numbered with the menu
29359 Edit\SpecialChar \menuseparator
29360 Math\SpecialChar \menuseparator
29362 \begin_inset space ~
29370 arg "math-number-toggle"
29374 The formula number is displayed in LyX behind the formula as number sign
29376 The number sign is replaced in the output by the formula number.
29379 \begin_layout Standard
29380 When numbering is turned on in multiline formulas, all lines will be numbered.
29381 But the numbering can be controlled with the menu
29383 Edit\SpecialChar \menuseparator
29384 Math\SpecialChar \menuseparator
29386 \begin_inset space ~
29390 \begin_inset space ~
29394 \begin_inset space ~
29402 arg "math-number-line-toggle"
29408 \begin_layout Standard
29409 Except of inline formulas, all formulas can be numbered with two different
29411 \begin_inset CommandInset ref
29413 reference "sec:Formula-Styles"
29420 \begin_layout Subsection
29425 \begin_layout Plain Layout
29426 Cross-references ! to formulas
29434 \begin_layout Standard
29435 All labeled formulas can be cross-referenced.
29436 A label is added by the menu
29438 Insert\SpecialChar \menuseparator
29441 or the toolbar button
29442 \begin_inset Graphics
29443 filename ../images/label-insert.png
29449 The cursor must hereby be inside a displayed formula.
29450 A dialog pops up displaying the prefix
29455 The label is inserted there behind the prefix.
29456 The predefined prefix means
29457 \begin_inset Quotes eld
29461 \begin_inset Quotes erd
29464 and makes it easier to find labels in large documents because it marks
29465 it as formula label to divide it from e.
29466 \begin_inset space \thinspace{}
29470 \begin_inset space \space{}
29474 To change a label, the menu
29476 Insert\SpecialChar \menuseparator
29482 \begin_layout Standard
29483 The name of the label is displayed in LyX within two parentheses behind
29485 A formula with a label is always numbered.
29488 \begin_layout Standard
29489 Cross-references are inserted via the menu
29491 Insert\SpecialChar \menuseparator
29494 or with the toolbar button
29495 \begin_inset Graphics
29496 filename ../images/dialog-show-new-inset_ref.png
29502 A formula cross-reference appears in the output as formula number.
29503 When in the cross-reference dialog window the format
29507 is chosen, the cross-reference appears in the output as formula number
29509 \begin_inset Newline newline
29512 By right-clicking on a cross-reference in LyX, one jumps to the formula
29513 that is referenced.
29516 \begin_layout Standard
29517 Here are as examples cross-references to formulas of the following subsections:
29518 \begin_inset Note Note
29521 \begin_layout Plain Layout
29522 Note the different cross-reference types.
29530 \begin_layout Standard
29532 \begin_inset CommandInset ref
29539 \begin_inset CommandInset ref
29547 \begin_inset CommandInset ref
29553 ) big Latin letters are used for the numbering in contrary to (
29554 \begin_inset CommandInset ref
29563 \begin_layout Standard
29564 \begin_inset VSpace medskip
29567 When the argument of
29575 \begin_layout Plain Layout
29583 \begin_inset CommandInset ref
29585 reference "sub:User-defined-Numbering"
29596 contains a box like in
29597 \begin_inset CommandInset ref
29599 reference "sub:Paragraph-Boxes"
29603 , the formula cannot be referenced.
29606 \begin_layout Subsection
29611 \begin_layout Plain Layout
29612 Formula numbering ! subnumbering
29620 \begin_layout Standard
29621 With the help of the commands
29625 begin{subequations}
29633 formulas can be subnumbered.
29634 Both commands are inserted in TeX-mode.
29637 \begin_layout Standard
29639 \begin_inset Formula \begin{equation}
29640 A=C-B\label{eq:a}\end{equation}
29648 \begin_layout Plain Layout
29652 addtocounter{equation}{-1}
29661 \begin_layout Plain Layout
29665 begin{subequations}
29671 \begin_inset VSpace -5mm
29675 \begin_inset Formula \begin{equation}
29676 B=C-A\label{eq:b}\end{equation}
29681 \begin_inset Formula \begin{equation}
29682 C=A+B\label{eq:c}\end{equation}
29689 \begin_layout Standard
29693 \begin_layout Plain Layout
29705 \begin_layout Standard
29706 To create the example, the following is done:
29709 \begin_layout Enumerate
29710 first formula is inserted
29713 \begin_layout Enumerate
29718 addtocounter{equation}{-1}
29720 begin{subequations}
29724 \begin_layout Plain Layout
29733 \begin_inset Newline newline
29738 is inserted after the first formula
29741 \begin_layout Enumerate
29742 second formula is inserted
29745 \begin_layout Enumerate
29746 third formula is inserted
29749 \begin_layout Enumerate
29756 is inserted after the third formula
29759 \begin_layout Standard
29760 Every formula between the commands
29772 is subnumbered as a, b,
29773 \begin_inset Newline linebreak
29776 c, \SpecialChar \ldots{}
29777 For multiline formulas every line will be subnumbered.
29778 All subnumbered formulas are treated as
29783 But as every numbered formula increases the counter
29787 by one, the command
29793 is needed to decrease it.
29794 Otherwise the formulas
29795 \begin_inset CommandInset ref
29802 \begin_inset CommandInset ref
29809 \begin_inset CommandInset ref
29815 would be numbered as
29816 \begin_inset CommandInset ref
29823 \begin_inset CommandInset ref
29830 \begin_inset CommandInset ref
29839 \begin_layout Standard
29840 By inserting the commands in TeX-mode, a space is created between the first
29843 \begin_inset space \thinspace{}
29846 mm vertical space is inserted after the command
29850 begin{subequations}
29853 When the formula style
29859 \begin_layout Plain Layout
29861 \begin_inset CommandInset ref
29863 reference "sec:Formula-Styles"
29875 \begin_inset space \thinspace{}
29878 mm space is inserted instead.
29881 \begin_layout Standard
29882 Here is an example for a multiline formula where the numbering was turned
29883 off for the second line:
29887 \begin_layout Plain Layout
29891 begin{subequations}
29897 \begin_inset Formula \begin{eqnarray}
29898 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29899 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29900 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29908 \begin_layout Plain Layout
29920 \begin_layout Subsection
29921 User-defined Numbering
29922 \begin_inset CommandInset label
29924 name "sub:User-defined-Numbering"
29932 \begin_layout Plain Layout
29933 Formula numbering ! user-defined
29941 \begin_layout Standard
29945 \begin_layout Plain Layout
29946 Formula numbering ! self-defined delimiters
29951 With the standard numbering parentheses are set around the formula number.
29952 To replace the parentheses for example by vertical bars, the following
29953 line is added to the LaTeX-preamble:
29956 \begin_layout Standard
29968 \begin_inset Note Note
29971 \begin_layout Plain Layout
29972 This macro is already declared in the LaTeX-preamble for testing.
29973 To activate it, remove the percent sign at the beginning.
29981 \begin_layout Standard
29982 To use other characters, the vertical bars besides the
29986 are replaced by one ore more characters.
29987 To get only the formula number the vertical bars are omitted.
29990 \begin_layout Standard
29991 \begin_inset VSpace bigskip
29994 When there should be an expression of your choice instead of the consecutive
29995 formula number in parentheses behind the formula, the command
30005 \begin_layout Plain Layout
30014 \begin_inset Formula \begin{equation}
30015 A+B=C\tag{something}\label{eq:tag}\end{equation}
30019 In this example the command
30027 \begin_layout Plain Layout
30038 was inserted to the formula.
30041 \begin_layout Standard
30050 \begin_layout Plain Layout
30061 is inserted instead, the star prevents the parentheses around the expression:
30062 \begin_inset Formula \[
30063 A+B=C\tag*{something}\]
30070 \begin_layout Standard
30071 \begin_inset VSpace bigskip
30074 To restart the formula numbering with new document parts or sections, the
30075 following command is used:
30078 \begin_layout Standard
30083 @addtoreset{equation}{part}
30089 \begin_layout Plain Layout
30094 \begin_layout Plain Layout
30105 \begin_layout Plain Layout
30118 \begin_layout Plain Layout
30129 \begin_layout Plain Layout
30142 \begin_inset Newline newline
30146 \begin_inset Newline newline
30153 @addtoreset{equation}{section}
30156 \begin_layout Standard
30157 To be able to use these commands in TeX-mode, the
30158 \begin_inset Quotes eld
30162 \begin_inset Quotes erd
30165 character has to be made
30166 \begin_inset Quotes eld
30170 \begin_inset Quotes erd
30173 for LaTeX using the command
30187 So the command sequence in TeX-mode is:
30190 \begin_layout Standard
30196 \begin_inset Newline newline
30201 @addtoreset{equation}{section}
30202 \begin_inset Newline newline
30210 \begin_layout Standard
30211 In the LaTeX-preamble
30223 can be omitted as they are automatically internally inserted by LyX.
30226 \begin_layout Standard
30241 \begin_layout Plain Layout
30246 is part of the LaTeX-package
30254 \begin_layout Plain Layout
30255 Packages ! carlisle
30260 that is part of every LaTeX standard installation.
30269 \begin_layout Plain Layout
30270 Packages ! remreset
30275 has to be loaded in the LaTeX-preamble with the line
30278 \begin_layout Standard
30283 usepackage{remreset}
30286 \begin_layout Standard
30297 \begin_layout Plain Layout
30302 \begin_layout Plain Layout
30313 \begin_layout Plain Layout
30326 \begin_layout Plain Layout
30337 \begin_layout Plain Layout
30349 can be used with the same scheme as
30358 \begin_layout Standard
30359 \begin_inset VSpace bigskip
30362 Sometimes formulas should be numbered in the following form:
30365 \begin_layout Standard
30368 (section number.formula number)
30371 \begin_layout Standard
30372 The formula number should start with every section with
30373 \begin_inset Quotes eld
30377 \begin_inset Quotes erd
30383 \begin_layout Standard
30384 For this case there is the command
30394 \begin_layout Plain Layout
30402 , which is used with the following scheme:
30405 \begin_layout Standard
30410 numberwithin{counter}{sectioning}
30413 \begin_layout Standard
30414 Counter denotes what kind of numbering is affected, sectioning denotes what
30415 number is before the dot.
30418 \begin_layout Standard
30419 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30422 \begin_layout Standard
30427 numberwithin{equation}{section}
30430 \begin_layout Standard
30431 This is the result:
30435 \begin_layout Plain Layout
30439 numberwithin{equation}{section}
30445 \begin_inset Formula \begin{equation}
30446 A+B=C\end{equation}
30453 \begin_layout Standard
30455 \begin_inset space \thinspace{}
30459 \begin_inset space \space{}
30462 tables so that the number of the part is the sectioning,
30463 \begin_inset Newline newline
30470 numberwithin{table}{part}
30475 \begin_layout Standard
30476 To go back to the standard numbering or to prevent this kind of numbering
30477 when it is defined by the document class, the following command is inserted
30478 as TeX-Code or to the LaTeX-preamble:
30481 \begin_layout Standard
30494 \begin_layout Plain Layout
30508 \begin_layout Plain Layout
30524 \begin_inset Newline newline
30532 \begin_inset Newline newline
30544 \begin_layout Standard
30551 uses internally the command
30557 , described above, that also needs to be reverted.
30561 \begin_layout Plain Layout
30568 \begin_layout Plain Layout
30572 @removefromreset{equation}{section}
30575 \begin_layout Plain Layout
30587 \begin_layout Subsection
30588 Numbering with Roman Numbers and Letters
30592 \begin_layout Plain Layout
30593 Formula numbering ! with letters
30602 \begin_layout Plain Layout
30603 Formula numbering ! with Roman numbers
30611 \begin_layout Standard
30612 Formulas can also be numbered with Roman numbers and Latin letters.
30613 To number for example with small Roman numbers, the command
30616 \begin_layout Standard
30628 \begin_layout Standard
30629 is inserted before the formula in TeX-mode.
30640 \begin_layout Plain Layout
30648 redefines the predefined command
30664 \begin_layout Plain Layout
30671 has the same scheme like the command
30677 that is described in
30678 \begin_inset CommandInset ref
30680 reference "sub:The-Command-newcommand"
30693 is the formula counter.
30700 is used as prefix for a counter, the value of the counter is output as
30702 When a formula is numbered, LaTeX sets internally the command
30708 behind the formula.
30717 \begin_layout Plain Layout
30727 outputs the counter as small Roman number.
30730 \begin_layout Standard
30731 All formulas behind the command
30741 are now numbered Roman.
30742 To switch to numbering with big Roman numbers, the command is inserted
30759 \begin_layout Plain Layout
30771 \begin_inset Quotes eld
30775 \begin_inset Quotes erd
30778 with small Latin letters there is the command
30788 \begin_layout Plain Layout
30796 , for big ones there is the command
30806 \begin_layout Plain Layout
30819 \begin_layout Standard
30820 \begin_inset Note Greyedout
30823 \begin_layout Plain Layout
30828 Only maximal 26 formulas can be numbered with Latin letters in one document.
30836 \begin_layout Standard
30840 \begin_layout Plain Layout
30856 \begin_layout Standard
30857 \begin_inset Formula \begin{equation}
30858 A=\textrm{small roman}\label{eq:rom}\end{equation}
30866 \begin_layout Plain Layout
30880 \begin_inset Formula \begin{equation}
30881 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30889 \begin_layout Plain Layout
30903 \begin_inset Formula \begin{equation}
30904 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30912 \begin_layout Plain Layout
30926 \begin_inset Formula \begin{equation}
30927 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30934 \begin_layout Standard
30935 To switch back to the default numbering, insert the command:
30938 \begin_layout Standard
30951 \begin_layout Plain Layout
30962 \begin_layout Standard
30966 \begin_layout Plain Layout
30980 \begin_inset Formula \begin{equation}
30981 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30988 \begin_layout Standard
30989 \begin_inset VSpace medskip
30992 As you see, formulas are numbered serially independent from the numbering
30994 When then numbering should start with
30995 \begin_inset Quotes eld
30999 \begin_inset Quotes erd
31002 when the style is changed, new equation counters have to be defined.
31003 A description about this can be found in the file
31004 \begin_inset CommandInset href
31006 target "Formula-numbering.lyx"
31013 \begin_layout Section
31014 User-defined Commands
31018 \begin_layout Plain Layout
31019 User-defined commands
31027 \begin_layout Standard
31028 \begin_inset Note Greyedout
31031 \begin_layout Plain Layout
31036 The names of user-defined commands and macros may only consist of Latin
31045 \begin_layout Subsection
31049 \begin_inset CommandInset label
31051 name "sub:The-Command-newcommand"
31059 \begin_layout Plain Layout
31060 User-defined commands !
31071 \begin_layout Plain Layout
31082 \begin_layout Standard
31083 Many LaTeX-commands are too long to be used frequently.
31084 But it is possible to define with the command
31090 new shorter commands.
31093 \begin_layout Standard
31094 The command scheme of
31103 \begin_layout Standard
31108 newcommand{new command name}[number of arguments][optional
31113 \begin_inset Newline newline
31120 \begin_layout Plain Layout
31135 \begin_layout Plain Layout
31142 {command definition}
31145 \begin_layout Standard
31146 \begin_inset Note Greyedout
31149 \begin_layout Plain Layout
31154 Assure that the name of the new command is not already used in your document
31155 or by LaTeX-packages that you use.
31156 When you for example define the command
31168 , you get an error message because
31174 is already defined as command for
31175 \begin_inset Quotes eld
31179 \begin_inset Formula $\le$
31183 \begin_inset Quotes erd
31194 \begin_layout Standard
31195 The number of arguments is an integer in the range 0
31196 \begin_inset space \thinspace{}
31200 \begin_inset space \thinspace{}
31203 9 and specifies how many arguments the new command should have.
31204 With the optional value a value for an optional argument can be predefined.
31205 When this is done, the
31213 rgument of the new command is automatically an optional one.
31216 \begin_layout Standard
31217 Here are some examples:
31220 \begin_layout Itemize
31221 To define the command
31233 , the LaTeX-preamble line is:
31234 \begin_inset VSpace medskip
31238 \begin_inset Newline newline
31252 \begin_layout Itemize
31253 To define the command
31265 , the argument (that should be underlined) must be taken into account.
31266 For this the preamble line is:
31267 \begin_inset VSpace medskip
31271 \begin_inset Newline newline
31285 \begin_inset VSpace medskip
31289 \begin_inset Newline newline
31296 acts as argument placeholder, the
31300 behind it denotes that it is the placeholder for the first argument.
31303 \begin_layout Itemize
31311 \begin_inset space \thinspace{}
31315 \begin_inset space \space{}
31325 \begin_inset VSpace medskip
31329 \begin_inset Newline newline
31340 framebox#1#2{$#3$}}
31343 \begin_inset VSpace medskip
31347 \begin_inset Newline newline
31350 The two Dollar signs creates the extra formula needed for
31357 \begin_inset CommandInset ref
31359 reference "sub:Boxes-with-Frame"
31366 \begin_layout Itemize
31367 To create a new command for
31373 where the color for the box needn't to be specified, the argument for the
31374 color is defined optional:
31375 \begin_inset VSpace medskip
31379 \begin_inset Newline newline
31390 fcolorbox{#2}{#1}{$#3$}}
31393 \begin_inset VSpace medskip
31397 \begin_inset Newline newline
31400 When the color is not specified when using
31406 , the predefined color
31413 \begin_layout Standard
31414 A test of the new defined commands:
31417 \begin_layout Standard
31419 \begin_inset Tabular
31420 <lyxtabular version="3" rows="6" columns="2">
31421 <features tabularvalignment="middle">
31422 <column alignment="center" valignment="top" width="0">
31423 <column alignment="center" valignment="top" width="0">
31425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31428 \begin_layout Plain Layout
31434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31437 \begin_layout Plain Layout
31439 \begin_inset Note Note
31442 \begin_layout Plain Layout
31449 is only used as spacer.
31461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31464 \begin_layout Plain Layout
31471 \begin_layout Plain Layout
31485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31488 \begin_layout Plain Layout
31489 \begin_inset Formula $A\gr B$
31499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31502 \begin_layout Plain Layout
31510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31513 \begin_layout Plain Layout
31514 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31527 \begin_layout Plain Layout
31531 \begin_inset Formula $\to$
31537 \begin_inset Formula $\to$
31548 \begin_layout Plain Layout
31562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31565 \begin_layout Plain Layout
31566 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31579 \begin_layout Plain Layout
31583 \begin_inset Formula $\to$
31594 \begin_layout Plain Layout
31608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31611 \begin_layout Plain Layout
31612 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31625 \begin_layout Plain Layout
31631 \begin_inset Formula $\to$
31642 \begin_layout Plain Layout
31656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31659 \begin_layout Plain Layout
31660 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31676 \begin_layout Subsection
31681 \begin_layout Plain Layout
31682 User-defined commands! Math macros
31691 \begin_layout Plain Layout
31700 \begin_layout Standard
31701 User-defined commands are especially convenient for complex expressions.
31702 When you are for example dealing in a document with quadratic equations,
31703 the same solution type occurs several times.
31704 The general form of a quadratic equation is
31705 \begin_inset Formula \[
31706 0=\lambda^{2}+p\lambda+q\]
31710 The general form of the solution is
31711 \begin_inset Formula \[
31712 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31719 \begin_layout Standard
31720 To define a command for the solution formula where only the three parameters
31722 \begin_inset Formula $\lambda$
31726 \begin_inset Formula $p$
31730 \begin_inset Formula $q$
31733 need to be specified and the index of
31734 \begin_inset Formula $\lambda$
31737 can be given optionally, the LaTeX-preamble line is
31738 \begin_inset Newline newline
31754 \begin_inset Newline newline
31761 \begin_layout Plain Layout
31776 \begin_layout Plain Layout
31787 frac{#3^{2}}{4}-#4}}
31790 \begin_layout Standard
31791 To create with this the solution formula, the command
31792 \begin_inset Newline newline
31802 \begin_inset Formula $\to$
31808 \begin_inset Formula $\to$
31815 is inserted to a formula
31820 \begin_layout Standard
31821 The definition of the new command is unintuitive because one has to know
31822 the schemes of all used LaTeX commands, e.
31823 \begin_inset space \thinspace{}
31827 \begin_inset space \space{}
31830 that a fraction is inserted in LaTeX as
31834 frac{numerator}{denominator}
31837 Furthermore one can easily forget a brace in the definition and cannot
31838 see in LyX what the new command is doing.
31839 To avoid these problems LyX offers the possibility to use math macros instead
31849 \begin_layout Standard
31850 A math macro is created by using the menu
31852 Insert\SpecialChar \menuseparator
31853 Math\SpecialChar \menuseparator
31856 or the toolbar button
31857 \begin_inset Graphics
31858 filename ../images/math-macro_newmacroname_newcommand.png
31864 The math macro toolbar appears together with the following box where the
31866 \begin_inset Newline newline
31870 \begin_inset space \hspace*{\fill}
31874 \begin_inset Graphics
31875 filename clipart/macrobox.png
31882 \begin_inset space \hspace*{\fill}
31886 \begin_inset Newline newline
31890 \begin_inset FormulaMacro
31891 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
31896 newmacroname is the default name of the macro that should be changed to
31897 something sensible.
31898 The wanted formula is inserted in the first blue box.
31899 An argument placeholder is inserted with the command
31906 \begin_inset space \thinspace{}
31910 \begin_inset space \space{}
31919 or by using the macro toolbar button
31920 \begin_inset Graphics
31921 filename ../images/math-macro-add-param.png
31927 Argument placeholders are displayed red.
31928 Maximum 9 arguments are possible.
31929 Optional arguments are created with the toolbar button
31930 \begin_inset Graphics
31931 filename ../images/math-macro-add-optional-param.png
31937 The first non-optional argument can be transformed to an optional one with
31939 \begin_inset Graphics
31940 filename ../images/math-macro-make-optional.png
31946 In the second blue box the appearance of the macro in LyX can be defined.
31947 Normally you want to see it as it is defined, so the box is kept empty.
31948 But when you have created a macro that needs lot of space on the screen,
31949 you can insert in the box for example
31950 \begin_inset Newline newline
31980 \begin_inset Newline newline
31985 For the macro only the arguments with the macro name in front of them will
31986 then be displayed in LyX, leading to a better overview.
31987 The formula appears in the output as defined in the first box.
31988 \begin_inset Newline newline
31991 The appearance of macros in formulas can furthermore be changed for single
31992 macros by setting the cursor in the macro and using the menu
31994 View\SpecialChar \menuseparator
31996 \begin_inset space ~
32000 \begin_inset space ~
32008 \begin_layout Standard
32009 To use a macro, the macro name is inserted as command to a formula, in our
32017 Our macro looks in LyX like this:
32018 \begin_inset Newline newline
32022 \begin_inset space \hspace*{\fill}
32026 \begin_inset Graphics
32027 filename clipart/macrouse.png
32034 \begin_inset space \hspace*{\fill}
32038 \begin_inset Newline newline
32041 Here is our macro example with the arguments
32042 \begin_inset Formula $x$
32046 \begin_inset Formula $\ln(x)$
32050 \begin_inset Formula $B$
32056 \begin_layout Standard
32057 \begin_inset Formula \[
32065 \begin_layout Standard
32066 A math macro is transformed internally to a
32072 command when exporting the document.
32079 command is not placed in the LaTeX-preamble, therefore macros can only
32080 be used in formulas that are in the document below the macro definition
32084 \begin_layout Standard
32085 Math macros can also be directly be created from a
32092 When writing for example the command
32095 \begin_inset Newline newline
32104 xleftarrow[#2]{#1}}
32105 \begin_inset Newline newline
32110 in LyX as normal text, highlighting it completely and using then the shortcut
32115 , the command will be transformed to a math macro.
32116 Using this method you need to be careful that the
32122 command is typed correctly, otherwise you get a faulty macro leading to
32126 \begin_layout Standard
32127 Math macros currently yet have the problem that further formulas in macro
32128 definitions are handled wrongly.
32129 Therefore the example
32136 \begin_inset CommandInset ref
32138 reference "sub:The-Command-newcommand"
32142 cannot be created as macro.
32145 \begin_layout Standard
32146 When the cursor is in a macro definition box, you will see the macro toolbar
32150 \begin_layout Standard
32151 \begin_inset VSpace defskip
32157 \begin_layout Standard
32158 \begin_inset Graphics
32159 filename clipart/MacroToolbar.png
32167 \begin_layout Plain Layout
32176 \begin_layout Standard
32177 \begin_inset VSpace defskip
32183 \begin_layout Standard
32184 The macro toolbar contains from left to right the following buttons:
32187 \begin_layout Standard
32188 \begin_inset VSpace defskip
32194 \begin_layout Standard
32195 \begin_inset Tabular
32196 <lyxtabular version="3" rows="9" columns="2">
32197 <features islongtable="true" tabularvalignment="middle">
32198 <column alignment="left" valignment="top" width="0">
32199 <column alignment="left" valignment="top" width="85col%">
32200 <row interlinespace="2.5mm">
32201 <cell alignment="center" valignment="top" usebox="none">
32204 \begin_layout Plain Layout
32205 \begin_inset Graphics
32206 filename ../images/math-macro-remove-param.png
32207 BoundingBox 0bp 5bp 20bp 25bp
32208 rotateOrigin center
32217 <cell alignment="center" valignment="top" usebox="none">
32220 \begin_layout Plain Layout
32223 Edit\SpecialChar \menuseparator
32224 Math\SpecialChar \menuseparator
32226 \begin_inset space ~
32229 Definition\SpecialChar \menuseparator
32236 <row interlinespace="2.5mm">
32237 <cell alignment="center" valignment="top" usebox="none">
32240 \begin_layout Plain Layout
32241 \begin_inset Graphics
32242 filename ../images/math-macro-add-param.png
32243 BoundingBox 0bp 5bp 20bp 25bp
32244 rotateOrigin center
32253 <cell alignment="center" valignment="top" usebox="none">
32256 \begin_layout Plain Layout
32259 Edit\SpecialChar \menuseparator
32260 Math\SpecialChar \menuseparator
32262 \begin_inset space ~
32265 Definition\SpecialChar \menuseparator
32266 Append Last Argument
32272 <row interlinespace="2.5mm">
32273 <cell alignment="center" valignment="top" usebox="none">
32276 \begin_layout Plain Layout
32277 \begin_inset Graphics
32278 filename ../images/math-macro-make-optional.png
32279 BoundingBox 0bp 5bp 20bp 25bp
32280 rotateOrigin center
32289 <cell alignment="center" valignment="top" usebox="none">
32292 \begin_layout Plain Layout
32295 Edit\SpecialChar \menuseparator
32296 Math\SpecialChar \menuseparator
32298 \begin_inset space ~
32301 Definition\SpecialChar \menuseparator
32302 Make First Non-Optional into
32303 \begin_inset Newline newline
32310 \begin_layout Plain Layout
32319 Edit\SpecialChar \menuseparator
32320 Math\SpecialChar \menuseparator
32322 \begin_inset space ~
32325 Definition\SpecialChar \menuseparator
32330 \begin_layout Plain Layout
32343 <row interlinespace="2.5mm">
32344 <cell alignment="center" valignment="top" usebox="none">
32347 \begin_layout Plain Layout
32348 \begin_inset Graphics
32349 filename ../images/math-macro-make-nonoptional.png
32350 BoundingBox 0bp 5bp 20bp 25bp
32351 rotateOrigin center
32360 <cell alignment="center" valignment="top" usebox="none">
32363 \begin_layout Plain Layout
32366 Edit\SpecialChar \menuseparator
32367 Math\SpecialChar \menuseparator
32369 \begin_inset space ~
32372 Definition\SpecialChar \menuseparator
32373 Make Last Optional into
32374 \begin_inset Newline newline
32381 \begin_layout Plain Layout
32390 Edit\SpecialChar \menuseparator
32391 Math\SpecialChar \menuseparator
32393 \begin_inset space ~
32396 Definition\SpecialChar \menuseparator
32401 \begin_layout Plain Layout
32408 Non-Optional Argument
32414 <row interlinespace="2.5mm">
32415 <cell alignment="center" valignment="top" usebox="none">
32418 \begin_layout Plain Layout
32419 \begin_inset Graphics
32420 filename ../images/math-macro-remove-optional-param.png
32421 BoundingBox 0bp 5bp 20bp 25bp
32422 rotateOrigin center
32431 <cell alignment="center" valignment="top" usebox="none">
32434 \begin_layout Plain Layout
32437 Edit\SpecialChar \menuseparator
32438 Math\SpecialChar \menuseparator
32440 \begin_inset space ~
32443 Definition\SpecialChar \menuseparator
32444 Remove Optional Argument
32450 <row interlinespace="2.5mm">
32451 <cell alignment="center" valignment="top" usebox="none">
32454 \begin_layout Plain Layout
32455 \begin_inset Graphics
32456 filename ../images/math-macro-add-optional-param.png
32457 BoundingBox 0bp 5bp 20bp 25bp
32458 rotateOrigin center
32467 <cell alignment="center" valignment="top" usebox="none">
32470 \begin_layout Plain Layout
32473 Edit\SpecialChar \menuseparator
32474 Math\SpecialChar \menuseparator
32476 \begin_inset space ~
32479 Definition\SpecialChar \menuseparator
32480 Insert Optional Argument
32486 <row interlinespace="2.5mm">
32487 <cell alignment="center" valignment="top" usebox="none">
32490 \begin_layout Plain Layout
32491 \begin_inset Graphics
32492 filename ../images/math-macro-remove-greedy-param.png
32493 BoundingBox 0bp 5bp 20bp 25bp
32494 rotateOrigin center
32503 <cell alignment="center" valignment="top" usebox="none">
32506 \begin_layout Plain Layout
32509 Edit\SpecialChar \menuseparator
32510 Math\SpecialChar \menuseparator
32512 \begin_inset space ~
32515 Definition\SpecialChar \menuseparator
32516 Remove Last Argument
32517 \begin_inset Newline newline
32524 \begin_layout Plain Layout
32533 Edit\SpecialChar \menuseparator
32534 Math\SpecialChar \menuseparator
32536 \begin_inset space ~
32539 Definition\SpecialChar \menuseparator
32544 \begin_layout Plain Layout
32551 Spitting Out To The Right
32557 <row interlinespace="2.5mm">
32558 <cell alignment="center" valignment="top" usebox="none">
32561 \begin_layout Plain Layout
32562 \begin_inset Graphics
32563 filename ../images/math-macro-append-greedy-param.png
32564 BoundingBox 0bp 5bp 20bp 25bp
32565 rotateOrigin center
32574 <cell alignment="center" valignment="top" usebox="none">
32577 \begin_layout Plain Layout
32580 Edit\SpecialChar \menuseparator
32581 Math\SpecialChar \menuseparator
32583 \begin_inset space ~
32586 Definition\SpecialChar \menuseparator
32588 \begin_inset Newline newline
32595 \begin_layout Plain Layout
32604 Edit\SpecialChar \menuseparator
32605 Math\SpecialChar \menuseparator
32607 \begin_inset space ~
32610 Definition\SpecialChar \menuseparator
32615 \begin_layout Plain Layout
32622 Eating From The Right
32628 <row interlinespace="2.5mm">
32629 <cell alignment="center" valignment="top" usebox="none">
32632 \begin_layout Plain Layout
32633 \begin_inset Graphics
32634 filename ../images/math-macro-add-greedy-optional-param.png
32635 BoundingBox 0bp 5bp 20bp 25bp
32636 rotateOrigin center
32645 <cell alignment="center" valignment="top" usebox="none">
32648 \begin_layout Plain Layout
32651 Edit\SpecialChar \menuseparator
32652 Math\SpecialChar \menuseparator
32654 \begin_inset space ~
32657 Definition\SpecialChar \menuseparator
32658 Append Optional Argument
32659 \begin_inset Newline newline
32666 \begin_layout Plain Layout
32675 Edit\SpecialChar \menuseparator
32676 Math\SpecialChar \menuseparator
32678 \begin_inset space ~
32681 Definition\SpecialChar \menuseparator
32686 \begin_layout Plain Layout
32693 Eating From The Right
32706 \begin_layout Standard
32707 \begin_inset Newpage newpage
32713 \begin_layout Section
32717 \begin_layout Standard
32718 LyX supports two types of commutative diagrams:
32726 that are explained in the following.
32729 \begin_layout Subsection
32734 \begin_layout Plain Layout
32743 \begin_layout Standard
32744 Diagrams of this type visualize relations by vertical and horizontal lines
32746 \begin_inset Formula \[
32747 \begin{CD}A@>>>B@>>>C\\
32749 F@<<<E@<<<D\end{CD}\]
32756 \begin_layout Standard
32757 To get them, the command
32765 \begin_layout Plain Layout
32775 is inserted to a formula.
32776 A blue box appears with two dashed lines where further commands can be
32781 arg "newline-insert newline"
32784 a new line is created.
32785 Horizontal relations are inserted in odd, vertical in even formula lines.
32788 \begin_layout Standard
32789 To create the relations there are the following commands:
32792 \begin_layout Itemize
32797 creates a left arrow,
32808 \begin_layout Itemize
32813 creates an up arrow,
32821 a vertical equal sign
32824 \begin_layout Itemize
32830 is a placeholder for non-existent relations
32833 \begin_layout Standard
32834 All arrows can be labeled as follows:
32837 \begin_layout Itemize
32838 Is text inserted between the first and second < or >, resp., it is placed
32840 When it is inserted between the second and third one, it appears under
32844 \begin_layout Itemize
32845 When text for vertical arrows is inserted between the first and second A
32846 or V, resp., it is placed left beside the arrow.
32847 When it is inserted between the second and third one, it appears right
32849 If the text contains an A or V, these letters must be set into a TeX-brace.
32852 \begin_layout Standard
32853 As example a diagram with all possible relations:
32856 \begin_layout Standard
32857 \begin_inset Formula \[
32858 \begin{CD}A@>j>>B@>>k>C@=F\\
32860 D@<<j<E@>k>>F@=C\end{CD}\]
32867 \begin_layout Standard
32868 The command for this is:
32869 \begin_inset Newline newline
32880 \begin_layout Plain Layout
32889 A@>j>>B@>>k>C@=F Ctrl+Return
32890 \begin_inset Newline newline
32897 \begin_layout Plain Layout
32912 \begin_layout Plain Layout
32925 \begin_layout Plain Layout
32937 \begin_inset Formula $\to$
32943 \begin_inset Newline newline
32950 \begin_layout Plain Layout
32965 \begin_layout Plain Layout
32978 \begin_layout Plain Layout
32988 \begin_layout Subsection
32993 \begin_layout Plain Layout
32994 Diagrams ! xymatrix
33002 \begin_layout Standard
33003 To be able to use xymatrices, the LaTeX-package
33008 A xymatrix is created by inserting the command
33015 Then you are able to add new matrix columns and rows like for normal matrices,
33017 \begin_inset CommandInset ref
33019 reference "sec:Matrices"
33026 \begin_layout Standard
33027 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33029 All possibilities to create commutative diagrams and decorations are explained
33034 that you find in the menu
33036 Help\SpecialChar \menuseparator
33038 \begin_inset space ~
33041 Manuals\SpecialChar \menuseparator
33043 \begin_inset space ~
33051 \begin_layout Standard
33052 \begin_inset Newpage newpage
33058 \begin_layout Section
33063 \begin_layout Plain Layout
33076 \begin_layout Plain Layout
33077 Other useful math tips can be found in
33078 \begin_inset CommandInset citation
33093 \begin_layout Plain Layout
33101 \begin_inset Note Note
33104 \begin_layout Plain Layout
33107 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33110 \begin_layout Plain Layout
33113 texorpdfstring is in section
33114 \begin_inset CommandInset ref
33116 reference "sub:Formulas-in-Section"
33129 \begin_layout Plain Layout
33139 \begin_layout Plain Layout
33144 \begin_layout Plain Layout
33151 Chemical characters
33155 \begin_layout Plain Layout
33170 \begin_layout Subsection
33171 Chemical Symbols and Equations
33172 \begin_inset CommandInset label
33174 name "sub:Chemical-Symbols-and"
33182 \begin_layout Plain Layout
33183 Chemical characters ! Symbols
33192 \begin_layout Plain Layout
33202 \begin_layout Plain Layout
33211 \begin_layout Standard
33212 An example text from chemistry:
33215 \begin_layout Quote
33217 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33220 -ion reacts with two
33221 \begin_inset Formula $\mathrm{Na^{+}}$
33224 -ions to sodium sulfate
33225 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33229 The chemical equation for this is:
33230 \begin_inset Formula \[
33231 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33238 \begin_layout Standard
33239 This chemical equation can directly be created as formula.
33240 To avoid that the symbols appear italic, everything is highlighted and
33241 changed by the shortcut
33247 to the upright font style.
33251 \begin_layout Plain Layout
33257 \begin_inset CommandInset ref
33259 reference "sub:Font-Styles"
33271 \begin_layout Subsection
33276 \begin_layout Plain Layout
33285 \begin_layout Standard
33286 Negative numbers often look ugly in formulas because the minus sign before
33287 the number is set with the same length as the minus operator sign.
33288 When writing the negative number in normal text, the minus sign appears
33292 \begin_layout Standard
33293 Thus, the problem disappears when converting the minus sign to mathematical
33297 \begin_layout Standard
33298 An example to visualize the problem:
33301 \begin_layout Standard
33303 \begin_inset Tabular
33304 <lyxtabular version="3" rows="3" columns="2">
33305 <features tabularvalignment="middle">
33306 <column alignment="right" valignment="top" width="0">
33307 <column alignment="left" valignment="top" width="0">
33309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33312 \begin_layout Plain Layout
33318 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33321 \begin_layout Plain Layout
33329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33332 \begin_layout Plain Layout
33338 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33341 \begin_layout Plain Layout
33342 \begin_inset Formula $x=-2$
33352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33355 \begin_layout Plain Layout
33361 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33364 \begin_layout Plain Layout
33365 \begin_inset Formula $x=\textrm{-}2$
33381 \begin_layout Subsection
33382 Comma as decimal Separator
33386 \begin_layout Plain Layout
33395 \begin_layout Standard
33396 In LaTeX a comma inside a formula is used, according to the English convention,
33397 as number group separator.
33398 So there will be space added behind all commas in formulas.
33401 \begin_layout Standard
33402 To avoid this, the comma is highlighted and changed to mathematical text
33412 \begin_layout Standard
33413 To use all formula commas in the document as decimal separator, the file
33422 \begin_layout Plain Layout
33427 is part of the LaTeX-package
33435 \begin_layout Plain Layout
33440 \begin_layout Plain Layout
33463 \begin_layout Plain Layout
33469 is loaded with the LaTeX-preamble line
33472 \begin_layout Standard
33480 \begin_layout Subsection
33482 \begin_inset CommandInset label
33484 name "sub:Physical-Vectors"
33492 \begin_layout Plain Layout
33501 \begin_layout Standard
33502 Predefined vectors are offered by the LaTeX-package
33510 \begin_layout Plain Layout
33515 should be part of every LaTeX standard installation.
33524 \begin_layout Plain Layout
33530 that is loaded with the LaTeX-preamble line
33533 \begin_layout Standard
33541 \begin_layout Standard
33545 \begin_layout Plain Layout
33555 \begin_inset Note Note
33558 \begin_layout Plain Layout
33559 The following table will only be displayed when the LaTeX-package
33568 The following commands are defined:
33571 \begin_layout Standard
33573 \begin_inset Tabular
33574 <lyxtabular version="3" rows="4" columns="2">
33575 <features tabularvalignment="middle">
33576 <column alignment="center" valignment="top" width="0">
33577 <column alignment="center" valignment="top" width="0">
33579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33582 \begin_layout Plain Layout
33588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33591 \begin_layout Plain Layout
33599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33602 \begin_layout Plain Layout
33612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33615 \begin_layout Plain Layout
33616 \begin_inset Formula $\Bra{\psi}$
33626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33629 \begin_layout Plain Layout
33639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33642 \begin_layout Plain Layout
33643 \begin_inset Formula $\Ket{\psi}$
33653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33656 \begin_layout Plain Layout
33668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33671 \begin_layout Plain Layout
33672 \begin_inset Formula $\Braket{\psi|\phi}$
33688 \begin_layout Standard
33695 assures that all vertical bars are set in the size of the surrounding brackets:
33696 \begin_inset Formula \[
33697 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33705 \begin_layout Plain Layout
33715 \begin_inset Note Note
33718 \begin_layout Plain Layout
33719 The following will be displayed when the LaTeX-package
33731 \begin_layout Standard
33732 You need to install the LaTeX-package
33736 to see the rest of this subsection in the output.
33739 \begin_layout Standard
33743 \begin_layout Plain Layout
33755 \begin_layout Standard
33762 can also be achieved using the command
33768 , that is described in
33769 \begin_inset CommandInset ref
33771 reference "sub:Automatic-Bracket-Size"
33778 \begin_layout Subsection
33779 Self-defined Fractions
33780 \begin_inset CommandInset label
33782 name "sub:Self-defined-Fractions"
33790 \begin_layout Plain Layout
33791 Fractions ! self-defined
33799 \begin_layout Standard
33800 To define custom commands for fractions, the command
33810 \begin_layout Plain Layout
33818 is used in the following scheme:
33821 \begin_layout Standard
33834 bracket}{fraction bar thickness}{style}
33835 \begin_inset Newline newline
33842 \begin_layout Plain Layout
33857 \begin_layout Plain Layout
33864 {numerator}{denominator}
33867 \begin_layout Standard
33868 The style is a number in the range of 0
33869 \begin_inset space \thinspace{}
33873 \begin_inset space \thinspace{}
33879 \begin_layout Standard
33881 \begin_inset Tabular
33882 <lyxtabular version="3" rows="5" columns="2">
33883 <features tabularvalignment="middle">
33884 <column alignment="center" valignment="top" width="0">
33885 <column alignment="center" valignment="top" width="0">
33887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33890 \begin_layout Plain Layout
33896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33899 \begin_layout Plain Layout
33907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33910 \begin_layout Plain Layout
33916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33919 \begin_layout Plain Layout
33920 display style formula
33927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33930 \begin_layout Plain Layout
33936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33939 \begin_layout Plain Layout
33947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33950 \begin_layout Plain Layout
33956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33959 \begin_layout Plain Layout
33967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33970 \begin_layout Plain Layout
33976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33979 \begin_layout Plain Layout
33993 \begin_layout Standard
33994 When no style is given, the size is adjusted to the surrounding environment
33995 like for the command
34004 \begin_layout Standard
34005 When no fraction bar thickness is given, the predefined value of 0.4
34006 \begin_inset space \thinspace{}
34012 \begin_layout Standard
34013 \begin_inset VSpace medskip
34016 For example, the commands
34029 \begin_inset CommandInset ref
34031 reference "sub:Fractions"
34035 are defined with the commands
34038 \begin_layout Standard
34047 genfrac{}{}{}{0}{#1}{#2}}
34050 \begin_layout Standard
34054 \begin_layout Standard
34063 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34066 \begin_layout Standard
34067 \begin_inset VSpace medskip
34070 To define a fraction where the fraction bar thickness can be given as optional
34071 argument, the following line is inserted to the LaTeX-preamble:
34074 \begin_layout Standard
34083 genfrac{}{}{#1}{}{#2}{#3}}
34086 \begin_layout Standard
34088 \begin_inset Formula \begin{align*}
34089 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34090 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34094 As one can see, the distance of the numerator and the denominator to the
34095 fraction bar is round about three times the bar thickness.
34098 \begin_layout Subsection
34103 \begin_layout Plain Layout
34112 \begin_layout Standard
34113 To cancel formulas or formula parts, the LaTeX-package
34121 \begin_layout Plain Layout
34126 is part of every LaTeX standard installation.
34135 \begin_layout Plain Layout
34141 has to be loaded with the LaTeX-preamble line
34144 \begin_layout Standard
34149 usepackage[samesize]{cancel}
34152 \begin_layout Standard
34153 There are four ways to cancel formulas:
34156 \begin_layout Standard
34158 \begin_inset Tabular
34159 <lyxtabular version="3" rows="5" columns="2">
34160 <features tabularvalignment="middle">
34161 <column alignment="center" valignment="top" width="0">
34162 <column alignment="center" valignment="top" width="0">
34164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34167 \begin_layout Plain Layout
34173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34176 \begin_layout Plain Layout
34178 \begin_inset Note Note
34181 \begin_layout Plain Layout
34194 are used here as spacer.
34206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34209 \begin_layout Plain Layout
34218 \begin_layout Plain Layout
34232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34235 \begin_layout Plain Layout
34236 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34249 \begin_layout Plain Layout
34258 \begin_layout Plain Layout
34272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34275 \begin_layout Plain Layout
34276 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34289 \begin_layout Plain Layout
34298 \begin_layout Plain Layout
34312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34315 \begin_layout Plain Layout
34316 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34329 \begin_layout Plain Layout
34333 \begin_inset Formula $\to$
34344 \begin_layout Plain Layout
34358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34361 \begin_layout Plain Layout
34362 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34378 \begin_layout Standard
34385 is especially suitable to visualize the reduction of fractions within formulas:
34386 \begin_inset Formula \[
34387 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34394 \begin_layout Subsection
34395 Formulas in Section Headings
34396 \begin_inset CommandInset label
34398 name "sub:Formulas-in-Section"
34406 \begin_layout Plain Layout
34407 Formula ! in section headings
34415 \begin_layout Standard
34416 When formulas are used in section headings, the following has to be taken
34420 \begin_layout Standard
34421 \begin_inset Note Greyedout
34424 \begin_layout Plain Layout
34433 \begin_layout Plain Layout
34434 Packages ! hyperref
34439 support is enabled in the document settings dialog under
34442 \begin_inset space ~
34447 , PDF-bookmarks are created for every section heading in the table of contents.
34448 If a section heading contains formulas, they are incorrectly displayed
34449 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34458 \begin_layout Standard
34459 Both problems can be solved by inserting at the end of the section heading
34460 a short title with the menu
34462 Insert\SpecialChar \menuseparator
34464 \begin_inset space ~
34470 Short titles are used as alternative for multiline section headings to
34471 keep the table of contents clearly arranged.
34472 Only the short title appears in the table of contents and therefore also
34473 in the PDF-bookmark.
34476 \begin_layout Standard
34477 When formulas should be used in the table of contents but
34481 is used, one can use the following command in TeX-mode:
34484 \begin_layout Standard
34489 texorpdfstring{part}{alternative}
34493 \begin_layout Plain Layout
34504 \begin_layout Standard
34505 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34506 This can be characters, formulas, footnotes, but also cross-references.
34507 The alternative is used instead of the part for the bookmark.
34510 \begin_layout Standard
34511 Here are two example headings:
34512 \begin_inset VSpace -3mm
34519 \begin_layout Plain Layout
34531 \begin_layout Subsubsection
34532 Heading without formula in table of contents
34533 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34537 \begin_inset OptArg
34540 \begin_layout Plain Layout
34541 Heading without formula in table of contents
34549 \begin_layout Subsubsection
34550 Heading with formula in table of contents
34554 \begin_layout Plain Layout
34564 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34571 \begin_layout Plain Layout
34581 \begin_layout Standard
34585 \begin_layout Plain Layout
34594 In the first heading a short title was used, in the second one
34603 \begin_layout Standard
34604 To get the same formatting as for the other headings, the complete heading
34613 \begin_layout Plain Layout
34615 \begin_inset CommandInset ref
34617 reference "sub:Bold-Formulas"
34629 \begin_layout Subsection
34630 Formulas in multi-column Text
34634 \begin_layout Plain Layout
34635 Formula ! in multi-column text
34643 \begin_layout Standard
34644 Formulas in multi-column text are often too wide to fit into a column and
34645 thus need to be set over the whole page width.
34646 This is done by using the LaTeX-package
34654 \begin_layout Plain Layout
34659 is part of every LaTeX standard installation.
34668 \begin_layout Plain Layout
34669 Packages ! multicol
34674 , that is loaded with the LaTeX-preamble line
34677 \begin_layout Standard
34682 usepackage{multicol}
34685 \begin_layout Standard
34686 \begin_inset Note Greyedout
34689 \begin_layout Plain Layout
34690 Note herby that the setting
34693 \begin_inset space ~
34700 Document\SpecialChar \menuseparator
34706 \begin_inset space ~
34726 \begin_layout Standard
34727 Before the multi-column text the command
34730 \begin_layout Standard
34735 begin{multicols}{column number}
34738 \begin_layout Standard
34739 is written in TeX-mode.
34740 The column number is a number in the range of 2
34741 \begin_inset space \thinspace{}
34745 \begin_inset space \thinspace{}
34749 Before the formula the multi-column text is ended by inserting the command
34752 \begin_layout Standard
34760 \begin_layout Standard
34764 \begin_layout Standard
34765 Due to the command some space is automatically added before the formula.
34767 \begin_inset space \thinspace{}
34770 mm vertical space is inserted before the formula.
34771 When the formula style
34777 \begin_layout Plain Layout
34779 \begin_inset CommandInset ref
34781 reference "sec:Formula-Styles"
34793 \begin_inset space \thinspace{}
34796 mm space is inserted instead.
34799 \begin_layout Standard
34800 As example a multi-column text with a displayed formula:
34803 \begin_layout Standard
34807 \begin_layout Plain Layout
34811 begin{multicols}{2}
34816 Das Spektrum wird fouriertransformiert.
34817 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34818 , Lösungsmittel) zu trennen.
34819 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34820 nun das Aussehen des Ausgangssignals.
34821 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34822 über alle Phasen integrieren muss.
34824 \begin_inset Formula $S$
34827 unser normiertes Ausgangssignal and
34828 \begin_inset Formula $P$
34831 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34835 \begin_layout Plain Layout
34845 \begin_inset VSpace -6mm
34849 \begin_inset Formula \begin{equation}
34850 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34858 \begin_layout Plain Layout
34862 begin{multicols}{2}
34868 \begin_inset Formula $S_{0}$
34871 das Signal ohne Gradient ist and the Normierungsbedingung
34872 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34876 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34878 \begin_inset Formula $\nicefrac{\pi}{2}$
34882 \begin_inset space \thinspace{}
34885 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34886 das Signal zusätzlich abschwächt.
34887 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34889 \begin_inset Formula $T_{2}$
34895 \begin_layout Standard
34899 \begin_layout Plain Layout
34911 \begin_layout Subsection
34912 Formulas with Description of Variables
34916 \begin_layout Plain Layout
34917 Formula ! with description of variables
34925 \begin_layout Standard
34926 To describe variables within a formula, like in formula
34927 \begin_inset CommandInset ref
34929 reference "eq:within"
34938 \begin_inset Formula $n$
34942 \begin_inset space ~
34945 matrix is used with left aligned columns for the
34946 \begin_inset Formula $n$
34953 \begin_layout Plain Layout
34955 \begin_inset CommandInset ref
34957 reference "sec:Matrices"
34966 To set the description in a smaller size, before the matrix e.
34967 \begin_inset space \thinspace{}
34971 \begin_inset space \space{}
34984 \begin_layout Plain Layout
34986 \begin_inset CommandInset ref
34988 reference "sub:Font-Sizes"
35000 \begin_layout Standard
35001 When the formula style
35007 \begin_layout Plain Layout
35009 \begin_inset CommandInset ref
35011 reference "sec:Formula-Styles"
35032 \begin_layout Plain Layout
35039 only works in formulas with the style
35044 \begin_inset CommandInset ref
35046 reference "sub:Variable-Space"
35055 is inserted before and after the matrix to have the same separation of
35056 the matrix from the equation and the side margin.
35059 \begin_layout Standard
35060 When the formula style
35064 is used, the method described in
35065 \begin_inset CommandInset ref
35067 reference "sub:Flalign-Environment"
35071 is used to indent formulas.
35073 \begin_inset CommandInset ref
35075 reference "eq:within"
35079 consists of five columns whereas in the first two columns contain the equation,
35080 the third the matrix, and the last one an empty TeX-brace.
35081 \begin_inset Formula \begin{flalign}
35082 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35083 \rho & \textrm{density}\\
35084 V & \textrm{volume}\\
35085 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35092 \begin_layout Subsection
35093 Upright small Greek Letters
35094 \begin_inset CommandInset label
35096 name "sub:Upright-small-Greek"
35104 \begin_layout Plain Layout
35105 Greek letters ! upright
35113 \begin_layout Standard
35114 Most of the math fonts only provide italic small Greek letters.
35115 But for symbols of elementary particles like pions and neutrinos, upright
35116 Greek letters are needed.
35125 \begin_layout Plain Layout
35130 is part of the LaTeX-package
35138 \begin_layout Plain Layout
35143 \begin_layout Plain Layout
35166 \begin_layout Plain Layout
35172 that is loaded with the LaTeX-preamble line
35175 \begin_layout Standard
35180 usepackage{upgreek}
35183 \begin_layout Standard
35189 \begin_layout Plain Layout
35199 \begin_inset Note Note
35202 \begin_layout Plain Layout
35203 The following table will only be displayed when the LaTeX-package
35212 They are created when the command for a small Greek letters is started
35218 For example the command
35225 \begin_inset Formula $\uptau$
35231 \begin_layout Standard
35232 With these commands reactions of elementary particles can be typeset:
35233 \begin_inset Formula \[
35234 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35241 \begin_layout Standard
35242 The upright letters are more bold and wider than the italic ones.
35243 They should therefore not be used for units like
35244 \begin_inset Quotes eld
35248 \begin_inset Quotes erd
35254 \begin_layout Standard
35258 \begin_layout Plain Layout
35268 \begin_inset Note Note
35271 \begin_layout Plain Layout
35272 The following will be displayed when the LaTeX-package
35284 \begin_layout Standard
35285 You need to install the LaTeX-package
35289 to see the rest of this subsection in the output.
35292 \begin_layout Standard
35296 \begin_layout Plain Layout
35308 \begin_layout Subsection
35309 Text Characters in Formulas
35310 \begin_inset CommandInset label
35312 name "sub:Text-Characters-in"
35320 \begin_layout Plain Layout
35329 \begin_layout Standard
35330 In some cases you might want to insert text characters directly into formulas.
35331 When for example the centered dot · is often used in formulas like
35332 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35335 , one would have to insert the command
35345 \begin_layout Plain Layout
35347 \begin_inset CommandInset ref
35349 reference "sub:Binary-Operators"
35358 all the time, because this character is defined in all encodings as text
35360 But the encoding can be changed by this LaTeX-preamble line:
35363 \begin_layout Standard
35368 Declare Inputtext{183}{
35378 f\SpecialChar \textcompwordmark{}
35382 \begin_layout Standard
35383 The character encoding (menu
35385 Document\SpecialChar \menuseparator
35386 Settings\SpecialChar \menuseparator
35389 ) specifies what character appears when a keyboard key is pressed.
35390 When the key for the character '·' is pressed, internally the command
35397 But this command is not available in a formula so that you would get LaTeX-erro
35399 With the changed encoding the right command is chosen automatically, depending
35400 on if the character was inserted into a formula or not.
35403 \begin_layout Standard
35404 The encoding of several characters is saved in definition files.
35405 Fore example the encoding
35409 is defined in the file
35413 that is in the installation folder of LaTeX.
35414 Encodings should only be changed via the LaTeX-preamble and not in the
35416 Otherwise own documents could not be edited by other LyX users working
35417 on other computers.
35420 \begin_layout Standard
35421 \begin_inset VSpace medskip
35424 Besides the centered dot, in this document the degree sign ° is defined
35425 with the following LaTeX-preamble line so that it can directly be inserted
35429 \begin_layout Standard
35434 DeclareInputtext{176}{
35444 f\SpecialChar \textcompwordmark{}
35448 \begin_layout Standard
35449 \begin_inset Newpage newpage
35455 \begin_layout Section
35461 \begin_layout Plain Layout
35470 \begin_layout Standard
35471 This section is a summary of the most important typographic rules, listed
35476 \begin_layout Plain Layout
35477 This collection was partly taken from the German semi-official dictionary
35479 \begin_inset Quotes eld
35483 \begin_inset Quotes erd
35487 \begin_inset CommandInset citation
35493 that lists some of the ISO rules.
35501 \begin_layout Itemize
35510 \begin_layout Plain Layout
35511 done with font styles, see
35512 \begin_inset CommandInset ref
35514 reference "sub:Font-Styles"
35524 \begin_inset space \thinspace{}
35528 \begin_inset Newline newline
35531 Between the value and the unit is the smallest space, see
35532 \begin_inset CommandInset ref
35534 reference "sub:Predefined-Space"
35539 \begin_inset Newline newline
35542 This convention is automatically fulfilled when the command
35549 When it is entered to a formula, two boxes appear.
35550 In the first one the value is inserted, in the second one the unit, and
35552 \begin_inset Formula $\unit[30]{km/h}$
35556 \begin_inset space \thinspace{}
35566 is not a real LaTeX command but the command
35572 , therefore you cannot use it in TeX code.
35575 \begin_layout Itemize
35576 Percent and perthousand signs are set like physical units:
35577 \begin_inset Newline newline
35581 \begin_inset space \thinspace{}
35587 \begin_layout Itemize
35588 The degree sign follows directly on the value: 15°, but not when it is used
35590 \begin_inset space \thinspace{}
35596 \begin_layout Itemize
35597 In numbers with more than four digits the smallest space is inserted before
35598 every third digit to group them:
35608 \begin_inset space \thinspace{}
35612 \begin_inset space \thinspace{}
35618 \begin_layout Itemize
35619 For dimensions like 120×90×40
35620 \begin_inset space \thinspace{}
35623 cm the multiplication sign
35624 \begin_inset Quotes eld
35628 \begin_inset Quotes erd
35632 It is available via the menu
35634 Insert\SpecialChar \menuseparator
35635 Special Character\SpecialChar \menuseparator
35639 With some keyboard definitions it can also be inserted directly.
35642 \begin_layout Itemize
35643 Functions with names consisting of several letters are set upright to avoid
35645 \begin_inset CommandInset ref
35647 reference "sub:Predefined-Functions"
35654 \begin_layout Itemize
35655 Indices consisting of several letters, are set upright:
35656 \begin_inset Formula $E_{\mathrm{kin}}$
35660 \begin_inset Newline newline
35663 Components of matrices are set italic:
35664 \begin_inset Formula $\hat{H}_{kl}$
35670 \begin_layout Itemize
35671 The differentiation/integration operator 'd', the Euler's number 'e', and
35672 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35676 \begin_layout Standard
35677 \begin_inset Newpage newpage
35683 \begin_layout Section
35688 \begin_layout Plain Layout
35697 \begin_layout Standard
35698 Some characters and symbols can be created with several commands.
35699 Here is a list of the synonym commands:
35702 \begin_layout Standard
35703 \begin_inset VSpace bigskip
35707 \begin_inset space \hfill{}
35711 \begin_inset Tabular
35712 <lyxtabular version="3" rows="12" columns="2">
35713 <features tabularvalignment="middle">
35714 <column alignment="center" valignment="top" width="0pt">
35715 <column alignment="center" valignment="top" width="0pt">
35717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35720 \begin_layout Plain Layout
35726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35729 \begin_layout Plain Layout
35731 \begin_inset Note Note
35734 \begin_layout Plain Layout
35741 is only used as spacer.
35753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35756 \begin_layout Plain Layout
35764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35767 \begin_layout Plain Layout
35771 \begin_layout Plain Layout
35784 \begin_layout Plain Layout
35798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35801 \begin_layout Plain Layout
35809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35812 \begin_layout Plain Layout
35822 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35825 \begin_layout Plain Layout
35833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35836 \begin_layout Plain Layout
35846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35849 \begin_layout Plain Layout
35857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35860 \begin_layout Plain Layout
35868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35871 \begin_layout Plain Layout
35879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35882 \begin_layout Plain Layout
35890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35893 \begin_layout Plain Layout
35901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35904 \begin_layout Plain Layout
35914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35917 \begin_layout Plain Layout
35925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35928 \begin_layout Plain Layout
35938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35941 \begin_layout Plain Layout
35949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35952 \begin_layout Plain Layout
35962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35965 \begin_layout Plain Layout
35973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35976 \begin_layout Plain Layout
35986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35989 \begin_layout Plain Layout
35997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36000 \begin_layout Plain Layout
36008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36011 \begin_layout Plain Layout
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36357 The LaTeX Companion
36360 Addison Wesley, 2004
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36388 LaTeX tips and tricks-
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36472 Packages ! hyperref
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36536 Auflage, Duden 2001
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