1 #LyX 1.6.3svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
41 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
43 \settowidth{\abc}{\space}
45 \renewcommand{\equationautorefname}{\hspace{-\abc}}
46 \renewcommand{\sectionautorefname}{sec.\negthinspace}
47 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % center multirows (e.g. in sec. 13.3)
86 \renewcommand{\multirowsetup}{\centering}
88 % define a color, used in sec.9.3
89 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
91 % declare operators (see sec. 10.4 and sec. 15.2)
92 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
93 \DeclareMathOperator{\sgn}{sgn}
95 \newcommand{\spce}{\textvisiblespace}
97 % example definitions for sec. 20.1
98 \newcommand{\gr}{\Longrightarrow}
99 \newcommand{\us}[1]{\underline{#1}}
100 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
101 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
102 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
104 % example macro from sec. 19.4
105 %\def\tagform@#1{\maketag@@@{|#1|}}
107 % macro from sec. 10.2
108 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
109 \def\mathclap {\mathpalette \mathclapinternal}
110 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
112 % redefine the greyed out note
113 \renewenvironment{lyxgreyedout}
114 {\textcolor{blue}\bgroup}{\egroup}
116 % ------------------------------------
117 % used to check for needed LaTeX packages
120 % check for package eurosym
121 % used for the Euro symbol
123 \IfFileExists{eurosym.sty}
124 {\usepackage[gennarrow]{eurosym}
125 \setboolean{eurosym}{true}}
126 {\setboolean{eurosym}{false}}
128 % needed in sec. 22.4
129 % check for package braket
131 \IfFileExists{braket.sty}
133 \setboolean{braket}{true}}
134 {\setboolean{braket}{false}}
136 % needed in sec. 22.10
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
145 \use_default_options false
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pdfusetitle false
174 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
181 \paperorientation portrait
184 \paragraph_separation skip
186 \quotes_language english
189 \paperpagestyle plain
193 \tracking_changes false
194 \output_changes false
202 LyX's detailed Math manual
210 \begin_layout Plain Layout
212 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_inset CommandInset href
218 name "lyx-docs@lists.lyx.org"
219 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
230 \begin_inset Note Note
233 \begin_layout Plain Layout
240 \begin_inset Newline newline
244 \begin_inset Newline newline
252 \begin_layout Standard
253 \begin_inset CommandInset toc
254 LatexCommand tableofcontents
261 \begin_layout Standard
262 \begin_inset Note Note
265 \begin_layout Plain Layout
266 To export this document to PDF, PS, or DVI the LaTeX-packages
279 If they are not installed you can export the document anyway but the sections
280 where the packages are required won't appear in the output.
283 \begin_layout Plain Layout
284 The latest PDF-version of this document can be found here:
285 \begin_inset Newline newline
290 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
298 \begin_layout Standard
299 \begin_inset Newpage newpage
305 \begin_layout Section
309 \begin_layout Standard
310 This document explains LyX's math features and is furthermore a collection
311 of LaTeX-commands used for mathematical characters and constructs.
312 The explanations are designed for the usage of commands.
313 It is therefore required that you have read the section
324 \begin_layout Standard
325 Most of the characters and many constructs explained in this manual are
326 also accessible via the menu
330 \SpecialChar \menuseparator
346 But everybody who has to write lots of formulas will notice that it is
347 much faster to use commands instead of the math toolbar.
348 Therefore this manual is focused on commands but also mentions the correspondin
349 g toolbar buttons when available.
352 \begin_layout Standard
353 If not specially mentioned the commands are only available within formulas.
354 To be able to use all commands explained in this document, the option
358 must be used in the document settings (menu
360 Document\SpecialChar \menuseparator
361 Settings\SpecialChar \menuseparator
372 \begin_layout Plain Layout
375 Use AMS math package automatically
381 \begin_layout Plain Layout
390 -math when math constructs are found that are supported by LyX.
398 \begin_layout Standard
399 This document doesn't list all
403 \begin_layout Plain Layout
416 \begin_layout Plain Layout
421 \begin_layout Plain Layout
430 -math commands is in the file
433 \begin_inset CommandInset href
436 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
442 , which is part of every LaTeX standard installation.
447 for lucidity reasons.
450 \begin_layout Section
454 \begin_layout Standard
455 To create an inline formula
459 \begin_layout Plain Layout
465 that is embedded into a text line, use one of the shortcuts
471 or the toolbar button
472 \begin_inset Graphics
473 filename ../images/math-mode.png
479 \begin_inset Newline newline
482 To create a display style formula
486 \begin_layout Plain Layout
487 Formula ! display style
492 that will appear bigger and in an own paragraph, use one of these shortcuts:
502 \begin_layout Standard
503 To change a display style formula to an inline formula, set the cursor into
504 the formula and use one of the shortcuts
512 Edit\SpecialChar \menuseparator
513 Math\SpecialChar \menuseparator
517 The same way is used to change an inline formula to a display style formula.
520 \begin_layout Standard
521 To display parts of an inline formula in the size of a display style formula,
530 \begin_layout Plain Layout
541 Then a new blue box appears in which the desired formula part is inserted.
544 \begin_layout Standard
545 Only inline formulas are allowed inside tables.
548 \begin_layout Standard
553 can be turned on in the menu
555 View\SpecialChar \menuseparator
559 When you click there on
560 \begin_inset Quotes eld
564 \begin_inset Quotes erd
567 the toolbar will be shown permanently at the bottom; this state is visualized
572 menu with a checkmark.
573 When you click in this state again on
574 \begin_inset Quotes eld
578 \begin_inset Quotes erd
589 is only shown when the cursor is within a formula; this state is visualized
590 by the renaming of the menu entry from
591 \begin_inset Quotes eld
595 \begin_inset Quotes erd
599 \begin_inset Quotes eld
607 \begin_inset Quotes erd
613 \begin_layout Standard
618 \begin_layout Plain Layout
624 is invoked by pressing the toolbar button
625 \begin_inset Graphics
626 filename ../images/ert-insert.png
633 Insert\SpecialChar \menuseparator
638 \begin_layout Plain Layout
654 \begin_inset Note Note
657 \begin_layout Plain Layout
658 In LyX there are three
659 \begin_inset Quotes eld
663 \begin_inset Quotes erd
666 that appear in the output with sub- and superscript letters: TeX, LaTeX,
670 \begin_layout Plain Layout
671 To avoid that these names are recognized as proper names, a TeX-brace pair
680 \begin_layout Standard
681 To change the LaTeX-preamble
685 \begin_layout Plain Layout
693 Document\SpecialChar \menuseparator
694 Settings\SpecialChar \menuseparator
699 \begin_layout Plain Layout
715 \begin_layout Standard
716 To edit matrices, case differentiations, and multiline formulas subsequently,
719 Edit\SpecialChar \menuseparator
724 Edit\SpecialChar \menuseparator
726 \begin_inset space \thinspace{}
730 \begin_inset space \thinspace{}
740 When lines and columns are swapped via the menu, the column or line where
741 the cursor is in is exchanged with the column to the right or the line
743 Is the cursor in the last column or row, the exchange is done with the
744 column to the left or the line above.
747 \begin_layout Standard
748 To write text in formulas
752 \begin_layout Plain Layout
753 For multiline formulas the command
760 \begin_inset CommandInset ref
762 reference "sub:Text-in-multiline"
779 \begin_layout Plain Layout
789 \begin_layout Plain Layout
796 This mode is invoked with the the shortcut
802 or by the insertion of the command
810 \begin_layout Plain Layout
821 The text appears black in LyX and can therefore be distinguished from the
822 other formula parts that appear blue.
823 In the output mathematical text is set upright, in contrary to other formula
827 \begin_layout Subsection*
831 \begin_layout Standard
832 Most of the LaTeX-commands for math constructs have the following scheme:
835 \begin_layout Standard
851 \begin_layout Standard
852 A command starts always with a backslash
853 \begin_inset Quotes gld
863 \begin_inset Quotes grd
867 To omit optional arguments, also omit the associated brackets.
868 The braces around the required arguments are named in this document as
873 \begin_layout Plain Layout
880 If you add in a formula a left brace to a command name, LyX creates automatical
882 In all other cases TeX-braces are created in formulas with the command
890 TeX-braces appear red in LyX, in contrary to normal braces that appear
892 In TeX-mode no command is needed to get TeX-braces.
893 TeX-braces don't appear in the output.
896 \begin_layout Standard
897 When commands without arguments, like commands for symbols are entered in
898 TeX-mode, a space character must
902 be behind the command to end it.
903 This space doesn't appear in the output.
904 When the space should appear in the output, the space must be followed
905 by a protected space in normal text.
908 \begin_layout Standard
909 A protected space is inserted with
912 arg "space-insert protected"
918 \begin_layout Subsection*
919 \begin_inset Newpage newpage
925 \begin_layout Itemize
930 \begin_layout Plain Layout
931 This visible space character can be created with the command
941 \begin_layout Plain Layout
949 , inserted in TeX-mode.
958 \begin_layout Plain Layout
971 denotes a space character to be input.
974 \begin_layout Itemize
976 \begin_inset Formula $\to$
979 denotes the usage of the corresponding arrow key on the keyboard.
982 \begin_layout Subsection*
986 \begin_layout Standard
988 \begin_inset Float table
994 \begin_layout Plain Layout
998 \begin_layout Plain Layout
999 \begin_inset CommandInset label
1001 name "tab:Available-units"
1013 \begin_layout Plain Layout
1015 \begin_inset Tabular
1016 <lyxtabular version="3" rows="13" columns="2">
1018 <column alignment="center" valignment="top" width="0">
1019 <column alignment="center" valignment="top" width="0">
1021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1024 \begin_layout Plain Layout
1030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1033 \begin_layout Plain Layout
1041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1044 \begin_layout Plain Layout
1050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1053 \begin_layout Plain Layout
1061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1064 \begin_layout Plain Layout
1070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1073 \begin_layout Plain Layout
1081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1084 \begin_layout Plain Layout
1090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1093 \begin_layout Plain Layout
1095 \begin_inset space \thinspace{}
1099 \begin_inset space \thinspace{}
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1112 \begin_layout Plain Layout
1118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1121 \begin_layout Plain Layout
1123 \begin_inset space \thinspace{}
1127 \begin_inset space \thinspace{}
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1140 \begin_layout Plain Layout
1146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1149 \begin_layout Plain Layout
1151 \begin_inset space \thinspace{}
1155 \begin_inset space \thinspace{}
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1168 \begin_layout Plain Layout
1174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1177 \begin_layout Plain Layout
1179 \begin_inset space \thinspace{}
1183 \begin_inset space \thinspace{}
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1196 \begin_layout Plain Layout
1202 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1205 \begin_layout Plain Layout
1207 \begin_inset space \thinspace{}
1211 \begin_inset space \thinspace{}
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1224 \begin_layout Plain Layout
1230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1233 \begin_layout Plain Layout
1235 \begin_inset space \thinspace{}
1239 \begin_inset Formula $\approx$
1243 \begin_inset space \thinspace{}
1253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1256 \begin_layout Plain Layout
1262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1265 \begin_layout Plain Layout
1267 \begin_inset space \thinspace{}
1271 \begin_inset space \thinspace{}
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1284 \begin_layout Plain Layout
1290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1293 \begin_layout Plain Layout
1297 \begin_inset Quotes eld
1303 \begin_inset Quotes erd
1313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1316 \begin_layout Plain Layout
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1325 \begin_layout Plain Layout
1327 \begin_inset Quotes eld
1335 \begin_inset Quotes erd
1345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1348 \begin_layout Plain Layout
1354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1357 \begin_layout Plain Layout
1359 \begin_inset space \thinspace{}
1363 \begin_inset Formula $\nicefrac{1}{18}$
1367 \begin_inset space \thinspace{}
1388 \begin_layout Standard
1389 \begin_inset Newpage newpage
1395 \begin_layout Section
1399 \begin_layout Subsection
1404 \begin_layout Plain Layout
1414 \begin_layout Plain Layout
1424 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1440 \begin_layout Plain Layout
1456 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1472 \begin_layout Plain Layout
1487 \begin_layout Standard
1488 Indices are created with an underscore
1489 \begin_inset Quotes eld
1493 \begin_inset Quotes erd
1496 or via the math toolbar button
1497 \begin_inset Graphics
1498 filename ../images/math-subscript.png
1503 , exponents with a caret
1504 \begin_inset Quotes eld
1508 \begin_inset Quotes erd
1511 or via the math toolbar button
1512 \begin_inset Graphics
1513 filename ../images/math-superscript.png
1521 \begin_layout Standard
1523 \begin_inset Tabular
1524 <lyxtabular version="3" rows="4" columns="2">
1526 <column alignment="center" valignment="top" width="0pt">
1527 <column alignment="center" valignment="top" width="0pt">
1529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1532 \begin_layout Plain Layout
1538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1541 \begin_layout Plain Layout
1543 \begin_inset Note Note
1546 \begin_layout Plain Layout
1553 is only used as spacer.
1565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1568 \begin_layout Plain Layout
1574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1577 \begin_layout Plain Layout
1578 \begin_inset Formula $B_{V}$
1588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1591 \begin_layout Plain Layout
1597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1600 \begin_layout Plain Layout
1601 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1614 \begin_layout Plain Layout
1619 \begin_layout Plain Layout
1633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1636 \begin_layout Plain Layout
1637 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1653 \begin_layout Standard
1654 As the caret is in some languages an accent, vowels will be accentuated
1655 in this case and not set as exponents
1659 \begin_layout Plain Layout
1660 Depending on the used keyboard settings this can also happen for other character
1667 To get in this case exponents, press
1671 after the caret as in the last example.
1674 \begin_layout Subsection
1676 \begin_inset CommandInset label
1678 name "sub:Fractions"
1686 \begin_layout Plain Layout
1695 \begin_layout Standard
1696 Fractions are generated with the command
1706 \begin_layout Plain Layout
1714 or via the math toolbar button
1715 \begin_inset Graphics
1716 filename ../images/math/frac.png
1722 The font size is adjusted automatically, depending on whether the fraction
1723 is in an inline or display style formula.
1724 With the math toolbar button
1725 \begin_inset Graphics
1726 filename ../images/math/frac-square.png
1731 you can select different fraction types.
1734 \begin_layout Standard
1743 \begin_layout Plain Layout
1753 a fraction can be created that has in any case the size of a display style
1763 \begin_layout Plain Layout
1773 the fraction appears always with the size of an inline formula.
1777 \begin_layout Standard
1778 A line with the fraction
1779 \begin_inset Formula $\frac{1}{2}$
1782 that was created with the command
1791 \begin_layout Standard
1792 A line with the fraction
1793 \begin_inset Formula $\dfrac{1}{2}$
1796 that was created with the command
1805 \begin_layout Standard
1807 \begin_inset Tabular
1808 <lyxtabular version="3" rows="4" columns="2">
1810 <column alignment="center" valignment="top" width="0pt">
1811 <column alignment="center" valignment="top" width="0pt">
1813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1816 \begin_layout Plain Layout
1822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1825 \begin_layout Plain Layout
1827 \begin_inset Note Note
1830 \begin_layout Plain Layout
1837 is only used as spacer.
1849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1852 \begin_layout Plain Layout
1859 \begin_layout Plain Layout
1869 \begin_inset Formula $\downarrow$
1877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1880 \begin_layout Plain Layout
1881 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1894 \begin_layout Plain Layout
1901 \begin_layout Plain Layout
1911 \begin_inset Formula $\downarrow$
1919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1922 \begin_layout Plain Layout
1923 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1936 \begin_layout Plain Layout
1943 \begin_layout Plain Layout
1956 \begin_layout Plain Layout
1971 \begin_layout Plain Layout
1981 \begin_inset Formula $\downarrow$
1985 \begin_inset Formula $\downarrow\downarrow$
1993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1996 \begin_layout Plain Layout
1997 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2013 \begin_layout Standard
2014 \begin_inset VSpace bigskip
2018 \begin_inset Newpage newpage
2021 For nested fractions the command
2031 \begin_layout Plain Layout
2041 \begin_inset VSpace -3mm
2047 \begin_layout Standard
2048 \begin_inset Formula \begin{align*}
2049 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2050 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2057 \begin_layout Standard
2058 The command for the example above is:
2061 \begin_layout Standard
2070 \begin_layout Plain Layout
2080 \begin_inset Formula $\downarrow$
2089 \begin_layout Plain Layout
2104 \begin_layout Plain Layout
2114 \begin_inset Formula $\downarrow$
2118 \begin_inset Formula $\downarrow$
2124 \begin_layout Standard
2125 \begin_inset VSpace medskip
2131 \begin_layout Standard
2138 sets the fraction always in the size of a displayed formula, also when
2139 it is part of another fraction.
2142 \begin_layout Standard
2143 It is possible to specify the alignment of the numerator.
2150 is used to left align it, the command
2163 centers the numerator.
2164 These fractions demonstrate the different alignments:
2167 \begin_layout Standard
2168 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2172 \begin_inset Formula $\cfrac{A}{B+C}$
2176 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2182 \begin_layout Standard
2183 \begin_inset Note Greyedout
2186 \begin_layout Plain Layout
2203 are no real LaTeX commands but represent the command
2207 cfrac[alignment]{numerator}{denominator}
2210 Therefore you cannot use them in TeX code.
2218 \begin_layout Standard
2219 \begin_inset VSpace medskip
2222 It is often advantageous to combine
2235 \begin_inset Formula \[
2236 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2243 \begin_layout Standard
2244 For inline fractions with a sloped fraction stroke you can use the command
2255 \begin_layout Plain Layout
2264 \begin_inset Formula $\nicefrac{5}{31}$
2277 \begin_layout Plain Layout
2286 \begin_inset Formula $\unitfrac{5}{31}$
2289 There is furthermore the command
2295 that offers to write a fraction in combination with a number:
2296 \begin_inset Formula $\unitfrac[2]{1}{3}$
2302 \begin_layout Standard
2303 \begin_inset Note Greyedout
2306 \begin_layout Plain Layout
2317 is not a real LaTeX command but the command
2318 \begin_inset Newline newline
2325 unitfrac[number]{numerator}{denominator}
2328 Therefore you cannot use it in TeX code.
2336 \begin_layout Standard
2337 How to define own fractions where the fraction stroke can be changed, is
2339 \begin_inset CommandInset ref
2341 reference "sub:Self-defined-Fractions"
2348 \begin_layout Subsection
2353 \begin_layout Plain Layout
2362 \begin_layout Standard
2363 Square roots are created with
2373 \begin_layout Plain Layout
2381 or the math toolbar button
2382 \begin_inset Graphics
2383 filename ../images/math/sqrt.png
2388 , all other roots with the command
2398 \begin_layout Plain Layout
2406 or with the math toolbar button
2407 \begin_inset Graphics
2408 filename ../images/math/root.png
2416 \begin_layout Standard
2418 \begin_inset Tabular
2419 <lyxtabular version="3" rows="3" columns="2">
2421 <column alignment="center" valignment="top" width="0pt">
2422 <column alignment="center" valignment="top" width="0pt">
2424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2427 \begin_layout Plain Layout
2433 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2436 \begin_layout Plain Layout
2438 \begin_inset Note Note
2441 \begin_layout Plain Layout
2448 is only used as spacer.
2460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2463 \begin_layout Plain Layout
2470 \begin_layout Plain Layout
2484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2487 \begin_layout Plain Layout
2488 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2498 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2501 \begin_layout Plain Layout
2508 \begin_layout Plain Layout
2518 \begin_inset Formula $\downarrow$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2529 \begin_layout Plain Layout
2530 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2546 \begin_layout Standard
2547 A square root can also be created with
2553 when the root index field is left empty.
2556 \begin_layout Standard
2557 With certain indices the distance to the root is too small, like in this
2559 \begin_inset Formula $\sqrt[\beta]{B}$
2563 \begin_inset Newline newline
2567 \begin_inset Formula $\beta$
2571 To avoid this, the commands
2581 \begin_layout Plain Layout
2599 \begin_layout Plain Layout
2607 are used with the following scheme:
2610 \begin_layout Standard
2624 \begin_layout Standard
2625 Distance is the number of Big Points (unit bp;
2626 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2629 ), that the index should be moved to the left or top, resp..
2630 The commands are written to the index.
2631 This way the command
2632 \begin_inset Newline newline
2642 \begin_inset Formula $\to$
2648 \begin_inset Formula $\to$
2657 \begin_layout Plain Layout
2667 \begin_inset Formula $\to$
2671 \begin_inset Newline newline
2676 produces a correct typeset formula:
2677 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2683 \begin_layout Subsection
2684 Binomial Coefficients
2688 \begin_layout Plain Layout
2689 Binomial coefficients
2697 \begin_layout Standard
2698 Binomial coefficients are inserted with the command
2708 \begin_layout Plain Layout
2716 or with the submenu of the math toolbar button
2717 \begin_inset Graphics
2718 filename ../images/math/frac-square.png
2724 Analog to fractions (
2744 \begin_layout Plain Layout
2764 \begin_layout Plain Layout
2773 For other brackets around binomial coeficients there are the commands
2783 \begin_layout Plain Layout
2801 \begin_layout Plain Layout
2812 \begin_layout Standard
2814 \begin_inset Tabular
2815 <lyxtabular version="3" rows="6" columns="2">
2817 <column alignment="center" valignment="top" width="0pt">
2818 <column alignment="center" valignment="top" width="0pt">
2820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2823 \begin_layout Plain Layout
2829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2832 \begin_layout Plain Layout
2834 \begin_inset Note Note
2837 \begin_layout Plain Layout
2844 is only used as spacer.
2856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2859 \begin_layout Plain Layout
2866 \begin_layout Plain Layout
2876 \begin_inset Formula $\downarrow$
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2887 \begin_layout Plain Layout
2888 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2901 \begin_layout Plain Layout
2908 \begin_layout Plain Layout
2918 \begin_inset Formula $\downarrow$
2926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2929 \begin_layout Plain Layout
2930 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2943 \begin_layout Plain Layout
2950 \begin_layout Plain Layout
2960 \begin_inset Formula $\downarrow$
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2971 \begin_layout Plain Layout
2972 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2985 \begin_layout Plain Layout
2992 \begin_layout Plain Layout
3002 \begin_inset Formula $\downarrow$
3010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3013 \begin_layout Plain Layout
3014 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3027 \begin_layout Plain Layout
3034 \begin_layout Plain Layout
3044 \begin_inset Formula $\downarrow$
3052 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3055 \begin_layout Plain Layout
3056 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3072 \begin_layout Subsection
3073 Case Differentiations
3077 \begin_layout Plain Layout
3078 Case differentiations
3086 \begin_layout Standard
3088 \begin_inset Tabular
3089 <lyxtabular version="3" rows="3" columns="2">
3091 <column alignment="center" valignment="top" width="0pt">
3092 <column alignment="center" valignment="top" width="0pt">
3094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3097 \begin_layout Plain Layout
3103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3106 \begin_layout Plain Layout
3114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3117 \begin_layout Plain Layout
3124 \begin_layout Plain Layout
3134 \begin_inset Formula $\to$
3141 \begin_layout Plain Layout
3154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3157 \begin_layout Plain Layout
3158 \begin_inset Formula $\begin{cases}
3169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3172 \begin_layout Plain Layout
3179 \begin_layout Plain Layout
3191 arg "newline-insert newline"
3199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3202 \begin_layout Plain Layout
3203 \begin_inset Formula $\begin{cases}
3204 A & \textrm{for }x>0\\
3205 B & \textrm{for }x=0\end{cases}$
3221 \begin_layout Standard
3228 or the usage of the math toolbar button
3229 \begin_inset Graphics
3230 filename ../images/math/cases.png
3235 you can create new lines with the shortcut
3238 arg "newline-insert newline"
3241 or the table toolbar button
3242 \begin_inset Graphics
3243 filename ../images/tabular-feature_append-row.png
3251 \begin_layout Standard
3258 is also available via the menu
3260 Insert\SpecialChar \menuseparator
3261 Math\SpecialChar \menuseparator
3267 \begin_layout Subsection
3272 \begin_layout Plain Layout
3281 \begin_layout Standard
3292 \begin_layout Plain Layout
3300 every character can be displayed canceled.
3301 The characters are quasi accentuated by a slash.
3304 \begin_layout Standard
3306 \begin_inset Tabular
3307 <lyxtabular version="3" rows="4" columns="2">
3309 <column alignment="center" valignment="top" width="0pt">
3310 <column alignment="center" valignment="top" width="0pt">
3312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3315 \begin_layout Plain Layout
3321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3324 \begin_layout Plain Layout
3332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3335 \begin_layout Plain Layout
3343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3346 \begin_layout Plain Layout
3347 \begin_inset Formula $\not=$
3357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3360 \begin_layout Plain Layout
3370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3373 \begin_layout Plain Layout
3374 \begin_inset Formula $\not\le$
3384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3387 \begin_layout Plain Layout
3397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3400 \begin_layout Plain Layout
3401 \begin_inset Formula $\not\parallel$
3417 \begin_layout Standard
3418 The last example shows, that not all negations look good.
3419 Therefore there are for some negations special commands (see
3420 \begin_inset CommandInset ref
3422 reference "sub:Mathematical-Symbols"
3427 \begin_inset CommandInset ref
3429 reference "sec:Relations"
3436 \begin_layout Subsection
3438 \begin_inset CommandInset label
3440 name "sub:Placeholders"
3448 \begin_layout Plain Layout
3458 \begin_layout Plain Layout
3459 Chemical characters ! Isotopes
3468 \begin_layout Plain Layout
3473 \begin_layout Plain Layout
3484 \begin_layout Plain Layout
3499 \begin_layout Standard
3501 \begin_inset space \thinspace{}
3505 \begin_inset space \space{}
3512 \begin_layout Plain Layout
3513 More about chemical symbols is written in
3514 \begin_inset CommandInset ref
3516 reference "sub:Chemical-Symbols-and"
3525 the following problem occurs:
3528 \begin_layout Standard
3530 \begin_inset Tabular
3531 <lyxtabular version="3" rows="2" columns="2">
3533 <column alignment="center" valignment="top" width="0pt">
3534 <column alignment="center" valignment="top" width="0pt">
3536 <cell alignment="center" valignment="top" usebox="none">
3539 \begin_layout Plain Layout
3540 Indices created with sub- and superscripts:
3545 <cell alignment="center" valignment="top" usebox="none">
3548 \begin_layout Plain Layout
3549 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3559 <cell alignment="center" valignment="top" usebox="none">
3562 \begin_layout Plain Layout
3568 <cell alignment="center" valignment="top" usebox="none">
3571 \begin_layout Plain Layout
3572 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3586 \begin_inset Note Note
3589 \begin_layout Plain Layout
3596 is only used as spacer.
3604 \begin_layout Standard
3605 The shorter index is by default placed below or above the first character
3606 of the longer index.
3607 To avoid this there is the command
3617 \begin_layout Plain Layout
3625 or the math toolbar button
3626 \begin_inset space \thinspace{}
3633 \begin_layout Plain Layout
3634 can be found in the submenu of the toolbar button
3635 \begin_inset Graphics
3636 filename ../images/math/space.png
3647 \begin_inset Graphics
3648 filename ../images/math/phantom.png
3653 that creates one or more phantom characters.
3660 a small blue box appears that is superposed with two red arrows.
3661 The arrows indicate that the complete width and height of the box content
3662 will be created as placeholder.
3663 Phantom characters are accordingly placeholders with the size of the characters.
3666 \begin_layout Standard
3668 \begin_inset Tabular
3669 <lyxtabular version="3" rows="4" columns="2">
3671 <column alignment="center" valignment="top" width="0">
3672 <column alignment="center" valignment="top" width="0">
3674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3677 \begin_layout Plain Layout
3683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3686 \begin_layout Plain Layout
3688 \begin_inset Note Note
3691 \begin_layout Plain Layout
3698 is only used as spacer.
3710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3713 \begin_layout Plain Layout
3718 \begin_layout Plain Layout
3733 \begin_layout Plain Layout
3743 \begin_inset Formula $\to$
3750 \begin_layout Plain Layout
3764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3767 \begin_layout Plain Layout
3768 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3781 \begin_layout Plain Layout
3786 \begin_layout Plain Layout
3801 \begin_layout Plain Layout
3811 \begin_inset Formula $\to$
3818 \begin_layout Plain Layout
3832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3835 \begin_layout Plain Layout
3836 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3849 \begin_layout Plain Layout
3856 \begin_layout Plain Layout
3871 \begin_layout Plain Layout
3881 \begin_inset Formula $\to$
3888 \begin_layout Plain Layout
3902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3905 \begin_layout Plain Layout
3906 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3922 \begin_layout Standard
3923 Furthermore there are the commands
3933 \begin_layout Plain Layout
3942 \begin_inset space ~
3946 \begin_inset Graphics
3947 filename ../images/math/vphantom.png
3962 \begin_layout Plain Layout
3971 \begin_inset space ~
3975 \begin_inset Graphics
3976 filename ../images/math/hphantom.png
3988 creates only space for the maximal height of the characters in the box
3989 but not for its width.
3996 creates only space for the width of the box content.
3997 Therefore the boxes of both commands have only one red arrow.
4000 \begin_layout Standard
4011 \begin_layout Plain Layout
4026 space for the height of the integral sign,
4030 \begin_layout Plain Layout
4037 creates an integral sign, see
4038 \begin_inset CommandInset ref
4040 reference "sub:Big-Operators"
4049 because this is the larger character.
4050 An example application is in
4051 \begin_inset CommandInset ref
4053 reference "sub:Multiline-Brackets"
4060 \begin_layout Subsection
4065 \begin_layout Plain Layout
4075 \begin_layout Plain Layout
4076 Formula ! underlined
4084 \begin_layout Standard
4086 \begin_inset Tabular
4087 <lyxtabular version="3" rows="4" columns="2">
4089 <column alignment="center" valignment="top" width="0pt">
4090 <column alignment="center" valignment="top" width="0pt">
4092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4095 \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
4106 \begin_inset Note Note
4109 \begin_layout Plain Layout
4116 is only used as spacer.
4128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4131 \begin_layout Plain Layout
4138 \begin_layout Plain Layout
4151 \begin_layout Plain Layout
4164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4167 \begin_layout Plain Layout
4168 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4178 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4181 \begin_layout Plain Layout
4188 \begin_layout Plain Layout
4201 \begin_layout Plain Layout
4214 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4217 \begin_layout Plain Layout
4218 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4231 \begin_layout Plain Layout
4238 \begin_layout Plain Layout
4253 \begin_layout Plain Layout
4267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4270 \begin_layout Plain Layout
4271 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4287 \begin_layout Standard
4288 In the last example it doesn't matter if first
4303 \begin_layout Standard
4304 To double underline e.
4305 \begin_inset space \thinspace{}
4309 \begin_inset space \space{}
4321 \begin_layout Standard
4322 It is possible to place up to 6 lines above or below characters.
4325 \begin_layout Standard
4326 \begin_inset VSpace bigskip
4329 Custom lines can be created using the command
4339 \begin_layout Plain Layout
4347 which has the following scheme:
4350 \begin_layout Standard
4355 rule[vertical offset]{length}{thickness}
4358 \begin_layout Standard
4359 The optional vertical offset shifts the line upwards (or downwards, when
4360 the value is negative).
4362 \begin_inset CommandInset ref
4364 reference "tab:Available-units"
4368 can be used for the values.
4369 Here are two example lines created with the commands
4370 \begin_inset Newline newline
4377 rule[-2ex]{3cm}{2pt}
4388 \begin_layout Standard
4390 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4396 \begin_layout Standard
4403 can also be used for text when it is inserted in TeX-mode.
4406 \begin_layout Subsection
4408 \begin_inset CommandInset label
4418 \begin_layout Plain Layout
4427 \begin_layout Standard
4428 There are different types of ellipses available.
4432 \begin_layout Plain Layout
4433 In the math toolbar in the submenu of the button
4434 \begin_inset Graphics
4435 filename ../images/math/ldots.png
4445 For listings dots at the baseline are used (
4455 \begin_layout Plain Layout
4463 ), while for operations dots are needed that are on the same height as the
4474 \begin_layout Plain Layout
4483 When using the command
4493 \begin_layout Plain Layout
4501 , LaTeX decides on the basis of the next character what type is used.
4504 \begin_layout Standard
4506 \begin_inset Tabular
4507 <lyxtabular version="3" rows="8" columns="2">
4509 <column alignment="center" valignment="top" width="0pt">
4510 <column alignment="center" valignment="top" width="0pt">
4512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4515 \begin_layout Plain Layout
4521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4524 \begin_layout Plain Layout
4532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4535 \begin_layout Plain Layout
4540 \begin_layout Plain Layout
4555 \begin_layout Plain Layout
4569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4572 \begin_layout Plain Layout
4573 \begin_inset Formula $A_{1},\dots,A_{n}$
4583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4586 \begin_layout Plain Layout
4591 \begin_layout Plain Layout
4606 \begin_layout Plain Layout
4620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4623 \begin_layout Plain Layout
4624 \begin_inset Formula $A_{1}+\dots+A_{n}$
4634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4637 \begin_layout Plain Layout
4642 \begin_layout Plain Layout
4657 \begin_layout Plain Layout
4671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4674 \begin_layout Plain Layout
4675 \begin_inset Formula $A_{1},\ldots,A_{n}$
4685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4688 \begin_layout Plain Layout
4693 \begin_layout Plain Layout
4708 \begin_layout Plain Layout
4722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4725 \begin_layout Plain Layout
4726 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4739 \begin_layout Plain Layout
4747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4750 \begin_layout Plain Layout
4751 \begin_inset Formula $\vdots$
4761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4764 \begin_layout Plain Layout
4772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4775 \begin_layout Plain Layout
4776 \begin_inset Formula $\ddots$
4786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4789 \begin_layout Plain Layout
4791 \begin_inset space \thinspace{}
4794 matrix with the different dots
4799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4802 \begin_layout Plain Layout
4803 \begin_inset Formula $\begin{array}{ccc}
4804 A_{11} & \cdots & A_{1m}\\
4805 \vdots & \ddots & \vdots\\
4806 A_{n1} & \cdots & A_{nm}\end{array}$
4822 \begin_layout Standard
4823 The ellipses available in menu
4825 Insert\SpecialChar \menuseparator
4827 \begin_inset space ~
4841 \begin_layout Standard
4842 \begin_inset VSpace medskip
4845 Specially for matrices there are ellipses that span over several columns.
4846 They are created with the command
4856 \begin_layout Plain Layout
4864 , that has the following scheme:
4867 \begin_layout Standard
4872 hdotsfor[distance]{number of columns}
4875 \begin_layout Standard
4876 The number of columns specifies how many columns should be spanned.
4877 Distance is a factor for the distance between the dots.
4880 \begin_layout Standard
4881 In the following matrix the command
4887 was inserted in the first box of the second line, to get an ellipsis with
4888 a dot distance twice as long as with the command
4895 \begin_inset Formula \[
4896 \left(\begin{array}{cccc}
4899 q & w & e & r\end{array}\right)\]
4903 Note that the matrix fields that should be spanned must be empty, otherwise
4904 you get LaTeX-errors.
4907 \begin_layout Standard
4908 \begin_inset VSpace bigskip
4911 Furthermore you can fill with the command
4921 \begin_layout Plain Layout
4929 the rest of a line with dots.
4930 The effect of these commands is the same like with
4937 \begin_inset CommandInset ref
4939 reference "sub:Variable-Space"
4946 \begin_layout Standard
4947 For example the command
4955 \begin_layout Plain Layout
4969 \begin_layout Standard
4970 \begin_inset Formula $A\dotfill B$
4976 \begin_layout Standard
4983 there is for a line the command
4993 \begin_layout Plain Layout
5004 \begin_layout Standard
5005 \begin_inset Formula $A\hrulefill B$
5011 \begin_layout Standard
5012 To use the commands for text, they have to be inserted in TeX-mode.
5015 \begin_layout Section
5017 \begin_inset CommandInset label
5027 \begin_layout Plain Layout
5036 \begin_layout Standard
5037 Matrices can be inserted via the math toolbar button
5038 \begin_inset Graphics
5039 filename ../images/dialog-show_mathmatrix.png
5046 Insert\SpecialChar \menuseparator
5047 Math\SpecialChar \menuseparator
5051 You will be asked for the number of matrix columns and rows, and the alignment.
5052 The vertical alignment is hereby only of importance for matrices in inline
5056 \begin_layout Standard
5057 The first matrix is top
5058 \begin_inset Formula $\begin{array}[t]{cccc}
5061 C & F & I & L\end{array}$
5065 \begin_inset Formula $\begin{array}{cccc}
5068 C & F & I & L\end{array}$
5071 , and the third bottom
5072 \begin_inset Formula $\begin{array}[b]{cccc}
5075 C & F & I & L\end{array}$
5081 \begin_layout Standard
5082 The horizontal alignment specifies how the column entries should be aligned.
5083 It is set by entering a letter for every column.
5088 denotes left aligned,
5097 To create for example a 4
5102 \begin_inset space ~
5105 matrix where the first column is left aligned, the second and third are
5106 centered, and the last one is right aligned, one enters for the horizontal
5112 Normally are in a matrix all columns centered, therefore the default is
5113 for every column is a
5120 \begin_layout Standard
5121 Horizontal alignment:
5124 \begin_layout Standard
5130 \begin_inset Formula $\begin{array}{lll}
5133 C & F & 10000\end{array}$
5141 \begin_inset Formula $\begin{array}{ccc}
5144 C & F & 10000\end{array}$
5152 \begin_inset Formula $\begin{array}{rrr}
5155 C & F & 10000\end{array}$
5161 \begin_layout Standard
5162 To add or delete rows and columns subsequently, the math toolbar buttons
5164 \begin_inset Graphics
5165 filename ../images/tabular-feature_append-row.png
5171 \begin_inset Graphics
5172 filename ../images/tabular-feature_delete-row.png
5178 \begin_inset space \thinspace{}
5183 Edit\SpecialChar \menuseparator
5187 New rows can also be created with
5190 arg "newline-insert newline"
5196 \begin_layout Standard
5197 \begin_inset VSpace bigskip
5200 Parentheses around a matrix can can either be created with the commands
5211 \begin_layout Plain Layout
5229 \begin_layout Plain Layout
5240 \begin_inset space ~
5246 \begin_inset CommandInset ref
5248 reference "sub:Automatic-Bracket-Size"
5252 , or by using the following commands:
5253 \begin_inset VSpace medskip
5259 \begin_layout Standard
5260 \begin_inset space \hfill{}
5264 \begin_inset Tabular
5265 <lyxtabular version="3" rows="4" columns="2">
5267 <column alignment="center" valignment="top" width="0">
5268 <column alignment="center" valignment="top" width="0">
5270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5273 \begin_layout Plain Layout
5279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5282 \begin_layout Plain Layout
5284 \begin_inset Note Note
5287 \begin_layout Plain Layout
5294 is only used as spacer.
5306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5309 \begin_layout Plain Layout
5316 \begin_layout Plain Layout
5330 \begin_inset space \thinspace{}
5338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5341 \begin_layout Plain Layout
5342 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5343 0 & \textrm{-}\mathrm{i}\\
5344 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5357 \begin_layout Plain Layout
5364 \begin_layout Plain Layout
5378 \begin_inset space \thinspace{}
5386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5389 \begin_layout Plain Layout
5390 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5391 0 & \textrm{-}\mathrm{i}\\
5392 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5405 \begin_layout Plain Layout
5412 \begin_layout Plain Layout
5426 \begin_inset space \thinspace{}
5434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5437 \begin_layout Plain Layout
5438 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5439 0 & \textrm{-}\mathrm{i}\\
5440 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5454 \begin_inset space \hfill{}
5458 \begin_inset Tabular
5459 <lyxtabular version="3" rows="4" columns="2">
5461 <column alignment="center" valignment="top" width="0">
5462 <column alignment="center" valignment="top" width="0">
5464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5467 \begin_layout Plain Layout
5473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5476 \begin_layout Plain Layout
5484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5487 \begin_layout Plain Layout
5494 \begin_layout Plain Layout
5508 \begin_inset space \thinspace{}
5516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5519 \begin_layout Plain Layout
5520 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5521 0 & \textrm{-}\mathrm{i}\\
5522 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5535 \begin_layout Plain Layout
5542 \begin_layout Plain Layout
5556 \begin_inset space \thinspace{}
5564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5567 \begin_layout Plain Layout
5568 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5569 0 & \textrm{-}\mathrm{i}\\
5570 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5583 \begin_layout Plain Layout
5590 \begin_layout Plain Layout
5604 \begin_inset space \thinspace{}
5612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5615 \begin_layout Plain Layout
5616 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5617 0 & \textrm{-}\mathrm{i}\\
5618 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5632 \begin_inset space \hfill{}
5638 \begin_layout Standard
5639 \begin_inset VSpace medskip
5643 \begin_inset space \thinspace{}
5647 \begin_inset space \space{}
5656 is inserted, a blue box appears between two vertical lines where the matrix
5660 \begin_layout Standard
5661 \begin_inset VSpace bigskip
5664 As all multiline formulas are matrices, the length
5674 \begin_layout Plain Layout
5682 that is described in
5683 \begin_inset CommandInset ref
5685 reference "sub:Column-Separation"
5689 can also be used to change the column separation of matrices.
5692 \begin_layout Standard
5693 To change the row separation, the command
5703 \begin_layout Plain Layout
5712 It is used as follows:
5715 \begin_layout Standard
5722 arraystretch}{stretch factor}
5726 \begin_layout Plain Layout
5737 \begin_layout Standard
5744 assigns the stretch factor to the predefined command
5752 \begin_inset space \thinspace{}
5756 \begin_inset space \space{}
5759 the row separation, use the factor 2.
5760 This is then used for all following matrices.
5761 To go back to the original separation, assign the factor 1 to
5770 \begin_layout Standard
5771 To set matrices into a text line, the command
5781 \begin_layout Plain Layout
5790 When it is inserted a blue box with two dashed lines appears.
5791 In this box the matrix is inserted.
5794 \begin_layout Standard
5796 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5797 C & D\end{smallmatrix}\right)$
5803 \begin_layout Section
5804 Brackets and Delimiters
5808 \begin_layout Plain Layout
5818 \begin_layout Plain Layout
5827 \begin_layout Subsection
5828 Vertical Brackets and Delimiters
5832 \begin_layout Plain Layout
5841 \begin_layout Standard
5842 \begin_inset space \hfill{}
5846 \begin_inset Tabular
5847 <lyxtabular version="3" rows="9" columns="2">
5849 <column alignment="center" valignment="top" width="0pt">
5850 <column alignment="center" valignment="top" width="0pt">
5852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5855 \begin_layout Plain Layout
5861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5864 \begin_layout Plain Layout
5872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5875 \begin_layout Plain Layout
5881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5884 \begin_layout Plain Layout
5885 \begin_inset Formula $($
5895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5898 \begin_layout Plain Layout
5904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5907 \begin_layout Plain Layout
5908 \begin_inset Formula $\{$
5918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5921 \begin_layout Plain Layout
5927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5930 \begin_layout Plain Layout
5931 \begin_inset Formula $[$
5941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5944 \begin_layout Plain Layout
5952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5955 \begin_layout Plain Layout
5956 \begin_inset Formula $\langle$
5966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5969 \begin_layout Plain Layout
5977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5980 \begin_layout Plain Layout
5981 \begin_inset Formula $\lceil$
5991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5994 \begin_layout Plain Layout
6002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6005 \begin_layout Plain Layout
6006 \begin_inset Formula $\lfloor$
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6029 \begin_inset Formula $/$
6039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6042 \begin_layout Plain Layout
6048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6051 \begin_layout Plain Layout
6052 \begin_inset Formula $|$
6066 \begin_inset space \hfill{}
6070 \begin_inset Tabular
6071 <lyxtabular version="3" rows="9" columns="2">
6073 <column alignment="center" valignment="top" width="0pt">
6074 <column alignment="center" valignment="top" width="0pt">
6076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6079 \begin_layout Plain Layout
6085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6088 \begin_layout Plain Layout
6096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6099 \begin_layout Plain Layout
6105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6108 \begin_layout Plain Layout
6109 \begin_inset Formula $)$
6119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6122 \begin_layout Plain Layout
6128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6131 \begin_layout Plain Layout
6132 \begin_inset Formula $\}$
6142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6145 \begin_layout Plain Layout
6151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6154 \begin_layout Plain Layout
6155 \begin_inset Formula $]$
6165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6168 \begin_layout Plain Layout
6176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6179 \begin_layout Plain Layout
6180 \begin_inset Formula $\rangle$
6190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6193 \begin_layout Plain Layout
6201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6204 \begin_layout Plain Layout
6205 \begin_inset Formula $\rceil$
6215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6218 \begin_layout Plain Layout
6226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6229 \begin_layout Plain Layout
6230 \begin_inset Formula $\rfloor$
6240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6243 \begin_layout Plain Layout
6253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6256 \begin_layout Plain Layout
6257 \begin_inset Formula $\backslash$
6267 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6270 \begin_layout Plain Layout
6278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6281 \begin_layout Plain Layout
6282 \begin_inset Formula $\|$
6296 \begin_inset space \hfill{}
6302 \begin_layout Standard
6305 \begin_inset Note Greyedout
6308 \begin_layout Plain Layout
6313 In TeX-mode the command
6323 \begin_layout Plain Layout
6331 must be used for the backslash, because the command
6339 produces there a line break.
6347 \begin_layout Standard
6348 For all characters listed above the size can be adjusted with the commands
6349 described in the following two subsections.
6350 When using these commands, the characters < and > can directly be used
6351 instead of the commands
6366 \begin_layout Subsubsection
6368 \begin_inset CommandInset label
6370 name "sub:Manual-Bracket-Size"
6378 \begin_layout Plain Layout
6379 Bracket size ! manual
6387 \begin_layout Standard
6388 The bracket size can be specified manually by the LaTeX-commands
6398 \begin_layout Plain Layout
6431 denotes the smallest and
6437 the largest bracket size.
6440 \begin_layout Standard
6441 These commands are used to emphasize levels of brackets:
6444 \begin_layout Standard
6446 \begin_inset Tabular
6447 <lyxtabular version="3" rows="2" columns="2">
6449 <column alignment="center" valignment="top" width="0pt">
6450 <column alignment="center" valignment="top" width="0pt">
6452 <cell alignment="center" valignment="top" usebox="none">
6455 \begin_layout Plain Layout
6456 all brackets in the same size:
6461 <cell alignment="center" valignment="top" usebox="none">
6464 \begin_layout Plain Layout
6465 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6475 <cell alignment="center" valignment="top" usebox="none">
6478 \begin_layout Plain Layout
6484 <cell alignment="center" valignment="top" usebox="none">
6487 \begin_layout Plain Layout
6488 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6502 \begin_inset Note Note
6505 \begin_layout Plain Layout
6512 is only used as spacer.
6520 \begin_layout Standard
6521 For the second formula the command
6531 \begin_layout Plain Layout
6545 \begin_layout Standard
6546 Here is an overview about all bracket sizes:
6549 \begin_layout Standard
6569 \begin_layout Plain Layout
6586 \begin_layout Plain Layout
6599 \begin_layout Plain Layout
6615 \begin_layout Standard
6617 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6623 \begin_layout Standard
6630 -commands there is the variant
6640 \begin_layout Plain Layout
6648 that adds a bit more space between the bracket and its content, and the
6665 \begin_layout Plain Layout
6675 , that don't add additional space.
6680 at the end of the command
6686 is for a left bracket; for a right bracket this will be replaced by an
6692 A left or right bracket can each be an opening or closing bracket.
6695 \begin_layout Standard
6696 In the following table is a comparison of the variants:
6699 \begin_layout Standard
6701 \begin_inset Tabular
6702 <lyxtabular version="3" rows="5" columns="2">
6704 <column alignment="center" valignment="middle" width="0">
6705 <column alignment="center" valignment="middle" width="0">
6707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6710 \begin_layout Plain Layout
6716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6719 \begin_layout Plain Layout
6721 \begin_inset Note Note
6724 \begin_layout Plain Layout
6731 is only used as spacer.
6743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6746 \begin_layout Plain Layout
6761 \begin_layout Plain Layout
6779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6782 \begin_layout Plain Layout
6783 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6796 \begin_layout Plain Layout
6811 \begin_layout Plain Layout
6829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6832 \begin_layout Plain Layout
6833 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6846 \begin_layout Plain Layout
6861 \begin_layout Plain Layout
6879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6882 \begin_layout Plain Layout
6883 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6896 \begin_layout Plain Layout
6908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6911 \begin_layout Plain Layout
6912 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6928 \begin_layout Subsubsection
6929 Automatic Bracket Size
6930 \begin_inset CommandInset label
6932 name "sub:Automatic-Bracket-Size"
6940 \begin_layout Plain Layout
6941 Bracket size ! automatic
6949 \begin_layout Standard
6950 Brackets with variable size can be inserted with the commands
6960 \begin_layout Plain Layout
6978 \begin_layout Plain Layout
6986 or via the math toolbar button
6987 \begin_inset Graphics
6988 filename ../images/dialog-show_mathdelimiter.png
7006 the wanted bracket must be inserted.
7007 The bracket size will then automatically be calculated for the output.
7010 \begin_layout Standard
7012 normal bracket: The command
7022 \begin_layout Plain Layout
7032 \begin_inset Formula $\downarrow$
7039 \begin_layout Plain Layout
7051 \begin_inset Formula \[
7059 \begin_layout Standard
7061 multiline bracket: The command
7073 \begin_layout Plain Layout
7083 \begin_inset Formula $\downarrow$
7090 \begin_layout Plain Layout
7104 \begin_inset Formula \[
7105 \ln\left(\frac{A}{C}\right)\]
7112 \begin_layout Standard
7128 \begin_inset space ~
7134 This has the advantage that you can see in LyX immediately the real bracket
7135 size and that the matching right bracket will be created too.
7136 \begin_inset Newline newline
7139 The command for the last example would then be:
7153 \begin_layout Plain Layout
7163 \begin_inset Formula $\downarrow$
7169 \begin_layout Standard
7170 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7171 For example the command
7181 \begin_layout Plain Layout
7191 \begin_inset Formula $\downarrow$
7198 \begin_layout Plain Layout
7214 \begin_inset Formula \[
7215 \left.\frac{A}{B}\right\} \]
7233 will be converted by LyX to brackets in the right size when the document
7234 is reloaded and an omitted bracket will appear as dashed line.
7237 \begin_layout Standard
7238 \begin_inset VSpace bigskip
7241 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7252 \begin_layout Plain Layout
7260 is additionally available for all brackets and limits.
7261 With this command the height of the following character is adapted to the
7262 one of the surrounding brackets, what is e.
7263 \begin_inset space \thinspace{}
7267 \begin_inset space \space{}
7270 needed for physical vectors:
7271 \begin_inset Formula \[
7272 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7276 For physical vectors there is a special LaTeX-package, described in
7277 \begin_inset CommandInset ref
7279 reference "sub:Physical-Vectors"
7286 \begin_layout Subsection
7291 \begin_layout Plain Layout
7292 Brackets ! horizontal
7300 \begin_layout Standard
7302 \begin_inset Tabular
7303 <lyxtabular version="3" rows="4" columns="2">
7305 <column alignment="center" valignment="top" width="0pt">
7306 <column alignment="center" valignment="top" width="0pt">
7308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7311 \begin_layout Plain Layout
7313 \begin_inset Note Note
7316 \begin_layout Plain Layout
7323 is only used as spacer.
7333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7336 \begin_layout Plain Layout
7344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7347 \begin_layout Plain Layout
7351 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7379 \begin_layout Plain Layout
7392 \begin_layout Plain Layout
7405 \begin_layout Plain Layout
7416 \begin_layout Plain Layout
7429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7432 \begin_layout Plain Layout
7433 \begin_inset Formula $\overbrace{A+B}^{3}$
7443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7446 \begin_layout Plain Layout
7450 \begin_layout Plain Layout
7465 \begin_layout Plain Layout
7478 \begin_layout Plain Layout
7491 \begin_layout Plain Layout
7502 \begin_layout Plain Layout
7515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7518 \begin_layout Plain Layout
7519 \begin_inset Formula $\underbrace{A+B}_{5}$
7529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7532 \begin_layout Plain Layout
7539 \begin_layout Plain Layout
7554 \begin_layout Plain Layout
7567 \begin_layout Plain Layout
7580 \begin_layout Plain Layout
7593 \begin_layout Plain Layout
7606 \begin_layout Plain Layout
7619 \begin_layout Plain Layout
7633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7636 \begin_layout Plain Layout
7637 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7653 \begin_layout Standard
7654 In the last example it doesn't matter if
7666 is inserted at first.
7669 \begin_layout Standard
7670 \begin_inset VSpace bigskip
7673 When brackets are needed that overlap each other, multiline formulas, as
7675 \begin_inset CommandInset ref
7677 reference "sec:Multiline-Formulas"
7682 \begin_inset Formula \begin{eqnarray*}
7683 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7684 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7688 In the first row the formula is inserted together with the first brace.
7689 It is hereby important that the space command
7693 \begin_layout Plain Layout
7694 Space commands are explained in
7695 \begin_inset CommandInset ref
7697 reference "sub:Predefined-Space"
7712 is inserted before the first
7713 \begin_inset Formula $d$
7716 , because the brace that ends behind the
7717 \begin_inset Formula $q$
7720 prevents that the following
7721 \begin_inset Quotes eld
7725 \begin_inset Quotes erd
7728 is surrounded by space.
7732 \begin_layout Plain Layout
7733 because a bracket is not handled as character, see
7734 \begin_inset CommandInset ref
7736 reference "sub:Binary-Operators"
7745 In the second row the second brace is inserted.
7746 As it should begin before the
7747 \begin_inset Formula $b$
7762 \begin_layout Plain Layout
7770 \begin_inset CommandInset ref
7772 reference "sub:Placeholders"
7781 This space is needed because the
7782 \begin_inset Quotes eld
7786 \begin_inset Quotes erd
7789 is also surrounded by space in the formula.
7790 The brace is placed under the command
7799 \begin_layout Standard
7800 It gets more complicated when brackets overlap each other, like in the following
7805 \begin_layout Plain Layout
7817 \begin_inset Formula \begin{eqnarray*}
7818 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7819 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7827 \begin_layout Plain Layout
7838 The first formula row is the same as the second row of the previous example,
7839 with the difference that the brace is above.
7840 The second row contains the formula together with the second brace.
7841 To avoid that there is space between the upper brace in the first row and
7842 the formula, the row spacing need to be reduced.
7843 This is not easily possible due to a bug in LyX
7847 \begin_layout Plain Layout
7848 \begin_inset CommandInset href
7850 name "LyX-bug #1505"
7851 target "http://www.lyx.org/trac/ticket/1505"
7861 As solution for the problem, the global formula row separation
7871 \begin_layout Plain Layout
7879 must be changed to -6
7880 \begin_inset space \thinspace{}
7883 pt before the formula with the command
7898 is set back after the formula to the standard value of 3
7899 \begin_inset space \thinspace{}
7902 pt using the same command.
7903 More about the row separation in formulas is explained in
7904 \begin_inset CommandInset ref
7906 reference "sub:Line-Separation"
7913 \begin_layout Section
7918 \begin_layout Plain Layout
7927 \begin_layout Standard
7928 Arrows can be inserted via the math toolbar button
7929 \begin_inset Graphics
7930 filename ../images/math/leftarrow.png
7935 or the commands listed in the following subsections.
7938 \begin_layout Standard
7939 \begin_inset Newpage newpage
7945 \begin_layout Subsection
7950 \begin_layout Plain Layout
7959 \begin_layout Standard
7960 \begin_inset space \hfill{}
7964 \begin_inset Tabular
7965 <lyxtabular version="3" rows="8" columns="2">
7967 <column alignment="center" valignment="top" width="0pt">
7968 <column alignment="center" valignment="top" width="0pt">
7970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7973 \begin_layout Plain Layout
7979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7982 \begin_layout Plain Layout
7990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7993 \begin_layout Plain Layout
8001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8004 \begin_layout Plain Layout
8005 \begin_inset Formula $\gets$
8015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8018 \begin_layout Plain Layout
8026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8029 \begin_layout Plain Layout
8030 \begin_inset Formula $\Leftarrow$
8040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8043 \begin_layout Plain Layout
8051 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8054 \begin_layout Plain Layout
8055 \begin_inset Formula $\longleftarrow$
8065 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8068 \begin_layout Plain Layout
8076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8079 \begin_layout Plain Layout
8080 \begin_inset Formula $\Longleftarrow$
8090 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8093 \begin_layout Plain Layout
8101 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8104 \begin_layout Plain Layout
8105 \begin_inset Formula $\leftharpoonup$
8115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\leftharpoondown$
8140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\hookleftarrow$
8169 \begin_inset space \hfill{}
8173 \begin_inset Tabular
8174 <lyxtabular version="3" rows="8" columns="2">
8176 <column alignment="center" valignment="top" width="0pt">
8177 <column alignment="center" valignment="top" width="0pt">
8179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8182 \begin_layout Plain Layout
8188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8191 \begin_layout Plain Layout
8199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\to$
8224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8227 \begin_layout Plain Layout
8235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8238 \begin_layout Plain Layout
8239 \begin_inset Formula $\Rightarrow$
8249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8252 \begin_layout Plain Layout
8260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8263 \begin_layout Plain Layout
8264 \begin_inset Formula $\longrightarrow$
8274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8277 \begin_layout Plain Layout
8285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8288 \begin_layout Plain Layout
8289 \begin_inset Formula $\Longrightarrow$
8299 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\rightharpoonup$
8324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\rightharpoondown$
8349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8363 \begin_layout Plain Layout
8364 \begin_inset Formula $\hookrightarrow$
8378 \begin_inset space \hfill{}
8384 \begin_layout Standard
8385 \begin_inset space \hfill{}
8389 \begin_inset Tabular
8390 <lyxtabular version="3" rows="6" columns="2">
8392 <column alignment="center" valignment="top" width="0pt">
8393 <column alignment="center" valignment="top" width="0pt">
8395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8398 \begin_layout Plain Layout
8404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8407 \begin_layout Plain Layout
8415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8418 \begin_layout Plain Layout
8426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8429 \begin_layout Plain Layout
8430 \begin_inset Formula $\leftrightarrow$
8440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8443 \begin_layout Plain Layout
8451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8454 \begin_layout Plain Layout
8455 \begin_inset Formula $\Leftrightarrow$
8465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8468 \begin_layout Plain Layout
8476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8479 \begin_layout Plain Layout
8480 \begin_inset Formula $\longleftrightarrow$
8490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8493 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8504 \begin_layout Plain Layout
8505 \begin_inset Formula $\Longleftrightarrow$
8515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8518 \begin_layout Plain Layout
8526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Plain Layout
8530 \begin_inset Formula $\rightleftharpoons$
8544 \begin_inset space \hspace{}
8549 \begin_inset space \hfill{}
8553 \begin_inset Tabular
8554 <lyxtabular version="3" rows="5" columns="2">
8556 <column alignment="center" valignment="top" width="0pt">
8557 <column alignment="center" valignment="top" width="0pt">
8559 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8562 \begin_layout Plain Layout
8568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8571 \begin_layout Plain Layout
8579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8582 \begin_layout Plain Layout
8590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8593 \begin_layout Plain Layout
8594 \begin_inset Formula $\mapsto$
8604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8607 \begin_layout Plain Layout
8615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8618 \begin_layout Plain Layout
8619 \begin_inset Formula $\longmapsto$
8629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8632 \begin_layout Plain Layout
8640 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8643 \begin_layout Plain Layout
8644 \begin_inset Formula $\leadsto$
8654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8657 \begin_layout Plain Layout
8665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8668 \begin_layout Plain Layout
8669 \begin_inset Formula $\dasharrow$
8683 \begin_inset space \hfill{}
8689 \begin_layout Standard
8690 \begin_inset VSpace medskip
8693 Arrows used as accent like e.
8694 \begin_inset space \thinspace{}
8698 \begin_inset space \space{}
8701 vector arrows are listed in
8702 \begin_inset CommandInset ref
8704 reference "sec:Accents"
8711 \begin_layout Standard
8712 \begin_inset VSpace bigskip
8715 Furthermore there are the labeled arrows
8719 \begin_layout Plain Layout
8735 \begin_layout Plain Layout
8753 \begin_layout Plain Layout
8760 \begin_layout Plain Layout
8775 When inserting one of these commands in a formula, an arrow with two blue
8776 boxes appear where the label can be inserted.
8777 The length of the arrow adapts to the label width.
8780 \begin_layout Standard
8782 \begin_inset Tabular
8783 <lyxtabular version="3" rows="3" columns="2">
8785 <column alignment="center" valignment="top" width="0pt">
8786 <column alignment="center" valignment="top" width="0pt">
8788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8791 \begin_layout Plain Layout
8797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8800 \begin_layout Plain Layout
8802 \begin_inset Note Note
8805 \begin_layout Plain Layout
8812 is only used as spacer.
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8827 \begin_layout Plain Layout
8834 \begin_layout Plain Layout
8844 \begin_inset Formula $\downarrow$
8848 \begin_inset Formula $\to$
8856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8859 \begin_layout Plain Layout
8860 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8873 \begin_layout Plain Layout
8880 \begin_layout Plain Layout
8890 \begin_inset Formula $\downarrow$
8894 \begin_inset Formula $\to$
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8905 \begin_layout Plain Layout
8906 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8922 \begin_layout Subsection
8923 Vertical and diagonal Arrows
8927 \begin_layout Plain Layout
8937 \begin_layout Plain Layout
8946 \begin_layout Standard
8947 \begin_inset space \hfill{}
8951 \begin_inset Tabular
8952 <lyxtabular version="3" rows="7" columns="2">
8954 <column alignment="center" valignment="top" width="0pt">
8955 <column alignment="center" valignment="top" width="0pt">
8957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8960 \begin_layout Plain Layout
8966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8969 \begin_layout Plain Layout
8977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8980 \begin_layout Plain Layout
8988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8991 \begin_layout Plain Layout
8992 \begin_inset Formula $\uparrow$
9002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9005 \begin_layout Plain Layout
9013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9016 \begin_layout Plain Layout
9017 \begin_inset Formula $\Uparrow$
9027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9030 \begin_layout Plain Layout
9038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9041 \begin_layout Plain Layout
9042 \begin_inset Formula $\updownarrow$
9052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9055 \begin_layout Plain Layout
9063 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9066 \begin_layout Plain Layout
9067 \begin_inset Formula $\Updownarrow$
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9091 \begin_layout Plain Layout
9092 \begin_inset Formula $\Downarrow$
9102 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9105 \begin_layout Plain Layout
9113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9116 \begin_layout Plain Layout
9117 \begin_inset Formula $\downarrow$
9131 \begin_inset space \hfill{}
9135 \begin_inset Tabular
9136 <lyxtabular version="3" rows="5" columns="2">
9138 <column alignment="center" valignment="top" width="0pt">
9139 <column alignment="center" valignment="top" width="0pt">
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9153 \begin_layout Plain Layout
9161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9164 \begin_layout Plain Layout
9172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9175 \begin_layout Plain Layout
9176 \begin_inset Formula $\nearrow$
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9189 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $\searrow$
9211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9214 \begin_layout Plain Layout
9222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9225 \begin_layout Plain Layout
9226 \begin_inset Formula $\swarrow$
9236 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9239 \begin_layout Plain Layout
9247 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9250 \begin_layout Plain Layout
9251 \begin_inset Formula $\nwarrow$
9265 \begin_inset space \hfill{}
9271 \begin_layout Standard
9272 \begin_inset VSpace medskip
9275 Vertical arrows can be used also as delimiter together with the commands
9277 \begin_inset CommandInset ref
9279 reference "sub:Manual-Bracket-Size"
9284 \begin_inset CommandInset ref
9286 reference "sub:Automatic-Bracket-Size"
9293 \begin_layout Standard
9294 \begin_inset Newpage newpage
9300 \begin_layout Section
9302 \begin_inset CommandInset label
9312 \begin_layout Plain Layout
9321 \begin_layout Standard
9322 Accents can be inserted via the math toolbar button
9323 \begin_inset Graphics
9324 filename ../images/math/hat.png
9329 or the commands listed in the following subsections.
9332 \begin_layout Subsection
9333 Accents for one Character
9337 \begin_layout Plain Layout
9350 \begin_layout Plain Layout
9352 \begin_inset CommandInset ref
9354 reference "sub:Accents-in-Text"
9367 \begin_layout Plain Layout
9375 \begin_inset Note Note
9378 \begin_layout Plain Layout
9381 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9384 \begin_layout Plain Layout
9387 texorpdfstring is in section
9388 \begin_inset CommandInset ref
9390 reference "sub:Formulas-in-Section"
9400 \begin_inset CommandInset label
9402 name "sub:Accents-for-one"
9410 \begin_layout Plain Layout
9411 Accents ! for one character
9419 \begin_layout Standard
9420 \begin_inset space \hfill{}
9424 \begin_inset Tabular
9425 <lyxtabular version="3" rows="8" columns="2">
9427 <column alignment="center" valignment="top" width="0pt">
9428 <column alignment="center" valignment="top" width="0pt">
9430 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9433 \begin_layout Plain Layout
9439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9442 \begin_layout Plain Layout
9444 \begin_inset Note Note
9447 \begin_layout Plain Layout
9454 is only used as spacer.
9466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9469 \begin_layout Plain Layout
9476 \begin_layout Plain Layout
9490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9493 \begin_layout Plain Layout
9494 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9504 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9507 \begin_layout Plain Layout
9514 \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 $\raisebox{5mm}{}\ddot{A}$
9542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9545 \begin_layout Plain Layout
9552 \begin_layout Plain Layout
9566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9569 \begin_layout Plain Layout
9570 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9583 \begin_layout Plain Layout
9591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9594 \begin_layout Plain Layout
9595 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9608 \begin_layout Plain Layout
9615 \begin_layout Plain Layout
9628 \begin_layout Plain Layout
9639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9642 \begin_layout Plain Layout
9643 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9653 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9656 \begin_layout Plain Layout
9663 \begin_layout Plain Layout
9677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9680 \begin_layout Plain Layout
9681 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9694 \begin_layout Plain Layout
9701 \begin_layout Plain Layout
9715 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9718 \begin_layout Plain Layout
9719 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9733 \begin_inset space \hfill{}
9737 \begin_inset Tabular
9738 <lyxtabular version="3" rows="7" columns="2">
9740 <column alignment="center" valignment="top" width="0pt">
9741 <column alignment="center" valignment="top" width="0pt">
9743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9746 \begin_layout Plain Layout
9752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9755 \begin_layout Plain Layout
9763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9766 \begin_layout Plain Layout
9773 \begin_layout Plain Layout
9787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9790 \begin_layout Plain Layout
9791 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9804 \begin_layout Plain Layout
9811 \begin_layout Plain Layout
9825 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9828 \begin_layout Plain Layout
9829 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9839 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9842 \begin_layout Plain Layout
9849 \begin_layout Plain Layout
9863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9866 \begin_layout Plain Layout
9867 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9880 \begin_layout Plain Layout
9887 \begin_layout Plain Layout
9901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9904 \begin_layout Plain Layout
9905 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9918 \begin_layout Plain Layout
9925 \begin_layout Plain Layout
9939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9942 \begin_layout Plain Layout
9943 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9956 \begin_layout Plain Layout
9963 \begin_layout Plain Layout
9977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9980 \begin_layout Plain Layout
9981 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9995 \begin_inset space \hfill{}
10001 \begin_layout Standard
10002 \begin_inset VSpace bigskip
10008 \begin_layout Standard
10009 You can directly insert accents like é to formulas.
10010 LyX will transform them to the corresponding accent command.
10015 \begin_layout Plain Layout
10021 it is better to insert a quotation mark before the vowel.
10022 These two characters are then treated by LaTeX as
10026 character when the formula part with the umlaut is marked as German.
10034 \begin_inset Quotes eld
10038 \begin_inset Quotes erd
10041 umlauts are created as demonstrated in the following example:
10044 \begin_layout Standard
10045 \begin_inset VSpace -2mm
10051 \begin_layout Standard
10053 \begin_inset Tabular
10054 <lyxtabular version="3" rows="3" columns="2">
10056 <column alignment="center" valignment="top" width="0">
10057 <column alignment="center" valignment="top" width="0">
10059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10062 \begin_layout Plain Layout
10068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10071 \begin_layout Plain Layout
10073 \begin_inset Note Note
10076 \begin_layout Plain Layout
10084 \begin_inset space \thinspace{}
10087 pt space are only used as spacer.
10099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10102 \begin_layout Plain Layout
10105 \begin_inset Quotes grd
10113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10116 \begin_layout Plain Layout
10117 \begin_inset space \hspace{}
10124 \begin_inset Formula $"i$
10134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10137 \begin_layout Plain Layout
10144 \begin_layout Plain Layout
10158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10161 \begin_layout Plain Layout
10162 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10178 \begin_layout Standard
10179 Another advantage to
10185 is that umlauts can directly be converted to mathematical text because
10186 the accent commands above are
10192 in mathematical text
10195 To convert an accented character to mathematical text, only the character
10196 under the accent may be converted.
10197 This applies also for all other conversions, e.
10198 \begin_inset space \thinspace{}
10202 \begin_inset space \space{}
10208 \begin_layout Standard
10209 In mathematical text, umlauts and other accented characters can directly
10213 \begin_layout Subsection
10214 Accents for Operators
10218 \begin_layout Plain Layout
10219 Accents ! for operators
10227 \begin_layout Standard
10238 \begin_layout Plain Layout
10256 \begin_layout Plain Layout
10264 characters can be placed above or below an operator, respectively, to accent
10276 \begin_layout Plain Layout
10284 characters can be set before and behind an operator.
10285 The command scheme is:
10288 \begin_layout Standard
10304 \begin_layout Standard
10311 must always be before the operator that should be accented.
10312 You can accent with several characters and even with other operators and
10320 for example only characters behind an operator, write nothing between the
10321 first braces but don't omit the braces.
10324 \begin_layout Standard
10325 For example the command
10330 \begin_inset Formula $\to$
10340 \begin_inset Formula $\to$
10349 \begin_layout Plain Layout
10365 \begin_inset Formula \[
10366 \sideset{}{'}\sum_{k=1}^{n}\]
10373 \begin_layout Standard
10382 \begin_layout Plain Layout
10397 \begin_layout Plain Layout
10409 \begin_inset Formula $\uparrow$
10417 \begin_inset Formula \[
10418 \overset{a}{\maltese}\]
10422 As seen in the last example, with
10434 also symbols and characters can be accented; with
10440 this is not possible.
10443 \begin_layout Subsection
10444 Accents for several Characters
10448 \begin_layout Plain Layout
10449 Accents ! for several characters
10457 \begin_layout Standard
10458 \begin_inset space \hfill{}
10462 \begin_inset Tabular
10463 <lyxtabular version="3" rows="5" columns="2">
10465 <column alignment="center" valignment="top" width="0pt">
10466 <column alignment="center" valignment="top" width="0pt">
10468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10471 \begin_layout Plain Layout
10477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10480 \begin_layout Plain Layout
10482 \begin_inset Note Note
10485 \begin_layout Plain Layout
10492 is only used as spacer.
10504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10507 \begin_layout Plain Layout
10514 \begin_layout Plain Layout
10528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10531 \begin_layout Plain Layout
10532 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10542 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10545 \begin_layout Plain Layout
10552 \begin_layout Plain Layout
10566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10569 \begin_layout Plain Layout
10570 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10583 \begin_layout Plain Layout
10590 \begin_layout Plain Layout
10604 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10607 \begin_layout Plain Layout
10608 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10621 \begin_layout Plain Layout
10624 underleftrightarrow
10628 \begin_layout Plain Layout
10642 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10645 \begin_layout Plain Layout
10646 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10660 \begin_inset space \hfill{}
10664 \begin_inset Tabular
10665 <lyxtabular version="3" rows="5" columns="2">
10667 <column alignment="center" valignment="top" width="0pt">
10668 <column alignment="center" valignment="top" width="0pt">
10670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10673 \begin_layout Plain Layout
10679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10682 \begin_layout Plain Layout
10690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10693 \begin_layout Plain Layout
10700 \begin_layout Plain Layout
10714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10717 \begin_layout Plain Layout
10718 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10728 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10731 \begin_layout Plain Layout
10738 \begin_layout Plain Layout
10752 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10755 \begin_layout Plain Layout
10756 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10766 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10769 \begin_layout Plain Layout
10776 \begin_layout Plain Layout
10790 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10793 \begin_layout Plain Layout
10794 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10807 \begin_layout Plain Layout
10814 \begin_layout Plain Layout
10828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10831 \begin_layout Plain Layout
10832 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10846 \begin_inset space \hfill{}
10852 \begin_layout Standard
10853 \begin_inset VSpace medskip
10856 With these commands as many characters as you like can be accented.
10869 will only be set in the output with a length of three characters, as shown
10870 in the following example:
10871 \begin_inset Formula \[
10872 \widetilde{A+B=C-D}\]
10879 \begin_layout Standard
10890 \begin_layout Plain Layout
10908 \begin_layout Plain Layout
10916 described in the previous subsection it is also possible to accent several
10926 \begin_layout Plain Layout
10936 \begin_inset Formula $\downarrow$
10942 \begin_inset Formula \[
10943 \underset{***}{A=B}\]
10950 \begin_layout Section
10952 \begin_inset CommandInset label
10962 \begin_layout Plain Layout
10971 \begin_layout Subsection
10973 \begin_inset CommandInset label
10975 name "sub:Predefined-Space"
10983 \begin_layout Plain Layout
10984 Space ! horizontal ! predefined
10992 \begin_layout Standard
10993 Sometimes it is necessary to insert horizontal space to a formula.
10994 This is done by inserting a protected space (shortcut
10997 arg "space-insert protected"
11002 \begin_inset Quotes eld
11011 \begin_layout Plain Layout
11023 \begin_inset Quotes erd
11026 appears and by pressing
11030 several times one can select one of eight different space sizes.
11031 The spaces can also be inserted using the math toolbar button
11032 \begin_inset Graphics
11033 filename ../images/math/space.png
11038 or special commands.
11039 Independent from the inserted command, one can select the size again by
11047 \begin_layout Standard
11050 \begin_inset VSpace -5mm
11054 \begin_inset Tabular
11055 <lyxtabular version="3" rows="3" columns="7">
11057 <column alignment="center" valignment="middle" width="6.8cm">
11058 <column alignment="center" valignment="top" width="0">
11059 <column alignment="center" valignment="top" width="0">
11060 <column alignment="center" valignment="top" width="0">
11061 <column alignment="center" valignment="top" width="0">
11062 <column alignment="center" valignment="top" width="0">
11063 <column alignment="center" valignment="top" width="0">
11065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11068 \begin_layout Plain Layout
11074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11077 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11088 \begin_layout Plain Layout
11096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11099 \begin_layout Plain Layout
11107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11110 \begin_layout Plain Layout
11118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11121 \begin_layout Plain Layout
11129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11132 \begin_layout Plain Layout
11142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11145 \begin_layout Plain Layout
11150 keystrokes after inserting the protected space
11155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11158 \begin_layout Plain Layout
11164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11167 \begin_layout Plain Layout
11173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11176 \begin_layout Plain Layout
11182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11185 \begin_layout Plain Layout
11191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11194 \begin_layout Plain Layout
11200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11203 \begin_layout Plain Layout
11211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11214 \begin_layout Plain Layout
11220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11223 \begin_layout Plain Layout
11224 \begin_inset Formula $A\, B$
11232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11235 \begin_layout Plain Layout
11236 \begin_inset Formula $A\: B$
11244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11247 \begin_layout Plain Layout
11248 \begin_inset Formula $A\; B$
11256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11259 \begin_layout Plain Layout
11260 \begin_inset Formula $A\quad B$
11268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11271 \begin_layout Plain Layout
11272 \begin_inset Formula $A\qquad B$
11280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11283 \begin_layout Plain Layout
11284 \begin_inset Formula $A\! B$
11300 \begin_layout Standard
11301 The last size seem to produce no space.
11302 It is displayed red in LyX contrary to the other sizes, because it is a
11304 There are two more negative spaces:
11307 \begin_layout Standard
11309 \begin_inset Tabular
11310 <lyxtabular version="3" rows="3" columns="3">
11312 <column alignment="center" valignment="middle" width="6.8cm">
11313 <column alignment="center" valignment="top" width="0pt">
11314 <column alignment="center" valignment="top" width="0pt">
11316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11319 \begin_layout Plain Layout
11325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11328 \begin_layout Plain Layout
11336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11339 \begin_layout Plain Layout
11349 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11352 \begin_layout Plain Layout
11357 keystrokes after inserting the protected space
11362 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11365 \begin_layout Plain Layout
11371 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11374 \begin_layout Plain Layout
11382 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11385 \begin_layout Plain Layout
11391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11394 \begin_layout Plain Layout
11395 \begin_inset Formula $A\negmedspace B$
11403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11406 \begin_layout Plain Layout
11407 \begin_inset Formula $A\negthickspace B$
11423 \begin_layout Standard
11424 Negative spaces can lead to characters overlapping each other.
11425 Thus they can be used to enforce ligatures, what is e.
11426 \begin_inset space \thinspace{}
11430 \begin_inset space \space{}
11433 useful for summation operators:
11436 \begin_layout Standard
11438 \begin_inset Tabular
11439 <lyxtabular version="3" rows="3" columns="2">
11441 <column alignment="center" valignment="top" width="0">
11442 <column alignment="center" valignment="top" width="0">
11444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11447 \begin_layout Plain Layout
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11456 \begin_layout Plain Layout
11458 \begin_inset Note Note
11461 \begin_layout Plain Layout
11468 is only used as spacer.
11480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11483 \begin_layout Plain Layout
11492 \begin_layout Plain Layout
11506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11509 \begin_layout Plain Layout
11510 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11523 \begin_layout Plain Layout
11534 \begin_layout Plain Layout
11548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11551 \begin_layout Plain Layout
11552 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11568 \begin_layout Standard
11569 Relations like for example equal signs, are always surrounded by space.
11570 To suppress this, the equal sign is placed into a TeX-brace.
11571 The following example demonstrates this:
11574 \begin_layout Standard
11576 \begin_inset Tabular
11577 <lyxtabular version="3" rows="2" columns="2">
11579 <column alignment="center" valignment="top" width="0pt">
11580 <column alignment="center" valignment="top" width="0pt">
11582 <cell alignment="center" valignment="top" usebox="none">
11585 \begin_layout Plain Layout
11591 <cell alignment="center" valignment="top" usebox="none">
11594 \begin_layout Plain Layout
11595 \begin_inset Formula $A=B$
11605 <cell alignment="center" valignment="top" usebox="none">
11608 \begin_layout Plain Layout
11609 \begin_inset Note Note
11612 \begin_layout Plain Layout
11619 is only used as spacer.
11625 \begin_inset Formula $\raisebox{5mm}{}$
11628 equation without space
11633 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11636 \begin_layout Plain Layout
11637 \begin_inset Formula $A{=}B$
11653 \begin_layout Standard
11655 The command for the last formula is:
11660 \begin_inset Formula $\to$
11666 \begin_layout Standard
11667 \begin_inset VSpace bigskip
11670 Spaces are needed for physical units, because the space between the value
11671 and the unit is the smallest one and not a normal space.
11672 For units in text, the smallest space is inserted via the menu
11674 Insert\SpecialChar \menuseparator
11675 Formatting\SpecialChar \menuseparator
11677 \begin_inset space ~
11685 arg "space-insert thin"
11691 \begin_layout Standard
11692 An example to visualize the difference:
11695 \begin_layout Standard
11696 \begin_inset Tabular
11697 <lyxtabular version="3" rows="2" columns="2">
11699 <column alignment="left" valignment="top" width="0">
11700 <column alignment="left" valignment="top" width="0">
11702 <cell alignment="center" valignment="top" usebox="none">
11705 \begin_layout Plain Layout
11707 \begin_inset Formula $\cdot$
11715 <cell alignment="center" valignment="top" usebox="none">
11718 \begin_layout Plain Layout
11719 space between value and unit
11726 <cell alignment="center" valignment="top" usebox="none">
11729 \begin_layout Plain Layout
11731 \begin_inset space \thinspace{}
11735 \begin_inset Formula $\cdot$
11743 <cell alignment="center" valignment="top" usebox="none">
11746 \begin_layout Plain Layout
11747 smallest space between value and unit
11760 \begin_layout Subsection
11765 \begin_layout Plain Layout
11778 \begin_layout Plain Layout
11779 for vertical space in formulas see
11780 \begin_inset CommandInset ref
11782 reference "sub:Line-Separation"
11795 \begin_layout Plain Layout
11803 \begin_inset Note Note
11806 \begin_layout Plain Layout
11809 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11812 \begin_layout Plain Layout
11815 texorpdfstring is in section
11816 \begin_inset CommandInset ref
11818 reference "sub:Formulas-in-Section"
11828 \begin_inset CommandInset label
11830 name "sub:Variable-Space"
11838 \begin_layout Plain Layout
11839 Space ! horizontal ! variable
11847 \begin_layout Standard
11848 Space with a defined length can be inserted with the command
11858 \begin_layout Plain Layout
11868 \begin_inset Quotes eld
11877 \begin_layout Plain Layout
11889 \begin_inset Quotes erd
11893 The length can be specified by left-clicking on the
11894 \begin_inset Quotes eld
11903 \begin_layout Plain Layout
11915 \begin_inset Quotes erd
11919 The length may also be negative.
11920 To insert so many space that the formula uses all available space, the
11931 \begin_layout Plain Layout
11942 \begin_layout Standard
11943 \begin_inset VSpace -1mm
11949 \begin_layout Standard
11951 \begin_inset Tabular
11952 <lyxtabular version="3" rows="4" columns="2">
11954 <column alignment="center" valignment="top" width="0">
11955 <column alignment="center" valignment="top" width="0">
11957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11960 \begin_layout Plain Layout
11968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11971 \begin_layout Plain Layout
11979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11982 \begin_layout Plain Layout
11989 \begin_layout Plain Layout
11999 \begin_inset Formula $\to$
12005 \begin_inset space \thinspace{}
12013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12016 \begin_layout Plain Layout
12017 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12030 \begin_layout Plain Layout
12037 \begin_layout Plain Layout
12047 \begin_inset Formula $\to$
12053 \begin_inset space \thinspace{}
12061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12064 \begin_layout Plain Layout
12065 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12078 \begin_layout Plain Layout
12085 \begin_layout Plain Layout
12099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12102 \begin_layout Plain Layout
12103 \begin_inset Formula $A=A\hfill B=B$
12119 \begin_layout Standard
12120 In the last example the available space is given by the longest column entry
12122 In an inline formula the space depends on the length of the line in which
12130 Thus, when the line uses the full width, no space will be created.
12137 only has an effect on displayed formulas when the formula style
12142 (Formula styles are explained in
12143 \begin_inset CommandInset ref
12145 reference "sec:Formula-Styles"
12152 \begin_layout Standard
12159 , there are the commands
12171 that fill the space with a pattern, see
12172 \begin_inset CommandInset ref
12174 reference "sub:Ellipses"
12181 \begin_layout Standard
12182 For text, variable space can be inserted via the menu
12184 Insert\SpecialChar \menuseparator
12185 Formatting\SpecialChar \menuseparator
12187 \begin_inset space ~
12195 \begin_layout Standard
12196 This is a line with
12197 \begin_inset space \hspace{}
12202 \begin_inset space \thinspace{}
12208 \begin_layout Standard
12209 This is a line with
12210 \begin_inset space \hfill{}
12216 \begin_layout Subsection
12217 Space besides inline Formulas
12221 \begin_layout Plain Layout
12222 Space ! besides inline formulas
12230 \begin_layout Standard
12231 The space that surrounds inline formulas can be adjusted with the length
12240 \begin_layout Plain Layout
12251 The value of a length is set with the command
12259 \begin_layout Plain Layout
12269 that has the following scheme:
12272 \begin_layout Standard
12277 setlength{length name}{value}
12280 \begin_layout Standard
12288 \begin_inset space \thinspace{}
12294 \begin_layout Standard
12304 \begin_layout Standard
12305 is inserted in TeX-mode.
12307 \begin_inset space \thinspace{}
12310 mm space will now be set around all inline formulas:
12314 \begin_layout Plain Layout
12328 \begin_layout Standard
12329 This is a line with an inline formula
12330 \begin_inset Formula $A=B$
12334 \begin_inset space \thinspace{}
12337 mm surrounding space.
12341 \begin_layout Plain Layout
12355 \begin_layout Standard
12356 To return to the predefined value,
12362 is set to the value 0
12363 \begin_inset space \thinspace{}
12369 \begin_layout Section
12374 \begin_layout Plain Layout
12384 \begin_layout Plain Layout
12389 \begin_layout Plain Layout
12400 \begin_layout Plain Layout
12415 \begin_layout Standard
12416 Boxes for text are described in chapter
12423 \begin_inset space ~
12431 \begin_layout Subsection
12433 \begin_inset CommandInset label
12435 name "sub:Boxes-with-Frame"
12443 \begin_layout Plain Layout
12452 \begin_layout Standard
12453 It is possible to frame formulas or parts of it with the commands
12463 \begin_layout Plain Layout
12481 \begin_layout Plain Layout
12492 \begin_layout Standard
12493 When one of these commands is inserted to a formula, a blue box appears
12494 within a frame to enter formula parts.
12501 an additional formula has to be created by
12505 within this box, because the box content will otherwise be treated as mathemati
12513 is used, a new formula is automatically created inside the frame.
12516 \begin_layout Standard
12523 is not suitable to frame displayed formulas because the formula will always
12524 be set in the size of the text.
12531 is in contrary not suitable to frame inline formulas, because the formula
12532 will always be set in the size of a displayed formula.
12535 \begin_layout Standard
12542 there is the command
12552 \begin_layout Plain Layout
12560 where additionally the frame width and the alignment can be specified.
12567 is used in the following scheme:
12570 \begin_layout Standard
12575 framebox[frame width][position]{box content}
12578 \begin_layout Standard
12579 The position can either be
12596 right aligns the formula in the box.
12597 When no position is given, the formula will be centered.
12598 \begin_inset Newline newline
12601 Is no width given, also no position can be given.
12602 In this case the frame width is adjusted to the box content like for
12611 \begin_layout Standard
12618 is inserted, a box appears containing three blue boxes.
12619 The first two boxes are surrounded by brackets and denote the two optional
12621 The third box is for formula parts like for
12630 \begin_layout Standard
12632 \begin_inset Tabular
12633 <lyxtabular version="3" rows="5" columns="2">
12635 <column alignment="center" valignment="top" width="0">
12636 <column alignment="center" valignment="top" width="0">
12638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12641 \begin_layout Plain Layout
12647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12650 \begin_layout Plain Layout
12652 \begin_inset Note Note
12655 \begin_layout Plain Layout
12662 is only used as spacer.
12674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12677 \begin_layout Plain Layout
12684 \begin_layout Plain Layout
12703 \begin_layout Plain Layout
12717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12720 \begin_layout Plain Layout
12721 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12734 \begin_layout Plain Layout
12741 \begin_layout Plain Layout
12756 \begin_layout Plain Layout
12770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12773 \begin_layout Plain Layout
12774 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12787 \begin_layout Plain Layout
12794 \begin_layout Plain Layout
12808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12811 \begin_layout Plain Layout
12812 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12825 \begin_layout Plain Layout
12832 \begin_layout Plain Layout
12842 \begin_inset Formula $\to$
12846 \begin_inset Formula $\to$
12859 \begin_layout Plain Layout
12869 \begin_inset Formula $\downarrow$
12877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12880 \begin_layout Plain Layout
12881 \begin_inset Formula $\raisebox{6mm}{}$
12885 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12889 \begin_inset Formula $\raisebox{-4mm}{}$
12905 \begin_layout Standard
12906 The frame thickness can also be adjusted.
12907 To do this the following commands have to be inserted in TeX-mode before
12911 \begin_layout Standard
12921 \begin_inset Quotes eld
12925 \begin_inset Quotes erd
12939 \begin_inset Quotes eld
12943 \begin_inset Quotes erd
12949 \begin_layout Standard
12950 \begin_inset Quotes eld
12954 \begin_inset Quotes erd
12957 specifies the minimal distance between the frame and the first character
12959 An example for this is the following framed formula:
12963 \begin_layout Plain Layout
12975 \begin_inset Formula \[
12980 Before this formula the commands
12983 \begin_layout Standard
13005 \begin_layout Standard
13006 were inserted in TeX-mode.
13007 The given values are used for all following boxes.
13010 \begin_layout Standard
13011 To return to the standard frame size, the command
13014 \begin_layout Standard
13039 \begin_layout Plain Layout
13053 \begin_layout Standard
13054 is inserted in TeX-mode before the next formula.
13057 \begin_layout Subsection
13058 Boxes without Frame
13059 \begin_inset CommandInset label
13061 name "sub:Boxes-without-Frame"
13069 \begin_layout Plain Layout
13070 Boxes ! without frame
13078 \begin_layout Standard
13079 For boxes without a frame there are the following box commands:
13089 \begin_layout Plain Layout
13107 \begin_layout Plain Layout
13125 \begin_layout Plain Layout
13136 \begin_layout Standard
13143 a box can be super- or subscripted.
13144 But in contrary to normal super- and subscripting, the characters in the
13145 box keep their font size.
13152 is used in the following scheme:
13155 \begin_layout Standard
13160 raisebox{height}{box content}
13163 \begin_layout Standard
13164 When the box should contain a formula, an extra formula is needed like for
13175 \begin_inset Note Greyedout
13178 \begin_layout Plain Layout
13189 this extra formula is created by pressing
13193 twice instead of once because LyX doesn't yet support
13207 \begin_layout Standard
13209 \begin_inset Tabular
13210 <lyxtabular version="3" rows="4" columns="2">
13212 <column alignment="center" valignment="top" width="0">
13213 <column alignment="center" valignment="top" width="0">
13215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13218 \begin_layout Plain Layout
13224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13227 \begin_layout Plain Layout
13235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13238 \begin_layout Plain Layout
13242 \begin_inset Formula $\to$
13248 \begin_inset Formula $\to$
13256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13259 \begin_layout Plain Layout
13260 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13273 \begin_layout Plain Layout
13277 \begin_inset Formula $\to$
13283 \begin_inset Formula $\to$
13291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13294 \begin_layout Plain Layout
13295 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13308 \begin_layout Plain Layout
13312 \begin_inset Formula $\to$
13331 \begin_layout Plain Layout
13345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13348 \begin_layout Plain Layout
13349 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13365 \begin_layout Standard
13390 , with the difference that there is no frame.
13393 \begin_layout Subsection
13395 \begin_inset CommandInset label
13397 name "sub:Colored-Boxes"
13405 \begin_layout Plain Layout
13414 \begin_layout Standard
13415 To be able to use all commands explained in this section, the LaTeX-package
13424 \begin_layout Plain Layout
13429 is part of every LaTeX standard installation.
13438 \begin_layout Plain Layout
13444 has to be loaded in the LaTeX-preamble with the line
13448 \begin_layout Plain Layout
13449 When text is colored somewhere in the document with a predefined color,
13450 LyX loads the LaTeX-package
13455 Thus it is possible that the package is loaded twice, but this doesn't
13462 \begin_inset Note Note
13465 \begin_layout Plain Layout
13466 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13475 \begin_layout Standard
13483 \begin_layout Standard
13484 \begin_inset VSpace medskip
13487 To color boxes, the command
13497 \begin_layout Plain Layout
13505 is used in the following scheme:
13508 \begin_layout Standard
13513 colorbox{color}{box content}
13516 \begin_layout Standard
13517 The box content can also be a box and a
13523 can also be part of another box (see the 2nd and 3rd example).
13524 When the box should contain a formula, an extra formula has to be created,
13525 the same way as for
13535 \begin_layout Plain Layout
13536 This also applies for the command
13550 \begin_layout Standard
13551 One of the following predefined colors can be chosen:
13554 \begin_layout Standard
13588 \begin_layout Standard
13590 \begin_inset Tabular
13591 <lyxtabular version="3" rows="4" columns="2">
13593 <column alignment="center" valignment="top" width="0">
13594 <column alignment="center" valignment="top" width="0">
13596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13599 \begin_layout Plain Layout
13605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13608 \begin_layout Plain Layout
13610 \begin_inset Note Note
13613 \begin_layout Plain Layout
13620 is only used as spacer.
13632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13635 \begin_layout Plain Layout
13639 \begin_inset Formula $\to$
13649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13652 \begin_layout Plain Layout
13653 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13666 \begin_layout Plain Layout
13670 \begin_inset Formula $\to$
13681 \begin_layout Plain Layout
13695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13698 \begin_layout Plain Layout
13699 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13712 \begin_layout Plain Layout
13719 \begin_layout Plain Layout
13731 \begin_inset Formula $\to$
13750 \begin_layout Plain Layout
13764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13767 \begin_layout Plain Layout
13768 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13784 \begin_layout Standard
13791 only colors the box but not the characters in the box.
13792 To color all characters, the whole formula is highlighted and the wanted
13793 color is chosen in the
13796 \begin_inset space ~
13802 The dialog can be called with the toolbar button
13803 \begin_inset Graphics
13804 filename ../images/dialog-show_character.png
13811 Edit\SpecialChar \menuseparator
13813 \begin_inset space ~
13816 Style\SpecialChar \menuseparator
13820 The formula number has then the same color as the formula.
13821 When the formula number should get another color than the formula characters,
13822 the color must be changed within the formula.
13825 \begin_layout Standard
13829 \begin_layout Standard
13832 \begin_inset Formula \begin{equation}
13833 \int A=B\label{eq:red}\end{equation}
13840 \begin_inset Formula \begin{equation}
13841 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13848 \begin_layout Standard
13850 \begin_inset CommandInset ref
13856 is completely colored red.
13857 \begin_inset Newline newline
13861 \begin_inset CommandInset ref
13863 reference "eq:redgreen"
13867 was first completely colored green to set the color for the formula number.
13868 Subsequently the formula characters were colored red.
13871 \begin_layout Standard
13872 \begin_inset VSpace bigskip
13875 To color the frame different than the rest of the box, the command
13885 \begin_layout Plain Layout
13893 is used in the following scheme:
13896 \begin_layout Standard
13901 fcolorbox{frame color}{color}{box content}
13904 \begin_layout Standard
13911 is an extension of the command
13918 The frame width is set, like for
13941 \begin_layout Plain Layout
13953 \begin_inset Formula \[
13954 \fcolorbox{cyan}{magenta}{A=B}\]
13962 \begin_layout Plain Layout
13976 \begin_layout Standard
13977 This formula was created with the command
13978 \begin_inset Newline newline
13986 \begin_inset Formula $\to$
13992 \begin_inset Formula $\to$
14002 \begin_layout Standard
14003 \begin_inset VSpace bigskip
14006 To use other colors than the predefined ones, they have to be defined first.
14009 \begin_layout Standard
14010 One can for example define the color
14011 \begin_inset Quotes eld
14019 \begin_inset Quotes erd
14022 with the LaTeX-preamble line:
14025 \begin_layout Standard
14030 definecolor{darkgreen}{cmyk}{0.5,
14048 \begin_layout Plain Layout
14059 \begin_layout Standard
14064 is the color space that denotes the colors
14081 The four comma separated numbers are the portion factor for the corresponding
14082 colors of the color space.
14083 The factors can be in the range of 0
14084 \begin_inset space \thinspace{}
14088 \begin_inset space \thinspace{}
14096 also the color space
14100 can be used for definitions.
14117 , so that there are in this case three portion factors for the corresponding
14119 Furthermore there is the color space
14123 with one portion factor for the gray value.
14126 \begin_layout Standard
14127 As example a framed box with the new defined color
14131 where the characters have been colored
14136 \begin_inset Formula \begin{equation}
14137 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14144 \begin_layout Standard
14145 Self-defined colors can also be used for text with the help of the command
14156 \begin_layout Plain Layout
14165 \begin_layout Standard
14169 \begin_layout Plain Layout
14173 textcolor{darkgreen}{
14179 \begin_inset Quotes eld
14183 \begin_inset Quotes erd
14190 \begin_layout Plain Layout
14200 \begin_layout Standard
14211 \begin_layout Plain Layout
14219 is used in the scheme
14223 textcolor{color}{characters to color}
14228 \begin_layout Subsection
14230 \begin_inset CommandInset label
14232 name "sub:Paragraph-Boxes"
14240 \begin_layout Plain Layout
14241 Boxes ! as paragraph
14249 \begin_layout Standard
14250 A box that can contain several lines and paragraphs, a so called paragraph
14251 box (parbox), can be created with the menu
14253 Insert\SpecialChar \menuseparator
14256 or the toolbar button
14257 \begin_inset Graphics
14258 filename ../images/box-insert.png
14266 \begin_layout Standard
14267 The following example shows a framed parbox in a line:
14270 \begin_layout Standard
14271 \begin_inset VSpace medskip
14275 \begin_inset Box Boxed
14284 height_special "totalheight"
14287 \begin_layout Plain Layout
14288 This is a paragraph box.
14290 \begin_inset space \thinspace{}
14293 cm long and can also contain formulas:
14294 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14305 \begin_layout Standard
14306 \begin_inset VSpace medskip
14312 \begin_layout Standard
14313 Such a box is created by right-clicking on the gray box inset.
14314 A dialog pops up showing the box properties.
14328 \begin_inset space \thinspace{}
14333 Vertical Box Alignment
14338 \begin_layout Standard
14339 \begin_inset VSpace medskip
14342 In LaTeX a parbox is created with the command
14352 \begin_layout Plain Layout
14360 that has the following scheme:
14363 \begin_layout Standard
14368 parbox[position]{width}{box content}
14371 \begin_layout Standard
14385 for bottom means that the box is aligned within the surrounding text with
14391 for top this is done with the first line.
14392 When no position is given, the box will be vertically centered, see section
14400 \begin_inset space ~
14405 manual for examples.
14408 \begin_layout Standard
14409 \begin_inset VSpace bigskip
14412 To frame formulas completely, including the formula number, the formula
14413 must be set into a parbox.
14414 To do this, the command
14428 is inserted in TeX-mode before the formula.
14437 \begin_layout Plain Layout
14447 is hereby the line width set for the document.
14448 Because the frame is outside the parbox, 2
14449 \begin_inset space \thinspace{}
14452 times the frame separation and the frame thickness must be subtracted from
14454 As this is not automatically done by LyX due to a bug
14458 \begin_layout Plain Layout
14459 \begin_inset CommandInset href
14461 name "LyX-bug #4483"
14462 target "http://www.lyx.org/trac/ticket/4483"
14471 , TeX-mode has to be used.
14472 To be able to multiply and subtract in arguments, the LaTeX-package
14480 \begin_layout Plain Layout
14485 is part of every LaTeX standard installation.
14494 \begin_layout Plain Layout
14500 must be loaded in the LaTeX-preamble with the line
14503 \begin_layout Standard
14511 \begin_layout Standard
14512 Behind the formula both boxes are closed by entering
14517 Here is an example:
14521 \begin_layout Plain Layout
14535 \begin_layout Standard
14539 \begin_layout Plain Layout
14557 \begin_inset Formula \begin{equation}
14558 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14566 \begin_layout Plain Layout
14577 \begin_layout Plain Layout
14591 \begin_layout Standard
14592 \begin_inset VSpace medskip
14595 As a parbox is used as argument of
14601 , there is in this case no difference between
14616 \begin_layout Standard
14617 \begin_inset VSpace bigskip
14620 Paragraph boxes are very useful to comment formulas directly.
14627 is used in combination with the command
14641 \begin_inset CommandInset ref
14643 reference "sub:User-defined-Numbering"
14650 \begin_layout Standard
14651 An example of a formula commented with
14660 \begin_layout Standard
14664 \begin_layout Plain Layout
14677 This is a description.
14678 It is distinctly separated from the formula and multiline.
14682 \begin_layout Plain Layout
14694 \begin_layout Standard
14695 Such a formula must be inserted completely in TeX-mode because LyX does
14696 not yet support the command
14703 The formula is created with the following command sequence:
14706 \begin_layout Standard
14719 is inserted in TeX-mode.
14723 \begin_layout Plain Layout
14724 When the formula style
14736 can also be replaced by
14743 (formula styles see
14744 \begin_inset CommandInset ref
14746 reference "sec:Formula-Styles"
14755 Then the description follows as normal text, and finally
14761 is inserted in TeX-mode.
14774 hereby create a displayed formula.
14777 \begin_layout Standard
14784 can be seen in this example that was
14785 \begin_inset Quotes eld
14789 \begin_inset Quotes erd
14792 using the mathematical textmode:
14793 \begin_inset Formula \[
14794 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14801 \begin_layout Section
14806 \begin_layout Plain Layout
14815 \begin_layout Subsection
14817 \begin_inset CommandInset label
14819 name "sub:Big-Operators"
14827 \begin_layout Plain Layout
14837 \begin_layout Plain Layout
14847 \begin_layout Plain Layout
14856 \begin_layout Standard
14857 To be able to use all integral operators listed here, the option
14859 Use esint package automatically
14861 must be set in the document settings under
14864 \begin_inset space ~
14872 \begin_layout Standard
14873 \begin_inset space \hfill{}
14877 \begin_inset Tabular
14878 <lyxtabular version="3" rows="11" columns="2">
14880 <column alignment="center" valignment="top" width="0pt">
14881 <column alignment="center" valignment="top" width="0pt">
14883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14886 \begin_layout Plain Layout
14892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14895 \begin_layout Plain Layout
14903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14906 \begin_layout Plain Layout
14913 \begin_layout Plain Layout
14926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14929 \begin_layout Plain Layout
14930 \begin_inset Formula $\int$
14940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14943 \begin_layout Plain Layout
14951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14954 \begin_layout Plain Layout
14955 \begin_inset Formula $\oint$
14965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14968 \begin_layout Plain Layout
14976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14979 \begin_layout Plain Layout
14980 \begin_inset Formula $\ointctrclockwise$
14990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14993 \begin_layout Plain Layout
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15004 \begin_layout Plain Layout
15005 \begin_inset Formula $\ointclockwise$
15015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15018 \begin_layout Plain Layout
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15029 \begin_layout Plain Layout
15030 \begin_inset Formula $\sqint$
15040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15043 \begin_layout Plain Layout
15051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15054 \begin_layout Plain Layout
15056 \begin_inset Formula $\fint$
15066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15069 \begin_layout Plain Layout
15077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15080 \begin_layout Plain Layout
15082 \begin_inset Formula $\landupint$
15092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15095 \begin_layout Plain Layout
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15106 \begin_layout Plain Layout
15108 \begin_inset Formula $\landdownint$
15118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15132 \begin_layout Plain Layout
15133 \begin_inset Formula $\bigcap$
15143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15146 \begin_layout Plain Layout
15154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15157 \begin_layout Plain Layout
15158 \begin_inset Formula $\bigcup$
15172 \begin_inset space \hfill{}
15176 \begin_inset Tabular
15177 <lyxtabular version="3" rows="11" columns="2">
15179 <column alignment="center" valignment="top" width="0pt">
15180 <column alignment="center" valignment="top" width="0pt">
15182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15185 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15205 \begin_layout Plain Layout
15212 \begin_layout Plain Layout
15225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15228 \begin_layout Plain Layout
15229 \begin_inset Formula $\sum$
15239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15242 \begin_layout Plain Layout
15249 \begin_layout Plain Layout
15262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15265 \begin_layout Plain Layout
15266 \begin_inset Formula $\prod$
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15279 \begin_layout Plain Layout
15287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15290 \begin_layout Plain Layout
15291 \begin_inset Formula $\coprod$
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15304 \begin_layout Plain Layout
15312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15315 \begin_layout Plain Layout
15316 \begin_inset Formula $\bigodot$
15326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15329 \begin_layout Plain Layout
15337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15340 \begin_layout Plain Layout
15341 \begin_inset Formula $\bigotimes$
15351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15354 \begin_layout Plain Layout
15362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15365 \begin_layout Plain Layout
15366 \begin_inset Formula $\bigoplus$
15376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15379 \begin_layout Plain Layout
15387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15390 \begin_layout Plain Layout
15391 \begin_inset Formula $\bigwedge$
15401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15404 \begin_layout Plain Layout
15412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15415 \begin_layout Plain Layout
15416 \begin_inset Formula $\bigvee$
15426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15429 \begin_layout Plain Layout
15437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15440 \begin_layout Plain Layout
15441 \begin_inset Formula $\bigsqcup$
15451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15454 \begin_layout Plain Layout
15462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15465 \begin_layout Plain Layout
15466 \begin_inset Formula $\biguplus$
15480 \begin_inset space \hfill{}
15486 \begin_layout Standard
15487 All big operators can also be inserted via the math toolbar button
15488 \begin_inset Graphics
15489 filename ../images/math/intop.png
15497 \begin_layout Standard
15498 The operators are called big because they are bigger than the sometimes
15499 equal looking binary operators.
15500 All big operators can have limits as described in the next subsection.
15503 \begin_layout Standard
15504 For all integral operators there is a second version available, ending on
15522 These operators are different from
15529 \begin_inset space \space{}
15532 in the style the operator limits are displayed, see
15533 \begin_inset CommandInset ref
15535 reference "sub:Operator-Limits"
15543 \begin_layout Subsubsection*
15544 Advices for Integrals
15547 \begin_layout Standard
15552 in an integral is an operator, that therefore has to be set upright.
15553 This is done by highlighting the
15557 and using the keyboard shortcut
15567 \begin_layout Plain Layout
15573 \begin_inset CommandInset ref
15575 reference "sub:Font-Styles"
15585 Finally the smallest space is inserted before the
15589 , as this is usual for operators.
15593 \begin_layout Standard
15595 \begin_inset Formula $\int A(x)dx$
15599 \begin_inset Newline newline
15606 \begin_layout Plain Layout
15616 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15622 \begin_layout Standard
15623 For multiple integrals there are the following commands:
15624 \begin_inset VSpace medskip
15630 \begin_layout Standard
15631 \begin_inset space \hfill{}
15635 \begin_inset Tabular
15636 <lyxtabular version="3" rows="4" columns="2">
15638 <column alignment="center" valignment="top" width="0">
15639 <column alignment="center" valignment="top" width="0">
15641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15653 \begin_layout Plain Layout
15655 \begin_inset Note Note
15658 \begin_layout Plain Layout
15665 is only used as spacer.
15677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15680 \begin_layout Plain Layout
15688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15691 \begin_layout Plain Layout
15692 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15702 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15705 \begin_layout Plain Layout
15713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15716 \begin_layout Plain Layout
15717 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15730 \begin_layout Plain Layout
15738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15741 \begin_layout Plain Layout
15742 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15756 \begin_inset space \hfill{}
15760 \begin_inset Tabular
15761 <lyxtabular version="3" rows="4" columns="2">
15763 <column alignment="center" valignment="top" width="0">
15764 <column alignment="center" valignment="top" width="0">
15766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15769 \begin_layout Plain Layout
15775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15778 \begin_layout Plain Layout
15786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15789 \begin_layout Plain Layout
15797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15800 \begin_layout Plain Layout
15801 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15814 \begin_layout Plain Layout
15822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15825 \begin_layout Plain Layout
15826 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15839 \begin_layout Plain Layout
15847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15850 \begin_layout Plain Layout
15851 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15865 \begin_inset space \hfill{}
15871 \begin_layout Subsection
15873 \begin_inset CommandInset label
15875 name "sub:Operator-Limits"
15883 \begin_layout Plain Layout
15892 \begin_layout Standard
15893 Limits are created by super- and subscripts:
15896 \begin_layout Standard
15898 \begin_inset Tabular
15899 <lyxtabular version="3" rows="2" columns="2">
15901 <column alignment="center" valignment="top" width="0pt">
15902 <column alignment="center" valignment="top" width="0pt">
15904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15907 \begin_layout Plain Layout
15913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15916 \begin_layout Plain Layout
15918 \begin_inset Note Note
15921 \begin_layout Plain Layout
15928 is only used as spacer.
15940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15943 \begin_layout Plain Layout
15952 \begin_layout Plain Layout
15962 \begin_inset Formula $\to$
15966 \begin_inset Formula $\to$
15974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15977 \begin_layout Plain Layout
15978 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15994 \begin_layout Standard
15995 Limits of inline formulas are set right beside the operator.
15996 Limits in displayed formulas are set above or below the operator, except
15997 for integral limits.
16000 \begin_layout Standard
16001 To force that the limits are set beside the operator, the cursor is set
16002 directly behind the operator and the limits type is changed with the menu
16005 Edit\SpecialChar \menuseparator
16006 Math\SpecialChar \menuseparator
16025 \begin_layout Standard
16026 The default limits type is this:
16027 \begin_inset Formula \[
16028 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16032 This is how it looks when the limits type was changed to
16039 \begin_inset Formula \[
16040 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16044 For integrals, except those ending with
16060 etc., the limits are by default set beside the operator.
16061 But for multiple integrals the limits are often set below the operator.
16062 In the following example the limits type was therefore set to
16066 and so set below the integrals:
16067 \begin_inset Formula \begin{equation}
16068 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16075 \begin_layout Standard
16076 \begin_inset VSpace medskip
16079 To specify conditions for limits, the commands
16089 \begin_layout Plain Layout
16107 \begin_layout Plain Layout
16116 To create for example this expression
16117 \begin_inset Formula \begin{equation}
16118 \sum_{\begin{subarray}{c}
16120 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16127 \begin_layout Standard
16128 the following has to be done:
16129 \begin_inset Newline newline
16144 \begin_layout Plain Layout
16156 One is now in a blue box under the summation operator and insert there
16165 \begin_layout Plain Layout
16177 The blue box is now within a purple box and now several lines can be written
16179 A new line is created by inserting a line break (
16182 arg "newline-insert newline"
16187 \begin_inset Newline newline
16192 0<k<1000 Ctrl+Return
16193 \begin_inset Newline newline
16198 is typed in, a new box appears below for the new line.
16201 \begin_layout Standard
16202 The alignment of the lines can be changed to left aligned with the
16212 Edit\SpecialChar \menuseparator
16216 To get right alignment,
16224 \begin_layout Plain Layout
16235 is inserted at the beginning of the line.
16238 \begin_layout Standard
16251 with the difference that the lines are always centered.
16254 \begin_layout Standard
16255 \begin_inset VSpace bigskip
16259 \begin_inset CommandInset ref
16261 reference "eq:substack"
16265 there can be too much space beside an operator, because the characters
16266 following the operator are set beside the limits.
16269 \begin_layout Standard
16270 To avoid this, the following macro can be used in the LaTeX-preamble:
16273 \begin_layout Standard
16287 \begin_inset Newline newline
16299 \begin_inset Newline newline
16306 mathclapinternal #1#2{
16310 mathsurround =0pt #1{#2}$}}
16313 \begin_layout Standard
16314 This defines the command
16324 \begin_layout Plain Layout
16332 that sets the width of the limit to 0
16333 \begin_inset space \thinspace{}
16337 The command scheme is
16340 \begin_layout Standard
16348 \begin_layout Standard
16349 where the limit can consist of several conditions.
16352 \begin_layout Standard
16354 \begin_inset CommandInset ref
16356 reference "eq:substack"
16360 , one uses the command
16363 \begin_layout Standard
16376 \begin_layout Plain Layout
16385 0<k<1000 Ctrl+Return
16388 \begin_layout Standard
16389 to create the lower limit.
16390 The summand is now directly behind the summation operator:
16391 \begin_inset Formula \[
16392 \sum_{\mathclap{\substack{0<k<1000\\
16393 \\k\,\in\,\mathbb{N}}
16401 \begin_layout Standard
16402 \begin_inset VSpace bigskip
16405 How to use one limit for several operators is described in
16406 \begin_inset CommandInset ref
16408 reference "sub:Self-defined-Operators"
16415 \begin_layout Standard
16416 \begin_inset Newpage newpage
16422 \begin_layout Subsection
16424 \begin_inset CommandInset label
16426 name "sub:Binary-Operators"
16434 \begin_layout Plain Layout
16443 \begin_layout Standard
16444 Binary operators are surrounded by space when there is a character before
16446 \begin_inset VSpace medskip
16452 \begin_layout Standard
16453 \begin_inset space \hfill{}
16457 \begin_inset Tabular
16458 <lyxtabular version="3" rows="13" columns="2">
16460 <column alignment="center" valignment="top" width="0pt">
16461 <column alignment="center" valignment="top" width="0pt">
16463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16466 \begin_layout Plain Layout
16468 \begin_inset Note Note
16471 \begin_layout Plain Layout
16478 is only used as spacer.
16488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16491 \begin_layout Plain Layout
16499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16502 \begin_layout Plain Layout
16508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16511 \begin_layout Plain Layout
16512 \begin_inset Formula $+$
16522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16525 \begin_layout Plain Layout
16531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16534 \begin_layout Plain Layout
16535 \begin_inset Formula $-$
16545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16548 \begin_layout Plain Layout
16556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16559 \begin_layout Plain Layout
16560 \begin_inset Formula $\pm$
16570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16573 \begin_layout Plain Layout
16581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16584 \begin_layout Plain Layout
16585 \begin_inset Formula $\mp$
16595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16598 \begin_layout Plain Layout
16606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16609 \begin_layout Plain Layout
16610 \begin_inset Formula $\cdot$
16620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16623 \begin_layout Plain Layout
16631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16634 \begin_layout Plain Layout
16635 \begin_inset Formula $\times$
16645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16648 \begin_layout Plain Layout
16656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16659 \begin_layout Plain Layout
16660 \begin_inset Formula $\div$
16670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16673 \begin_layout Plain Layout
16677 \begin_layout Plain Layout
16690 \begin_layout Plain Layout
16702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16705 \begin_layout Plain Layout
16706 \begin_inset Formula $*$
16716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16719 \begin_layout Plain Layout
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16730 \begin_layout Plain Layout
16731 \begin_inset Formula $\star$
16741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16744 \begin_layout Plain Layout
16752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16755 \begin_layout Plain Layout
16756 \begin_inset Formula $\circ$
16766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16769 \begin_layout Plain Layout
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16780 \begin_layout Plain Layout
16781 \begin_inset Formula $\diamond$
16791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16794 \begin_layout Plain Layout
16802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16805 \begin_layout Plain Layout
16806 \begin_inset Formula $\bullet$
16820 \begin_inset space \hfill{}
16824 \begin_inset Tabular
16825 <lyxtabular version="3" rows="13" columns="2">
16827 <column alignment="center" valignment="top" width="0pt">
16828 <column alignment="center" valignment="top" width="0pt">
16830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16833 \begin_layout Plain Layout
16839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16842 \begin_layout Plain Layout
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16864 \begin_layout Plain Layout
16865 \begin_inset Formula $\nabla$
16875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16878 \begin_layout Plain Layout
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16890 \begin_inset Formula $\bigtriangledown$
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16903 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $\bigtriangleup$
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16939 \begin_layout Plain Layout
16940 \begin_inset Formula $\Box$
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16953 \begin_layout Plain Layout
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16964 \begin_layout Plain Layout
16965 \begin_inset Formula $\cap$
16975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16978 \begin_layout Plain Layout
16986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16989 \begin_layout Plain Layout
16990 \begin_inset Formula $\cup$
17000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17003 \begin_layout Plain Layout
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17014 \begin_layout Plain Layout
17015 \begin_inset Formula $\dagger$
17025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17028 \begin_layout Plain Layout
17036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17039 \begin_layout Plain Layout
17040 \begin_inset Formula $\ddagger$
17050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17053 \begin_layout Plain Layout
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17064 \begin_layout Plain Layout
17065 \begin_inset Formula $\wr$
17075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17078 \begin_layout Plain Layout
17086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17089 \begin_layout Plain Layout
17090 \begin_inset Formula $\bigcirc$
17100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17103 \begin_layout Plain Layout
17111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17114 \begin_layout Plain Layout
17115 \begin_inset Formula $\wedge$
17125 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17128 \begin_layout Plain Layout
17136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17139 \begin_layout Plain Layout
17140 \begin_inset Formula $\vee$
17154 \begin_inset space \hfill{}
17158 \begin_inset Tabular
17159 <lyxtabular version="3" rows="13" columns="2">
17161 <column alignment="center" valignment="top" width="0pt">
17162 <column alignment="center" valignment="top" width="0pt">
17164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17167 \begin_layout Plain Layout
17173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17176 \begin_layout Plain Layout
17184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17198 \begin_layout Plain Layout
17199 \begin_inset Formula $\oplus$
17209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17212 \begin_layout Plain Layout
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17223 \begin_layout Plain Layout
17224 \begin_inset Formula $\ominus$
17234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17237 \begin_layout Plain Layout
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17248 \begin_layout Plain Layout
17249 \begin_inset Formula $\otimes$
17259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17262 \begin_layout Plain Layout
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17273 \begin_layout Plain Layout
17274 \begin_inset Formula $\oslash$
17284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17287 \begin_layout Plain Layout
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17298 \begin_layout Plain Layout
17299 \begin_inset Formula $\odot$
17309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17312 \begin_layout Plain Layout
17320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17323 \begin_layout Plain Layout
17324 \begin_inset Formula $\amalg$
17334 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17337 \begin_layout Plain Layout
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17348 \begin_layout Plain Layout
17349 \begin_inset Formula $\uplus$
17359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17362 \begin_layout Plain Layout
17370 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17373 \begin_layout Plain Layout
17374 \begin_inset Formula $\setminus$
17384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17387 \begin_layout Plain Layout
17395 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17398 \begin_layout Plain Layout
17399 \begin_inset Formula $\sqcap$
17409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17412 \begin_layout Plain Layout
17420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17423 \begin_layout Plain Layout
17424 \begin_inset Formula $\sqcup$
17434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17437 \begin_layout Plain Layout
17445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17448 \begin_layout Plain Layout
17449 \begin_inset Formula $\triangleleft$
17459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17462 \begin_layout Plain Layout
17470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17473 \begin_layout Plain Layout
17474 \begin_inset Formula $\triangleright$
17488 \begin_inset space \hfill{}
17494 \begin_layout Standard
17495 All binary operators can also be inserted via the math toolbar button
17496 \begin_inset Graphics
17497 filename ../images/math/pm.png
17505 \begin_layout Standard
17506 To typeset the Laplace operator also
17523 \begin_inset Formula $\nabla^{2}$
17526 ) can be used instead of
17535 \begin_layout Standard
17542 Insert\SpecialChar \menuseparator
17554 \begin_layout Subsection
17555 Self-defined Operators
17556 \begin_inset CommandInset label
17558 name "sub:Self-defined-Operators"
17566 \begin_layout Plain Layout
17567 Operators ! self-defined
17575 \begin_layout Standard
17576 With the help of the command
17580 DeclareMathOperator
17586 \begin_layout Plain Layout
17591 DeclareMathOperator
17596 custom operators can be defined in the LaTeX-preamble.
17597 Its command scheme is:
17600 \begin_layout Standard
17605 DeclareMathOperator{new command}{display}
17608 \begin_layout Standard
17609 Display can be characters or symbols that define how the operator looks
17611 To define a big operator a * is set behind the command.
17612 All self-defined big operators can have limits as described in
17613 \begin_inset CommandInset ref
17615 reference "sub:Operator-Limits"
17622 \begin_layout Standard
17623 For example the LaTeX-preamble line
17626 \begin_layout Standard
17631 DeclareMathOperator*{
17638 \begin_layout Standard
17639 defines the command
17645 , that inserts a big operator consisting of the lozenge symbol from
17646 \begin_inset CommandInset ref
17648 reference "sub:Miscellaneous-Symbols"
17653 \begin_inset Formula \[
17654 \Lozenge_{n=1}^{\infty}\]
17658 The command for this formula is:
17669 \begin_inset Formula $\to$
17675 \begin_layout Standard
17676 \begin_inset VSpace bigskip
17679 When self-defined operators are not used several times in the document,
17680 they can also be defined with the commands
17690 \begin_layout Plain Layout
17708 \begin_layout Plain Layout
17716 , which have the following scheme:
17719 \begin_layout Standard
17733 \begin_layout Standard
17740 defines big operators,
17749 \begin_layout Standard
17757 \begin_inset space \thinspace{}
17761 \begin_inset space \space{}
17764 be used to use one limit for several operators:
17767 \begin_layout Standard
17768 \begin_inset Formula \[
17769 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17776 \begin_layout Standard
17777 The command for the formula above is:
17778 \begin_inset Newline newline
17797 \begin_layout Plain Layout
17809 \begin_inset Formula $\to$
17818 \begin_layout Plain Layout
17832 \begin_layout Section
17837 \begin_layout Plain Layout
17846 \begin_layout Subsection
17848 \begin_inset CommandInset label
17850 name "sub:Font-Styles"
17858 \begin_layout Plain Layout
17867 \begin_layout Standard
17868 Latin letters in formulas can be set in one of the following font styles:
17869 \begin_inset VSpace -2mm
17875 \begin_layout Standard
17877 \begin_inset Tabular
17878 <lyxtabular version="3" rows="6" columns="3">
17880 <column alignment="center" valignment="top" width="0">
17881 <column alignment="center" valignment="top" width="0">
17882 <column alignment="center" valignment="top" width="0">
17884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17887 \begin_layout Plain Layout
17893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17896 \begin_layout Plain Layout
17902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17905 \begin_layout Plain Layout
17913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17916 \begin_layout Plain Layout
17925 \begin_layout Plain Layout
17941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17944 \begin_layout Plain Layout
17945 \begin_inset Formula $\mathbb{ABC}$
17953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17956 \begin_layout Plain Layout
17969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17972 \begin_layout Plain Layout
17981 \begin_layout Plain Layout
17997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18000 \begin_layout Plain Layout
18001 \begin_inset Formula $\mathbf{AbC}$
18009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18012 \begin_layout Plain Layout
18025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18028 \begin_layout Plain Layout
18037 \begin_layout Plain Layout
18053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18056 \begin_layout Plain Layout
18057 \begin_inset Formula $\boldsymbol{AbC}$
18065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18068 \begin_layout Plain Layout
18071 arg "font-boldsymbol"
18081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18084 \begin_layout Plain Layout
18093 \begin_layout Plain Layout
18109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18112 \begin_layout Plain Layout
18113 \begin_inset Formula $\mathcal{ABC}$
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18124 \begin_layout Plain Layout
18137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18140 \begin_layout Plain Layout
18149 \begin_layout Plain Layout
18165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18168 \begin_layout Plain Layout
18169 \begin_inset Formula $\mathfrak{AbC}$
18177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18180 \begin_layout Plain Layout
18194 \begin_layout Standard
18196 \begin_inset Tabular
18197 <lyxtabular version="3" rows="5" columns="3">
18199 <column alignment="center" valignment="top" width="0">
18200 <column alignment="center" valignment="top" width="0">
18201 <column alignment="center" valignment="top" width="0">
18203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18215 \begin_layout Plain Layout
18221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18224 \begin_layout Plain Layout
18232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18235 \begin_layout Plain Layout
18244 \begin_layout Plain Layout
18260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18263 \begin_layout Plain Layout
18264 \begin_inset Formula $\mathit{AbC}$
18272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18275 \begin_layout Plain Layout
18283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18286 \begin_layout Plain Layout
18295 \begin_layout Plain Layout
18311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18314 \begin_layout Plain Layout
18315 \begin_inset Formula $\mathrm{AbC}$
18323 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18326 \begin_layout Plain Layout
18339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18342 \begin_layout Plain Layout
18351 \begin_layout Plain Layout
18367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18370 \begin_layout Plain Layout
18371 \begin_inset Formula $\mathsf{AbC}$
18379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18382 \begin_layout Plain Layout
18395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18398 \begin_layout Plain Layout
18407 \begin_layout Plain Layout
18423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18426 \begin_layout Plain Layout
18427 \begin_inset Formula $\mathtt{AbC}$
18435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18438 \begin_layout Plain Layout
18441 arg "font-typewriter"
18457 \begin_layout Standard
18458 \begin_inset Note Greyedout
18461 \begin_layout Plain Layout
18478 can only be used for big letters.
18486 \begin_layout Standard
18487 Predefined is the style
18496 \begin_layout Standard
18497 The style commands work also for letters in mathematical constructs:
18498 \begin_inset Formula \[
18499 \mathfrak{A=\frac{b}{C}}\]
18506 \begin_layout Standard
18507 Characters in mathematical text don't appear in a math font style but in
18508 the text font style
18515 That their style can't be set correctly via the text style dialog is a
18520 \begin_layout Plain Layout
18521 \begin_inset CommandInset href
18523 name "LyX-bug #4629"
18524 target "http://www.lyx.org/trac/ticket/4629"
18536 \begin_layout Standard
18537 Instead of the style commands the dialog
18539 Edit\SpecialChar \menuseparator
18540 Math\SpecialChar \menuseparator
18543 or the toolbar button
18544 \begin_inset Graphics
18545 filename ../images/math/font.png
18553 \begin_layout Subsection
18555 \begin_inset CommandInset label
18557 name "sub:Bold-Formulas"
18565 \begin_layout Plain Layout
18574 \begin_layout Standard
18575 To make a complete formula bold, the command
18581 from the previous subsection cannot be used, because it doesn't work for
18582 small Greek letters.
18583 Furthermore it prints Latin letters always upright, like in the following
18587 \begin_layout Standard
18588 \begin_inset Formula \[
18589 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18596 \begin_layout Standard
18597 To display the formula correctly, the command
18604 \begin_inset Formula \[
18605 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18609 It is also possible to set the formula in a
18611 boldmath environment
18614 This environment is created by inserting the command
18622 \begin_layout Plain Layout
18633 To end the environment, the command
18641 \begin_layout Plain Layout
18651 is inserted in TeX-mode.
18655 \begin_layout Plain Layout
18665 \begin_inset Formula \[
18666 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18674 \begin_layout Plain Layout
18686 \begin_layout Subsection
18691 \begin_layout Plain Layout
18700 \begin_layout Standard
18701 Formulas can be colored like normal text: Highlight a formula or a formula
18707 Here is a formula in magenta:
18708 \begin_inset Formula \[
18709 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18716 \begin_layout Standard
18717 You can also define your own colors as described in
18718 \begin_inset CommandInset ref
18720 reference "sub:Colored-Boxes"
18725 They can be used with the TeX code command
18735 \begin_layout Plain Layout
18746 \begin_layout Standard
18751 textcolor{color}{characters or formula}
18754 \begin_layout Standard
18755 The following example was colored completely dark green and partly red:
18758 \begin_layout Standard
18762 \begin_layout Plain Layout
18766 textcolor{darkgreen}{
18772 \begin_inset Formula \[
18773 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18781 \begin_layout Plain Layout
18791 \begin_layout Standard
18792 Due to a bug in LyX only complete formulas can be colored with self-defined
18797 \begin_layout Plain Layout
18798 \begin_inset CommandInset href
18800 name "LyX-bug #5269"
18801 target "http://www.lyx.org/trac/ticket/5269"
18813 \begin_layout Subsection
18815 \begin_inset CommandInset label
18817 name "sub:Font-Sizes"
18825 \begin_layout Plain Layout
18834 \begin_layout Standard
18835 For characters in formulas there are, analog to characters in text, the
18836 following size commands:
18839 \begin_layout Standard
18883 \begin_inset Newline newline
18905 \begin_layout Standard
18906 The size produced by the commands depends on the document font size, that
18907 corresponds with the command
18914 The other commands produce smaller or larger sizes than
18921 The font size can however not exceed a certain value.
18922 Is for example the document font size 12
18923 \begin_inset space \thinspace{}
18932 switches to the same size as
18942 \begin_layout Standard
18943 A size command is inserted in TeX-mode before the formula and sets the size
18944 for all following formula and text characters.
18945 To switch back to the initial size, the command
18951 is inserted behind the formula in TeX-mode.
18954 \begin_layout Standard
18955 Within a formula the size can only be changed for symbols or letters in
18957 To do this, the size command is inserted in mathematical text.
18958 All following characters until the end of the mathematical text or until
18959 another size command will have the selected size.
18961 \begin_inset VSpace -2mm
18967 \begin_layout Standard
18971 \begin_layout Plain Layout
18981 \begin_inset Formula \[
18982 A=\frac{B}{c}\cdot\maltese\]
18987 \begin_inset Formula \[
18988 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18996 \begin_layout Plain Layout
19008 \begin_layout Standard
19009 \begin_inset VSpace medskip
19012 Before both formulas the command
19019 The command for the second formula is:
19020 \begin_inset Newline newline
19031 \begin_layout Plain Layout
19046 \begin_layout Plain Layout
19061 \begin_layout Plain Layout
19076 \begin_layout Plain Layout
19086 \begin_inset Formula $\to$
19090 \begin_inset Formula $\to$
19094 \begin_inset Newline newline
19098 \begin_inset space \hspace*{}
19112 \begin_layout Plain Layout
19127 \begin_layout Plain Layout
19142 \begin_layout Plain Layout
19154 \begin_layout Standard
19155 If a symbol cannot be displayed in different sizes, it will always be displayed
19156 in the default size.
19159 \begin_layout Section
19164 \begin_layout Plain Layout
19173 \begin_layout Standard
19174 All Greek letters can also be inserted via the toolbar button
19175 \begin_inset Graphics
19176 filename ../images/math/alpha.png
19184 \begin_layout Subsection
19189 \begin_layout Plain Layout
19190 Greek letters ! small
19198 \begin_layout Standard
19199 \begin_inset space \hfill{}
19203 \begin_inset Tabular
19204 <lyxtabular version="3" rows="11" columns="2">
19206 <column alignment="center" valignment="top" width="0pt">
19207 <column alignment="center" valignment="top" width="0pt">
19209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19212 \begin_layout Plain Layout
19218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19221 \begin_layout Plain Layout
19229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19232 \begin_layout Plain Layout
19240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19243 \begin_layout Plain Layout
19244 \begin_inset Formula $\alpha$
19254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19257 \begin_layout Plain Layout
19265 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19268 \begin_layout Plain Layout
19269 \begin_inset Formula $\beta$
19279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19282 \begin_layout Plain Layout
19290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19293 \begin_layout Plain Layout
19294 \begin_inset Formula $\gamma$
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19307 \begin_layout Plain Layout
19315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19318 \begin_layout Plain Layout
19319 \begin_inset Formula $\delta$
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19332 \begin_layout Plain Layout
19340 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19343 \begin_layout Plain Layout
19344 \begin_inset Formula $\epsilon$
19354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19357 \begin_layout Plain Layout
19365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19368 \begin_layout Plain Layout
19369 \begin_inset Formula $\varepsilon$
19379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19382 \begin_layout Plain Layout
19390 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19393 \begin_layout Plain Layout
19394 \begin_inset Formula $\zeta$
19404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19407 \begin_layout Plain Layout
19415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19418 \begin_layout Plain Layout
19419 \begin_inset Formula $\eta$
19429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19432 \begin_layout Plain Layout
19440 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19443 \begin_layout Plain Layout
19444 \begin_inset Formula $\theta$
19454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19457 \begin_layout Plain Layout
19465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19468 \begin_layout Plain Layout
19469 \begin_inset Formula $\vartheta$
19483 \begin_inset space \hfill{}
19487 \begin_inset Tabular
19488 <lyxtabular version="3" rows="12" columns="2">
19490 <column alignment="center" valignment="top" width="0pt">
19491 <column alignment="center" valignment="top" width="0pt">
19493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19496 \begin_layout Plain Layout
19502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19505 \begin_layout Plain Layout
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19516 \begin_layout Plain Layout
19524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19527 \begin_layout Plain Layout
19528 \begin_inset Formula $\iota$
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19541 \begin_layout Plain Layout
19549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19552 \begin_layout Plain Layout
19553 \begin_inset Formula $\kappa$
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19566 \begin_layout Plain Layout
19574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19577 \begin_layout Plain Layout
19578 \begin_inset Formula $\varkappa$
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19591 \begin_layout Plain Layout
19599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19602 \begin_layout Plain Layout
19603 \begin_inset Formula $\lambda$
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19616 \begin_layout Plain Layout
19624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19627 \begin_layout Plain Layout
19628 \begin_inset Formula $\mu$
19638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19641 \begin_layout Plain Layout
19649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19652 \begin_layout Plain Layout
19653 \begin_inset Formula $\nu$
19663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19666 \begin_layout Plain Layout
19674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19677 \begin_layout Plain Layout
19678 \begin_inset Formula $\xi$
19688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19691 \begin_layout Plain Layout
19697 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19700 \begin_layout Plain Layout
19701 \begin_inset Formula $o$
19711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19714 \begin_layout Plain Layout
19722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19725 \begin_layout Plain Layout
19726 \begin_inset Formula $\pi$
19736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19739 \begin_layout Plain Layout
19747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19750 \begin_layout Plain Layout
19751 \begin_inset Formula $\varpi$
19761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19764 \begin_layout Plain Layout
19772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19775 \begin_layout Plain Layout
19776 \begin_inset Formula $\rho$
19790 \begin_inset space \hfill{}
19794 \begin_inset Tabular
19795 <lyxtabular version="3" rows="11" columns="2">
19797 <column alignment="center" valignment="top" width="0pt">
19798 <column alignment="center" valignment="top" width="0pt">
19800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19803 \begin_layout Plain Layout
19809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19812 \begin_layout Plain Layout
19820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19823 \begin_layout Plain Layout
19831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19834 \begin_layout Plain Layout
19835 \begin_inset Formula $\varrho$
19845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19859 \begin_layout Plain Layout
19860 \begin_inset Formula $\sigma$
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19873 \begin_layout Plain Layout
19881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19884 \begin_layout Plain Layout
19885 \begin_inset Formula $\varsigma$
19895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19898 \begin_layout Plain Layout
19906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19909 \begin_layout Plain Layout
19910 \begin_inset Formula $\tau$
19920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19923 \begin_layout Plain Layout
19931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19934 \begin_layout Plain Layout
19935 \begin_inset Formula $\upsilon$
19945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19948 \begin_layout Plain Layout
19956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19959 \begin_layout Plain Layout
19960 \begin_inset Formula $\phi$
19970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19973 \begin_layout Plain Layout
19981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19984 \begin_layout Plain Layout
19985 \begin_inset Formula $\varphi$
19995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19998 \begin_layout Plain Layout
20006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20009 \begin_layout Plain Layout
20010 \begin_inset Formula $\chi$
20020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20023 \begin_layout Plain Layout
20031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Plain Layout
20035 \begin_inset Formula $\psi$
20045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20048 \begin_layout Plain Layout
20056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20059 \begin_layout Plain Layout
20060 \begin_inset Formula $\omega$
20074 \begin_inset space \hfill{}
20080 \begin_layout Standard
20081 \begin_inset VSpace medskip
20087 \begin_layout Standard
20088 How to create upright Greek letters is explained in
20089 \begin_inset CommandInset ref
20091 reference "sub:Upright-small-Greek"
20098 \begin_layout Subsection
20103 \begin_layout Plain Layout
20104 Greek letters ! big
20112 \begin_layout Standard
20113 \begin_inset space \hfill{}
20117 \begin_inset Tabular
20118 <lyxtabular version="3" rows="7" columns="2">
20120 <column alignment="center" valignment="top" width="0pt">
20121 <column alignment="center" valignment="top" width="0pt">
20123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20126 \begin_layout Plain Layout
20132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20135 \begin_layout Plain Layout
20143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20146 \begin_layout Plain Layout
20154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20157 \begin_layout Plain Layout
20158 \begin_inset Formula $\Gamma$
20168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20171 \begin_layout Plain Layout
20179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20182 \begin_layout Plain Layout
20183 \begin_inset Formula $\Delta$
20193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20196 \begin_layout Plain Layout
20204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20207 \begin_layout Plain Layout
20208 \begin_inset Formula $\Theta$
20218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20221 \begin_layout Plain Layout
20229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20232 \begin_layout Plain Layout
20233 \begin_inset Formula $\Lambda$
20243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20246 \begin_layout Plain Layout
20254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20257 \begin_layout Plain Layout
20258 \begin_inset Formula $\Xi$
20268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20271 \begin_layout Plain Layout
20279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20282 \begin_layout Plain Layout
20283 \begin_inset Formula $\Pi$
20297 \begin_inset space \hfill{}
20301 \begin_inset Tabular
20302 <lyxtabular version="3" rows="6" columns="2">
20304 <column alignment="center" valignment="top" width="0pt">
20305 <column alignment="center" valignment="top" width="0pt">
20307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20310 \begin_layout Plain Layout
20316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20319 \begin_layout Plain Layout
20327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20330 \begin_layout Plain Layout
20338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20341 \begin_layout Plain Layout
20342 \begin_inset Formula $\Sigma$
20352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20355 \begin_layout Plain Layout
20363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20366 \begin_layout Plain Layout
20367 \begin_inset Formula $\Upsilon$
20377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20380 \begin_layout Plain Layout
20388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20391 \begin_layout Plain Layout
20392 \begin_inset Formula $\Phi$
20402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20405 \begin_layout Plain Layout
20413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20416 \begin_layout Plain Layout
20417 \begin_inset Formula $\Psi$
20427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20430 \begin_layout Plain Layout
20438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20441 \begin_layout Plain Layout
20442 \begin_inset Formula $\Omega$
20456 \begin_inset space \hfill{}
20462 \begin_layout Standard
20463 \begin_inset VSpace medskip
20466 That the big Greek letters appear upright is caused by a design bug when
20468 To get correct italic big letters, begin every command with
20473 For example the command
20480 \begin_inset Formula $\varGamma$
20486 \begin_layout Subsection
20491 \begin_layout Plain Layout
20492 Greek letters ! bold
20500 \begin_layout Standard
20501 Greek letters cannot be set with different font styles like Latin letters.
20502 They can only be made bold with the command
20512 \begin_layout Plain Layout
20523 \begin_layout Standard
20525 \begin_inset Tabular
20526 <lyxtabular version="3" rows="3" columns="2">
20528 <column alignment="center" valignment="top" width="0">
20529 <column alignment="center" valignment="top" width="0">
20531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20534 \begin_layout Plain Layout
20540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20543 \begin_layout Plain Layout
20551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20554 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20598 \begin_layout Plain Layout
20599 \begin_inset Formula $\theta\boldsymbol{\theta}$
20615 \begin_layout Section
20620 \begin_layout Plain Layout
20633 \begin_layout Plain Layout
20634 A list with all symbols of most of the LaTeX-packages can be found in
20635 \begin_inset CommandInset citation
20650 \begin_layout Plain Layout
20658 \begin_inset Note Note
20661 \begin_layout Plain Layout
20664 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20667 \begin_layout Plain Layout
20670 texorpdfstring is in section
20671 \begin_inset CommandInset ref
20673 reference "sub:Formulas-in-Section"
20686 \begin_layout Plain Layout
20695 \begin_layout Standard
20696 Many of the symbols listed in this section can also be inserted via the
20698 \begin_inset Graphics
20699 filename ../images/math/nabla.png
20705 \begin_inset Graphics
20706 filename ../images/math/digamma.png
20714 \begin_layout Subsection
20715 Mathematical Symbols
20716 \begin_inset CommandInset label
20718 name "sub:Mathematical-Symbols"
20726 \begin_layout Plain Layout
20727 Symbols ! mathematical
20735 \begin_layout Standard
20736 \begin_inset space \hfill{}
20740 \begin_inset Tabular
20741 <lyxtabular version="3" rows="10" columns="2">
20743 <column alignment="center" valignment="top" width="0pt">
20744 <column alignment="center" valignment="top" width="0pt">
20746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20749 \begin_layout Plain Layout
20755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Plain Layout
20766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20769 \begin_layout Plain Layout
20777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20780 \begin_layout Plain Layout
20781 \begin_inset Formula $\neg$
20791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20794 \begin_layout Plain Layout
20802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20805 \begin_layout Plain Layout
20806 \begin_inset Formula $\Im$
20816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20819 \begin_layout Plain Layout
20827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20830 \begin_layout Plain Layout
20831 \begin_inset Formula $\Re$
20841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20844 \begin_layout Plain Layout
20852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20855 \begin_layout Plain Layout
20856 \begin_inset Formula $\aleph$
20866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20869 \begin_layout Plain Layout
20877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20880 \begin_layout Plain Layout
20881 \begin_inset Formula $\partial$
20891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20894 \begin_layout Plain Layout
20902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20905 \begin_layout Plain Layout
20906 \begin_inset Formula $\infty$
20916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20919 \begin_layout Plain Layout
20927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20930 \begin_layout Plain Layout
20931 \begin_inset Formula $\wp$
20941 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20944 \begin_layout Plain Layout
20952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20955 \begin_layout Plain Layout
20956 \begin_inset Formula $\imath$
20966 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20969 \begin_layout Plain Layout
20977 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20980 \begin_layout Plain Layout
20981 \begin_inset Formula $\jmath$
20995 \begin_inset space \hfill{}
20999 \begin_inset Tabular
21000 <lyxtabular version="3" rows="10" columns="2">
21002 <column alignment="center" valignment="top" width="0pt">
21003 <column alignment="center" valignment="top" width="0pt">
21005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21008 \begin_layout Plain Layout
21014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21017 \begin_layout Plain Layout
21019 \begin_inset Note Note
21022 \begin_layout Plain Layout
21029 is only used as spacer.
21041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21044 \begin_layout Plain Layout
21052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21055 \begin_layout Plain Layout
21056 \begin_inset Formula $\forall$
21066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21069 \begin_layout Plain Layout
21077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21080 \begin_layout Plain Layout
21081 \begin_inset Formula $\exists$
21091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21094 \begin_layout Plain Layout
21102 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21105 \begin_layout Plain Layout
21106 \begin_inset Formula $\nexists$
21116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21119 \begin_layout Plain Layout
21127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21130 \begin_layout Plain Layout
21131 \begin_inset Formula $\emptyset$
21141 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21144 \begin_layout Plain Layout
21152 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21155 \begin_layout Plain Layout
21156 \begin_inset Formula $\varnothing$
21166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21169 \begin_layout Plain Layout
21177 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21180 \begin_layout Plain Layout
21181 \begin_inset Formula $\dag$
21191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21194 \begin_layout Plain Layout
21202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21205 \begin_layout Plain Layout
21206 \begin_inset Formula $\ddag$
21216 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21219 \begin_layout Plain Layout
21227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21230 \begin_layout Plain Layout
21234 \begin_layout Plain Layout
21244 \begin_inset Formula $\complement$
21251 \begin_layout Plain Layout
21265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21268 \begin_layout Plain Layout
21276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21279 \begin_layout Plain Layout
21280 \begin_inset Formula $\Bbbk$
21294 \begin_inset space \hfill{}
21298 \begin_inset Tabular
21299 <lyxtabular version="3" rows="10" columns="2">
21301 <column alignment="center" valignment="top" width="0pt">
21302 <column alignment="center" valignment="top" width="0pt">
21304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21307 \begin_layout Plain Layout
21313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21327 \begin_layout Plain Layout
21335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21338 \begin_layout Plain Layout
21339 \begin_inset Formula $\prime$
21349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21352 \begin_layout Plain Layout
21360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21363 \begin_layout Plain Layout
21364 \begin_inset Formula $\backprime$
21374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21377 \begin_layout Plain Layout
21385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21388 \begin_layout Plain Layout
21389 \begin_inset Formula $\mho$
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21402 \begin_layout Plain Layout
21410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21413 \begin_layout Plain Layout
21414 \begin_inset Formula $\triangle$
21424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21427 \begin_layout Plain Layout
21435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21438 \begin_layout Plain Layout
21439 \begin_inset Formula $\angle$
21449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\measuredangle$
21474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21489 \begin_inset Formula $\sphericalangle$
21499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21502 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $\top$
21524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\bot$
21553 \begin_inset space \hfill{}
21559 \begin_layout Subsection
21560 Miscellaneous Symbols
21561 \begin_inset CommandInset label
21563 name "sub:Miscellaneous-Symbols"
21571 \begin_layout Plain Layout
21572 Symbols ! miscellaneous
21580 \begin_layout Standard
21583 \begin_inset Tabular
21584 <lyxtabular version="3" rows="10" columns="2">
21586 <column alignment="center" valignment="top" width="0pt">
21587 <column alignment="center" valignment="top" width="0pt">
21589 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21592 \begin_layout Plain Layout
21598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21612 \begin_layout Plain Layout
21620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21623 \begin_layout Plain Layout
21624 \begin_inset Formula $\flat$
21634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21637 \begin_layout Plain Layout
21645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21648 \begin_layout Plain Layout
21649 \begin_inset Formula $\natural$
21659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21662 \begin_layout Plain Layout
21670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21673 \begin_layout Plain Layout
21674 \begin_inset Formula $\sharp$
21684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21687 \begin_layout Plain Layout
21695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21698 \begin_layout Plain Layout
21699 \begin_inset Formula $\surd$
21709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21712 \begin_layout Plain Layout
21720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21723 \begin_layout Plain Layout
21724 \begin_inset Formula $\checkmark$
21734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21737 \begin_layout Plain Layout
21745 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21748 \begin_layout Plain Layout
21749 \begin_inset Formula $\yen$
21759 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21762 \begin_layout Plain Layout
21770 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21773 \begin_layout Plain Layout
21774 \begin_inset Formula $\pounds$
21784 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21787 \begin_layout Plain Layout
21793 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21796 \begin_layout Plain Layout
21797 \begin_inset Formula $\$$
21807 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21810 \begin_layout Plain Layout
21816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21819 \begin_layout Plain Layout
21820 \begin_inset Formula $§$
21834 \begin_inset Tabular
21835 <lyxtabular version="3" rows="10" columns="2">
21837 <column alignment="center" valignment="top" width="0">
21838 <column alignment="center" valignment="top" width="0">
21840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21843 \begin_layout Plain Layout
21849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21852 \begin_layout Plain Layout
21860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21863 \begin_layout Plain Layout
21871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21874 \begin_layout Plain Layout
21875 \begin_inset Formula $\hbar$
21885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21888 \begin_layout Plain Layout
21896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21899 \begin_layout Plain Layout
21900 \begin_inset Formula $\hslash$
21910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21924 \begin_layout Plain Layout
21925 \begin_inset Formula $\clubsuit$
21935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21938 \begin_layout Plain Layout
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21949 \begin_layout Plain Layout
21950 \begin_inset Formula $\spadesuit$
21960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21974 \begin_layout Plain Layout
21975 \begin_inset Formula $\bigstar$
21985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21988 \begin_layout Plain Layout
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21999 \begin_layout Plain Layout
22000 \begin_inset Formula $\blacklozenge$
22010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22013 \begin_layout Plain Layout
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22024 \begin_layout Plain Layout
22025 \begin_inset Formula $\blacktriangle$
22035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22038 \begin_layout Plain Layout
22046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22049 \begin_layout Plain Layout
22050 \begin_inset Formula $\blacktriangledown$
22060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22063 \begin_layout Plain Layout
22071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22074 \begin_layout Plain Layout
22075 \begin_inset Formula $\bullet$
22089 \begin_inset Tabular
22090 <lyxtabular version="3" rows="10" columns="2">
22092 <column alignment="center" valignment="top" width="0pt">
22093 <column alignment="center" valignment="top" width="0pt">
22095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22098 \begin_layout Plain Layout
22104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22107 \begin_layout Plain Layout
22115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22118 \begin_layout Plain Layout
22126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22129 \begin_layout Plain Layout
22130 \begin_inset Formula $\diamondsuit$
22140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22143 \begin_layout Plain Layout
22151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22154 \begin_layout Plain Layout
22155 \begin_inset Formula $\Diamond$
22165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22168 \begin_layout Plain Layout
22176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22179 \begin_layout Plain Layout
22180 \begin_inset Formula $\heartsuit$
22190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22193 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22204 \begin_layout Plain Layout
22205 \begin_inset Formula $\P$
22215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22218 \begin_layout Plain Layout
22226 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22229 \begin_layout Plain Layout
22230 \begin_inset Formula $\copyright$
22240 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22243 \begin_layout Plain Layout
22251 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22254 \begin_layout Plain Layout
22255 \begin_inset Formula $\circledR$
22265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22268 \begin_layout Plain Layout
22276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22279 \begin_layout Plain Layout
22280 \begin_inset Formula $\maltese$
22290 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22293 \begin_layout Plain Layout
22301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22304 \begin_layout Plain Layout
22305 \begin_inset Formula $\diagup$
22315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22318 \begin_layout Plain Layout
22326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22329 \begin_layout Plain Layout
22330 \begin_inset Formula $\diagdown$
22346 \begin_layout Standard
22347 \begin_inset VSpace medskip
22350 More symbols are listed in
22351 \begin_inset CommandInset ref
22353 reference "sub:Miscellaneous-special-Characters"
22360 \begin_layout Standard
22361 Some symbols can be displayed in different sizes, see
22362 \begin_inset CommandInset ref
22364 reference "sub:Font-Sizes"
22371 \begin_layout Subsection
22376 \begin_layout Plain Layout
22377 Symbols ! Euro-symbol
22386 \begin_layout Plain Layout
22393 \begin_layout Plain Layout
22410 \begin_layout Standard
22411 To use the Euro symbol in formulas, the LaTeX-package
22419 \begin_layout Plain Layout
22425 must be installed and loaded with the LaTeX-preamble line
22428 \begin_layout Standard
22433 usepackage[gennarrow]{eurosym}
22436 \begin_layout Standard
22437 The Euro symbol can now be inserted with the command
22447 \begin_layout Plain Layout
22458 \begin_layout Standard
22459 The Euro symbol can directly be inserted with the € key in mathematical
22460 text, without having
22475 can also be inserted in TeX-mode.
22476 The official currency symbol can then be inserted with the command
22486 \begin_layout Plain Layout
22494 , that is only available in TeX-mode.
22497 \begin_layout Standard
22501 \begin_layout Plain Layout
22511 \begin_inset Note Note
22514 \begin_layout Plain Layout
22515 The following table will only be displayed when the LaTeX-package
22527 \begin_layout Standard
22528 An overview about the different Euro symbols:
22531 \begin_layout Standard
22533 \begin_inset Tabular
22534 <lyxtabular version="3" rows="4" columns="3">
22536 <column alignment="center" valignment="top" width="0pt">
22537 <column alignment="center" valignment="top" width="0pt">
22538 <column alignment="center" valignment="top" width="0pt">
22540 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22543 \begin_layout Plain Layout
22549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22552 \begin_layout Plain Layout
22558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22561 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22572 \begin_layout Plain Layout
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22581 \begin_layout Plain Layout
22589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22592 \begin_layout Plain Layout
22593 \begin_inset Formula $\euro$
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22606 \begin_layout Plain Layout
22612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22615 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\mbox{€}$
22635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22638 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22647 \begin_layout Plain Layout
22655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22658 \begin_layout Plain Layout
22662 \begin_layout Plain Layout
22684 \begin_layout Standard
22688 \begin_layout Plain Layout
22698 \begin_inset Note Note
22701 \begin_layout Plain Layout
22702 The following will be displayed when the LaTeX-package
22714 \begin_layout Standard
22715 You need to install the LaTeX-package
22719 to see the rest of this subsection in the output.
22722 \begin_layout Standard
22726 \begin_layout Plain Layout
22738 \begin_layout Section
22740 \begin_inset CommandInset label
22742 name "sec:Relations"
22750 \begin_layout Plain Layout
22760 \begin_layout Plain Layout
22765 \begin_layout Plain Layout
22776 \begin_layout Plain Layout
22791 \begin_layout Standard
22792 All relations can also be inserted via the toolbar button
22793 \begin_inset Graphics
22794 filename ../images/math/leq.png
22802 \begin_layout Standard
22803 \begin_inset space \hfill{}
22807 \begin_inset Tabular
22808 <lyxtabular version="3" rows="17" columns="2">
22810 <column alignment="center" valignment="top" width="0pt">
22811 <column alignment="center" valignment="top" width="0pt">
22813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22816 \begin_layout Plain Layout
22822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22825 \begin_layout Plain Layout
22833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22845 \begin_layout Plain Layout
22846 \begin_inset Formula $<$
22856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22859 \begin_layout Plain Layout
22867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22870 \begin_layout Plain Layout
22871 \begin_inset Formula $\le$
22881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22884 \begin_layout Plain Layout
22892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22895 \begin_layout Plain Layout
22896 \begin_inset Formula $\ll$
22906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22909 \begin_layout Plain Layout
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22920 \begin_layout Plain Layout
22921 \begin_inset Formula $\prec$
22931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22934 \begin_layout Plain Layout
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22945 \begin_layout Plain Layout
22946 \begin_inset Formula $\preceq$
22956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22959 \begin_layout Plain Layout
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22970 \begin_layout Plain Layout
22971 \begin_inset Formula $\subset$
22981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22995 \begin_layout Plain Layout
22996 \begin_inset Formula $\subseteq$
23006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23009 \begin_layout Plain Layout
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23020 \begin_layout Plain Layout
23021 \begin_inset Formula $\sqsubseteq$
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23034 \begin_layout Plain Layout
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23045 \begin_layout Plain Layout
23046 \begin_inset Formula $\in$
23056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23059 \begin_layout Plain Layout
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23070 \begin_layout Plain Layout
23071 \begin_inset Formula $\vdash$
23081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23084 \begin_layout Plain Layout
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23095 \begin_layout Plain Layout
23096 \begin_inset Formula $\smile$
23106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23109 \begin_layout Plain Layout
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23120 \begin_layout Plain Layout
23121 \begin_inset Formula $\lhd$
23131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23134 \begin_layout Plain Layout
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23145 \begin_layout Plain Layout
23146 \begin_inset Formula $\unlhd$
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23171 \begin_inset Formula $\gtrless$
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23195 \begin_layout Plain Layout
23196 \begin_inset Formula $\mid$
23206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23220 \begin_layout Plain Layout
23221 \begin_inset Formula $\nmid$
23235 \begin_inset space \hfill{}
23239 \begin_inset Tabular
23240 <lyxtabular version="3" rows="17" columns="2">
23242 <column alignment="center" valignment="top" width="0pt">
23243 <column alignment="center" valignment="top" width="0pt">
23245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23248 \begin_layout Plain Layout
23254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23257 \begin_layout Plain Layout
23265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23268 \begin_layout Plain Layout
23274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23277 \begin_layout Plain Layout
23278 \begin_inset Formula $=$
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23291 \begin_layout Plain Layout
23299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23302 \begin_layout Plain Layout
23303 \begin_inset Formula $\not=$
23313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23316 \begin_layout Plain Layout
23324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23327 \begin_layout Plain Layout
23328 \begin_inset Formula $\equiv$
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23341 \begin_layout Plain Layout
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Plain Layout
23353 \begin_inset Formula $\sim$
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23378 \begin_inset Formula $\simeq$
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23391 \begin_layout Plain Layout
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Plain Layout
23403 \begin_inset Formula $\approx$
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23427 \begin_layout Plain Layout
23428 \begin_inset Formula $\cong$
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23441 \begin_layout Plain Layout
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23452 \begin_layout Plain Layout
23453 \begin_inset Formula $\bowtie$
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23466 \begin_layout Plain Layout
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23477 \begin_layout Plain Layout
23478 \begin_inset Formula $\notin$
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23491 \begin_layout Plain Layout
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23502 \begin_layout Plain Layout
23503 \begin_inset Formula $\perp$
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23516 \begin_layout Plain Layout
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23527 \begin_layout Plain Layout
23528 \begin_inset Formula $\propto$
23538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23541 \begin_layout Plain Layout
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23552 \begin_layout Plain Layout
23553 \begin_inset Formula $\asymp$
23563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23566 \begin_layout Plain Layout
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23577 \begin_layout Plain Layout
23578 \begin_inset Formula $\doteq$
23588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23591 \begin_layout Plain Layout
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23602 \begin_layout Plain Layout
23603 \begin_inset Formula $\circeq$
23613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23616 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23627 \begin_layout Plain Layout
23628 \begin_inset Formula $\models$
23638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\widehat{=}$
23667 \begin_inset space \hfill{}
23671 \begin_inset Tabular
23672 <lyxtabular version="3" rows="17" columns="2">
23674 <column alignment="center" valignment="top" width="0pt">
23675 <column alignment="center" valignment="top" width="0pt">
23677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23680 \begin_layout Plain Layout
23686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23689 \begin_layout Plain Layout
23697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23700 \begin_layout Plain Layout
23706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23709 \begin_layout Plain Layout
23710 \begin_inset Formula $>$
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23723 \begin_layout Plain Layout
23731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23734 \begin_layout Plain Layout
23735 \begin_inset Formula $\ge$
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23748 \begin_layout Plain Layout
23756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23759 \begin_layout Plain Layout
23760 \begin_inset Formula $\gg$
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23773 \begin_layout Plain Layout
23781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23784 \begin_layout Plain Layout
23785 \begin_inset Formula $\succ$
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23798 \begin_layout Plain Layout
23806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23809 \begin_layout Plain Layout
23810 \begin_inset Formula $\succeq$
23820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23823 \begin_layout Plain Layout
23831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23834 \begin_layout Plain Layout
23835 \begin_inset Formula $\supset$
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23848 \begin_layout Plain Layout
23856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23859 \begin_layout Plain Layout
23860 \begin_inset Formula $\supseteq$
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23873 \begin_layout Plain Layout
23881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23884 \begin_layout Plain Layout
23885 \begin_inset Formula $\sqsupseteq$
23895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23898 \begin_layout Plain Layout
23906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23909 \begin_layout Plain Layout
23910 \begin_inset Formula $\ni$
23920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23923 \begin_layout Plain Layout
23931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23934 \begin_layout Plain Layout
23935 \begin_inset Formula $\dashv$
23945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23948 \begin_layout Plain Layout
23956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23959 \begin_layout Plain Layout
23960 \begin_inset Formula $\frown$
23970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23973 \begin_layout Plain Layout
23981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23984 \begin_layout Plain Layout
23985 \begin_inset Formula $\rhd$
23995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23998 \begin_layout Plain Layout
24006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24009 \begin_layout Plain Layout
24010 \begin_inset Formula $\unrhd$
24020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24023 \begin_layout Plain Layout
24031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24034 \begin_layout Plain Layout
24035 \begin_inset Formula $\lessgtr$
24045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24048 \begin_layout Plain Layout
24056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24059 \begin_layout Plain Layout
24060 \begin_inset Formula $\parallel$
24070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24073 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24085 \begin_inset Formula $\nparallel$
24099 \begin_inset space \hfill{}
24105 \begin_layout Standard
24106 \begin_inset VSpace medskip
24121 are bigger than the equal looking operators
24136 \begin_layout Standard
24137 Relations are, in contrary to symbols, always surrounded by space.
24140 \begin_layout Standard
24141 Relations with labels can be created with the command
24151 \begin_layout Plain Layout
24162 \begin_layout Standard
24164 \begin_inset Tabular
24165 <lyxtabular version="3" rows="2" columns="2">
24167 <column alignment="center" valignment="top" width="0">
24168 <column alignment="center" valignment="top" width="0">
24170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24173 \begin_layout Plain Layout
24179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24182 \begin_layout Plain Layout
24184 \begin_inset Note Note
24187 \begin_layout Plain Layout
24194 is only used as spacer.
24206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24216 \begin_layout Plain Layout
24233 \begin_layout Plain Layout
24243 \begin_inset Formula $\downarrow$
24252 \begin_layout Plain Layout
24265 \begin_layout Plain Layout
24279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24282 \begin_layout Plain Layout
24283 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24299 \begin_layout Section
24303 \begin_layout Subsection
24304 Predefined Functions
24305 \begin_inset CommandInset label
24307 name "sub:Predefined-Functions"
24315 \begin_layout Plain Layout
24316 Functions ! predefined
24324 \begin_layout Standard
24325 In general, variables are set
24329 in mathematical expressions, but not function names, because
24330 \begin_inset Formula $sin$
24333 could be misunderstood as
24334 \begin_inset Formula $s\cdot i\cdot n$
24338 Therefore there are predefined functions, that are additionally a bit separated
24340 They are inserted as commands starting with a backslash before their name.
24343 \begin_layout Standard
24345 \begin_inset Tabular
24346 <lyxtabular version="3" rows="2" columns="4">
24348 <column alignment="center" valignment="top" width="0pt">
24349 <column alignment="center" valignment="top" width="0pt">
24350 <column alignment="center" valignment="top" width="0pt">
24351 <column alignment="center" valignment="top" width="0pt">
24353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24365 \begin_layout Plain Layout
24371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24403 \begin_layout Plain Layout
24404 \begin_inset Formula $Asin(x)+B$
24412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24415 \begin_layout Plain Layout
24423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24426 \begin_layout Plain Layout
24427 \begin_inset Formula $A\sin(x)+B$
24443 \begin_layout Standard
24444 The following functions are predefined:
24447 \begin_layout Standard
24448 \begin_inset VSpace -2mm
24454 \begin_layout Standard
24456 \begin_inset Tabular
24457 <lyxtabular version="3" rows="9" columns="4">
24459 <column alignment="center" valignment="top" width="0pt">
24460 <column alignment="center" valignment="top" width="0pt">
24461 <column alignment="center" valignment="top" width="0pt">
24462 <column alignment="center" valignment="top" width="0pt">
24464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24467 \begin_layout Plain Layout
24473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24476 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24485 \begin_layout Plain Layout
24491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24494 \begin_layout Plain Layout
24502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24505 \begin_layout Plain Layout
24513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24516 \begin_layout Plain Layout
24524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24527 \begin_layout Plain Layout
24535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24538 \begin_layout Plain Layout
24548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24551 \begin_layout Plain Layout
24559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24562 \begin_layout Plain Layout
24570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24573 \begin_layout Plain Layout
24581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24584 \begin_layout Plain Layout
24594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24597 \begin_layout Plain Layout
24605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24608 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24619 \begin_layout Plain Layout
24627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24630 \begin_layout Plain Layout
24640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24643 \begin_layout Plain Layout
24651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24654 \begin_layout Plain Layout
24662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24665 \begin_layout Plain Layout
24673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24676 \begin_layout Plain Layout
24686 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24689 \begin_layout Plain Layout
24697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24700 \begin_layout Plain Layout
24708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24722 \begin_layout Plain Layout
24732 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24735 \begin_layout Plain Layout
24743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24746 \begin_layout Plain Layout
24754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24757 \begin_layout Plain Layout
24765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24768 \begin_layout Plain Layout
24778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24781 \begin_layout Plain Layout
24789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24792 \begin_layout Plain Layout
24800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24803 \begin_layout Plain Layout
24811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24814 \begin_layout Plain Layout
24824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24827 \begin_layout Plain Layout
24835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24838 \begin_layout Plain Layout
24846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24849 \begin_layout Plain Layout
24857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24860 \begin_layout Plain Layout
24876 \begin_layout Standard
24877 They can also be inserted with the math toolbar button
24878 \begin_inset Graphics
24879 filename ../images/math/functions.png
24887 \begin_layout Subsection
24888 Self-defined Functions
24892 \begin_layout Plain Layout
24893 Functions ! self-defined
24901 \begin_layout Standard
24902 To use a function that is not predefined, like for example the sign function
24903 sgn(x), there are two possibilities:
24906 \begin_layout Itemize
24907 Define the function by inserting the following line to the LaTeX-preamble
24911 \begin_layout Plain Layout
24916 DeclareMathOperator
24919 \begin_inset CommandInset ref
24921 reference "sub:Self-defined-Operators"
24931 \begin_inset Newline newline
24935 \begin_inset VSpace -3mm
24939 \begin_inset Newline newline
24946 DeclareMathOperator{
24954 \begin_layout Plain Layout
24959 DeclareMathOperator
24965 \begin_inset Newline newline
24969 \begin_inset VSpace -2mm
24973 \begin_inset Newline newline
24976 Now the new defined function can be called with the command
24985 \begin_layout Itemize
24986 Write the the formula as usual, mark the formula name, in our example the
24991 , and change it to mathematical text.
24992 At last a space is inserted between prefactor and function.
24995 \begin_layout Standard
24996 The result is the same with both methods as with a predefined function
25000 \begin_layout Plain Layout
25001 In LyX self-defined functions are displayed red, predefined ones black.
25009 \begin_layout Standard
25011 \begin_inset Tabular
25012 <lyxtabular version="3" rows="3" columns="2">
25014 <column alignment="center" valignment="top" width="0pt">
25015 <column alignment="center" valignment="top" width="0pt">
25017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25020 \begin_layout Plain Layout
25026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25029 \begin_layout Plain Layout
25037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25040 \begin_layout Plain Layout
25048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25051 \begin_layout Plain Layout
25052 \begin_inset Formula $A\sgn(x)+B$
25062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25065 \begin_layout Plain Layout
25069 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25080 \begin_layout Plain Layout
25081 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25097 \begin_layout Standard
25098 The first method is more suitable when the self-defined function should
25099 be used several times.
25102 \begin_layout Subsection
25107 \begin_layout Plain Layout
25116 \begin_layout Standard
25117 For limits there are defined besides
25127 \begin_layout Plain Layout
25147 furthermore the following functions:
25150 \begin_layout Standard
25152 \begin_inset Tabular
25153 <lyxtabular version="3" rows="5" columns="2">
25155 <column alignment="center" valignment="top" width="0">
25156 <column alignment="center" valignment="top" width="0">
25158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25170 \begin_layout Plain Layout
25172 \begin_inset Note Note
25175 \begin_layout Plain Layout
25182 is only used as spacer.
25194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25197 \begin_layout Plain Layout
25205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25208 \begin_layout Plain Layout
25209 \begin_inset Formula $\varliminf$
25219 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25222 \begin_layout Plain Layout
25230 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25233 \begin_layout Plain Layout
25234 \begin_inset Formula $\varlimsup$
25244 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25247 \begin_layout Plain Layout
25255 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25258 \begin_layout Plain Layout
25259 \begin_inset Formula $\varprojlim$
25269 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25272 \begin_layout Plain Layout
25280 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25283 \begin_layout Plain Layout
25284 \begin_inset Formula $\varinjlim$
25288 \begin_inset Formula $\raisebox{-2.5mm}{}$
25304 \begin_layout Standard
25305 \begin_inset VSpace medskip
25308 The limit is created by inserting a subscript.
25309 It is set right beside the function in an inline formula:
25312 \begin_layout Standard
25314 \begin_inset Tabular
25315 <lyxtabular version="3" rows="2" columns="2">
25317 <column alignment="center" valignment="top" width="0pt">
25318 <column alignment="center" valignment="top" width="0pt">
25320 <cell alignment="center" valignment="top" usebox="none">
25323 \begin_layout Plain Layout
25329 <cell alignment="center" valignment="top" usebox="none">
25332 \begin_layout Plain Layout
25333 \begin_inset space \hspace{}
25338 \begin_inset Note Note
25341 \begin_layout Plain Layout
25348 are used here as spacer.
25360 <cell alignment="center" valignment="top" usebox="none">
25363 \begin_layout Plain Layout
25372 \begin_layout Plain Layout
25385 \begin_layout Plain Layout
25399 <cell alignment="center" valignment="top" usebox="none">
25402 \begin_layout Plain Layout
25403 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25419 \begin_layout Standard
25420 In a displayed formula the limit is set below the formula, as usual:
25421 \begin_inset Formula \[
25429 \begin_layout Subsection
25434 \begin_layout Plain Layout
25435 Functions ! modulo-
25443 \begin_layout Standard
25444 The modulo-function is special, because it exists in four variants.
25447 \begin_layout Standard
25448 The variants in a displayed formula:
25449 \begin_inset Formula \begin{align*}
25450 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25451 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25452 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25453 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25454 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25461 \begin_layout Standard
25462 In an inline formula less space is set before the function names for all
25466 \begin_layout Section
25471 \begin_layout Plain Layout
25480 \begin_layout Subsection
25481 Special Characters in Mathematical Text
25484 \begin_layout Standard
25485 The following commands can only be used in mathematical text or in TeX-mode:
25488 \begin_layout Standard
25489 \begin_inset space \hfill{}
25493 \begin_inset Tabular
25494 <lyxtabular version="3" rows="8" columns="2">
25496 <column alignment="block" valignment="top" width="0">
25497 <column alignment="block" valignment="top" width="0">
25499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25502 \begin_layout Plain Layout
25508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25511 \begin_layout Plain Layout
25519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25522 \begin_layout Plain Layout
25530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25533 \begin_layout Plain Layout
25534 \begin_inset Formula $\textrm{œ}$
25544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25547 \begin_layout Plain Layout
25555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25558 \begin_layout Plain Layout
25559 \begin_inset Formula $\textrm{Œ}$
25569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25572 \begin_layout Plain Layout
25580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25583 \begin_layout Plain Layout
25584 \begin_inset Formula $\textrm{æ}$
25594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25597 \begin_layout Plain Layout
25605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25608 \begin_layout Plain Layout
25609 \begin_inset Formula $\textrm{Æ}$
25619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25622 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25633 \begin_layout Plain Layout
25634 \begin_inset Formula $\textrm{\aa}$
25644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25647 \begin_layout Plain Layout
25654 \begin_layout Plain Layout
25661 \begin_layout Plain Layout
25682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25685 \begin_layout Plain Layout
25686 \begin_inset Formula $\textrm{Å}$
25696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25699 \begin_layout Plain Layout
25707 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25710 \begin_layout Plain Layout
25711 \begin_inset Formula $\textrm{ı}$
25725 \begin_inset space \hfill{}
25729 \begin_inset Tabular
25730 <lyxtabular version="3" rows="8" columns="2">
25732 <column alignment="block" valignment="top" width="0">
25733 <column alignment="center" valignment="top" width="0">
25735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25738 \begin_layout Plain Layout
25740 \begin_inset Note Note
25743 \begin_layout Plain Layout
25745 \begin_inset space \thinspace{}
25748 mm is used for separation, because otherwise the output will be ¡ and ¿
25759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25762 \begin_layout Plain Layout
25770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25773 \begin_layout Plain Layout
25781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25784 \begin_layout Plain Layout
25785 \begin_inset Formula $\textrm{ø}$
25795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25798 \begin_layout Plain Layout
25806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25809 \begin_layout Plain Layout
25810 \begin_inset Formula $\textrm{Ø}$
25820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25823 \begin_layout Plain Layout
25831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25834 \begin_layout Plain Layout
25835 \begin_inset Formula $\textrm{ł}$
25845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25848 \begin_layout Plain Layout
25856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25859 \begin_layout Plain Layout
25860 \begin_inset Formula $\textrm{Ł}$
25870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25873 \begin_layout Plain Layout
25875 \begin_inset space \hspace{}
25883 \begin_layout Plain Layout
25897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25900 \begin_layout Plain Layout
25901 \begin_inset Formula $\textrm{!`}$
25911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25914 \begin_layout Plain Layout
25916 \begin_inset space \hspace{}
25924 \begin_layout Plain Layout
25938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25941 \begin_layout Plain Layout
25942 \begin_inset Formula $\textrm{?`}$
25952 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25955 \begin_layout Plain Layout
25963 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25966 \begin_layout Plain Layout
25967 \begin_inset Formula $\textrm{ȷ}$
25981 \begin_inset space \hfill{}
25987 \begin_layout Standard
25989 \begin_inset Formula $\textrm{\textrm{Å}}$
25993 \begin_inset Formula $\textrm{\textrm{Ø}}$
25996 can also be inserted via the math toolbar button
25997 \begin_inset Graphics
25998 filename ../images/math/digamma.png
26006 \begin_layout Standard
26007 An exception are the commands
26010 \begin_inset space \hspace{}
26019 \begin_inset space \hspace{}
26025 , because they can be inserted in LyX directly to text.
26028 \begin_layout Subsection
26030 \begin_inset CommandInset label
26032 name "sub:Accents-in-Text"
26040 \begin_layout Plain Layout
26049 \begin_layout Standard
26050 With the following commands all letters can be accented.
26051 The commands must be inserted in TeX-mode.
26054 \begin_layout Standard
26055 \begin_inset space \hfill{}
26059 \begin_inset Tabular
26060 <lyxtabular version="3" rows="8" columns="2">
26062 <column alignment="block" valignment="top" width="0">
26063 <column alignment="block" valignment="top" width="0">
26065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26068 \begin_layout Plain Layout
26074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26077 \begin_layout Plain Layout
26085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26088 \begin_layout Plain Layout
26092 \begin_inset Quotes grd
26100 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26103 \begin_layout Plain Layout
26107 \begin_layout Plain Layout
26123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26126 \begin_layout Plain Layout
26134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26137 \begin_layout Plain Layout
26141 \begin_layout Plain Layout
26157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26160 \begin_layout Plain Layout
26167 \begin_layout Plain Layout
26181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26184 \begin_layout Plain Layout
26188 \begin_layout Plain Layout
26204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26207 \begin_layout Plain Layout
26215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26218 \begin_layout Plain Layout
26222 \begin_layout Plain Layout
26238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26241 \begin_layout Plain Layout
26248 \begin_layout Plain Layout
26262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26265 \begin_layout Plain Layout
26269 \begin_layout Plain Layout
26285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26288 \begin_layout Plain Layout
26295 \begin_layout Plain Layout
26309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26312 \begin_layout Plain Layout
26316 \begin_layout Plain Layout
26332 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26335 \begin_layout Plain Layout
26342 \begin_layout Plain Layout
26356 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26359 \begin_layout Plain Layout
26363 \begin_layout Plain Layout
26383 \begin_inset space \hfill{}
26387 \begin_inset Tabular
26388 <lyxtabular version="3" rows="8" columns="2">
26390 <column alignment="block" valignment="top" width="0">
26391 <column alignment="center" valignment="top" width="0">
26393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26396 \begin_layout Plain Layout
26402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26405 \begin_layout Plain Layout
26413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26416 \begin_layout Plain Layout
26423 \begin_layout Plain Layout
26437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26440 \begin_layout Plain Layout
26444 \begin_layout Plain Layout
26460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26463 \begin_layout Plain Layout
26471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26474 \begin_layout Plain Layout
26478 \begin_layout Plain Layout
26494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26497 \begin_layout Plain Layout
26504 \begin_layout Plain Layout
26515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26518 \begin_layout Plain Layout
26522 \begin_layout Plain Layout
26538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26541 \begin_layout Plain Layout
26549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26552 \begin_layout Plain Layout
26556 \begin_layout Plain Layout
26572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26575 \begin_layout Plain Layout
26582 \begin_layout Plain Layout
26596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26599 \begin_layout Plain Layout
26603 \begin_layout Plain Layout
26619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26622 \begin_layout Plain Layout
26629 \begin_layout Plain Layout
26643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26646 \begin_layout Plain Layout
26650 \begin_layout Plain Layout
26666 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26669 \begin_layout Plain Layout
26676 \begin_layout Plain Layout
26690 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26693 \begin_layout Plain Layout
26697 \begin_layout Plain Layout
26717 \begin_inset space \hfill{}
26723 \begin_layout Standard
26724 \begin_inset VSpace medskip
26733 also two different characters can be accented.
26742 \begin_layout Plain Layout
26757 \begin_layout Plain Layout
26769 \begin_layout Standard
26782 can in combination with vowels directly be inserted with the keyboard without
26784 The same applies for the tilde
26788 \begin_layout Plain Layout
26789 This only applies for keyboards where the tilde is defined as accent.
26798 in combination with
26813 \begin_layout Standard
26856 , and accents inserted directly with the keyboard are also available in
26858 For the other accents there are special math commands to be used in formulas,
26860 \begin_inset CommandInset ref
26862 reference "sub:Accents-for-one"
26869 \begin_layout Standard
26870 \begin_inset VSpace bigskip
26873 Furthermore, with the command
26883 \begin_layout Plain Layout
26891 all numbers and letters can be set into a circle, quasi accented with a
26892 circle, similar to the the copyright symbol.
26895 \begin_layout Standard
26897 \begin_inset Tabular
26898 <lyxtabular version="3" rows="3" columns="2">
26900 <column alignment="center" valignment="top" width="0">
26901 <column alignment="center" valignment="top" width="0">
26903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26906 \begin_layout Plain Layout
26912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26915 \begin_layout Plain Layout
26917 \begin_inset Note Note
26920 \begin_layout Plain Layout
26927 is only used as spacer.
26939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26942 \begin_layout Plain Layout
26950 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26953 \begin_layout Plain Layout
26957 \begin_layout Plain Layout
26973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26976 \begin_layout Plain Layout
26987 raisebox{-1.5pt}{W}}
26992 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26995 \begin_layout Plain Layout
26996 \begin_inset Formula $\raisebox{4.5mm}{}$
27003 \begin_layout Plain Layout
27021 \begin_inset Formula $\raisebox{-2mm}{}$
27037 \begin_layout Standard
27038 One has to take care that the character fits in the circle.
27049 \begin_layout Plain Layout
27051 \begin_inset CommandInset ref
27053 reference "sub:Font-Sizes"
27062 specifies thereby the size of the circle.
27073 \begin_layout Plain Layout
27075 \begin_inset CommandInset ref
27077 reference "sub:Boxes-without-Frame"
27086 the character can be centered.
27089 \begin_layout Subsection
27094 \begin_layout Plain Layout
27103 \begin_layout Standard
27104 Minuscule numbers are created with the command
27114 \begin_layout Plain Layout
27123 The command can be used in formulas and in TeX-mode.
27124 The command scheme is:
27127 \begin_layout Standard
27132 oldstylenums{number}
27135 \begin_layout Standard
27140 oldstylenums{0123456789
27143 \begin_inset Formula $\oldstylenums{0123456789}$
27149 \begin_layout Subsection
27150 Miscellaneous special Characters
27151 \begin_inset CommandInset label
27153 name "sub:Miscellaneous-special-Characters"
27161 \begin_layout Plain Layout
27162 Special characters ! miscellaneous
27170 \begin_layout Standard
27171 The following characters can only be inserted to formulas by using commands:
27174 \begin_layout Standard
27176 \begin_inset Tabular
27177 <lyxtabular version="3" rows="4" columns="2">
27179 <column alignment="center" valignment="top" width="0">
27180 <column alignment="center" valignment="top" width="0">
27182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27185 \begin_layout Plain Layout
27191 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27194 \begin_layout Plain Layout
27202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27205 \begin_layout Plain Layout
27212 \begin_layout Plain Layout
27226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27229 \begin_layout Plain Layout
27230 \begin_inset Formula $\mathcircumflex$
27240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27243 \begin_layout Plain Layout
27251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27254 \begin_layout Plain Layout
27255 \begin_inset Formula $\_$
27265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27268 \begin_layout Plain Layout
27273 \begin_layout Plain Layout
27288 \begin_layout Plain Layout
27301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27304 \begin_layout Plain Layout
27305 \begin_inset Formula $^{\circ}$
27321 \begin_layout Standard
27322 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27323 contains the following line
27327 \begin_layout Plain Layout
27328 More about this is described in
27329 \begin_inset CommandInset ref
27331 reference "sub:Text-Characters-in"
27343 \begin_layout Standard
27348 DeclareInputtext{176}{
27361 \begin_layout Section
27363 \begin_inset CommandInset label
27365 name "sec:Formula-Styles"
27373 \begin_layout Plain Layout
27382 \begin_layout Itemize
27383 There are two different alignment styles:
27387 \begin_layout Description
27388 Centered is the predefined standard
27391 \begin_layout Description
27392 Indented for this the option
27396 must be inserted in the menu
27398 Document\SpecialChar \menuseparator
27404 \begin_inset space ~
27410 \begin_layout Standard
27415 is used, the indentation can be adjusted with the length
27425 \begin_layout Plain Layout
27434 Should the distance be 15
27435 \begin_inset space \thinspace{}
27438 mm, the following command line is inserted in the LaTeX-preamble
27441 \begin_layout Standard
27451 \begin_layout Standard
27452 When no length is specified, the predefined value of 30
27453 \begin_inset space \thinspace{}
27460 \begin_layout Itemize
27461 And two different numbering styles:
27465 \begin_layout Description
27466 Right is the predefined standard
27469 \begin_layout Description
27470 Left for this the option
27474 must be inserted in the menu
27476 Document\SpecialChar \menuseparator
27482 \begin_inset space ~
27489 \begin_layout Standard
27498 can also be used together.
27499 In this case both options are inserted, separated by a comma.
27502 \begin_layout Standard
27503 The chosen styles are used for all displayed formulas of the document.
27504 When both, centered and indented formulas should be created in a document,
27510 The indented formulas are then set in a flalign environment, see
27511 \begin_inset CommandInset ref
27513 reference "sub:Flalign-Environment"
27520 \begin_layout Section
27522 \begin_inset CommandInset label
27524 name "sec:Multiline-Formulas"
27532 \begin_layout Plain Layout
27533 Formula ! multiline
27541 \begin_layout Subsection
27545 \begin_layout Standard
27546 In LyX multiline formulas are created by pressing
27551 arg "newline-insert newline"
27557 This creates either an
27559 eqnarray environment
27561 that is described in
27562 \begin_inset CommandInset ref
27564 reference "sub:Eqnarray-Environment"
27568 or, when the option
27570 Use AMS math package
27572 in the document settings is selected, an
27576 that is described in
27577 \begin_inset CommandInset ref
27579 reference "sub:Standard-align-Environment"
27586 \begin_layout Standard
27587 There are other multiline formula environments that can be created via the
27590 Insert\SpecialChar \menuseparator
27594 These environments are described in the following sections.
27597 \begin_layout Standard
27598 In all multiline formula environments a new line is created by pressing
27602 arg "newline-insert newline"
27606 To add or delete lines, the math toolbar buttons
27607 \begin_inset Graphics
27608 filename ../images/tabular-feature_append-row.png
27614 \begin_inset Graphics
27615 filename ../images/tabular-feature_delete-row.png
27620 , respectively, or the menu
27622 Edit\SpecialChar \menuseparator
27628 \begin_layout Subsubsection
27630 \begin_inset CommandInset label
27632 name "sub:Line-Separation"
27640 \begin_layout Plain Layout
27641 Formula ! multiline ! Line separation
27649 \begin_layout Standard
27650 There is sometimes not enough space in multiline formulas between the lines:
27651 \begin_inset Formula \begin{eqnarray*}
27652 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}\\
27653 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*}
27660 \begin_layout Standard
27661 In LaTeX additional line space is specified as optional argument of the
27663 This is not yet possible in LyX
27667 \begin_layout Plain Layout
27669 \begin_inset CommandInset href
27671 name "LyX-bug #1505"
27672 target "http://www.lyx.org/trac/ticket/1505"
27681 , therefore the whole formula must be inserted in TeX-mode.
27682 To add in our example space, the command
27690 is inserted at the end of the first line.
27695 \begin_layout Plain Layout
27702 \begin_layout Plain Layout
27704 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27707 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27714 \begin_layout Plain Layout
27718 left(B^{2}+x_{0}^{2}
27726 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27731 \begin_layout Plain Layout
27743 \begin_layout Standard
27744 \begin_inset VSpace bigskip
27747 To set the the line separation for all lines in a formula, the length
27757 \begin_layout Plain Layout
27767 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27778 \begin_inset space \thinspace{}
27783 \begin_inset space \thinspace{}
27786 mm additional line separation as in the previous example, the command
27789 \begin_layout Standard
27799 \begin_layout Standard
27800 is inserted in TeX-mode before the formula.
27801 This requires that the LaTeX-package
27809 \begin_layout Plain Layout
27814 is part of every LaTeX standard installation.
27823 \begin_layout Plain Layout
27829 was loaded in LaTeX-preamble with the line
27832 \begin_layout Standard
27840 \begin_layout Standard
27845 \begin_layout Plain Layout
27857 \begin_inset Formula \begin{eqnarray*}
27858 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}\\
27859 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*}
27866 \begin_layout Standard
27870 \begin_layout Plain Layout
27881 To get back to the predefined distance,
27887 is set to the value 3
27888 \begin_inset space \thinspace{}
27894 \begin_layout Subsubsection
27896 \begin_inset CommandInset label
27898 name "sub:Column-Separation"
27906 \begin_layout Plain Layout
27907 Formula ! multiline ! Column separation
27915 \begin_layout Standard
27916 Multiline formulas form a matrix.
27917 A formula in the eqnarray environment is for example a matrix with three
27919 By changing the column separation in this environment, the space beside
27920 the relation sign can be changed.
27923 \begin_layout Standard
27924 The column separation is specified with the length
27934 \begin_layout Plain Layout
27943 \begin_inset Newline newline
27946 column separation = 2
27947 \begin_inset space \thinspace{}
27957 \begin_inset Newline newline
27963 \begin_layout Standard
27973 \begin_layout Standard
27974 inserted in TeX-mode, sets for all following formulas a column separation
27976 \begin_inset space \thinspace{}
27980 To get back to the predefined distance,
27987 \begin_inset space \thinspace{}
27993 \begin_layout Standard
27995 \begin_inset space \thinspace{}
27998 cm column separation:
28002 \begin_layout Plain Layout
28014 \begin_inset Formula \begin{eqnarray*}
28016 C & \ne & A\end{eqnarray*}
28020 A formula with the predefined column separation for matrices of 10
28021 \begin_inset space \thinspace{}
28028 \begin_layout Plain Layout
28040 \begin_inset Formula \begin{eqnarray*}
28042 C & \ne & A\end{eqnarray*}
28049 \begin_layout Subsubsection
28054 \begin_layout Plain Layout
28063 \begin_layout Standard
28064 Long formulas can be typeset using these methods:
28067 \begin_layout Itemize
28068 When one side of the equation is much shorther than the line width, this
28069 one is chosen for the left side and the right side is typeset over two
28071 \begin_inset Formula \begin{eqnarray}
28072 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 \\
28073 & & -\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}
28077 The minus sign at the beginning of the second line does normally not appear
28078 as operator because it is the first character of the line.
28079 Thus it would not be surrounded by space and could not be distinguished
28080 from the fraction bar.
28082 \begin_inset space \thinspace{}
28085 pt space was inserted behind the minus sign with the command
28095 \begin_layout Plain Layout
28103 \begin_inset CommandInset ref
28105 reference "sub:Variable-Space"
28118 \begin_layout Plain Layout
28129 \begin_layout Itemize
28130 When both sides of the equation are too long, the command
28140 \begin_layout Plain Layout
28149 It is inserted to the first column of the first line and effects that all
28150 further insertions overwrite the following columns:
28151 \begin_inset Formula \begin{eqnarray}
28152 \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 \\
28153 & & -\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 \\
28154 & & =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}
28158 After the insertion of
28164 , the cursor is in a purple box that is a bit shifted to the left from the
28166 In this the formula is inserted.
28167 \begin_inset Newline newline
28170 The content of the further lines is inserted to the second or another formula
28172 The greater the column number where it was inserted, the larger the indentation.
28173 \begin_inset VSpace medskip
28177 \begin_inset Newline newline
28181 \begin_inset Note Greyedout
28184 \begin_layout Plain Layout
28185 Note the following when using
28194 \begin_layout Itemize
28195 The formula doesn't use the full page width.
28197 \begin_inset space \thinspace{}
28201 \begin_inset space \space{}
28205 \begin_inset Formula $-B^{2}$
28208 is added to the first line in the above example, it would have been outside
28210 To better use the width, negative space can be inserted at the beginning
28214 \begin_layout Itemize
28215 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28220 \begin_layout Plain Layout
28221 \begin_inset CommandInset href
28223 name "LyX-bug #1429"
28224 target "http://www.lyx.org/trac/ticket/1429"
28233 One can only set the cursor at the beginning of the line and move it with
28242 \begin_layout Itemize
28243 Other methods to set long formulas are offered by the environments described
28245 \begin_inset CommandInset ref
28247 reference "sub:Multline-Environment"
28252 \begin_inset CommandInset ref
28254 reference "sub:Multiline-Formula-Parts"
28261 \begin_layout Subsubsection
28263 \begin_inset CommandInset label
28265 name "sub:Multiline-Brackets"
28273 \begin_layout Plain Layout
28274 Brackets ! for multiline expressions
28282 \begin_layout Standard
28283 For brackets spanning multiple lines the following problem occurs:
28284 \begin_inset Formula \begin{eqnarray*}
28285 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28286 & & \left.\cdots+B-D\right]\end{eqnarray*}
28293 \begin_layout Standard
28294 The closing bracket is smaller than the opening bracket because brackets
28295 with variable size may not span multiple lines.
28298 \begin_layout Standard
28299 To set the bracket size for the second line correctly, the first line is
28310 \begin_layout Plain Layout
28318 and the second line with
28326 \begin_layout Plain Layout
28340 \begin_inset CommandInset ref
28342 reference "sub:Automatic-Bracket-Size"
28357 \begin_layout Plain Layout
28383 \begin_layout Plain Layout
28402 \begin_layout Plain Layout
28421 \begin_layout Plain Layout
28433 \begin_inset Formula $\downarrow$
28442 \begin_layout Plain Layout
28450 is inserted, because the multiplication operator with its limits is the
28451 largest symbol in the first line and this should be the size for the bracket
28452 in the second line.
28455 \begin_layout Standard
28456 The result is this:
28457 \begin_inset Formula \begin{eqnarray*}
28458 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28459 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28466 \begin_layout Subsection
28470 \begin_layout Standard
28471 Align environments can be used for every kind of multiline formulas.
28472 They are specially useful to set several formulas side by side.
28475 \begin_layout Standard
28476 Align environments consist of columns.
28477 The odd columns are right aligned, the even ones left aligned.
28478 Every line in an Align environment can be numbered.
28481 \begin_layout Standard
28482 Align environments are created via the menu
28484 Insert\SpecialChar \menuseparator
28490 Edit\SpecialChar \menuseparator
28491 Math\SpecialChar \menuseparator
28492 Change Formula Type
28494 already existing formulas can be converted to Align environments.
28497 \begin_layout Standard
28498 To add or delete columns, the math toolbar buttons
28499 \begin_inset Graphics
28500 filename ../images/tabular-feature_append-column.png
28506 \begin_inset Graphics
28507 filename ../images/tabular-feature_delete-column.png
28512 , respectively, or the menu
28514 Edit\SpecialChar \menuseparator
28520 \begin_layout Subsubsection
28521 Standard align Environment
28522 \begin_inset CommandInset label
28524 name "sub:Standard-align-Environment"
28532 \begin_layout Plain Layout
28533 Formula ! multiline ! align environment
28541 \begin_layout Standard
28542 This Align environment is created by presssing
28545 arg "newline-insert newline"
28548 in a formula or by the menu
28550 Insert\SpecialChar \menuseparator
28551 Math\SpecialChar \menuseparator
28552 AMS align Environment
28557 \begin_layout Standard
28558 An example for two formulas set side by side, that are created with a four
28559 column align environment:
28560 \begin_inset Formula \begin{align*}
28561 A & =\sin(B) & C & =D\\
28562 C & \ne A & B & \ne D\end{align*}
28566 As it can be seen, the formulas in this environment are placed so as if
28575 \begin_layout Plain Layout
28583 \begin_inset CommandInset ref
28585 reference "sub:Variable-Space"
28596 before the first and after every even column.
28597 When the formula style
28603 \begin_layout Plain Layout
28605 \begin_inset CommandInset ref
28607 reference "sec:Formula-Styles"
28618 is used, the formula is set without the
28624 before the first column.
28627 \begin_layout Subsubsection
28628 Alignat Environment
28632 \begin_layout Plain Layout
28633 Formula ! multiline ! alignat environment
28641 \begin_layout Standard
28642 The alignat environment has no predefined column separation.
28643 It can be inserted manually with the spaces that are described
28644 \begin_inset CommandInset ref
28646 reference "sub:Space"
28653 \begin_layout Standard
28654 The above example in the alignat environment where 1
28655 \begin_inset space \thinspace{}
28658 cm space was inserted at the beginning of the second formula:
28659 \begin_inset Formula \begin{alignat*}{2}
28660 A & =\sin(B) & \hspace{1cm}C & =D\\
28661 C & \ne A & B & \ne D\end{alignat*}
28665 Because the column separation can be set separately for every column, this
28666 environment is especially suitable to set three and more formulas side
28670 \begin_layout Subsubsection
28671 Flalign Environment
28672 \begin_inset CommandInset label
28674 name "sub:Flalign-Environment"
28682 \begin_layout Plain Layout
28683 Formula ! multiline ! flalign environment
28691 \begin_layout Standard
28692 In this environment the first two columns are always set as much as possible
28693 to the left and the last two ones to the right.
28695 \begin_inset Formula \begin{flalign*}
28696 A & =1 & B & =2 & C & =3\\
28697 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28704 \begin_layout Standard
28705 By creating a flalign environment with an odd number of columns where an
28706 empty TeX-brace is inserted to the last column, several formulas in a document
28707 can be set to the left, although the formula style
28712 As example the indented formula
28713 \begin_inset CommandInset ref
28715 reference "eq:VolInt"
28720 \begin_inset Formula \begin{flalign}
28721 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28725 The first two columns contain the formula.
28726 To indent it as with the formula style
28731 \begin_inset space \thinspace{}
28734 pt space was inserted at the beginning of the first column.
28737 \begin_layout Subsection
28738 Eqnarray Environment
28739 \begin_inset CommandInset label
28741 name "sub:Eqnarray-Environment"
28749 \begin_layout Plain Layout
28750 Formula ! multiline ! eqnarray environment
28758 \begin_layout Standard
28759 When this environment has been created, three blue boxes appear.
28760 The content of the first box is right aligned, the content of the last
28762 The content of the middle box appears centered and a bit smaller, because
28763 it is designed to insert there only relation characters.
28764 \begin_inset Formula \begin{eqnarray*}
28765 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28767 A & = & A\end{eqnarray*}
28774 \begin_layout Subsection
28779 \begin_layout Plain Layout
28780 Formula ! multiline ! gather environment
28788 \begin_layout Standard
28789 This environment consists of only one centered column.
28790 Every line can be numbered.
28791 \begin_inset Formula \begin{gather}
28793 X=\textrm{-}1\end{gather}
28800 \begin_layout Subsection
28801 Multline Environment
28802 \begin_inset CommandInset label
28804 name "sub:Multline-Environment"
28812 \begin_layout Plain Layout
28813 Formula ! multiline ! multline environment
28821 \begin_layout Standard
28822 The multline environment consists, like the gather environment, of only
28824 But the first line is left aligned, the last one right aligned.
28825 All other lines are centered.
28826 Therefore this environment is suitable for long formulas.
28828 \begin_inset CommandInset ref
28830 reference "eq:lefteqn"
28834 in the multline environment:
28835 \begin_inset Formula \begin{multline}
28836 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}\\
28837 -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}\\
28838 =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}
28845 \begin_layout Standard
28846 In the output only the last (first) line of a multline environment appears
28847 numbered when the document numbering is right (left).
28851 \begin_layout Plain Layout
28852 numbering styles see
28853 \begin_inset CommandInset ref
28855 reference "sec:Formula-Styles"
28867 \begin_layout Standard
28876 \begin_layout Plain Layout
28894 \begin_layout Plain Layout
28904 a centered line can be right or left aligned, respectively.
28905 The commands are used as follows:
28908 \begin_layout Standard
28913 shoveright{line content}
28919 shoveleft{line content}
28922 \begin_layout Standard
28923 \begin_inset VSpace medskip
28934 \begin_layout Plain Layout
28944 specifies the distance of the first line from the left page margin.
28945 Predefined is the length 0
28946 \begin_inset space \thinspace{}
28952 \begin_layout Standard
28953 As example the above formula where the command
28956 \begin_layout Standard
28966 \begin_layout Standard
28967 was inserted in TeX-mode before:
28971 \begin_layout Plain Layout
28983 \begin_inset Formula \begin{multline}
28984 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}\\
28985 \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}}\\
28986 =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}
28994 \begin_layout Plain Layout
29005 The second line was left aligned using
29014 \begin_layout Subsection
29015 Multiline Formula Parts
29016 \begin_inset CommandInset label
29018 name "sub:Multiline-Formula-Parts"
29026 \begin_layout Plain Layout
29027 Formula ! multiline ! formula parts
29035 \begin_layout Standard
29036 To display only parts of a formula with multiple lines, one of the following
29037 environments are used:
29054 They can be inserted via the menu
29056 Insert\SpecialChar \menuseparator
29059 or by using the commands described in this section.
29062 \begin_layout Standard
29063 The first three have the same properties as the corresponding multiline
29064 formula environments, but it is possible to set further formula parts beside
29067 \begin_inset Formula \[
29068 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29069 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29070 \right\} \textrm{Uncertainty relations}\]
29077 \begin_layout Standard
29078 To get this formula, a displayed formula is created where the command
29086 \begin_layout Plain Layout
29097 A purple box appears around the blue formula box where now columns and
29098 lines can be added.
29099 Outside the multiline environment other formula parts can be set, like
29103 \begin_layout Standard
29104 The aligned environment is also suitable for long formulas whose lines are
29105 horizontally aligned.
29106 Using aligned in a displayed formula has the advantage that the formula
29107 number is vertically centered behind the lines.
29109 \begin_inset CommandInset ref
29111 reference "eq:shortlong"
29115 in the aligned environment:
29116 \begin_inset Formula \begin{equation}
29117 \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}|}\\
29118 & -\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}
29126 \begin_layout Standard
29127 To use the environments
29149 \begin_layout Plain Layout
29167 \begin_layout Plain Layout
29185 \begin_layout Plain Layout
29193 are inserted, respectively.
29194 The split environment has the same properties as the aligned environment
29195 but it can only have two columns.
29198 \begin_layout Subsection
29199 Text in multiline Formulas
29200 \begin_inset CommandInset label
29202 name "sub:Text-in-multiline"
29210 \begin_layout Plain Layout
29220 \begin_layout Plain Layout
29221 Formula ! multiline ! text
29229 \begin_layout Standard
29230 In the Align environments, and the multline and gather environment, text
29231 can be inserted that will appear in a separate line and doesn't affect
29232 the column alignment.
29233 To do this, the command
29241 \begin_layout Plain Layout
29251 is used in the following scheme:
29254 \begin_layout Standard
29262 \begin_layout Standard
29263 The text should not be longer than a line because it cannot be hyphenated.
29264 As LyX doesn't yet support
29270 directly, the text is written as mathematical text.
29277 must hereby be at the beginning of a line and appears in the output above
29279 An example where the text was inserted at the beginning of the second line:
29280 \begin_inset Formula \begin{align}
29281 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29282 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29289 \begin_layout Section
29294 \begin_layout Plain Layout
29304 \begin_layout Plain Layout
29305 Formula ! numbering|see
29309 \begin_layout Plain Layout
29320 \begin_layout Plain Layout
29335 \begin_layout Subsection
29339 \begin_layout Standard
29340 Numbered formulas can be created with the menu
29342 Insert\SpecialChar \menuseparator
29343 Math\SpecialChar \menuseparator
29345 \begin_inset space ~
29353 \begin_inset space ~
29359 Existing formulas can be numbered with the menu
29361 Edit\SpecialChar \menuseparator
29362 Math\SpecialChar \menuseparator
29364 \begin_inset space ~
29372 arg "math-number-toggle"
29376 The formula number is displayed in LyX behind the formula as number sign
29378 The number sign is replaced in the output by the formula number.
29381 \begin_layout Standard
29382 When numbering is turned on in multiline formulas, all lines will be numbered.
29383 But the numbering can be controlled with the menu
29385 Edit\SpecialChar \menuseparator
29386 Math\SpecialChar \menuseparator
29388 \begin_inset space ~
29392 \begin_inset space ~
29396 \begin_inset space ~
29404 arg "math-number-line-toggle"
29410 \begin_layout Standard
29411 Except for inline formulas, all formulas can be numbered with two different
29413 \begin_inset CommandInset ref
29415 reference "sec:Formula-Styles"
29422 \begin_layout Subsection
29427 \begin_layout Plain Layout
29428 Cross-references ! to formulas
29436 \begin_layout Standard
29437 All labeled formulas can be cross-referenced.
29438 A label is added by the menu
29440 Insert\SpecialChar \menuseparator
29443 or the toolbar button
29444 \begin_inset Graphics
29445 filename ../images/label-insert.png
29451 The cursor must hereby be inside a displayed formula.
29452 A dialog pops up displaying the prefix
29457 The label is inserted there behind the prefix.
29458 The predefined prefix means
29459 \begin_inset Quotes eld
29463 \begin_inset Quotes erd
29466 and makes it easier to find labels in large documents because it marks
29467 it as formula label to divide it from e.
29468 \begin_inset space \thinspace{}
29472 \begin_inset space \space{}
29476 To change a label, the menu
29478 Insert\SpecialChar \menuseparator
29484 \begin_layout Standard
29485 The name of the label is displayed in LyX within two parentheses behind
29487 A formula with a label is always numbered.
29490 \begin_layout Standard
29491 Cross-references are inserted via the menu
29493 Insert\SpecialChar \menuseparator
29496 or with the toolbar button
29497 \begin_inset Graphics
29498 filename ../images/dialog-show-new-inset_ref.png
29504 A formula cross-reference appears in the output as formula number.
29505 When in the cross-reference dialog window the format
29509 is chosen, the cross-reference appears in the output as formula number
29511 \begin_inset Newline newline
29514 By right-clicking on a cross-reference in LyX, one jumps to the formula
29515 that is referenced.
29518 \begin_layout Standard
29519 Here are as examples cross-references to formulas of the following subsections:
29520 \begin_inset Note Note
29523 \begin_layout Plain Layout
29524 Note the different cross-reference types.
29532 \begin_layout Standard
29534 \begin_inset CommandInset ref
29541 \begin_inset CommandInset ref
29549 \begin_inset CommandInset ref
29555 ) big Latin letters are used for the numbering in contrary to (
29556 \begin_inset CommandInset ref
29565 \begin_layout Standard
29566 \begin_inset VSpace medskip
29569 When the argument of
29577 \begin_layout Plain Layout
29585 \begin_inset CommandInset ref
29587 reference "sub:User-defined-Numbering"
29598 contains a box like in
29599 \begin_inset CommandInset ref
29601 reference "sub:Paragraph-Boxes"
29605 , the formula cannot be referenced.
29608 \begin_layout Subsection
29613 \begin_layout Plain Layout
29614 Formula numbering ! subnumbering
29622 \begin_layout Standard
29623 With the help of the commands
29627 begin{subequations}
29635 formulas can be subnumbered.
29636 Both commands are inserted in TeX-mode.
29639 \begin_layout Standard
29641 \begin_inset Formula \begin{equation}
29642 A=C-B\label{eq:a}\end{equation}
29650 \begin_layout Plain Layout
29654 addtocounter{equation}{-1}
29663 \begin_layout Plain Layout
29667 begin{subequations}
29673 \begin_inset VSpace -5mm
29677 \begin_inset Formula \begin{equation}
29678 B=C-A\label{eq:b}\end{equation}
29683 \begin_inset Formula \begin{equation}
29684 C=A+B\label{eq:c}\end{equation}
29691 \begin_layout Standard
29695 \begin_layout Plain Layout
29707 \begin_layout Standard
29708 To create the example, the following is done:
29711 \begin_layout Enumerate
29712 first formula is inserted
29715 \begin_layout Enumerate
29720 addtocounter{equation}{-1}
29722 begin{subequations}
29726 \begin_layout Plain Layout
29735 \begin_inset Newline newline
29740 is inserted after the first formula
29743 \begin_layout Enumerate
29744 second formula is inserted
29747 \begin_layout Enumerate
29748 third formula is inserted
29751 \begin_layout Enumerate
29758 is inserted after the third formula
29761 \begin_layout Standard
29762 Every formula between the commands
29774 is subnumbered as a, b,
29775 \begin_inset Newline linebreak
29778 c, \SpecialChar \ldots{}
29779 For multiline formulas every line will be subnumbered.
29780 All subnumbered formulas are treated as
29785 But as every numbered formula increases the counter
29789 by one, the command
29795 is needed to decrease it.
29796 Otherwise the formulas
29797 \begin_inset CommandInset ref
29804 \begin_inset CommandInset ref
29811 \begin_inset CommandInset ref
29817 would be numbered as
29818 \begin_inset CommandInset ref
29825 \begin_inset CommandInset ref
29832 \begin_inset CommandInset ref
29841 \begin_layout Standard
29842 By inserting the commands in TeX-mode, a space is created between the first
29845 \begin_inset space \thinspace{}
29848 mm vertical space is inserted after the command
29852 begin{subequations}
29855 When the formula style
29861 \begin_layout Plain Layout
29863 \begin_inset CommandInset ref
29865 reference "sec:Formula-Styles"
29877 \begin_inset space \thinspace{}
29880 mm space is inserted instead.
29883 \begin_layout Standard
29884 Here is an example for a multiline formula where the numbering was turned
29885 off for the second line:
29889 \begin_layout Plain Layout
29893 begin{subequations}
29899 \begin_inset Formula \begin{eqnarray}
29900 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29901 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29902 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29910 \begin_layout Plain Layout
29922 \begin_layout Subsection
29923 User-defined Numbering
29924 \begin_inset CommandInset label
29926 name "sub:User-defined-Numbering"
29934 \begin_layout Plain Layout
29935 Formula numbering ! user-defined
29943 \begin_layout Standard
29947 \begin_layout Plain Layout
29948 Formula numbering ! self-defined delimiters
29953 With the standard numbering parentheses are set around the formula number.
29954 To replace the parentheses for example by vertical bars, the following
29955 line is added to the LaTeX-preamble:
29958 \begin_layout Standard
29970 \begin_inset Note Note
29973 \begin_layout Plain Layout
29974 This macro is already declared in the LaTeX-preamble for testing.
29975 To activate it, remove the percent sign at the beginning.
29983 \begin_layout Standard
29984 To use other characters, the vertical bars besides the
29988 are replaced by one ore more characters.
29989 To get only the formula number the vertical bars are omitted.
29992 \begin_layout Standard
29993 \begin_inset VSpace bigskip
29996 When there should be an expression of your choice instead of the consecutive
29997 formula number in parentheses behind the formula, the command
30007 \begin_layout Plain Layout
30016 \begin_inset Formula \begin{equation}
30017 A+B=C\tag{something}\label{eq:tag}\end{equation}
30021 In this example the command
30029 \begin_layout Plain Layout
30040 was inserted to the formula.
30043 \begin_layout Standard
30052 \begin_layout Plain Layout
30063 is inserted instead, the star prevents the parentheses around the expression:
30064 \begin_inset Formula \[
30065 A+B=C\tag*{something}\]
30072 \begin_layout Standard
30073 \begin_inset VSpace bigskip
30076 To restart the formula numbering with new document parts or sections, the
30077 following command is used:
30080 \begin_layout Standard
30085 @addtoreset{equation}{part}
30091 \begin_layout Plain Layout
30096 \begin_layout Plain Layout
30107 \begin_layout Plain Layout
30120 \begin_layout Plain Layout
30131 \begin_layout Plain Layout
30144 \begin_inset Newline newline
30148 \begin_inset Newline newline
30155 @addtoreset{equation}{section}
30158 \begin_layout Standard
30159 To be able to use these commands in TeX-mode, the
30160 \begin_inset Quotes eld
30164 \begin_inset Quotes erd
30167 character has to be made
30168 \begin_inset Quotes eld
30172 \begin_inset Quotes erd
30175 for LaTeX using the command
30189 So the command sequence in TeX-mode is:
30192 \begin_layout Standard
30198 \begin_inset Newline newline
30203 @addtoreset{equation}{section}
30204 \begin_inset Newline newline
30212 \begin_layout Standard
30213 In the LaTeX-preamble
30225 can be omitted as they are automatically internally inserted by LyX.
30228 \begin_layout Standard
30243 \begin_layout Plain Layout
30248 is part of the LaTeX-package
30256 \begin_layout Plain Layout
30257 Packages ! carlisle
30262 that is part of every LaTeX standard installation.
30271 \begin_layout Plain Layout
30272 Packages ! remreset
30277 has to be loaded in the LaTeX-preamble with the line
30280 \begin_layout Standard
30285 usepackage{remreset}
30288 \begin_layout Standard
30299 \begin_layout Plain Layout
30304 \begin_layout Plain Layout
30315 \begin_layout Plain Layout
30328 \begin_layout Plain Layout
30339 \begin_layout Plain Layout
30351 can be used with the same scheme as
30360 \begin_layout Standard
30361 \begin_inset VSpace bigskip
30364 Sometimes formulas should be numbered in the following form:
30367 \begin_layout Standard
30370 (section number.formula number)
30373 \begin_layout Standard
30374 The formula number should start with every section with
30375 \begin_inset Quotes eld
30379 \begin_inset Quotes erd
30385 \begin_layout Standard
30386 For this case there is the command
30396 \begin_layout Plain Layout
30404 , which is used with the following scheme:
30407 \begin_layout Standard
30412 numberwithin{counter}{sectioning}
30415 \begin_layout Standard
30416 Counter denotes what kind of numbering is affected, sectioning denotes what
30417 number is before the dot.
30420 \begin_layout Standard
30421 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30424 \begin_layout Standard
30429 numberwithin{equation}{section}
30432 \begin_layout Standard
30433 This is the result:
30437 \begin_layout Plain Layout
30441 numberwithin{equation}{section}
30447 \begin_inset Formula \begin{equation}
30448 A+B=C\end{equation}
30455 \begin_layout Standard
30457 \begin_inset space \thinspace{}
30461 \begin_inset space \space{}
30464 tables so that the number of the part is the sectioning,
30465 \begin_inset Newline newline
30472 numberwithin{table}{part}
30477 \begin_layout Standard
30478 To go back to the standard numbering or to prevent this kind of numbering
30479 when it is defined by the document class, the following command is inserted
30480 as TeX-Code or to the LaTeX-preamble:
30483 \begin_layout Standard
30496 \begin_layout Plain Layout
30510 \begin_layout Plain Layout
30526 \begin_inset Newline newline
30534 \begin_inset Newline newline
30546 \begin_layout Standard
30553 uses internally the command
30559 , described above, that also needs to be reverted.
30563 \begin_layout Plain Layout
30570 \begin_layout Plain Layout
30574 @removefromreset{equation}{section}
30577 \begin_layout Plain Layout
30589 \begin_layout Subsection
30590 Numbering with Roman Numbers and Letters
30594 \begin_layout Plain Layout
30595 Formula numbering ! with letters
30604 \begin_layout Plain Layout
30605 Formula numbering ! with Roman numbers
30613 \begin_layout Standard
30614 Formulas can also be numbered with Roman numbers and Latin letters.
30615 To number for example with small Roman numbers, the command
30618 \begin_layout Standard
30630 \begin_layout Standard
30631 is inserted before the formula in TeX-mode.
30642 \begin_layout Plain Layout
30650 redefines the predefined command
30666 \begin_layout Plain Layout
30673 has the same scheme like the command
30679 that is described in
30680 \begin_inset CommandInset ref
30682 reference "sub:The-Command-newcommand"
30695 is the formula counter.
30702 is used as prefix for a counter, the value of the counter is output as
30704 When a formula is numbered, LaTeX sets internally the command
30710 behind the formula.
30719 \begin_layout Plain Layout
30729 outputs the counter as small Roman number.
30732 \begin_layout Standard
30733 All formulas behind the command
30743 are now numbered Roman.
30744 To switch to numbering with big Roman numbers, the command is inserted
30761 \begin_layout Plain Layout
30773 \begin_inset Quotes eld
30777 \begin_inset Quotes erd
30780 with small Latin letters there is the command
30790 \begin_layout Plain Layout
30798 , for big ones there is the command
30808 \begin_layout Plain Layout
30821 \begin_layout Standard
30822 \begin_inset Note Greyedout
30825 \begin_layout Plain Layout
30830 Only maximal 26 formulas can be numbered with Latin letters in one document.
30838 \begin_layout Standard
30842 \begin_layout Plain Layout
30858 \begin_layout Standard
30859 \begin_inset Formula \begin{equation}
30860 A=\textrm{small roman}\label{eq:rom}\end{equation}
30868 \begin_layout Plain Layout
30882 \begin_inset Formula \begin{equation}
30883 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30891 \begin_layout Plain Layout
30905 \begin_inset Formula \begin{equation}
30906 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30914 \begin_layout Plain Layout
30928 \begin_inset Formula \begin{equation}
30929 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30936 \begin_layout Standard
30937 To switch back to the default numbering, insert the command:
30940 \begin_layout Standard
30953 \begin_layout Plain Layout
30964 \begin_layout Standard
30968 \begin_layout Plain Layout
30982 \begin_inset Formula \begin{equation}
30983 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30990 \begin_layout Standard
30991 \begin_inset VSpace medskip
30994 As you see, formulas are numbered serially independent from the numbering
30996 When then numbering should start with
30997 \begin_inset Quotes eld
31001 \begin_inset Quotes erd
31004 when the style is changed, new equation counters have to be defined.
31005 A description about this can be found in the file
31006 \begin_inset CommandInset href
31008 target "Formula-numbering.lyx"
31015 \begin_layout Section
31016 User-defined Commands
31020 \begin_layout Plain Layout
31021 User-defined commands
31029 \begin_layout Standard
31030 \begin_inset Note Greyedout
31033 \begin_layout Plain Layout
31038 The names of user-defined commands and macros may only consist of Latin
31047 \begin_layout Subsection
31051 \begin_inset CommandInset label
31053 name "sub:The-Command-newcommand"
31061 \begin_layout Plain Layout
31062 User-defined commands !
31073 \begin_layout Plain Layout
31084 \begin_layout Standard
31085 Many LaTeX-commands are too long to be used frequently.
31086 But it is possible to define with the command
31092 new shorter commands.
31095 \begin_layout Standard
31096 The command scheme of
31105 \begin_layout Standard
31110 newcommand{new command name}[number of arguments][optional
31115 \begin_inset Newline newline
31122 \begin_layout Plain Layout
31137 \begin_layout Plain Layout
31144 {command definition}
31147 \begin_layout Standard
31148 \begin_inset Note Greyedout
31151 \begin_layout Plain Layout
31156 Assure that the name of the new command is not already used in your document
31157 or by LaTeX-packages that you use.
31158 When you for example define the command
31170 , you get an error message because
31176 is already defined as command for
31177 \begin_inset Quotes eld
31181 \begin_inset Formula $\le$
31185 \begin_inset Quotes erd
31196 \begin_layout Standard
31197 The number of arguments is an integer in the range 0
31198 \begin_inset space \thinspace{}
31202 \begin_inset space \thinspace{}
31205 9 and specifies how many arguments the new command should have.
31206 With the optional value a value for an optional argument can be predefined.
31207 When this is done, the
31215 rgument of the new command is automatically an optional one.
31218 \begin_layout Standard
31219 Here are some examples:
31222 \begin_layout Itemize
31223 To define the command
31235 , the LaTeX-preamble line is:
31236 \begin_inset VSpace medskip
31240 \begin_inset Newline newline
31254 \begin_layout Itemize
31255 To define the command
31267 , the argument (that should be underlined) must be taken into account.
31268 For this the preamble line is:
31269 \begin_inset VSpace medskip
31273 \begin_inset Newline newline
31287 \begin_inset VSpace medskip
31291 \begin_inset Newline newline
31298 acts as argument placeholder, the
31302 behind it denotes that it is the placeholder for the first argument.
31305 \begin_layout Itemize
31313 \begin_inset space \thinspace{}
31317 \begin_inset space \space{}
31327 \begin_inset VSpace medskip
31331 \begin_inset Newline newline
31342 framebox#1#2{$#3$}}
31345 \begin_inset VSpace medskip
31349 \begin_inset Newline newline
31352 The two Dollar signs creates the extra formula needed for
31359 \begin_inset CommandInset ref
31361 reference "sub:Boxes-with-Frame"
31368 \begin_layout Itemize
31369 To create a new command for
31375 where the color for the box needn't to be specified, the argument for the
31376 color is defined optional:
31377 \begin_inset VSpace medskip
31381 \begin_inset Newline newline
31392 fcolorbox{#2}{#1}{$#3$}}
31395 \begin_inset VSpace medskip
31399 \begin_inset Newline newline
31402 When the color is not specified when using
31408 , the predefined color
31415 \begin_layout Standard
31416 A test of the new defined commands:
31419 \begin_layout Standard
31421 \begin_inset Tabular
31422 <lyxtabular version="3" rows="6" columns="2">
31424 <column alignment="center" valignment="top" width="0">
31425 <column alignment="center" valignment="top" width="0">
31427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31430 \begin_layout Plain Layout
31436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31439 \begin_layout Plain Layout
31441 \begin_inset Note Note
31444 \begin_layout Plain Layout
31451 is only used as spacer.
31463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31466 \begin_layout Plain Layout
31473 \begin_layout Plain Layout
31487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31490 \begin_layout Plain Layout
31491 \begin_inset Formula $A\gr B$
31501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31504 \begin_layout Plain Layout
31512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31515 \begin_layout Plain Layout
31516 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31529 \begin_layout Plain Layout
31533 \begin_inset Formula $\to$
31539 \begin_inset Formula $\to$
31550 \begin_layout Plain Layout
31564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31567 \begin_layout Plain Layout
31568 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31581 \begin_layout Plain Layout
31585 \begin_inset Formula $\to$
31596 \begin_layout Plain Layout
31610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31613 \begin_layout Plain Layout
31614 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31627 \begin_layout Plain Layout
31633 \begin_inset Formula $\to$
31644 \begin_layout Plain Layout
31658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31661 \begin_layout Plain Layout
31662 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31678 \begin_layout Subsection
31683 \begin_layout Plain Layout
31684 User-defined commands! Math macros
31693 \begin_layout Plain Layout
31702 \begin_layout Standard
31703 User-defined commands are especially convenient for complex expressions.
31704 When you are for example dealing in a document with quadratic equations,
31705 the same solution type occurs several times.
31706 The general form of a quadratic equation is
31707 \begin_inset Formula \[
31708 0=\lambda^{2}+p\lambda+q\]
31712 The general form of the solution is
31713 \begin_inset Formula \[
31714 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
31721 \begin_layout Standard
31722 To define a command for the solution formula where only the three parameters
31724 \begin_inset Formula $\lambda$
31728 \begin_inset Formula $p$
31732 \begin_inset Formula $q$
31735 need to be specified and the index of
31736 \begin_inset Formula $\lambda$
31739 can be given optionally, the LaTeX-preamble line is
31740 \begin_inset Newline newline
31756 \begin_inset Newline newline
31763 \begin_layout Plain Layout
31778 \begin_layout Plain Layout
31789 frac{#3^{2}}{4}-#4}}
31792 \begin_layout Standard
31793 To create with this the solution formula, the command
31794 \begin_inset Newline newline
31804 \begin_inset Formula $\to$
31810 \begin_inset Formula $\to$
31817 is inserted to a formula
31822 \begin_layout Standard
31823 The definition of the new command is unintuitive because one has to know
31824 the schemes of all used LaTeX commands, e.
31825 \begin_inset space \thinspace{}
31829 \begin_inset space \space{}
31832 that a fraction is inserted in LaTeX as
31836 frac{numerator}{denominator}
31839 Furthermore one can easily forget a brace in the definition and cannot
31840 see in LyX what the new command is doing.
31841 To avoid these problems LyX offers the possibility to use math macros instead
31851 \begin_layout Standard
31852 A math macro is created by using the menu
31854 Insert\SpecialChar \menuseparator
31855 Math\SpecialChar \menuseparator
31858 or the toolbar button
31859 \begin_inset Graphics
31860 filename ../images/math-macro_newmacroname_newcommand.png
31866 The math macro toolbar appears together with the following box where the
31868 \begin_inset Newline newline
31872 \begin_inset space \hspace*{\fill}
31876 \begin_inset Graphics
31877 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
32032 \begin_inset space \hspace*{\fill}
32036 \begin_inset Newline newline
32039 Here is our macro example with the arguments
32040 \begin_inset Formula $x$
32044 \begin_inset Formula $\ln(x)$
32048 \begin_inset Formula $B$
32054 \begin_layout Standard
32055 \begin_inset Formula \[
32063 \begin_layout Standard
32064 A math macro is transformed internally to a
32070 command when exporting the document.
32077 command is not placed in the LaTeX-preamble, therefore macros can only
32078 be used in formulas that are in the document below the macro definition
32082 \begin_layout Standard
32083 Math macros can also be directly be created from a
32090 When writing for example the command
32093 \begin_inset Newline newline
32102 xleftarrow[#2]{#1}}
32103 \begin_inset Newline newline
32108 in LyX as normal text, highlighting it completely and using then the shortcut
32113 , the command will be transformed to a math macro.
32114 Using this method you need to be careful that the
32120 command is typed correctly, otherwise you get a faulty macro leading to
32124 \begin_layout Standard
32125 Math macros currently yet have the problem that further formulas in macro
32126 definitions are handled wrongly.
32127 Therefore the example
32134 \begin_inset CommandInset ref
32136 reference "sub:The-Command-newcommand"
32140 cannot be created as macro.
32143 \begin_layout Standard
32144 When the cursor is in a macro definition box, you will see the macro toolbar
32148 \begin_layout Standard
32149 \begin_inset VSpace defskip
32155 \begin_layout Standard
32156 \begin_inset Graphics
32157 filename clipart/MacroToolbar.png
32165 \begin_layout Plain Layout
32174 \begin_layout Standard
32175 \begin_inset VSpace defskip
32181 \begin_layout Standard
32182 The macro toolbar contains from left to right the following buttons:
32185 \begin_layout Standard
32186 \begin_inset VSpace defskip
32192 \begin_layout Standard
32193 \begin_inset Tabular
32194 <lyxtabular version="3" rows="9" columns="2">
32195 <features islongtable="true">
32196 <column alignment="left" valignment="top" width="0">
32197 <column alignment="left" valignment="top" width="85col%">
32198 <row interlinespace="2.5mm">
32199 <cell alignment="center" valignment="top" usebox="none">
32202 \begin_layout Plain Layout
32203 \begin_inset Graphics
32204 filename ../images/math-macro-remove-param.png
32205 BoundingBox 0bp 5bp 20bp 25bp
32206 rotateOrigin center
32215 <cell alignment="center" valignment="top" usebox="none">
32218 \begin_layout Plain Layout
32221 Edit\SpecialChar \menuseparator
32222 Math\SpecialChar \menuseparator
32224 \begin_inset space ~
32227 Definition\SpecialChar \menuseparator
32228 Remove Last Argument
32234 <row interlinespace="2.5mm">
32235 <cell alignment="center" valignment="top" usebox="none">
32238 \begin_layout Plain Layout
32239 \begin_inset Graphics
32240 filename ../images/math-macro-add-param.png
32241 BoundingBox 0bp 5bp 20bp 25bp
32242 rotateOrigin center
32251 <cell alignment="center" valignment="top" usebox="none">
32254 \begin_layout Plain Layout
32257 Edit\SpecialChar \menuseparator
32258 Math\SpecialChar \menuseparator
32260 \begin_inset space ~
32263 Definition\SpecialChar \menuseparator
32270 <row interlinespace="2.5mm">
32271 <cell alignment="center" valignment="top" usebox="none">
32274 \begin_layout Plain Layout
32275 \begin_inset Graphics
32276 filename ../images/math-macro-make-optional.png
32277 BoundingBox 0bp 5bp 20bp 25bp
32278 rotateOrigin center
32287 <cell alignment="center" valignment="top" usebox="none">
32290 \begin_layout Plain Layout
32293 Edit\SpecialChar \menuseparator
32294 Math\SpecialChar \menuseparator
32296 \begin_inset space ~
32299 Definition\SpecialChar \menuseparator
32300 Make First Non-Optional into
32301 \begin_inset Newline newline
32308 \begin_layout Plain Layout
32317 Edit\SpecialChar \menuseparator
32318 Math\SpecialChar \menuseparator
32320 \begin_inset space ~
32323 Definition\SpecialChar \menuseparator
32328 \begin_layout Plain Layout
32341 <row interlinespace="2.5mm">
32342 <cell alignment="center" valignment="top" usebox="none">
32345 \begin_layout Plain Layout
32346 \begin_inset Graphics
32347 filename ../images/math-macro-make-nonoptional.png
32348 BoundingBox 0bp 5bp 20bp 25bp
32349 rotateOrigin center
32358 <cell alignment="center" valignment="top" usebox="none">
32361 \begin_layout Plain Layout
32364 Edit\SpecialChar \menuseparator
32365 Math\SpecialChar \menuseparator
32367 \begin_inset space ~
32370 Definition\SpecialChar \menuseparator
32371 Make Last Optional into
32372 \begin_inset Newline newline
32379 \begin_layout Plain Layout
32388 Edit\SpecialChar \menuseparator
32389 Math\SpecialChar \menuseparator
32391 \begin_inset space ~
32394 Definition\SpecialChar \menuseparator
32399 \begin_layout Plain Layout
32406 Non-Optional Argument
32412 <row interlinespace="2.5mm">
32413 <cell alignment="center" valignment="top" usebox="none">
32416 \begin_layout Plain Layout
32417 \begin_inset Graphics
32418 filename ../images/math-macro-remove-optional-param.png
32419 BoundingBox 0bp 5bp 20bp 25bp
32420 rotateOrigin center
32429 <cell alignment="center" valignment="top" usebox="none">
32432 \begin_layout Plain Layout
32435 Edit\SpecialChar \menuseparator
32436 Math\SpecialChar \menuseparator
32438 \begin_inset space ~
32441 Definition\SpecialChar \menuseparator
32442 Remove Optional Argument
32448 <row interlinespace="2.5mm">
32449 <cell alignment="center" valignment="top" usebox="none">
32452 \begin_layout Plain Layout
32453 \begin_inset Graphics
32454 filename ../images/math-macro-add-optional-param.png
32455 BoundingBox 0bp 5bp 20bp 25bp
32456 rotateOrigin center
32465 <cell alignment="center" valignment="top" usebox="none">
32468 \begin_layout Plain Layout
32471 Edit\SpecialChar \menuseparator
32472 Math\SpecialChar \menuseparator
32474 \begin_inset space ~
32477 Definition\SpecialChar \menuseparator
32478 Insert Optional Argument
32484 <row interlinespace="2.5mm">
32485 <cell alignment="center" valignment="top" usebox="none">
32488 \begin_layout Plain Layout
32489 \begin_inset Graphics
32490 filename ../images/math-macro-remove-greedy-param.png
32491 BoundingBox 0bp 5bp 20bp 25bp
32492 rotateOrigin center
32501 <cell alignment="center" valignment="top" usebox="none">
32504 \begin_layout Plain Layout
32507 Edit\SpecialChar \menuseparator
32508 Math\SpecialChar \menuseparator
32510 \begin_inset space ~
32513 Definition\SpecialChar \menuseparator
32514 Remove Last Argument
32515 \begin_inset Newline newline
32522 \begin_layout Plain Layout
32531 Edit\SpecialChar \menuseparator
32532 Math\SpecialChar \menuseparator
32534 \begin_inset space ~
32537 Definition\SpecialChar \menuseparator
32542 \begin_layout Plain Layout
32549 Spitting Out To The Right
32555 <row interlinespace="2.5mm">
32556 <cell alignment="center" valignment="top" usebox="none">
32559 \begin_layout Plain Layout
32560 \begin_inset Graphics
32561 filename ../images/math-macro-append-greedy-param.png
32562 BoundingBox 0bp 5bp 20bp 25bp
32563 rotateOrigin center
32572 <cell alignment="center" valignment="top" usebox="none">
32575 \begin_layout Plain Layout
32578 Edit\SpecialChar \menuseparator
32579 Math\SpecialChar \menuseparator
32581 \begin_inset space ~
32584 Definition\SpecialChar \menuseparator
32586 \begin_inset Newline newline
32593 \begin_layout Plain Layout
32602 Edit\SpecialChar \menuseparator
32603 Math\SpecialChar \menuseparator
32605 \begin_inset space ~
32608 Definition\SpecialChar \menuseparator
32613 \begin_layout Plain Layout
32620 Eating From The Right
32626 <row interlinespace="2.5mm">
32627 <cell alignment="center" valignment="top" usebox="none">
32630 \begin_layout Plain Layout
32631 \begin_inset Graphics
32632 filename ../images/math-macro-add-greedy-optional-param.png
32633 BoundingBox 0bp 5bp 20bp 25bp
32634 rotateOrigin center
32643 <cell alignment="center" valignment="top" usebox="none">
32646 \begin_layout Plain Layout
32649 Edit\SpecialChar \menuseparator
32650 Math\SpecialChar \menuseparator
32652 \begin_inset space ~
32655 Definition\SpecialChar \menuseparator
32656 Append Optional Argument
32657 \begin_inset Newline newline
32664 \begin_layout Plain Layout
32673 Edit\SpecialChar \menuseparator
32674 Math\SpecialChar \menuseparator
32676 \begin_inset space ~
32679 Definition\SpecialChar \menuseparator
32684 \begin_layout Plain Layout
32691 Eating From The Right
32704 \begin_layout Standard
32705 \begin_inset Newpage newpage
32711 \begin_layout Section
32715 \begin_layout Standard
32716 LyX supports two types of commutative diagrams:
32724 that are explained in the following.
32727 \begin_layout Subsection
32732 \begin_layout Plain Layout
32741 \begin_layout Standard
32742 Diagrams of this type visualize relations by vertical and horizontal lines
32744 \begin_inset Formula \[
32745 \begin{CD}A@>>>B@>>>C\\
32747 F@<<<E@<<<D\end{CD}\]
32754 \begin_layout Standard
32755 To get them, the command
32763 \begin_layout Plain Layout
32773 is inserted to a formula.
32774 A blue box appears with two dashed lines where further commands can be
32779 arg "newline-insert newline"
32782 a new line is created.
32783 Horizontal relations are inserted in odd, vertical in even formula lines.
32786 \begin_layout Standard
32787 To create the relations there are the following commands:
32790 \begin_layout Itemize
32795 creates a left arrow,
32806 \begin_layout Itemize
32811 creates an up arrow,
32819 a vertical equal sign
32822 \begin_layout Itemize
32828 is a placeholder for non-existent relations
32831 \begin_layout Standard
32832 All arrows can be labeled as follows:
32835 \begin_layout Itemize
32836 Is text inserted between the first and second < or >, resp., it is placed
32838 When it is inserted between the second and third one, it appears under
32842 \begin_layout Itemize
32843 When text for vertical arrows is inserted between the first and second A
32844 or V, resp., it is placed left beside the arrow.
32845 When it is inserted between the second and third one, it appears right
32847 If the text contains an A or V, these letters must be set into a TeX-brace.
32850 \begin_layout Standard
32851 As example a diagram with all possible relations:
32854 \begin_layout Standard
32855 \begin_inset Formula \[
32856 \begin{CD}A@>j>>B@>>k>C@=F\\
32858 D@<<j<E@>k>>F@=C\end{CD}\]
32865 \begin_layout Standard
32866 The command for this is:
32867 \begin_inset Newline newline
32878 \begin_layout Plain Layout
32887 A@>j>>B@>>k>C@=F Ctrl+Return
32888 \begin_inset Newline newline
32895 \begin_layout Plain Layout
32910 \begin_layout Plain Layout
32923 \begin_layout Plain Layout
32935 \begin_inset Formula $\to$
32941 \begin_inset Newline newline
32948 \begin_layout Plain Layout
32963 \begin_layout Plain Layout
32976 \begin_layout Plain Layout
32986 \begin_layout Subsection
32991 \begin_layout Plain Layout
32992 Diagrams ! xymatrix
33000 \begin_layout Standard
33001 To be able to use xymatrices, the LaTeX-package
33006 A xymatrix is created by inserting the command
33013 Then you are able to add new matrix columns and rows like for normal matrices,
33015 \begin_inset CommandInset ref
33017 reference "sec:Matrices"
33024 \begin_layout Standard
33025 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
33027 All possibilities to create commutative diagrams and decorations are explained
33032 that you find in the menu
33034 Help\SpecialChar \menuseparator
33036 \begin_inset space ~
33039 Manuals\SpecialChar \menuseparator
33041 \begin_inset space ~
33049 \begin_layout Standard
33050 \begin_inset Newpage newpage
33056 \begin_layout Section
33061 \begin_layout Plain Layout
33074 \begin_layout Plain Layout
33075 Other useful math tips can be found in
33076 \begin_inset CommandInset citation
33091 \begin_layout Plain Layout
33099 \begin_inset Note Note
33102 \begin_layout Plain Layout
33105 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
33108 \begin_layout Plain Layout
33111 texorpdfstring is in section
33112 \begin_inset CommandInset ref
33114 reference "sub:Formulas-in-Section"
33127 \begin_layout Plain Layout
33137 \begin_layout Plain Layout
33142 \begin_layout Plain Layout
33149 Chemical characters
33153 \begin_layout Plain Layout
33168 \begin_layout Subsection
33169 Chemical Symbols and Equations
33170 \begin_inset CommandInset label
33172 name "sub:Chemical-Symbols-and"
33180 \begin_layout Plain Layout
33181 Chemical characters ! Symbols
33190 \begin_layout Plain Layout
33200 \begin_layout Plain Layout
33209 \begin_layout Standard
33210 An example text from chemistry:
33213 \begin_layout Quote
33215 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
33218 -ion reacts with two
33219 \begin_inset Formula $\mathrm{Na^{+}}$
33222 -ions to sodium sulfate
33223 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
33227 The chemical equation for this is:
33228 \begin_inset Formula \[
33229 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
33236 \begin_layout Standard
33237 This chemical equation can directly be created as formula.
33238 To avoid that the symbols appear italic, everything is highlighted and
33239 changed by the shortcut
33245 to the upright font style.
33249 \begin_layout Plain Layout
33255 \begin_inset CommandInset ref
33257 reference "sub:Font-Styles"
33269 \begin_layout Subsection
33274 \begin_layout Plain Layout
33283 \begin_layout Standard
33284 Negative numbers often look ugly in formulas because the minus sign before
33285 the number is set with the same length as the minus operator sign.
33286 When writing the negative number in normal text, the minus sign appears
33290 \begin_layout Standard
33291 Thus, the problem disappears when converting the minus sign to mathematical
33295 \begin_layout Standard
33296 An example to visualize the problem:
33299 \begin_layout Standard
33301 \begin_inset Tabular
33302 <lyxtabular version="3" rows="3" columns="2">
33304 <column alignment="right" valignment="top" width="0">
33305 <column alignment="left" valignment="top" width="0">
33307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33310 \begin_layout Plain Layout
33316 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
33319 \begin_layout Plain Layout
33327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33330 \begin_layout Plain Layout
33336 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33339 \begin_layout Plain Layout
33340 \begin_inset Formula $x=-2$
33350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33353 \begin_layout Plain Layout
33359 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
33362 \begin_layout Plain Layout
33363 \begin_inset Formula $x=\textrm{-}2$
33379 \begin_layout Subsection
33380 Comma as decimal Separator
33384 \begin_layout Plain Layout
33393 \begin_layout Standard
33394 In LaTeX a comma inside a formula is used, according to the English convention,
33395 as number group separator.
33396 So there will be space added behind all commas in formulas.
33399 \begin_layout Standard
33400 To avoid this, the comma is highlighted and changed to mathematical text
33410 \begin_layout Standard
33411 To use all formula commas in the document as decimal separator, the file
33420 \begin_layout Plain Layout
33425 is part of the LaTeX-package
33433 \begin_layout Plain Layout
33438 \begin_layout Plain Layout
33461 \begin_layout Plain Layout
33467 is loaded with the LaTeX-preamble line
33470 \begin_layout Standard
33478 \begin_layout Subsection
33480 \begin_inset CommandInset label
33482 name "sub:Physical-Vectors"
33490 \begin_layout Plain Layout
33499 \begin_layout Standard
33500 Predefined vectors are offered by the LaTeX-package
33508 \begin_layout Plain Layout
33513 should be part of every LaTeX standard installation.
33522 \begin_layout Plain Layout
33528 that is loaded with the LaTeX-preamble line
33531 \begin_layout Standard
33539 \begin_layout Standard
33543 \begin_layout Plain Layout
33553 \begin_inset Note Note
33556 \begin_layout Plain Layout
33557 The following table will only be displayed when the LaTeX-package
33566 The following commands are defined:
33569 \begin_layout Standard
33571 \begin_inset Tabular
33572 <lyxtabular version="3" rows="4" columns="2">
33574 <column alignment="center" valignment="top" width="0">
33575 <column alignment="center" valignment="top" width="0">
33577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33580 \begin_layout Plain Layout
33586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33589 \begin_layout Plain Layout
33597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33600 \begin_layout Plain Layout
33610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33613 \begin_layout Plain Layout
33614 \begin_inset Formula $\Bra{\psi}$
33624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33627 \begin_layout Plain Layout
33637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33640 \begin_layout Plain Layout
33641 \begin_inset Formula $\Ket{\psi}$
33651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33654 \begin_layout Plain Layout
33666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33669 \begin_layout Plain Layout
33670 \begin_inset Formula $\Braket{\psi|\phi}$
33686 \begin_layout Standard
33693 assures that all vertical bars are set in the size of the surrounding brackets:
33694 \begin_inset Formula \[
33695 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
33703 \begin_layout Plain Layout
33713 \begin_inset Note Note
33716 \begin_layout Plain Layout
33717 The following will be displayed when the LaTeX-package
33729 \begin_layout Standard
33730 You need to install the LaTeX-package
33734 to see the rest of this subsection in the output.
33737 \begin_layout Standard
33741 \begin_layout Plain Layout
33753 \begin_layout Standard
33760 can also be achieved using the command
33766 , that is described in
33767 \begin_inset CommandInset ref
33769 reference "sub:Automatic-Bracket-Size"
33776 \begin_layout Subsection
33777 Self-defined Fractions
33778 \begin_inset CommandInset label
33780 name "sub:Self-defined-Fractions"
33788 \begin_layout Plain Layout
33789 Fractions ! self-defined
33797 \begin_layout Standard
33798 To define custom commands for fractions, the command
33808 \begin_layout Plain Layout
33816 is used in the following scheme:
33819 \begin_layout Standard
33832 bracket}{fraction bar thickness}{style}
33833 \begin_inset Newline newline
33840 \begin_layout Plain Layout
33855 \begin_layout Plain Layout
33862 {numerator}{denominator}
33865 \begin_layout Standard
33866 The style is a number in the range of 0
33867 \begin_inset space \thinspace{}
33871 \begin_inset space \thinspace{}
33877 \begin_layout Standard
33879 \begin_inset Tabular
33880 <lyxtabular version="3" rows="5" columns="2">
33882 <column alignment="center" valignment="top" width="0">
33883 <column alignment="center" valignment="top" width="0">
33885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33888 \begin_layout Plain Layout
33894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33897 \begin_layout Plain Layout
33905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33908 \begin_layout Plain Layout
33914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33917 \begin_layout Plain Layout
33918 display style formula
33925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33928 \begin_layout Plain Layout
33934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33937 \begin_layout Plain Layout
33945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33948 \begin_layout Plain Layout
33954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33957 \begin_layout Plain Layout
33965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33968 \begin_layout Plain Layout
33974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33977 \begin_layout Plain Layout
33991 \begin_layout Standard
33992 When no style is given, the size is adjusted to the surrounding environment
33993 like for the command
34002 \begin_layout Standard
34003 When no fraction bar thickness is given, the predefined value of 0.4
34004 \begin_inset space \thinspace{}
34010 \begin_layout Standard
34011 \begin_inset VSpace medskip
34014 For example, the commands
34027 \begin_inset CommandInset ref
34029 reference "sub:Fractions"
34033 are defined with the commands
34036 \begin_layout Standard
34045 genfrac{}{}{}{0}{#1}{#2}}
34048 \begin_layout Standard
34052 \begin_layout Standard
34061 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34064 \begin_layout Standard
34065 \begin_inset VSpace medskip
34068 To define a fraction where the fraction bar thickness can be given as optional
34069 argument, the following line is inserted to the LaTeX-preamble:
34072 \begin_layout Standard
34081 genfrac{}{}{#1}{}{#2}{#3}}
34084 \begin_layout Standard
34086 \begin_inset Formula \begin{align*}
34087 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34088 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34092 As one can see, the distance of the numerator and the denominator to the
34093 fraction bar is round about three times the bar thickness.
34096 \begin_layout Subsection
34101 \begin_layout Plain Layout
34110 \begin_layout Standard
34111 To cancel formulas or formula parts, the LaTeX-package
34119 \begin_layout Plain Layout
34124 is part of every LaTeX standard installation.
34133 \begin_layout Plain Layout
34139 has to be loaded with the LaTeX-preamble line
34142 \begin_layout Standard
34147 usepackage[samesize]{cancel}
34150 \begin_layout Standard
34151 There are four ways to cancel formulas:
34154 \begin_layout Standard
34156 \begin_inset Tabular
34157 <lyxtabular version="3" rows="5" columns="2">
34159 <column alignment="center" valignment="top" width="0">
34160 <column alignment="center" valignment="top" width="0">
34162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34165 \begin_layout Plain Layout
34171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34174 \begin_layout Plain Layout
34176 \begin_inset Note Note
34179 \begin_layout Plain Layout
34186 are used here as spacer.
34198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34201 \begin_layout Plain Layout
34210 \begin_layout Plain Layout
34224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34227 \begin_layout Plain Layout
34228 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34241 \begin_layout Plain Layout
34250 \begin_layout Plain Layout
34264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34267 \begin_layout Plain Layout
34268 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
34278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34281 \begin_layout Plain Layout
34290 \begin_layout Plain Layout
34304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34307 \begin_layout Plain Layout
34308 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
34318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34321 \begin_layout Plain Layout
34325 \begin_inset Formula $\to$
34336 \begin_layout Plain Layout
34350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34353 \begin_layout Plain Layout
34354 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
34370 \begin_layout Standard
34377 is especially suitable to visualize the reduction of fractions within formulas:
34378 \begin_inset Formula \[
34379 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
34386 \begin_layout Subsection
34387 Formulas in Section Headings
34388 \begin_inset CommandInset label
34390 name "sub:Formulas-in-Section"
34398 \begin_layout Plain Layout
34399 Formula ! in section headings
34407 \begin_layout Standard
34408 When formulas are used in section headings, the following has to be taken
34412 \begin_layout Standard
34413 \begin_inset Note Greyedout
34416 \begin_layout Plain Layout
34425 \begin_layout Plain Layout
34426 Packages ! hyperref
34431 support is enabled in the document settings dialog under
34434 \begin_inset space ~
34439 , PDF-bookmarks are created for every section heading in the table of contents.
34440 If a section heading contains formulas, they are incorrectly displayed
34441 in the bookmark text, because formulas in bookmarks infringe the PDF convention
34450 \begin_layout Standard
34451 Both problems can be solved by inserting at the end of the section heading
34452 a short title with the menu
34454 Insert\SpecialChar \menuseparator
34456 \begin_inset space ~
34462 Short titles are used as alternative for multiline section headings to
34463 keep the table of contents clearly arranged.
34464 Only the short title appears in the table of contents and therefore also
34465 in the PDF-bookmark.
34468 \begin_layout Standard
34469 When formulas should be used in the table of contents but
34473 is used, one can use the following command in TeX-mode:
34476 \begin_layout Standard
34481 texorpdfstring{part}{alternative}
34485 \begin_layout Plain Layout
34496 \begin_layout Standard
34497 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
34498 This can be characters, formulas, footnotes, but also cross-references.
34499 The alternative is used instead of the part for the bookmark.
34502 \begin_layout Standard
34503 Here are two example headings:
34504 \begin_inset VSpace -3mm
34511 \begin_layout Plain Layout
34523 \begin_layout Subsubsection
34524 Heading without formula in table of contents
34525 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34529 \begin_inset OptArg
34532 \begin_layout Plain Layout
34533 Heading without formula in table of contents
34541 \begin_layout Subsubsection
34542 Heading with formula in table of contents
34546 \begin_layout Plain Layout
34556 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
34563 \begin_layout Plain Layout
34573 \begin_layout Standard
34577 \begin_layout Plain Layout
34586 In the first heading a short title was used, in the second one
34595 \begin_layout Standard
34596 To get the same formatting as for the other headings, the complete heading
34605 \begin_layout Plain Layout
34607 \begin_inset CommandInset ref
34609 reference "sub:Bold-Formulas"
34621 \begin_layout Subsection
34622 Formulas in multi-column Text
34626 \begin_layout Plain Layout
34627 Formula ! in multi-column text
34635 \begin_layout Standard
34636 Formulas in multi-column text are often too wide to fit into a column and
34637 thus need to be set over the whole page width.
34638 This is done by using the LaTeX-package
34646 \begin_layout Plain Layout
34651 is part of every LaTeX standard installation.
34660 \begin_layout Plain Layout
34661 Packages ! multicol
34666 , that is loaded with the LaTeX-preamble line
34669 \begin_layout Standard
34674 usepackage{multicol}
34677 \begin_layout Standard
34678 \begin_inset Note Greyedout
34681 \begin_layout Plain Layout
34682 Note herby that the setting
34685 \begin_inset space ~
34692 Document\SpecialChar \menuseparator
34698 \begin_inset space ~
34718 \begin_layout Standard
34719 Before the multi-column text the command
34722 \begin_layout Standard
34727 begin{multicols}{column number}
34730 \begin_layout Standard
34731 is written in TeX-mode.
34732 The column number is a number in the range of 2
34733 \begin_inset space \thinspace{}
34737 \begin_inset space \thinspace{}
34741 Before the formula the multi-column text is ended by inserting the command
34744 \begin_layout Standard
34752 \begin_layout Standard
34756 \begin_layout Standard
34757 Due to the command some space is automatically added before the formula.
34759 \begin_inset space \thinspace{}
34762 mm vertical space is inserted before the formula.
34763 When the formula style
34769 \begin_layout Plain Layout
34771 \begin_inset CommandInset ref
34773 reference "sec:Formula-Styles"
34785 \begin_inset space \thinspace{}
34788 mm space is inserted instead.
34791 \begin_layout Standard
34792 As example a multi-column text with a displayed formula:
34795 \begin_layout Standard
34799 \begin_layout Plain Layout
34803 begin{multicols}{2}
34808 Das Spektrum wird fouriertransformiert.
34809 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34810 , Lösungsmittel) zu trennen.
34811 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34812 nun das Aussehen des Ausgangssignals.
34813 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34814 über alle Phasen integrieren muss.
34816 \begin_inset Formula $S$
34819 unser normiertes Ausgangssignal and
34820 \begin_inset Formula $P$
34823 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34827 \begin_layout Plain Layout
34837 \begin_inset VSpace -6mm
34841 \begin_inset Formula \begin{equation}
34842 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
34850 \begin_layout Plain Layout
34854 begin{multicols}{2}
34860 \begin_inset Formula $S_{0}$
34863 das Signal ohne Gradient ist and the Normierungsbedingung
34864 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34868 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34870 \begin_inset Formula $\nicefrac{\pi}{2}$
34874 \begin_inset space \thinspace{}
34877 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34878 das Signal zusätzlich abschwächt.
34879 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34881 \begin_inset Formula $T_{2}$
34887 \begin_layout Standard
34891 \begin_layout Plain Layout
34903 \begin_layout Subsection
34904 Formulas with Description of Variables
34908 \begin_layout Plain Layout
34909 Formula ! with description of variables
34917 \begin_layout Standard
34918 To describe variables within a formula, like in formula
34919 \begin_inset CommandInset ref
34921 reference "eq:within"
34930 \begin_inset Formula $n$
34934 \begin_inset space ~
34937 matrix is used with left aligned columns for the
34938 \begin_inset Formula $n$
34945 \begin_layout Plain Layout
34947 \begin_inset CommandInset ref
34949 reference "sec:Matrices"
34958 To set the description in a smaller size, before the matrix e.
34959 \begin_inset space \thinspace{}
34963 \begin_inset space \space{}
34976 \begin_layout Plain Layout
34978 \begin_inset CommandInset ref
34980 reference "sub:Font-Sizes"
34992 \begin_layout Standard
34993 When the formula style
34999 \begin_layout Plain Layout
35001 \begin_inset CommandInset ref
35003 reference "sec:Formula-Styles"
35024 \begin_layout Plain Layout
35031 only works in formulas with the style
35036 \begin_inset CommandInset ref
35038 reference "sub:Variable-Space"
35047 is inserted before and after the matrix to have the same separation of
35048 the matrix from the equation and the side margin.
35051 \begin_layout Standard
35052 When the formula style
35056 is used, the method described in
35057 \begin_inset CommandInset ref
35059 reference "sub:Flalign-Environment"
35063 is used to indent formulas.
35065 \begin_inset CommandInset ref
35067 reference "eq:within"
35071 consists of five columns whereas in the first two columns contain the equation,
35072 the third the matrix, and the last one an empty TeX-brace.
35073 \begin_inset Formula \begin{flalign}
35074 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35075 \rho & \textrm{density}\\
35076 V & \textrm{volume}\\
35077 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35084 \begin_layout Subsection
35085 Upright small Greek Letters
35086 \begin_inset CommandInset label
35088 name "sub:Upright-small-Greek"
35096 \begin_layout Plain Layout
35097 Greek letters ! upright
35105 \begin_layout Standard
35106 Most of the math fonts only provide italic small Greek letters.
35107 But for symbols of elementary particles like pions and neutrinos, upright
35108 Greek letters are needed.
35117 \begin_layout Plain Layout
35122 is part of the LaTeX-package
35130 \begin_layout Plain Layout
35135 \begin_layout Plain Layout
35158 \begin_layout Plain Layout
35164 that is loaded with the LaTeX-preamble line
35167 \begin_layout Standard
35172 usepackage{upgreek}
35175 \begin_layout Standard
35181 \begin_layout Plain Layout
35191 \begin_inset Note Note
35194 \begin_layout Plain Layout
35195 The following table will only be displayed when the LaTeX-package
35204 They are created when the command for a small Greek letters is started
35210 For example the command
35217 \begin_inset Formula $\uptau$
35223 \begin_layout Standard
35224 With these commands reactions of elementary particles can be typeset:
35225 \begin_inset Formula \[
35226 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35233 \begin_layout Standard
35234 The upright letters are more bold and wider than the italic ones.
35235 They should therefore not be used for units like
35236 \begin_inset Quotes eld
35240 \begin_inset Quotes erd
35246 \begin_layout Standard
35250 \begin_layout Plain Layout
35260 \begin_inset Note Note
35263 \begin_layout Plain Layout
35264 The following will be displayed when the LaTeX-package
35276 \begin_layout Standard
35277 You need to install the LaTeX-package
35281 to see the rest of this subsection in the output.
35284 \begin_layout Standard
35288 \begin_layout Plain Layout
35300 \begin_layout Subsection
35301 Text Characters in Formulas
35302 \begin_inset CommandInset label
35304 name "sub:Text-Characters-in"
35312 \begin_layout Plain Layout
35321 \begin_layout Standard
35322 In some cases you might want to insert text characters directly into formulas.
35323 When for example the centered dot · is often used in formulas like
35324 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
35327 , one would have to insert the command
35337 \begin_layout Plain Layout
35339 \begin_inset CommandInset ref
35341 reference "sub:Binary-Operators"
35350 all the time, because this character is defined in all encodings as text
35352 But the encoding can be changed by this LaTeX-preamble line:
35355 \begin_layout Standard
35360 Declare Inputtext{183}{
35370 f\SpecialChar \textcompwordmark{}
35374 \begin_layout Standard
35375 The character encoding (menu
35377 Document\SpecialChar \menuseparator
35378 Settings\SpecialChar \menuseparator
35381 ) specifies what character appears when a keyboard key is pressed.
35382 When the key for the character '·' is pressed, internally the command
35389 But this command is not available in a formula so that you would get LaTeX-erro
35391 With the changed encoding the right command is chosen automatically, depending
35392 on if the character was inserted into a formula or not.
35395 \begin_layout Standard
35396 The encoding of several characters is saved in definition files.
35397 Fore example the encoding
35401 is defined in the file
35405 that is in the installation folder of LaTeX.
35406 Encodings should only be changed via the LaTeX-preamble and not in the
35408 Otherwise own documents could not be edited by other LyX users working
35409 on other computers.
35412 \begin_layout Standard
35413 \begin_inset VSpace medskip
35416 Besides the centered dot, in this document the degree sign ° is defined
35417 with the following LaTeX-preamble line so that it can directly be inserted
35421 \begin_layout Standard
35426 DeclareInputtext{176}{
35436 f\SpecialChar \textcompwordmark{}
35440 \begin_layout Standard
35441 \begin_inset Newpage newpage
35447 \begin_layout Section
35453 \begin_layout Plain Layout
35462 \begin_layout Standard
35463 This section is a summary of the most important typographic rules, listed
35468 \begin_layout Plain Layout
35469 This collection was partly taken from the German semi-official dictionary
35471 \begin_inset Quotes eld
35475 \begin_inset Quotes erd
35479 \begin_inset CommandInset citation
35485 that lists some of the ISO rules.
35493 \begin_layout Itemize
35502 \begin_layout Plain Layout
35503 done with font styles, see
35504 \begin_inset CommandInset ref
35506 reference "sub:Font-Styles"
35516 \begin_inset space \thinspace{}
35520 \begin_inset Newline newline
35523 Between the value and the unit is the smallest space, see
35524 \begin_inset CommandInset ref
35526 reference "sub:Predefined-Space"
35531 \begin_inset Newline newline
35534 This convention is automatically fulfilled when the command
35541 When it is entered to a formula, two boxes appear.
35542 In the first one the value is inserted, in the second one the unit, and
35544 \begin_inset Formula $\unit[30]{km/h}$
35548 \begin_inset space \thinspace{}
35558 is not a real LaTeX command but the command
35564 , therefore you cannot use it in TeX code.
35567 \begin_layout Itemize
35568 Percent and perthousand signs are set like physical units:
35569 \begin_inset Newline newline
35573 \begin_inset space \thinspace{}
35579 \begin_layout Itemize
35580 The degree sign follows directly on the value: 15°, but not when it is used
35582 \begin_inset space \thinspace{}
35588 \begin_layout Itemize
35589 In numbers with more than four digits the smallest space is inserted before
35590 every third digit to group them:
35600 \begin_inset space \thinspace{}
35604 \begin_inset space \thinspace{}
35610 \begin_layout Itemize
35611 For dimensions like 120×90×40
35612 \begin_inset space \thinspace{}
35615 cm the multiplication sign
35616 \begin_inset Quotes eld
35620 \begin_inset Quotes erd
35624 It is available via the menu
35626 Insert\SpecialChar \menuseparator
35627 Special Character\SpecialChar \menuseparator
35631 With some keyboard definitions it can also be inserted directly.
35634 \begin_layout Itemize
35635 Functions with names consisting of several letters are set upright to avoid
35637 \begin_inset CommandInset ref
35639 reference "sub:Predefined-Functions"
35646 \begin_layout Itemize
35647 Indices consisting of several letters, are set upright:
35648 \begin_inset Formula $E_{\mathrm{kin}}$
35652 \begin_inset Newline newline
35655 Components of matrices are set italic:
35656 \begin_inset Formula $\hat{H}_{kl}$
35662 \begin_layout Itemize
35663 The differentiation/integration operator 'd', the Euler's number 'e', and
35664 the imaginary unit 'i' should be set upright, to avoid mixing them up with
35668 \begin_layout Standard
35669 \begin_inset Newpage newpage
35675 \begin_layout Section
35680 \begin_layout Plain Layout
35689 \begin_layout Standard
35690 Some characters and symbols can be created with several commands.
35691 Here is a list of the synonym commands:
35694 \begin_layout Standard
35695 \begin_inset VSpace bigskip
35699 \begin_inset space \hfill{}
35703 \begin_inset Tabular
35704 <lyxtabular version="3" rows="12" columns="2">
35706 <column alignment="center" valignment="top" width="0pt">
35707 <column alignment="center" valignment="top" width="0pt">
35709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35712 \begin_layout Plain Layout
35718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35721 \begin_layout Plain Layout
35723 \begin_inset Note Note
35726 \begin_layout Plain Layout
35733 is only used as spacer.
35745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35748 \begin_layout Plain Layout
35756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35759 \begin_layout Plain Layout
35763 \begin_layout Plain Layout
35776 \begin_layout Plain Layout
35790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35793 \begin_layout Plain Layout
35801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35804 \begin_layout Plain Layout
35814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35817 \begin_layout Plain Layout
35825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35828 \begin_layout Plain Layout
35838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35841 \begin_layout Plain Layout
35849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35852 \begin_layout Plain Layout
35860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35863 \begin_layout Plain Layout
35871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35874 \begin_layout Plain Layout
35882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35885 \begin_layout Plain Layout
35893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35896 \begin_layout Plain Layout
35906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35909 \begin_layout Plain Layout
35917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35920 \begin_layout Plain Layout
35930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35933 \begin_layout Plain Layout
35941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35944 \begin_layout Plain Layout
35954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35957 \begin_layout Plain Layout
35965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35968 \begin_layout Plain Layout
35978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35981 \begin_layout Plain Layout
35989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35992 \begin_layout Plain Layout
36000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36003 \begin_layout Plain Layout
36011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36014 \begin_layout Plain Layout
36026 \begin_inset space \hfill{}
36030 \begin_inset Tabular
36031 <lyxtabular version="3" rows="12" columns="2">
36033 <column alignment="center" valignment="top" width="0pt">
36034 <column alignment="center" valignment="top" width="0pt">
36036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36039 \begin_layout Plain Layout
36045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36048 \begin_layout Plain Layout
36056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36059 \begin_layout Plain Layout
36067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36070 \begin_layout Plain Layout
36082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36085 \begin_layout Plain Layout
36093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36096 \begin_layout Plain Layout
36106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36109 \begin_layout Plain Layout
36117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36120 \begin_layout Plain Layout
36130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36133 \begin_layout Plain Layout
36141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36144 \begin_layout Plain Layout
36152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36155 \begin_layout Plain Layout
36163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36166 \begin_layout Plain Layout
36174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36177 \begin_layout Plain Layout
36185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36188 \begin_layout Plain Layout
36198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36201 \begin_layout Plain Layout
36209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36212 \begin_layout Plain Layout
36222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36225 \begin_layout Plain Layout
36233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36236 \begin_layout Plain Layout
36246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36249 \begin_layout Plain Layout
36257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36260 \begin_layout Plain Layout
36270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36273 \begin_layout Plain Layout
36281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36284 \begin_layout Plain Layout
36294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36297 \begin_layout Plain Layout
36305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36308 \begin_layout Plain Layout
36322 \begin_inset space \hfill{}
36328 \begin_layout Standard
36329 \begin_inset Newpage newpage
36335 \begin_layout Bibliography
36336 \begin_inset CommandInset bibitem
36337 LatexCommand bibitem
36349 The LaTeX Companion
36352 Addison Wesley, 2004
36355 \begin_layout Bibliography
36356 \begin_inset CommandInset bibitem
36357 LatexCommand bibitem
36363 \begin_inset CommandInset href
36366 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
36370 of LaTeX's math abilities
36373 \begin_layout Bibliography
36374 \begin_inset CommandInset bibitem
36375 LatexCommand bibitem
36380 LaTeX tips and tricks-
36381 \begin_inset CommandInset href
36384 target "http://tug.org/TeXnik/"
36391 \begin_layout Bibliography
36392 \begin_inset CommandInset bibitem
36393 LatexCommand bibitem
36399 \begin_inset CommandInset href
36402 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
36410 \begin_layout Plain Layout
36422 \begin_layout Bibliography
36423 \begin_inset CommandInset bibitem
36424 LatexCommand bibitem
36430 \begin_inset CommandInset href
36433 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
36437 of all symbols available with LaTeX-packages
36440 \begin_layout Bibliography
36441 \begin_inset CommandInset bibitem
36442 LatexCommand bibitem
36448 \begin_inset CommandInset href
36450 name "Documentation"
36451 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
36455 of the LaTeX-package
36463 \begin_layout Plain Layout
36464 Packages ! hyperref
36472 \begin_layout Bibliography
36473 \begin_inset CommandInset bibitem
36474 LatexCommand bibitem
36480 \begin_inset CommandInset href
36483 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
36494 \begin_inset CommandInset ref
36496 reference "sub:Operator-Limits"
36504 \begin_layout Plain Layout
36515 \begin_layout Bibliography
36516 \begin_inset CommandInset bibitem
36517 LatexCommand bibitem
36528 Auflage, Duden 2001
36531 \begin_layout Subsubsection*
36532 \begin_inset CommandInset index_print
36533 LatexCommand printindex