1 #LyX 1.6.0alpha1 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
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 % link all cross references and URLs
27 \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
28 bookmarksopen, bookmarksopenlevel=1,
29 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
30 pdfpagelayout=OneColumn, pdfnewwindow=true,
31 pdfstartview=XYZ, plainpages=false, pdfpagelabels,
32 pdfauthor={LyX Team}, pdftex,
33 pdftitle={LyX's Math Manual},
34 pdfsubject={LyX-documentation about math},
35 pdfkeywords={LyX, Mathed}]{hyperref}
37 \else % if dvi or ps is produced
39 % link all cross references and URLs in DVI output
40 \usepackage[ps2pdf, colorlinks=true,
41 linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
43 \fi % end if pdflatex is used
45 % Folgendes Problem lösen:
46 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
47 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
48 % die Kapitelnummer geschrieben.
49 % Als Lösung wird mehr Platz zwischen Nummer und
50 % Überschrift eingefügt.
51 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
52 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
54 % To be able to enter the character ° and · directly in LyX,
56 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
57 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
59 % increase link area for cross-references and autoname them,
61 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
62 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
63 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
64 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
66 \settowidth{\abc}{\space}
67 \renewcommand{\equationautorefname}{\hspace{-\abc}}
69 % don't load packages twice
70 % see first footnote in sec. 9.3
71 \@ifundefined{textcolor}{\usepackage{color}}{}
73 % the pages of the TOC are numbered roman
74 % and a PDF-bookmark for the TOC is added
76 \let\myTOC\tableofcontents
77 \renewcommand{\tableofcontents}{%
79 \pdfbookmark[1]{Contents}{}
82 \pagenumbering{arabic}}
84 % insert additional vertical space of 1.5 mm between footnotes,
87 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
89 % provides caption formatting
90 \setkomafont{captionlabel}{\bfseries}
96 \usepackage[samesize]{cancel}
98 % enables calculation of values,
101 % for multiple table row and column cells
102 \usepackage{multirow}
103 \usepackage{multicol}
105 % needed for diagrams
108 % needed in sec. 19.4
109 \usepackage{remreset}
111 % center multirows (e.g. in sec. 13.3)
112 \renewcommand{\multirowsetup}{\centering}
114 % define a color, used in sec.9.3
115 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
117 % declare operators (see sec. 10.4 and sec. 15.2)
118 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
119 \DeclareMathOperator{\sgn}{sgn}
121 \newcommand{\spce}{\textvisiblespace}
123 % example definitions for sec. 20.1
124 \newcommand{\gr}{\Longrightarrow}
125 \newcommand{\us}[1]{\underline{#1}}
126 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
127 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
128 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
130 % example macro from sec. 19.4
131 %\def\tagform@#1{\maketag@@@{|#1|}}
133 % macro from sec. 10.2
134 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
135 \def\mathclap {\mathpalette \mathclapinternal}
136 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
138 % redefine the greyed out note
139 \renewenvironment{lyxgreyedout}
140 {\textcolor{blue}\bgroup}{\egroup}
142 % check for package eurosym
143 % used for the Euro symbol
145 \IfFileExists{eurosym.sty}
146 {\usepackage[gennarrow]{eurosym}
147 \setboolean{eurosym}{true}}
148 {\setboolean{eurosym}{false}}
150 % needed in sec. 22.4
151 % check for package braket
153 \IfFileExists{braket.sty}
155 \setboolean{braket}{true}}
156 {\setboolean{braket}{false}}
158 % needed in sec. 22.10
159 % check for package upgreek
161 \IfFileExists{upgreek.sty}
162 {\usepackage{upgreek}
163 \setboolean{upgreek}{true}}
164 {\setboolean{upgreek}{false}}
166 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
171 \font_typewriter default
172 \font_default_family default
187 \paperorientation portrait
190 \paragraph_separation skip
192 \quotes_language english
195 \paperpagestyle plain
199 \tracking_changes false
200 \output_changes false
203 \extra_embedded_files ""
209 LyX's detailed Math manual
217 \begin_layout Plain Layout
219 If you have comments or error corrections, please send them to the LyX Documenta
226 \begin_layout Plain Layout
230 href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
235 lyx-docs@lists.lyx.org
239 \begin_layout Plain Layout
252 \begin_inset Note Note
255 \begin_layout Plain Layout
262 \begin_inset Newline newline
266 \begin_inset Newline newline
274 \begin_layout Standard
275 \begin_inset CommandInset toc
276 LatexCommand tableofcontents
283 \begin_layout Standard
284 \begin_inset Note Note
287 \begin_layout Plain Layout
288 To export this document to PDF, PS, or DVI the LaTeX-packages
301 If they are not installed you can export the document anyway but the sections
302 where the packages are required won't appear in the output.
305 \begin_layout Plain Layout
306 The latest PDF-version of this document can be found here:
307 \begin_inset Newline newline
312 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
320 \begin_layout Standard
321 \begin_inset Newpage newpage
327 \begin_layout Section
329 \begin_inset CommandInset label
331 name "sec:Introduction"
338 \begin_layout Standard
339 This document explains LyX's math features and is furthermore a collection
340 of LaTeX-commands used for mathematical characters and constructs.
341 The explanations are designed for the usage of commands.
342 It is therefore required that you have read the section
353 \begin_layout Standard
354 Most of the characters and many constructs explained in this manual are
355 also accessible via the menu
359 \SpecialChar \menuseparator
375 But everybody who has to write lots of formulas will notice that it is
376 much faster to use commands instead of the math toolbar.
377 Therefore this manual is focused on commands but also mentions the correspondin
378 g toolbar buttons when available.
381 \begin_layout Standard
382 If not specially mentioned the commands are only available within formulas.
383 To be able to use all commands explained in this document, the option
387 must be used in the document settings (menu
389 Document\SpecialChar \menuseparator
390 Settings\SpecialChar \menuseparator
401 \begin_layout Plain Layout
404 Use AMS math package automatically
410 \begin_layout Plain Layout
419 -math when math constructs are found that are supported by LyX.
427 \begin_layout Standard
428 This document doesn't list all
432 \begin_layout Plain Layout
445 \begin_layout Plain Layout
450 \begin_layout Plain Layout
459 -math commands is in the file
463 \begin_layout Plain Layout
467 href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
480 \begin_layout Plain Layout
487 , which is part of every LaTeX standard installation.
492 for lucidity reasons.
495 \begin_layout Section
497 \begin_inset CommandInset label
499 name "sec:General-Instructions"
506 \begin_layout Standard
507 To create an inline formula
511 \begin_layout Plain Layout
517 that is embedded into a text line, press
521 or the toolbar button
522 \begin_inset Graphics
523 filename ../images/math-mode.png
530 \begin_inset Newline newline
533 To create a display style formula
537 \begin_layout Plain Layout
538 Formula ! display style
543 that will appear bigger and in an own paragraph, press
550 \begin_layout Standard
551 To change a display style formula to an inline formula, set the cursor into
552 the formula and press
558 Edit\SpecialChar \menuseparator
559 Math\SpecialChar \menuseparator
563 The same way is used to change an inline formula to a display style formula.
566 \begin_layout Standard
567 To display parts of an inline formula in the size of a display style formula,
576 \begin_layout Plain Layout
587 Then a new blue box appears in which the desired formula part is inserted.
590 \begin_layout Standard
591 Only inline formulas are allowed inside tables.
594 \begin_layout Standard
599 can be turned on in the menu
601 View\SpecialChar \menuseparator
605 When you click there on
606 \begin_inset Quotes eld
610 \begin_inset Quotes erd
613 the toolbar will be shown permanently at the bottom; this state is visualized
618 menu with a checkmark.
619 When you click in this state again on
620 \begin_inset Quotes eld
624 \begin_inset Quotes erd
635 is only shown when the cursor is within a formula; this state is visualized
636 by the renaming of the menu entry from
637 \begin_inset Quotes eld
641 \begin_inset Quotes erd
645 \begin_inset Quotes eld
653 \begin_inset Quotes erd
659 \begin_layout Standard
664 \begin_layout Plain Layout
669 \begin_layout Plain Layout
677 \begin_layout Plain Layout
688 \begin_layout Plain Layout
705 is invoked by pressing the toolbar button
706 \begin_inset Graphics
707 filename ../images/ert-insert.png
715 Insert\SpecialChar \menuseparator
720 \begin_layout Plain Layout
731 \begin_layout Plain Layout
745 \begin_inset Note Note
748 \begin_layout Plain Layout
749 In LyX there are three
750 \begin_inset Quotes eld
754 \begin_inset Quotes erd
757 that appear in the output with sub- and superscript letters: TeX, LaTeX,
761 \begin_layout Plain Layout
762 To avoid that these names are recognized as proper names, TeX-braces are
763 set around one of the letters of the name.
771 \begin_layout Standard
772 To change the LaTeX-preamble
776 \begin_layout Plain Layout
784 Document\SpecialChar \menuseparator
785 Settings\SpecialChar \menuseparator
790 \begin_layout Plain Layout
801 \begin_layout Plain Layout
817 \begin_layout Standard
818 To edit matrices, case differentiations, and multiline formulas subsequently,
821 Edit\SpecialChar \menuseparator
826 Edit\SpecialChar \menuseparator
828 \begin_inset Space \thinspace{}
832 \begin_inset Space \thinspace{}
842 When lines and columns are swapped via the menu, the column or line where
843 the cursor is in is exchanged with the column to the right or the line
845 Is the cursor in the last column or row, the exchange is done with the
846 column to the left or the line above.
849 \begin_layout Standard
850 To write text in formulas
854 \begin_layout Plain Layout
855 For multiline formulas the command
862 \begin_inset CommandInset ref
864 reference "sub:Text-in-multiline"
881 \begin_layout Plain Layout
891 \begin_layout Plain Layout
898 This mode is invoked with the the shortcut
906 or by the insertion of the command
914 \begin_layout Plain Layout
925 The text appears black in LyX and can therefore be distinguished from the
926 other formula parts that appear blue.
927 In the output mathematical text is set upright, in contrary to other formula
931 \begin_layout Subsection*
935 \begin_layout Standard
936 Most of the LaTeX-commands for math constructs have the following scheme:
939 \begin_layout Standard
955 \begin_layout Standard
956 A command starts always with a backslash
957 \begin_inset Quotes gld
967 \begin_inset Quotes grd
971 To omit optional arguments, also omit the associated brackets.
972 The braces around the required arguments are named in this document as
977 \begin_layout Plain Layout
982 \begin_layout Plain Layout
990 \begin_layout Plain Layout
1001 \begin_layout Plain Layout
1019 If you add in a formula a left brace to a command name, LyX creates automatical
1021 In all other cases TeX-braces are created in formulas with the command
1029 TeX-braces appear red in LyX, in contrary to normal braces that appear
1031 In TeX-mode no command is needed to get TeX-braces.
1032 TeX-braces don't appear in the output.
1035 \begin_layout Standard
1036 When commands without arguments, like commands for symbols are entered in
1037 TeX-mode, a space character must
1041 be behind the command to end it.
1042 This space doesn't appear in the output.
1043 When the space should appear in the output, the space must be followed
1044 by a protected space in normal text.
1047 \begin_layout Standard
1048 A protected space is inserted with
1055 \begin_layout Subsection*
1056 \begin_inset Newpage newpage
1062 \begin_layout Itemize
1067 \begin_layout Plain Layout
1068 This visible space character can be created with the command
1078 \begin_layout Plain Layout
1086 , inserted in TeX-mode.
1095 \begin_layout Plain Layout
1105 \begin_inset Space ~
1108 denotes a space character to be input.
1111 \begin_layout Itemize
1113 \begin_inset Formula $\to$
1116 denotes the usage of the corresponding arrow key on the keyboard.
1119 \begin_layout Subsection*
1123 \begin_layout Standard
1125 \begin_inset Float table
1131 \begin_layout Plain Layout
1133 \begin_inset Caption
1135 \begin_layout Plain Layout
1136 \begin_inset CommandInset label
1138 name "tab:Used-units"
1150 \begin_layout Plain Layout
1152 \begin_inset Tabular
1153 <lyxtabular version="3" rows="13" columns="2">
1155 <column alignment="center" valignment="top" width="0">
1156 <column alignment="center" valignment="top" width="0">
1158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1161 \begin_layout Plain Layout
1167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1170 \begin_layout Plain Layout
1178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1181 \begin_layout Plain Layout
1187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1190 \begin_layout Plain Layout
1198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1201 \begin_layout Plain Layout
1207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1210 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1221 \begin_layout Plain Layout
1227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1230 \begin_layout Plain Layout
1232 \begin_inset Space \thinspace{}
1236 \begin_inset Space \thinspace{}
1246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1249 \begin_layout Plain Layout
1255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1258 \begin_layout Plain Layout
1260 \begin_inset Space \thinspace{}
1264 \begin_inset Space \thinspace{}
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1277 \begin_layout Plain Layout
1283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1286 \begin_layout Plain Layout
1288 \begin_inset Space \thinspace{}
1292 \begin_inset Space \thinspace{}
1302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1305 \begin_layout Plain Layout
1311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1314 \begin_layout Plain Layout
1316 \begin_inset Space \thinspace{}
1320 \begin_inset Space \thinspace{}
1330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1333 \begin_layout Plain Layout
1339 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1342 \begin_layout Plain Layout
1344 \begin_inset Space \thinspace{}
1348 \begin_inset Space \thinspace{}
1358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1361 \begin_layout Plain Layout
1367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1370 \begin_layout Plain Layout
1372 \begin_inset Space \thinspace{}
1376 \begin_inset Formula $\approx$
1380 \begin_inset Space \thinspace{}
1390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1393 \begin_layout Plain Layout
1399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1402 \begin_layout Plain Layout
1404 \begin_inset Space \thinspace{}
1408 \begin_inset Space \thinspace{}
1418 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1421 \begin_layout Plain Layout
1427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1430 \begin_layout Plain Layout
1434 \begin_inset Quotes eld
1440 \begin_inset Quotes erd
1450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1453 \begin_layout Plain Layout
1459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1462 \begin_layout Plain Layout
1464 \begin_inset Quotes eld
1472 \begin_inset Quotes erd
1482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1485 \begin_layout Plain Layout
1491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1494 \begin_layout Plain Layout
1496 \begin_inset Space \thinspace{}
1500 \begin_inset Formula $\nicefrac{1}{18}$
1504 \begin_inset Space \thinspace{}
1525 \begin_layout Standard
1526 \begin_inset Newpage newpage
1532 \begin_layout Section
1536 \begin_layout Subsection
1541 \begin_layout Plain Layout
1551 \begin_layout Plain Layout
1561 \begin_layout Plain Layout
1566 \begin_layout Plain Layout
1577 \begin_layout Plain Layout
1593 \begin_layout Plain Layout
1598 \begin_layout Plain Layout
1609 \begin_layout Plain Layout
1624 \begin_layout Standard
1625 Indices are created with an underscore
1626 \begin_inset Quotes eld
1630 \begin_inset Quotes erd
1633 or via the math toolbar button
1634 \begin_inset Graphics
1635 filename ../images/math-subscript.png
1641 , exponents with a caret
1642 \begin_inset Quotes eld
1646 \begin_inset Quotes erd
1649 or via the math toolbar button
1650 \begin_inset Graphics
1651 filename ../images/math-superscript.png
1660 \begin_layout Standard
1662 \begin_inset Tabular
1663 <lyxtabular version="3" rows="4" columns="2">
1665 <column alignment="center" valignment="top" width="0pt">
1666 <column alignment="center" valignment="top" width="0pt">
1668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1671 \begin_layout Plain Layout
1677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1680 \begin_layout Plain Layout
1682 \begin_inset Note Note
1685 \begin_layout Plain Layout
1692 is only used as spacer.
1704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1707 \begin_layout Plain Layout
1713 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1716 \begin_layout Plain Layout
1717 \begin_inset Formula $B_{V}$
1727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1730 \begin_layout Plain Layout
1736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1739 \begin_layout Plain Layout
1740 \begin_inset Formula $\raisebox {5mm}{}B^{V}$
1750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1753 \begin_layout Plain Layout
1758 \begin_layout Plain Layout
1772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1775 \begin_layout Plain Layout
1776 \begin_inset Formula $\raisebox {5mm}{}B^{A}$
1792 \begin_layout Standard
1793 As the caret is in some languages an accent, vowels will be accentuated
1794 in this case and not set as exponents
1798 \begin_layout Plain Layout
1799 Depending on the used keyboard settings this can also happen for other character
1806 To get in this case exponents, press
1810 after the caret as in the last example.
1813 \begin_layout Subsection
1815 \begin_inset CommandInset label
1817 name "sub:Fractions"
1825 \begin_layout Plain Layout
1834 \begin_layout Standard
1835 Fractions are generated with the command
1845 \begin_layout Plain Layout
1853 or via the math toolbar button
1854 \begin_inset Graphics
1855 filename ../images/math/frac.png
1862 The font size is adjusted automatically, depending on whether the fraction
1863 is in an inline or display style formula.
1864 With the math toolbar button
1865 \begin_inset Graphics
1866 filename ../images/math/frac-square.png
1872 you can select different fraction types.
1875 \begin_layout Standard
1884 \begin_layout Plain Layout
1894 a fraction can be created that has in any case the size of a display style
1904 \begin_layout Plain Layout
1914 the fraction appears always with the size of an inline formula.
1918 \begin_layout Standard
1919 A line with the fraction
1920 \begin_inset Formula $\frac{1}{2}$
1923 that was created with the command
1932 \begin_layout Standard
1933 A line with the fraction
1934 \begin_inset Formula $\dfrac{1}{2}$
1937 that was created with the command
1946 \begin_layout Standard
1948 \begin_inset Tabular
1949 <lyxtabular version="3" rows="4" columns="2">
1951 <column alignment="center" valignment="top" width="0pt">
1952 <column alignment="center" valignment="top" width="0pt">
1954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1957 \begin_layout Plain Layout
1963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1966 \begin_layout Plain Layout
1968 \begin_inset Note Note
1971 \begin_layout Plain Layout
1978 is only used as spacer.
1990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1993 \begin_layout Plain Layout
2000 \begin_layout Plain Layout
2010 \begin_inset Formula $\downarrow$
2018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2021 \begin_layout Plain Layout
2022 \begin_inset Formula $\raisebox {4.5mm}{}\frac{A}{B}\raisebox {-2.5mm}{}$
2032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2035 \begin_layout Plain Layout
2042 \begin_layout Plain Layout
2052 \begin_inset Formula $\downarrow$
2060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2063 \begin_layout Plain Layout
2064 \begin_inset Formula $\raisebox {7mm}{}\dfrac{A}{B}\raisebox {-4mm}{}$
2074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2077 \begin_layout Plain Layout
2084 \begin_layout Plain Layout
2097 \begin_layout Plain Layout
2112 \begin_layout Plain Layout
2122 \begin_inset Formula $\downarrow$
2126 \begin_inset Formula $\downarrow\downarrow$
2134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2137 \begin_layout Plain Layout
2138 \begin_inset Formula $\raisebox {8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox {-4mm}{}$
2154 \begin_layout Standard
2155 \begin_inset VSpace bigskip
2159 \begin_inset Newpage newpage
2162 For nested fractions the command
2172 \begin_layout Plain Layout
2182 \begin_inset VSpace -3mm
2188 \begin_layout Standard
2189 \begin_inset Formula \begin{align*}
2190 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2191 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac {A}{B+\cfrac {C+\cfrac {E}{F}}{D}}\end{align*}
2198 \begin_layout Standard
2199 The command for the example above is:
2202 \begin_layout Standard
2208 \begin_inset Formula $\to$
2218 \begin_inset Formula $\to$
2224 \begin_inset Formula $\to\to$
2232 \begin_layout Standard
2233 \begin_inset VSpace medskip
2239 \begin_layout Standard
2246 sets the fraction always in the size of a displayed formula, also when
2247 it is part of another fraction.
2254 has the following command scheme:
2257 \begin_layout Standard
2262 cfrac[numerator position]{numerator}{denominator}
2265 \begin_layout Standard
2266 The numerator position can be
2279 l or r aligns the numerator to the left or right, resp.
2280 \begin_inset Space ~
2283 with the fraction stroke.
2288 or no position is given, the numerator appears centered.
2289 These fractions demonstrate the different alignments:
2290 \begin_inset Newline newline
2296 \begin_inset Formula $\cfrac [l]{A}{B+C}$
2300 \begin_inset Formula $\cfrac {A}{B+C}$
2304 \begin_inset Formula $\cfrac [r]{A}{B+C}$
2310 \begin_layout Standard
2311 \begin_inset VSpace medskip
2314 It is often advantageous to combine
2327 \begin_inset Formula \[
2328 \cfrac {A}{B+\cfrac {C+\frac{E}{F}}{D}}\]
2335 \begin_layout Standard
2336 For inline fractions with a sloped fraction stroke you can use the command
2345 \begin_layout Plain Layout
2356 \begin_inset Formula $\nicefrac{5}{31}$
2362 \begin_layout Standard
2363 How to define own fractions where the fraction stroke can be changed, is
2365 \begin_inset CommandInset ref
2367 reference "sub:Self-defined-Fractions"
2374 \begin_layout Subsection
2379 \begin_layout Plain Layout
2388 \begin_layout Standard
2389 Square roots are created with
2399 \begin_layout Plain Layout
2407 or the math toolbar button
2408 \begin_inset Graphics
2409 filename ../images/math/sqrt.png
2415 , all other roots with the command
2425 \begin_layout Plain Layout
2433 or with the math toolbar button
2434 \begin_inset Graphics
2435 filename ../images/math/root.png
2444 \begin_layout Standard
2446 \begin_inset Tabular
2447 <lyxtabular version="3" rows="3" columns="2">
2449 <column alignment="center" valignment="top" width="0pt">
2450 <column alignment="center" valignment="top" width="0pt">
2452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2455 \begin_layout Plain Layout
2461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2464 \begin_layout Plain Layout
2466 \begin_inset Note Note
2469 \begin_layout Plain Layout
2476 is only used as spacer.
2488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2491 \begin_layout Plain Layout
2498 \begin_layout Plain Layout
2512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt{A-B}$
2526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2529 \begin_layout Plain Layout
2536 \begin_layout Plain Layout
2546 \begin_inset Formula $\downarrow$
2554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2557 \begin_layout Plain Layout
2558 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt[3]{A-B}$
2574 \begin_layout Standard
2575 A square root can also be created with
2581 when the root index field is left empty.
2584 \begin_layout Standard
2585 With certain indices the distance to the root is too small, like in this
2587 \begin_inset Formula $\sqrt[\beta]{B}$
2591 \begin_inset Newline newline
2595 \begin_inset Formula $\beta$
2599 To avoid this, the commands
2609 \begin_layout Plain Layout
2627 \begin_layout Plain Layout
2635 are used with the following scheme:
2638 \begin_layout Standard
2652 \begin_layout Standard
2653 Distance is the number of Big Points (unit bp;
2654 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2657 ), that the index should be moved to the left or top, resp..
2658 The commands are written to the index.
2659 This way the command
2660 \begin_inset Newline newline
2670 \begin_inset Formula $\to$
2676 \begin_inset Formula $\to$
2685 \begin_layout Plain Layout
2695 \begin_inset Formula $\to$
2699 \begin_inset Newline newline
2704 produces a correct typeset formula:
2705 \begin_inset Formula $\sqrt[\leftroot {-1}\uproot {2}\beta]{B}$
2711 \begin_layout Subsection
2712 Binomial coefficients
2716 \begin_layout Plain Layout
2717 Binomial coefficient s
2725 \begin_layout Standard
2726 Binomial coefficients are inserted with the command
2736 \begin_layout Plain Layout
2744 or with the submenu of the math toolbar button
2745 \begin_inset Graphics
2746 filename ../images/math/frac-square.png
2753 Analog to fractions (
2773 \begin_layout Plain Layout
2793 \begin_layout Plain Layout
2804 \begin_layout Standard
2806 \begin_inset Tabular
2807 <lyxtabular version="3" rows="4" columns="2">
2809 <column alignment="center" valignment="top" width="0pt">
2810 <column alignment="center" valignment="top" width="0pt">
2812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2815 \begin_layout Plain Layout
2821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2824 \begin_layout Plain Layout
2826 \begin_inset Note Note
2829 \begin_layout Plain Layout
2836 is only used as spacer.
2848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2851 \begin_layout Plain Layout
2858 \begin_layout Plain Layout
2868 \begin_inset Formula $\downarrow$
2876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2879 \begin_layout Plain Layout
2880 \begin_inset Formula $\raisebox {5mm}{}\binom{A}{B}\raisebox {-2.5mm}{}$
2890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2893 \begin_layout Plain Layout
2900 \begin_layout Plain Layout
2910 \begin_inset Formula $\downarrow$
2918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2921 \begin_layout Plain Layout
2922 \begin_inset Formula $\raisebox {5mm}{}\dbinom{A}{B}\raisebox {-2.5mm}{}$
2932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2935 \begin_layout Plain Layout
2942 \begin_layout Plain Layout
2952 \begin_inset Formula $\downarrow$
2960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2963 \begin_layout Plain Layout
2964 \begin_inset Formula $\raisebox {5mm}{}\tbinom{A}{B}\raisebox {-2.5mm}{}$
2980 \begin_layout Subsection
2981 Case differentiations
2985 \begin_layout Plain Layout
2986 Case differentiations
2994 \begin_layout Standard
2996 \begin_inset Tabular
2997 <lyxtabular version="3" rows="3" columns="2">
2999 <column alignment="center" valignment="top" width="0pt">
3000 <column alignment="center" valignment="top" width="0pt">
3002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3005 \begin_layout Plain Layout
3011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3014 \begin_layout Plain Layout
3022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3025 \begin_layout Plain Layout
3032 \begin_layout Plain Layout
3042 \begin_inset Formula $\to$
3049 \begin_layout Plain Layout
3062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3065 \begin_layout Plain Layout
3066 \begin_inset Formula $\begin{cases}
3077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3080 \begin_layout Plain Layout
3087 \begin_layout Plain Layout
3101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3104 \begin_layout Plain Layout
3105 \begin_inset Formula $\begin{cases}
3106 A & \textrm{for }x>0\\
3107 B & \textrm{for }x=0\end{cases}$
3123 \begin_layout Standard
3130 or the usage of the math toolbar button
3131 \begin_inset Graphics
3132 filename ../images/math/cases.png
3138 you can create new lines with the shortcut
3142 or the table toolbar button
3143 \begin_inset Graphics
3144 filename ../images/tabular-feature_append-row.png
3153 \begin_layout Standard
3160 is also available via the menu
3162 Insert\SpecialChar \menuseparator
3163 Math\SpecialChar \menuseparator
3169 \begin_layout Subsection
3174 \begin_layout Plain Layout
3183 \begin_layout Standard
3194 \begin_layout Plain Layout
3202 every character can be displayed canceled.
3203 The characters are quasi accentuated by a slash.
3206 \begin_layout Standard
3208 \begin_inset Tabular
3209 <lyxtabular version="3" rows="4" columns="2">
3211 <column alignment="center" valignment="top" width="0pt">
3212 <column alignment="center" valignment="top" width="0pt">
3214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3217 \begin_layout Plain Layout
3223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3226 \begin_layout Plain Layout
3234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3237 \begin_layout Plain Layout
3245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3248 \begin_layout Plain Layout
3249 \begin_inset Formula $\not=$
3259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3262 \begin_layout Plain Layout
3272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3275 \begin_layout Plain Layout
3276 \begin_inset Formula $\not\le$
3286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3289 \begin_layout Plain Layout
3299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3302 \begin_layout Plain Layout
3303 \begin_inset Formula $\not\parallel$
3319 \begin_layout Standard
3320 The last example shows, that not all negations look good.
3321 Therefore there are for some negations special commands (see
3322 \begin_inset CommandInset ref
3324 reference "sub:Mathematical-Symbols"
3329 \begin_inset CommandInset ref
3331 reference "sec:Relations"
3338 \begin_layout Subsection
3340 \begin_inset CommandInset label
3342 name "sub:Placeholders"
3350 \begin_layout Plain Layout
3360 \begin_layout Plain Layout
3361 Chemical characters ! Isotopes
3370 \begin_layout Plain Layout
3375 \begin_layout Plain Layout
3386 \begin_layout Plain Layout
3401 \begin_layout Standard
3403 \begin_inset Space \thinspace{}
3407 \begin_inset Space ~
3414 \begin_layout Plain Layout
3415 More about chemical symbols is written in
3416 \begin_inset CommandInset ref
3418 reference "sub:Chemical-Symbols-and"
3427 the following problem occurs:
3430 \begin_layout Standard
3432 \begin_inset Tabular
3433 <lyxtabular version="3" rows="2" columns="2">
3435 <column alignment="center" valignment="top" width="0pt">
3436 <column alignment="center" valignment="top" width="0pt">
3438 <cell alignment="center" valignment="top" usebox="none">
3441 \begin_layout Plain Layout
3442 Indices created with sub- and superscripts:
3447 <cell alignment="center" valignment="top" usebox="none">
3450 \begin_layout Plain Layout
3451 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox {-3mm}{}$
3461 <cell alignment="center" valignment="top" usebox="none">
3464 \begin_layout Plain Layout
3470 <cell alignment="center" valignment="top" usebox="none">
3473 \begin_layout Plain Layout
3474 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3488 \begin_inset Note Note
3491 \begin_layout Plain Layout
3498 is only used as spacer.
3506 \begin_layout Standard
3507 The shorter index is by default placed below or above the first character
3508 of the longer index.
3509 To avoid this there is the command
3519 \begin_layout Plain Layout
3527 or the math toolbar button
3528 \begin_inset Space \thinspace{}
3535 \begin_layout Plain Layout
3536 can be found in the submenu of the toolbar button
3537 \begin_inset Graphics
3538 filename ../images/math/space.png
3550 \begin_inset Graphics
3551 filename ../images/math/phantom.png
3557 that creates one or more phantom characters.
3564 a small blue box appears that is superposed with two red arrows.
3565 The arrows indicate that the complete width and height of the box content
3566 will be created as placeholder.
3567 Phantom characters are accordingly placeholders with the size of the characters.
3570 \begin_layout Standard
3572 \begin_inset Tabular
3573 <lyxtabular version="3" rows="4" columns="2">
3575 <column alignment="center" valignment="top" width="0">
3576 <column alignment="center" valignment="top" width="0">
3578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3581 \begin_layout Plain Layout
3587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3590 \begin_layout Plain Layout
3592 \begin_inset Note Note
3595 \begin_layout Plain Layout
3602 is only used as spacer.
3614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3617 \begin_layout Plain Layout
3622 \begin_layout Plain Layout
3637 \begin_layout Plain Layout
3647 \begin_inset Formula $\to$
3654 \begin_layout Plain Layout
3668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3671 \begin_layout Plain Layout
3672 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox {-2.5mm}{}$
3682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3685 \begin_layout Plain Layout
3690 \begin_layout Plain Layout
3705 \begin_layout Plain Layout
3715 \begin_inset Formula $\to$
3722 \begin_layout Plain Layout
3736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3739 \begin_layout Plain Layout
3740 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox {-2.5mm}{}$
3750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3753 \begin_layout Plain Layout
3760 \begin_layout Plain Layout
3775 \begin_layout Plain Layout
3785 \begin_inset Formula $\to$
3792 \begin_layout Plain Layout
3806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3809 \begin_layout Plain Layout
3810 \begin_inset Formula $\raisebox {4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox {-2.5mm}{}$
3826 \begin_layout Standard
3827 Furthermore there are the commands
3837 \begin_layout Plain Layout
3846 \begin_inset Space ~
3850 \begin_inset Graphics
3851 filename ../images/math/vphantom.png
3867 \begin_layout Plain Layout
3876 \begin_inset Space ~
3880 \begin_inset Graphics
3881 filename ../images/math/hphantom.png
3894 creates only space for the maximal height of the characters in the box
3895 but not for its width.
3902 creates only space for the width of the box content.
3903 Therefore the boxes of both commands have only one red arrow.
3906 \begin_layout Standard
3917 \begin_layout Plain Layout
3932 space for the height of the integral sign,
3936 \begin_layout Plain Layout
3943 creates an integral sign, see
3944 \begin_inset CommandInset ref
3946 reference "sub:Big-Operators"
3955 because this is the larger character.
3956 An example application is in
3957 \begin_inset CommandInset ref
3959 reference "sub:Multiline-Brackets"
3966 \begin_layout Subsection
3971 \begin_layout Plain Layout
3981 \begin_layout Plain Layout
3982 Formula ! underlined
3990 \begin_layout Standard
3992 \begin_inset Tabular
3993 <lyxtabular version="3" rows="4" columns="2">
3995 <column alignment="center" valignment="top" width="0pt">
3996 <column alignment="center" valignment="top" width="0pt">
3998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4001 \begin_layout Plain Layout
4007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4010 \begin_layout Plain Layout
4012 \begin_inset Note Note
4015 \begin_layout Plain Layout
4022 is only used as spacer.
4034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4037 \begin_layout Plain Layout
4044 \begin_layout Plain Layout
4057 \begin_layout Plain Layout
4070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4073 \begin_layout Plain Layout
4074 \begin_inset Formula $\raisebox {5mm}{}\overline{A+B}$
4084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4087 \begin_layout Plain Layout
4094 \begin_layout Plain Layout
4107 \begin_layout Plain Layout
4120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4123 \begin_layout Plain Layout
4124 \begin_inset Formula $\underline{A+B}\raisebox {-2.5mm}{}$
4134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4137 \begin_layout Plain Layout
4144 \begin_layout Plain Layout
4159 \begin_layout Plain Layout
4173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4176 \begin_layout Plain Layout
4177 \begin_inset Formula $\raisebox {5mm}{}\overline{\underline{A+B}}\raisebox {-2.5mm}{}$
4193 \begin_layout Standard
4194 In the last example it doesn't matter if first
4209 \begin_layout Standard
4210 To double underline e.
4211 \begin_inset Space \thinspace{}
4224 \begin_layout Standard
4225 It is possible to place up to 6 lines above or below characters.
4228 \begin_layout Subsection
4233 \begin_layout Plain Layout
4242 \begin_layout Standard
4243 There are different types of ellipses available.
4247 \begin_layout Plain Layout
4248 In the math toolbar in the submenu of the button
4249 \begin_inset Graphics
4250 filename ../images/math/ldots.png
4261 For listings dots at the baseline are used (
4271 \begin_layout Plain Layout
4279 ), while for operations dots are needed that are on the same height as the
4290 \begin_layout Plain Layout
4299 When using the command
4309 \begin_layout Plain Layout
4317 , LaTeX decides on the basis of the next character what type is used.
4320 \begin_layout Standard
4322 \begin_inset Tabular
4323 <lyxtabular version="3" rows="8" columns="2">
4325 <column alignment="center" valignment="top" width="0pt">
4326 <column alignment="center" valignment="top" width="0pt">
4328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4331 \begin_layout Plain Layout
4337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4340 \begin_layout Plain Layout
4348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4351 \begin_layout Plain Layout
4356 \begin_layout Plain Layout
4371 \begin_layout Plain Layout
4385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4388 \begin_layout Plain Layout
4389 \begin_inset Formula $A_{1},\dots,A_{n}$
4399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4402 \begin_layout Plain Layout
4407 \begin_layout Plain Layout
4422 \begin_layout Plain Layout
4436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4439 \begin_layout Plain Layout
4440 \begin_inset Formula $A_{1}+\dots+A_{n}$
4450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4453 \begin_layout Plain Layout
4458 \begin_layout Plain Layout
4473 \begin_layout Plain Layout
4487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4490 \begin_layout Plain Layout
4491 \begin_inset Formula $A_{1},\ldots,A_{n}$
4501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4504 \begin_layout Plain Layout
4509 \begin_layout Plain Layout
4524 \begin_layout Plain Layout
4538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4541 \begin_layout Plain Layout
4542 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4555 \begin_layout Plain Layout
4563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4566 \begin_layout Plain Layout
4567 \begin_inset Formula $\vdots$
4577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4580 \begin_layout Plain Layout
4588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4591 \begin_layout Plain Layout
4592 \begin_inset Formula $\ddots$
4602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4605 \begin_layout Plain Layout
4607 \begin_inset Space \thinspace{}
4610 matrix with the different dots
4615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4618 \begin_layout Plain Layout
4619 \begin_inset Formula $\begin{array}{ccc}
4620 A_{11} & \cdots & A_{1m}\\
4621 \vdots & \ddots & \vdots\\
4622 A_{n1} & \cdots & A_{nm}\end{array}$
4638 \begin_layout Standard
4639 The ellipses available in menu
4641 Insert\SpecialChar \menuseparator
4643 \begin_inset Space ~
4657 \begin_layout Standard
4658 \begin_inset VSpace medskip
4661 Specially for matrices there are ellipses that span over several columns.
4662 They are created with the command
4672 \begin_layout Plain Layout
4680 , that has the following scheme:
4683 \begin_layout Standard
4688 hdotsfor[distance]{number of columns}
4691 \begin_layout Standard
4692 The number of columns specifies how many columns should be spanned.
4693 Distance is a factor for the distance between the dots.
4696 \begin_layout Standard
4697 In the following matrix the command
4703 was inserted in the first box of the second line, to get an ellipsis with
4704 a dot distance twice as long as with the command
4711 \begin_inset Formula \[
4712 \left(\begin{array}{cccc}
4715 q & w & e & r\end{array}\right)\]
4719 Note that the matrix fields that should be spanned must be empty, otherwise
4720 you get LaTeX-errors.
4723 \begin_layout Standard
4724 \begin_inset VSpace bigskip
4727 Furthermore you can fill with the command
4737 \begin_layout Plain Layout
4745 the rest of a line with dots.
4746 The effect of these commands is the same like with
4753 \begin_inset CommandInset ref
4755 reference "sub:Variable-Space"
4762 \begin_layout Standard
4763 For example the command
4771 \begin_layout Plain Layout
4785 \begin_layout Standard
4786 \begin_inset Formula $A\dotfill B$
4792 \begin_layout Standard
4799 there is for a line the command
4809 \begin_layout Plain Layout
4820 \begin_layout Standard
4821 \begin_inset Formula $A\hrulefill B$
4827 \begin_layout Standard
4828 To use the commands for text, they have to be inserted in TeX-mode.
4831 \begin_layout Section
4833 \begin_inset CommandInset label
4843 \begin_layout Plain Layout
4852 \begin_layout Standard
4853 Matrices can be inserted via the math toolbar button
4854 \begin_inset Graphics
4855 filename ../images/dialog-show_mathmatrix.png
4863 Insert\SpecialChar \menuseparator
4864 Math\SpecialChar \menuseparator
4868 You will be asked for the number of matrix columns and rows, and the alignment.
4869 The vertical alignment is hereby only of importance for matrices in inline
4873 \begin_layout Standard
4874 The first matrix is top
4875 \begin_inset Formula $\begin{array}[t]{cccc}
4878 C & F & I & L\end{array}$
4882 \begin_inset Formula $\begin{array}{cccc}
4885 C & F & I & L\end{array}$
4888 , and the third bottom
4889 \begin_inset Formula $\begin{array}[b]{cccc}
4892 C & F & I & L\end{array}$
4898 \begin_layout Standard
4899 The horizontal alignment specifies how the column entries should be aligned.
4900 It is set by entering a letter for every column.
4905 denotes left aligned,
4914 To create for example a 4
4919 \begin_inset Space ~
4922 matrix where the first column is left aligned, the second and third are
4923 centered, and the last one is right aligned, one enters for the horizontal
4929 Normally are in a matrix all columns centered, therefore the default is
4930 for every column is a
4937 \begin_layout Standard
4938 Horizontal alignment:
4941 \begin_layout Standard
4947 \begin_inset Formula $\begin{array}{lll}
4950 C & F & 10000\end{array}$
4958 \begin_inset Formula $\begin{array}{ccc}
4961 C & F & 10000\end{array}$
4969 \begin_inset Formula $\begin{array}{rrr}
4972 C & F & 10000\end{array}$
4978 \begin_layout Standard
4979 To add or delete rows and columns subsequently, the math toolbar buttons
4981 \begin_inset Graphics
4982 filename ../images/tabular-feature_append-row.png
4989 \begin_inset Graphics
4990 filename ../images/tabular-feature_delete-row.png
4997 \begin_inset Space \thinspace{}
5002 Edit\SpecialChar \menuseparator
5006 New rows can also be created with
5013 \begin_layout Standard
5014 \begin_inset VSpace bigskip
5017 Parentheses around a matrix can can either be created with the commands
5028 \begin_layout Plain Layout
5046 \begin_layout Plain Layout
5057 \begin_inset Space ~
5063 \begin_inset CommandInset ref
5065 reference "sub:Automatic-Bracket-Size"
5069 , or by using the following commands:
5070 \begin_inset VSpace medskip
5076 \begin_layout Standard
5077 \begin_inset Space \hfill{}
5081 \begin_inset Tabular
5082 <lyxtabular version="3" rows="4" columns="2">
5084 <column alignment="center" valignment="top" width="0">
5085 <column alignment="center" valignment="top" width="0">
5087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5090 \begin_layout Plain Layout
5096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5099 \begin_layout Plain Layout
5101 \begin_inset Note Note
5104 \begin_layout Plain Layout
5111 is only used as spacer.
5123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5126 \begin_layout Plain Layout
5133 \begin_layout Plain Layout
5147 \begin_inset Space \thinspace{}
5155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5158 \begin_layout Plain Layout
5159 \begin_inset Formula $\raisebox {7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5160 0 & \textrm{-}\mathrm{i}\\
5161 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox {-5.3mm}{}$
5171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5174 \begin_layout Plain Layout
5181 \begin_layout Plain Layout
5195 \begin_inset Space \thinspace{}
5203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5206 \begin_layout Plain Layout
5207 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5208 0 & \textrm{-}\mathrm{i}\\
5209 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox {-5.3mm}{}$
5219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5222 \begin_layout Plain Layout
5229 \begin_layout Plain Layout
5243 \begin_inset Space \thinspace{}
5251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5254 \begin_layout Plain Layout
5255 \begin_inset Formula $\raisebox {7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5256 0 & \textrm{-}\mathrm{i}\\
5257 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox {-5.3mm}{}$
5271 \begin_inset Space \hfill{}
5275 \begin_inset Tabular
5276 <lyxtabular version="3" rows="4" columns="2">
5278 <column alignment="center" valignment="top" width="0">
5279 <column alignment="center" valignment="top" width="0">
5281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5284 \begin_layout Plain Layout
5290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5293 \begin_layout Plain Layout
5301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5304 \begin_layout Plain Layout
5311 \begin_layout Plain Layout
5325 \begin_inset Space \thinspace{}
5333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5336 \begin_layout Plain Layout
5337 \begin_inset Formula $\raisebox {7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5338 0 & \textrm{-}\mathrm{i}\\
5339 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox {-5.3mm}{}$
5349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5352 \begin_layout Plain Layout
5359 \begin_layout Plain Layout
5373 \begin_inset Space \thinspace{}
5381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5384 \begin_layout Plain Layout
5385 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5386 0 & \textrm{-}\mathrm{i}\\
5387 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox {-5.3mm}{}$
5397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5400 \begin_layout Plain Layout
5407 \begin_layout Plain Layout
5421 \begin_inset Space \thinspace{}
5429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5432 \begin_layout Plain Layout
5433 \begin_inset Formula $\raisebox {7.5mm}{}\begin{matrix}\begin{array}{cc}
5434 0 & \textrm{-}\mathrm{i}\\
5435 \mathrm{i} & 0\end{array}\end{matrix}\raisebox {-5.3mm}{}$
5449 \begin_inset Space \hfill{}
5455 \begin_layout Standard
5456 \begin_inset VSpace medskip
5460 \begin_inset Space \thinspace{}
5464 \begin_inset Space ~
5473 is inserted, a blue box appears between two vertical lines where the matrix
5477 \begin_layout Standard
5478 \begin_inset VSpace bigskip
5481 As all multiline formulas are matrices, the length
5491 \begin_layout Plain Layout
5499 that is described in
5500 \begin_inset CommandInset ref
5502 reference "sub:Column-Separation"
5506 can also be used to change the column separation of matrices.
5509 \begin_layout Standard
5510 To change the row separation, the command
5520 \begin_layout Plain Layout
5529 It is used as follows:
5532 \begin_layout Standard
5539 arraystretch}{stretch factor}
5543 \begin_layout Plain Layout
5554 \begin_layout Standard
5561 assigns the stretch factor to the predefined command
5569 \begin_inset Space \thinspace{}
5573 \begin_inset Space ~
5576 the row separation, use the factor 2.
5577 This is then used for all following matrices.
5578 To go back to the original separation, assign the factor 1 to
5587 \begin_layout Standard
5588 To set matrices into a text line, the command
5598 \begin_layout Plain Layout
5607 When it is inserted a blue box with two dashed lines appears.
5608 In this box the matrix is inserted.
5611 \begin_layout Standard
5613 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5614 C & D\end{smallmatrix}\right)$
5620 \begin_layout Section
5621 Brackets and Delimiters
5625 \begin_layout Plain Layout
5635 \begin_layout Plain Layout
5644 \begin_layout Subsection
5645 Vertical Brackets and Delimiters
5649 \begin_layout Plain Layout
5658 \begin_layout Standard
5659 \begin_inset Space \hfill{}
5663 \begin_inset Tabular
5664 <lyxtabular version="3" rows="9" columns="2">
5666 <column alignment="center" valignment="top" width="0pt">
5667 <column alignment="center" valignment="top" width="0pt">
5669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5672 \begin_layout Plain Layout
5678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5681 \begin_layout Plain Layout
5689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5692 \begin_layout Plain Layout
5698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5701 \begin_layout Plain Layout
5702 \begin_inset Formula $($
5712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5715 \begin_layout Plain Layout
5721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5724 \begin_layout Plain Layout
5725 \begin_inset Formula $\{$
5735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5738 \begin_layout Plain Layout
5744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5747 \begin_layout Plain Layout
5748 \begin_inset Formula $[$
5758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5761 \begin_layout Plain Layout
5769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5772 \begin_layout Plain Layout
5773 \begin_inset Formula $\langle$
5783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5786 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5797 \begin_layout Plain Layout
5798 \begin_inset Formula $\lceil$
5808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5811 \begin_layout Plain Layout
5819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5822 \begin_layout Plain Layout
5823 \begin_inset Formula $\lfloor$
5833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5836 \begin_layout Plain Layout
5842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5845 \begin_layout Plain Layout
5846 \begin_inset Formula $/$
5856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5859 \begin_layout Plain Layout
5865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5868 \begin_layout Plain Layout
5869 \begin_inset Formula $|$
5883 \begin_inset Space \hfill{}
5887 \begin_inset Tabular
5888 <lyxtabular version="3" rows="9" columns="2">
5890 <column alignment="center" valignment="top" width="0pt">
5891 <column alignment="center" valignment="top" width="0pt">
5893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5896 \begin_layout Plain Layout
5902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5905 \begin_layout Plain Layout
5913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5916 \begin_layout Plain Layout
5922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5925 \begin_layout Plain Layout
5926 \begin_inset Formula $)$
5936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5939 \begin_layout Plain Layout
5945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5948 \begin_layout Plain Layout
5949 \begin_inset Formula $\}$
5959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5962 \begin_layout Plain Layout
5968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5971 \begin_layout Plain Layout
5972 \begin_inset Formula $]$
5982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5985 \begin_layout Plain Layout
5993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5996 \begin_layout Plain Layout
5997 \begin_inset Formula $\rangle$
6007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6010 \begin_layout Plain Layout
6018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6021 \begin_layout Plain Layout
6022 \begin_inset Formula $\rceil$
6032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6035 \begin_layout Plain Layout
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6046 \begin_layout Plain Layout
6047 \begin_inset Formula $\rfloor$
6057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6060 \begin_layout Plain Layout
6070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6073 \begin_layout Plain Layout
6074 \begin_inset Formula $\backslash$
6084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6087 \begin_layout Plain Layout
6095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6098 \begin_layout Plain Layout
6099 \begin_inset Formula $\|$
6113 \begin_inset Space \hfill{}
6119 \begin_layout Standard
6122 \begin_inset Note Greyedout
6125 \begin_layout Plain Layout
6130 In TeX-mode the command
6140 \begin_layout Plain Layout
6148 must be used for the backslash, because the command
6156 produces there a line break.
6164 \begin_layout Standard
6165 For all characters listed above the size can be adjusted with the commands
6166 described in the following two subsections.
6167 When using these commands, the characters < and > can directly be used
6168 instead of the commands
6183 \begin_layout Subsubsection
6185 \begin_inset CommandInset label
6187 name "sub:Manual-Bracket-Size"
6195 \begin_layout Plain Layout
6196 Bracket size ! manual
6204 \begin_layout Standard
6205 The bracket size can be specified manually by the LaTeX-commands
6215 \begin_layout Plain Layout
6248 denotes the smallest and
6254 the largest bracket size.
6257 \begin_layout Standard
6258 These commands are used to emphasize levels of brackets:
6261 \begin_layout Standard
6263 \begin_inset Tabular
6264 <lyxtabular version="3" rows="2" columns="2">
6266 <column alignment="center" valignment="top" width="0pt">
6267 <column alignment="center" valignment="top" width="0pt">
6269 <cell alignment="center" valignment="top" usebox="none">
6272 \begin_layout Plain Layout
6273 all brackets in the same size:
6278 <cell alignment="center" valignment="top" usebox="none">
6281 \begin_layout Plain Layout
6282 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox {-4mm}{}$
6292 <cell alignment="center" valignment="top" usebox="none">
6295 \begin_layout Plain Layout
6301 <cell alignment="center" valignment="top" usebox="none">
6304 \begin_layout Plain Layout
6305 \begin_inset Formula $\Big ((A+B)(A-B)\Big )^{C}$
6319 \begin_inset Note Note
6322 \begin_layout Plain Layout
6329 is only used as spacer.
6337 \begin_layout Standard
6338 For the second formula the command
6348 \begin_layout Plain Layout
6362 \begin_layout Standard
6363 Here is an overview about all bracket sizes:
6366 \begin_layout Standard
6386 \begin_layout Plain Layout
6403 \begin_layout Plain Layout
6416 \begin_layout Plain Layout
6432 \begin_layout Standard
6434 \begin_inset Formula $\Bigg (\exp\bigg <\Big [\big \{\ln(3x)\big \}^{2}\sin(x)\Big ]^{A}\bigg >\Bigg )^{0,5}$
6440 \begin_layout Standard
6441 \begin_inset Newpage newpage
6450 -commands there is the variant
6460 \begin_layout Plain Layout
6468 that adds a bit more space between the bracket and its content, and the
6485 \begin_layout Plain Layout
6495 , that don't add additional space.
6500 at the end of the command
6506 is for a left bracket; for a right bracket this will be replaced by an
6512 A left or right bracket can each be an opening or closing bracket.
6515 \begin_layout Standard
6516 In the following table is a comparison of the variants:
6519 \begin_layout Standard
6521 \begin_inset Tabular
6522 <lyxtabular version="3" rows="5" columns="2">
6524 <column alignment="center" valignment="middle" width="0">
6525 <column alignment="center" valignment="middle" width="0">
6527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6530 \begin_layout Plain Layout
6536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6539 \begin_layout Plain Layout
6541 \begin_inset Note Note
6544 \begin_layout Plain Layout
6551 is only used as spacer.
6563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6566 \begin_layout Plain Layout
6581 \begin_layout Plain Layout
6599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6602 \begin_layout Plain Layout
6603 \begin_inset Formula $\raisebox {5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox {-3.25mm}{}$
6613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6616 \begin_layout Plain Layout
6631 \begin_layout Plain Layout
6649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6652 \begin_layout Plain Layout
6653 \begin_inset Formula $\raisebox {5.5mm}{}\Big (\big (\ln(3x)\big )^{2}\Big )\raisebox {-3.25mm}{}$
6663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6666 \begin_layout Plain Layout
6681 \begin_layout Plain Layout
6699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6702 \begin_layout Plain Layout
6703 \begin_inset Formula $\raisebox {5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox {-3.25mm}{}$
6713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6716 \begin_layout Plain Layout
6728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6731 \begin_layout Plain Layout
6732 \begin_inset Formula $\raisebox {4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox {-2mm}{}$
6748 \begin_layout Subsubsection
6749 Automatic Bracket Size
6750 \begin_inset CommandInset label
6752 name "sub:Automatic-Bracket-Size"
6760 \begin_layout Plain Layout
6761 Bracket size ! automatic
6769 \begin_layout Standard
6770 Brackets with variable size can be inserted with the commands
6780 \begin_layout Plain Layout
6798 \begin_layout Plain Layout
6806 or via the math toolbar button
6807 \begin_inset Graphics
6808 filename ../images/dialog-show_mathdelimiter.png
6827 the wanted bracket must be inserted.
6828 The bracket size will then automatically be calculated for the output.
6831 \begin_layout Standard
6833 normal bracket: The command
6843 \begin_layout Plain Layout
6853 \begin_inset Formula $\downarrow$
6860 \begin_layout Plain Layout
6872 \begin_inset Formula \[
6880 \begin_layout Standard
6882 multiline bracket: The command
6894 \begin_layout Plain Layout
6904 \begin_inset Formula $\downarrow$
6911 \begin_layout Plain Layout
6925 \begin_inset Formula \[
6926 \ln\left(\frac{A}{C}\right)\]
6933 \begin_layout Standard
6949 \begin_inset Space ~
6955 This has the advantage that you can see in LyX immediately the real bracket
6956 size and that the matching right bracket will be created too.
6957 \begin_inset Newline newline
6960 The command for the last example would then be:
6974 \begin_layout Plain Layout
6984 \begin_inset Formula $\downarrow$
6990 \begin_layout Standard
6991 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6992 For example the command
7002 \begin_layout Plain Layout
7012 \begin_inset Formula $\downarrow$
7019 \begin_layout Plain Layout
7035 \begin_inset Formula \[
7036 \left.\frac{A}{B}\right\} \]
7054 will be converted by LyX to brackets in the right size when the document
7055 is reloaded and an omitted bracket will appear as dashed line.
7058 \begin_layout Standard
7059 \begin_inset VSpace bigskip
7062 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7073 \begin_layout Plain Layout
7081 is additionally available for all brackets and limits.
7082 With this command the height of the following character is adapted to the
7083 one of the surrounding brackets, what is e.
7084 \begin_inset Space \thinspace{}
7088 \begin_inset Space ~
7091 needed for physical vectors:
7092 \begin_inset Formula \[
7093 \left\langle \phi\:\middle |\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7097 For physical vectors there is a special LaTeX-package, described in
7098 \begin_inset CommandInset ref
7100 reference "sub:Physical-Vectors"
7107 \begin_layout Subsection
7112 \begin_layout Plain Layout
7113 Brackets ! horizontal
7121 \begin_layout Standard
7123 \begin_inset Tabular
7124 <lyxtabular version="3" rows="4" columns="2">
7126 <column alignment="center" valignment="top" width="0pt">
7127 <column alignment="center" valignment="top" width="0pt">
7129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7132 \begin_layout Plain Layout
7134 \begin_inset Note Note
7137 \begin_layout Plain Layout
7144 is only used as spacer.
7154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7157 \begin_layout Plain Layout
7165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7168 \begin_layout Plain Layout
7172 \begin_layout Plain Layout
7187 \begin_layout Plain Layout
7200 \begin_layout Plain Layout
7213 \begin_layout Plain Layout
7226 \begin_layout Plain Layout
7237 \begin_layout Plain Layout
7250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7253 \begin_layout Plain Layout
7254 \begin_inset Formula $\overbrace{A+B}^{3}$
7264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7267 \begin_layout Plain Layout
7271 \begin_layout Plain Layout
7286 \begin_layout Plain Layout
7299 \begin_layout Plain Layout
7312 \begin_layout Plain Layout
7323 \begin_layout Plain Layout
7336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7339 \begin_layout Plain Layout
7340 \begin_inset Formula $\underbrace{A+B}_{5}$
7350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7353 \begin_layout Plain Layout
7360 \begin_layout Plain Layout
7375 \begin_layout Plain Layout
7388 \begin_layout Plain Layout
7401 \begin_layout Plain Layout
7414 \begin_layout Plain Layout
7427 \begin_layout Plain Layout
7440 \begin_layout Plain Layout
7454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7457 \begin_layout Plain Layout
7458 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7474 \begin_layout Standard
7475 In the last example it doesn't matter if
7487 is inserted at first.
7490 \begin_layout Standard
7491 \begin_inset VSpace bigskip
7494 When brackets are needed that overlap each other, multiline formulas, as
7496 \begin_inset CommandInset ref
7498 reference "sec:Multiline-Formulas"
7503 \begin_inset Formula \begin{eqnarray*}
7504 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7505 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7509 In the first row the formula is inserted together with the first brace.
7510 It is hereby important that the space command
7514 \begin_layout Plain Layout
7515 Space commands are explained in
7516 \begin_inset CommandInset ref
7518 reference "sub:Predefined-Space"
7533 is inserted before the first
7534 \begin_inset Formula $d$
7537 , because the brace that ends behind the
7538 \begin_inset Formula $q$
7541 prevents that the following
7542 \begin_inset Quotes eld
7546 \begin_inset Quotes erd
7549 is surrounded by space.
7553 \begin_layout Plain Layout
7554 because a bracket is not handled as character, see
7555 \begin_inset CommandInset ref
7557 reference "sub:Binary-Operators"
7566 In the second row the second brace is inserted.
7567 As it should begin before the
7568 \begin_inset Formula $b$
7583 \begin_layout Plain Layout
7591 \begin_inset CommandInset ref
7593 reference "sub:Placeholders"
7602 This space is needed because the
7603 \begin_inset Quotes eld
7607 \begin_inset Quotes erd
7610 is also surrounded by space in the formula.
7611 The brace is placed under the command
7620 \begin_layout Standard
7621 It gets more complicated when brackets overlap each other, like in the following
7626 \begin_layout Plain Layout
7638 \begin_inset Formula \begin{eqnarray*}
7639 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7640 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7648 \begin_layout Plain Layout
7659 The first formula row is the same as the second row of the previous example,
7660 with the difference that the brace is above.
7661 The second row contains the formula together with the second brace.
7662 To avoid that there is space between the upper brace in the first row and
7663 the formula, the row spacing need to be reduced.
7664 This is not easily possible due to a bug in LyX
7668 \begin_layout Plain Layout
7672 \begin_layout Plain Layout
7676 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
7685 \begin_layout Plain Layout
7698 As solution for the problem, the global formula row separation
7708 \begin_layout Plain Layout
7716 must be changed to -6
7717 \begin_inset Space \thinspace{}
7720 pt before the formula with the command
7735 is set back after the formula to the standard value of 3
7736 \begin_inset Space \thinspace{}
7739 pt using the same command.
7740 More about the row separation in formulas is explained in
7741 \begin_inset CommandInset ref
7743 reference "sub:Line-Separation"
7750 \begin_layout Section
7755 \begin_layout Plain Layout
7764 \begin_layout Standard
7765 Arrows can be inserted via the math toolbar button
7766 \begin_inset Graphics
7767 filename ../images/math/leftarrow.png
7773 or the commands listed in the following subsections.
7776 \begin_layout Subsection
7781 \begin_layout Plain Layout
7790 \begin_layout Standard
7791 \begin_inset Space \hfill{}
7795 \begin_inset Tabular
7796 <lyxtabular version="3" rows="8" columns="2">
7798 <column alignment="center" valignment="top" width="0pt">
7799 <column alignment="center" valignment="top" width="0pt">
7801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7804 \begin_layout Plain Layout
7810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7813 \begin_layout Plain Layout
7821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7824 \begin_layout Plain Layout
7832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7835 \begin_layout Plain Layout
7836 \begin_inset Formula $\gets$
7846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7849 \begin_layout Plain Layout
7857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7860 \begin_layout Plain Layout
7861 \begin_inset Formula $\Leftarrow$
7871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7874 \begin_layout Plain Layout
7882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7885 \begin_layout Plain Layout
7886 \begin_inset Formula $\longleftarrow$
7896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7899 \begin_layout Plain Layout
7907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7910 \begin_layout Plain Layout
7911 \begin_inset Formula $\Longleftarrow$
7921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7924 \begin_layout Plain Layout
7932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7935 \begin_layout Plain Layout
7936 \begin_inset Formula $\leftharpoonup$
7946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7949 \begin_layout Plain Layout
7957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7960 \begin_layout Plain Layout
7961 \begin_inset Formula $\leftharpoondown$
7971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7974 \begin_layout Plain Layout
7982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7985 \begin_layout Plain Layout
7986 \begin_inset Formula $\hookleftarrow$
8000 \begin_inset Space \hfill{}
8004 \begin_inset Tabular
8005 <lyxtabular version="3" rows="8" columns="2">
8007 <column alignment="center" valignment="top" width="0pt">
8008 <column alignment="center" valignment="top" width="0pt">
8010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8013 \begin_layout Plain Layout
8019 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8022 \begin_layout Plain Layout
8030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8033 \begin_layout Plain Layout
8041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8044 \begin_layout Plain Layout
8045 \begin_inset Formula $\to$
8055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8058 \begin_layout Plain Layout
8066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8069 \begin_layout Plain Layout
8070 \begin_inset Formula $\Rightarrow$
8080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8083 \begin_layout Plain Layout
8091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8094 \begin_layout Plain Layout
8095 \begin_inset Formula $\longrightarrow$
8105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8108 \begin_layout Plain Layout
8116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8119 \begin_layout Plain Layout
8120 \begin_inset Formula $\Longrightarrow$
8130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8133 \begin_layout Plain Layout
8141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8144 \begin_layout Plain Layout
8145 \begin_inset Formula $\rightharpoonup$
8155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8158 \begin_layout Plain Layout
8166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8169 \begin_layout Plain Layout
8170 \begin_inset Formula $\rightharpoondown$
8180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8183 \begin_layout Plain Layout
8191 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8194 \begin_layout Plain Layout
8195 \begin_inset Formula $\hookrightarrow$
8209 \begin_inset Space \hfill{}
8215 \begin_layout Standard
8216 \begin_inset Space \hfill{}
8220 \begin_inset Tabular
8221 <lyxtabular version="3" rows="6" columns="2">
8223 <column alignment="center" valignment="top" width="0pt">
8224 <column alignment="center" valignment="top" width="0pt">
8226 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8229 \begin_layout Plain Layout
8235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8238 \begin_layout Plain Layout
8246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8249 \begin_layout Plain Layout
8257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8260 \begin_layout Plain Layout
8261 \begin_inset Formula $\leftrightarrow$
8271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8274 \begin_layout Plain Layout
8282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8285 \begin_layout Plain Layout
8286 \begin_inset Formula $\Leftrightarrow$
8296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8299 \begin_layout Plain Layout
8307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8310 \begin_layout Plain Layout
8311 \begin_inset Formula $\longleftrightarrow$
8321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8324 \begin_layout Plain Layout
8332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8335 \begin_layout Plain Layout
8336 \begin_inset Formula $\Longleftrightarrow$
8346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8349 \begin_layout Plain Layout
8357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8360 \begin_layout Plain Layout
8361 \begin_inset Formula $\rightleftharpoons$
8375 \begin_inset Space \hspace{}
8380 \begin_inset Space \hfill{}
8384 \begin_inset Tabular
8385 <lyxtabular version="3" rows="5" columns="2">
8387 <column alignment="center" valignment="top" width="0pt">
8388 <column alignment="center" valignment="top" width="0pt">
8390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8393 \begin_layout Plain Layout
8399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8402 \begin_layout Plain Layout
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8413 \begin_layout Plain Layout
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8424 \begin_layout Plain Layout
8425 \begin_inset Formula $\mapsto$
8435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8438 \begin_layout Plain Layout
8446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8449 \begin_layout Plain Layout
8450 \begin_inset Formula $\longmapsto$
8460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8463 \begin_layout Plain Layout
8471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8474 \begin_layout Plain Layout
8475 \begin_inset Formula $\leadsto$
8485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8488 \begin_layout Plain Layout
8496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8499 \begin_layout Plain Layout
8500 \begin_inset Formula $\dasharrow$
8514 \begin_inset Space \hfill{}
8520 \begin_layout Standard
8521 \begin_inset VSpace medskip
8524 Arrows used as accent like e.
8525 \begin_inset Space \thinspace{}
8529 \begin_inset Space ~
8532 vector arrows are listed in
8533 \begin_inset CommandInset ref
8535 reference "sec:Accents"
8542 \begin_layout Standard
8543 \begin_inset VSpace bigskip
8546 Furthermore there are the labeled arrows
8550 \begin_layout Plain Layout
8566 \begin_layout Plain Layout
8584 \begin_layout Plain Layout
8588 \begin_inset VSpace 4mm
8597 When inserting one of these commands in a formula, an arrow with two blue
8598 boxes appear where the label can be inserted.
8599 The length of the arrow adapts to the label width.
8602 \begin_layout Standard
8604 \begin_inset Tabular
8605 <lyxtabular version="3" rows="3" columns="2">
8607 <column alignment="center" valignment="top" width="0pt">
8608 <column alignment="center" valignment="top" width="0pt">
8610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8613 \begin_layout Plain Layout
8619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8622 \begin_layout Plain Layout
8624 \begin_inset Note Note
8627 \begin_layout Plain Layout
8634 is only used as spacer.
8646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8649 \begin_layout Plain Layout
8656 \begin_layout Plain Layout
8666 \begin_inset Formula $\downarrow$
8670 \begin_inset Formula $\to$
8678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8681 \begin_layout Plain Layout
8682 \begin_inset Formula $\raisebox {5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox {-4mm}{}$
8692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8695 \begin_layout Plain Layout
8702 \begin_layout Plain Layout
8712 \begin_inset Formula $\downarrow$
8716 \begin_inset Formula $\to$
8724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8727 \begin_layout Plain Layout
8728 \begin_inset Formula $\raisebox {5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox {-4mm}{}$
8744 \begin_layout Subsection
8745 Vertical and diagonal Arrows
8749 \begin_layout Plain Layout
8759 \begin_layout Plain Layout
8768 \begin_layout Standard
8769 \begin_inset Space \hfill{}
8773 \begin_inset Tabular
8774 <lyxtabular version="3" rows="7" columns="2">
8776 <column alignment="center" valignment="top" width="0pt">
8777 <column alignment="center" valignment="top" width="0pt">
8779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8782 \begin_layout Plain Layout
8788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8791 \begin_layout Plain Layout
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8802 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\uparrow$
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8827 \begin_layout Plain Layout
8835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\Uparrow$
8849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8852 \begin_layout Plain Layout
8860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8863 \begin_layout Plain Layout
8864 \begin_inset Formula $\updownarrow$
8874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8877 \begin_layout Plain Layout
8885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8888 \begin_layout Plain Layout
8889 \begin_inset Formula $\Updownarrow$
8899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8902 \begin_layout Plain Layout
8910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8913 \begin_layout Plain Layout
8914 \begin_inset Formula $\Downarrow$
8924 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8927 \begin_layout Plain Layout
8935 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8938 \begin_layout Plain Layout
8939 \begin_inset Formula $\downarrow$
8953 \begin_inset Space \hfill{}
8957 \begin_inset Tabular
8958 <lyxtabular version="3" rows="5" columns="2">
8960 <column alignment="center" valignment="top" width="0pt">
8961 <column alignment="center" valignment="top" width="0pt">
8963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8966 \begin_layout Plain Layout
8972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8975 \begin_layout Plain Layout
8983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8986 \begin_layout Plain Layout
8994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8997 \begin_layout Plain Layout
8998 \begin_inset Formula $\nearrow$
9008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9011 \begin_layout Plain Layout
9019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9022 \begin_layout Plain Layout
9023 \begin_inset Formula $\searrow$
9033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9036 \begin_layout Plain Layout
9044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9047 \begin_layout Plain Layout
9048 \begin_inset Formula $\swarrow$
9058 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9061 \begin_layout Plain Layout
9069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9072 \begin_layout Plain Layout
9073 \begin_inset Formula $\nwarrow$
9087 \begin_inset Space \hfill{}
9093 \begin_layout Standard
9094 \begin_inset VSpace medskip
9097 Vertical arrows can be used also as delimiter together with the commands
9099 \begin_inset CommandInset ref
9101 reference "sub:Manual-Bracket-Size"
9106 \begin_inset CommandInset ref
9108 reference "sub:Automatic-Bracket-Size"
9115 \begin_layout Standard
9116 \begin_inset Newpage newpage
9122 \begin_layout Section
9124 \begin_inset CommandInset label
9134 \begin_layout Plain Layout
9143 \begin_layout Standard
9144 Accents can be inserted via the math toolbar button
9145 \begin_inset Graphics
9146 filename ../images/math/hat.png
9152 or the commands listed in the following subsections.
9155 \begin_layout Subsection
9156 Accents for one Character
9160 \begin_layout Plain Layout
9173 \begin_layout Plain Layout
9175 \begin_inset CommandInset ref
9177 reference "sub:Accents-in-Text"
9190 \begin_layout Plain Layout
9198 \begin_inset Note Note
9201 \begin_layout Plain Layout
9204 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9207 \begin_layout Plain Layout
9210 texorpdfstring is in section
9211 \begin_inset CommandInset ref
9213 reference "sub:Formulas-in-Section"
9223 \begin_inset CommandInset label
9225 name "sub:Accents-for-one"
9233 \begin_layout Plain Layout
9234 Accents ! for one character
9242 \begin_layout Standard
9243 \begin_inset Space \hfill{}
9247 \begin_inset Tabular
9248 <lyxtabular version="3" rows="8" columns="2">
9250 <column alignment="center" valignment="top" width="0pt">
9251 <column alignment="center" valignment="top" width="0pt">
9253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9256 \begin_layout Plain Layout
9262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9265 \begin_layout Plain Layout
9267 \begin_inset Note Note
9270 \begin_layout Plain Layout
9277 is only used as spacer.
9289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9292 \begin_layout Plain Layout
9299 \begin_layout Plain Layout
9313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9316 \begin_layout Plain Layout
9317 \begin_inset Formula $\raisebox {5mm}{}\dot{A}$
9327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9330 \begin_layout Plain Layout
9337 \begin_layout Plain Layout
9351 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9354 \begin_layout Plain Layout
9355 \begin_inset Formula $\raisebox {5mm}{}\ddot{A}$
9365 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9368 \begin_layout Plain Layout
9375 \begin_layout Plain Layout
9389 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9392 \begin_layout Plain Layout
9393 \begin_inset Formula $\raisebox {5mm}{}\dddot{A}$
9403 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9406 \begin_layout Plain Layout
9414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9417 \begin_layout Plain Layout
9418 \begin_inset Formula $\raisebox {5mm}{}\ddddot {A}$
9428 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9431 \begin_layout Plain Layout
9438 \begin_layout Plain Layout
9451 \begin_layout Plain Layout
9462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9465 \begin_layout Plain Layout
9466 \begin_inset Formula $\raisebox {5mm}{}\vec{A}$
9476 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9479 \begin_layout Plain Layout
9486 \begin_layout Plain Layout
9500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9503 \begin_layout Plain Layout
9504 \begin_inset Formula $\raisebox {5mm}{}\bar{A}$
9514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9517 \begin_layout Plain Layout
9524 \begin_layout Plain Layout
9538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9541 \begin_layout Plain Layout
9542 \begin_inset Formula $\raisebox {5mm}{}\mathring{A}$
9556 \begin_inset Space \hfill{}
9560 \begin_inset Tabular
9561 <lyxtabular version="3" rows="7" columns="2">
9563 <column alignment="center" valignment="top" width="0pt">
9564 <column alignment="center" valignment="top" width="0pt">
9566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9569 \begin_layout Plain Layout
9575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9578 \begin_layout Plain Layout
9586 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9589 \begin_layout Plain Layout
9596 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Plain Layout
9614 \begin_inset Formula $\raisebox {5mm}{}\tilde{A}$
9624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9634 \begin_layout Plain Layout
9648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9651 \begin_layout Plain Layout
9652 \begin_inset Formula $\raisebox {5mm}{}\hat{A}$
9662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9665 \begin_layout Plain Layout
9672 \begin_layout Plain Layout
9686 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9689 \begin_layout Plain Layout
9690 \begin_inset Formula $\raisebox {5mm}{}\check{A}$
9700 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9703 \begin_layout Plain Layout
9710 \begin_layout Plain Layout
9724 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9727 \begin_layout Plain Layout
9728 \begin_inset Formula $\raisebox {5mm}{}\acute{A}$
9738 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9741 \begin_layout Plain Layout
9748 \begin_layout Plain Layout
9762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9765 \begin_layout Plain Layout
9766 \begin_inset Formula $\raisebox {5mm}{}\grave{A}$
9776 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9779 \begin_layout Plain Layout
9786 \begin_layout Plain Layout
9800 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9803 \begin_layout Plain Layout
9804 \begin_inset Formula $\raisebox {5mm}{}\breve{A}$
9818 \begin_inset Space \hfill{}
9824 \begin_layout Standard
9825 \begin_inset VSpace bigskip
9832 \begin_layout Plain Layout
9838 in formulas, a quotation mark is inserted before the vowel.
9839 These two characters are then treated by LaTeX as
9843 character when the formula part with the umlaut is marked as German.
9851 \begin_inset Quotes eld
9855 \begin_inset Quotes erd
9858 umlauts are created as demonstrated in the following example:
9861 \begin_layout Standard
9862 \begin_inset VSpace -2mm
9868 \begin_layout Standard
9870 \begin_inset Tabular
9871 <lyxtabular version="3" rows="3" columns="2">
9873 <column alignment="center" valignment="top" width="0">
9874 <column alignment="center" valignment="top" width="0">
9876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9879 \begin_layout Plain Layout
9885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9888 \begin_layout Plain Layout
9890 \begin_inset Note Note
9893 \begin_layout Plain Layout
9900 is only used as spacer.
9912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9915 \begin_layout Plain Layout
9918 \begin_inset Quotes grd
9926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9929 \begin_layout Plain Layout
9932 \begin_inset Formula $"i$
9942 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9945 \begin_layout Plain Layout
9952 \begin_layout Plain Layout
9966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9969 \begin_layout Plain Layout
9970 \begin_inset Formula $\raisebox {5mm}{}\ddot{i}$
9986 \begin_layout Standard
9987 Another advantage to
9993 is that umlauts can directly be converted to mathematical text because
9994 the accent commands above are
10000 in mathematical text
10003 To convert an accented character to mathematical text, only the character
10004 under the accent may be converted.
10005 This applies also for all other conversions, e.
10006 \begin_inset Space \thinspace{}
10010 \begin_inset Space ~
10016 \begin_layout Standard
10017 In mathematical text, umlauts and other accented characters can directly
10021 \begin_layout Subsection
10022 Accents for Operators
10026 \begin_layout Plain Layout
10027 Accents ! for operators
10035 \begin_layout Standard
10046 \begin_layout Plain Layout
10064 \begin_layout Plain Layout
10072 characters can be placed above or below an operator, respectively, to accent
10084 \begin_layout Plain Layout
10092 characters can be set before and behind an operator.
10093 The command scheme is:
10096 \begin_layout Standard
10112 \begin_layout Standard
10119 must always be before the operator that should be accented.
10120 You can accent with several characters and even with other operators and
10128 for example only characters behind an operator, write nothing between the
10129 first braces but don't omit the braces.
10132 \begin_layout Standard
10133 For example the command
10138 \begin_inset Formula $\to$
10148 \begin_inset Formula $\to$
10157 \begin_layout Plain Layout
10173 \begin_inset Formula \[
10174 \sideset {}{'}\sum_{k=1}^{n}\]
10181 \begin_layout Standard
10190 \begin_layout Plain Layout
10205 \begin_layout Plain Layout
10217 \begin_inset Formula $\uparrow$
10225 \begin_inset Formula \[
10226 \overset{a}{\maltese}\]
10230 As seen in the last example, with
10242 also symbols and characters can be accented; with
10248 this is not possible.
10251 \begin_layout Subsection
10252 Accents for several Characters
10253 \begin_inset CommandInset label
10255 name "sub:Accents-for-several"
10263 \begin_layout Plain Layout
10264 Accents ! for several characters
10272 \begin_layout Standard
10273 \begin_inset Space \hfill{}
10277 \begin_inset Tabular
10278 <lyxtabular version="3" rows="5" columns="2">
10280 <column alignment="center" valignment="top" width="0pt">
10281 <column alignment="center" valignment="top" width="0pt">
10283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10286 \begin_layout Plain Layout
10292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10295 \begin_layout Plain Layout
10297 \begin_inset Note Note
10300 \begin_layout Plain Layout
10307 is only used as spacer.
10319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10322 \begin_layout Plain Layout
10329 \begin_layout Plain Layout
10343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10346 \begin_layout Plain Layout
10347 \begin_inset Formula $\raisebox {6mm}{}\overleftarrow{A=B}\raisebox {-2mm}{}$
10357 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10360 \begin_layout Plain Layout
10367 \begin_layout Plain Layout
10381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10384 \begin_layout Plain Layout
10385 \begin_inset Formula $\raisebox {5mm}{}\underleftarrow{A=B}\raisebox {-3mm}{}$
10395 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10398 \begin_layout Plain Layout
10405 \begin_layout Plain Layout
10419 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10422 \begin_layout Plain Layout
10423 \begin_inset Formula $\raisebox {6mm}{}\overleftrightarrow{A=B}\raisebox {-2mm}{}$
10433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10436 \begin_layout Plain Layout
10439 underleftrightarrow
10443 \begin_layout Plain Layout
10457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10460 \begin_layout Plain Layout
10461 \begin_inset Formula $\raisebox {5mm}{}\underleftrightarrow{A=B}\raisebox {-3mm}{}$
10475 \begin_inset Space \hfill{}
10479 \begin_inset Tabular
10480 <lyxtabular version="3" rows="5" columns="2">
10482 <column alignment="center" valignment="top" width="0pt">
10483 <column alignment="center" valignment="top" width="0pt">
10485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10488 \begin_layout Plain Layout
10494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10497 \begin_layout Plain Layout
10505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10508 \begin_layout Plain Layout
10515 \begin_layout Plain Layout
10529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10532 \begin_layout Plain Layout
10533 \begin_inset Formula $\raisebox {6mm}{}\overrightarrow{A=B}\raisebox {-2mm}{}$
10543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10546 \begin_layout Plain Layout
10553 \begin_layout Plain Layout
10567 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10570 \begin_layout Plain Layout
10571 \begin_inset Formula $\raisebox {5mm}{}\underrightarrow{A=B}\raisebox {-3mm}{}$
10581 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10584 \begin_layout Plain Layout
10591 \begin_layout Plain Layout
10605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10608 \begin_layout Plain Layout
10609 \begin_inset Formula $\raisebox {6mm}{}\widetilde{A=B}\raisebox {-2mm}{}$
10619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10622 \begin_layout Plain Layout
10629 \begin_layout Plain Layout
10643 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10646 \begin_layout Plain Layout
10647 \begin_inset Formula $\raisebox {6mm}{}\widehat{A=B}\raisebox {-2mm}{}$
10661 \begin_inset Space \hfill{}
10667 \begin_layout Standard
10668 \begin_inset VSpace medskip
10671 With these commands as many characters as you like can be accented.
10684 will only be set in the output with a length of three characters, as shown
10685 in the following example:
10686 \begin_inset Formula \[
10687 \widetilde{A+B=C-D}\]
10694 \begin_layout Standard
10705 \begin_layout Plain Layout
10723 \begin_layout Plain Layout
10731 described in the previous subsection it is also possible to accent several
10741 \begin_layout Plain Layout
10751 \begin_inset Formula $\downarrow$
10757 \begin_inset Formula \[
10758 \underset{***}{A=B}\]
10765 \begin_layout Section
10767 \begin_inset CommandInset label
10777 \begin_layout Plain Layout
10786 \begin_layout Subsection
10788 \begin_inset CommandInset label
10790 name "sub:Predefined-Space"
10798 \begin_layout Plain Layout
10799 Space ! horizontal ! predefined
10807 \begin_layout Standard
10808 Sometimes it is necessary to insert horizontal space to a formula.
10809 This is done by inserting a protected space (shortcut
10815 \begin_inset Quotes eld
10825 \begin_layout Plain Layout
10838 \begin_inset Quotes erd
10841 appears and by pressing
10845 several times one can select one of eight different space sizes.
10846 The spaces can also be inserted using the math toolbar button
10847 \begin_inset Graphics
10848 filename ../images/math/space.png
10854 or special commands.
10855 Independent from the inserted command, one can select the size again by
10863 \begin_layout Standard
10866 \begin_inset VSpace -5mm
10870 \begin_inset Tabular
10871 <lyxtabular version="3" rows="3" columns="7">
10873 <column alignment="center" valignment="middle" width="6.8cm">
10874 <column alignment="center" valignment="top" width="0">
10875 <column alignment="center" valignment="top" width="0">
10876 <column alignment="center" valignment="top" width="0">
10877 <column alignment="center" valignment="top" width="0">
10878 <column alignment="center" valignment="top" width="0">
10879 <column alignment="center" valignment="top" width="0">
10881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10884 \begin_layout Plain Layout
10890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10893 \begin_layout Plain Layout
10901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10904 \begin_layout Plain Layout
10912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10915 \begin_layout Plain Layout
10923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10926 \begin_layout Plain Layout
10934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10937 \begin_layout Plain Layout
10945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10948 \begin_layout Plain Layout
10958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10961 \begin_layout Plain Layout
10966 keystrokes after inserting the protected space
10971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10974 \begin_layout Plain Layout
10980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10983 \begin_layout Plain Layout
10989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10992 \begin_layout Plain Layout
10998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11019 \begin_layout Plain Layout
11027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11030 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11040 \begin_inset Formula $A\, B$
11048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11051 \begin_layout Plain Layout
11052 \begin_inset Formula $A\: B$
11060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11063 \begin_layout Plain Layout
11064 \begin_inset Formula $A\; B$
11072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11075 \begin_layout Plain Layout
11076 \begin_inset Formula $A\quad B$
11084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11087 \begin_layout Plain Layout
11088 \begin_inset Formula $A\qquad B$
11096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11099 \begin_layout Plain Layout
11100 \begin_inset Formula $A\! B$
11116 \begin_layout Standard
11117 The last size seem to produce no space.
11118 It is displayed red in LyX contrary to the other sizes, because it is a
11120 There are two more negative spaces:
11123 \begin_layout Standard
11125 \begin_inset Tabular
11126 <lyxtabular version="3" rows="3" columns="3">
11128 <column alignment="center" valignment="middle" width="6.8cm">
11129 <column alignment="center" valignment="top" width="0pt">
11130 <column alignment="center" valignment="top" width="0pt">
11132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11155 \begin_layout Plain Layout
11165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11173 keystrokes after inserting the protected space
11178 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11187 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11190 \begin_layout Plain Layout
11198 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11210 \begin_layout Plain Layout
11211 \begin_inset Formula $A\negmedspace B$
11219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11223 \begin_inset Formula $A\negthickspace B$
11239 \begin_layout Standard
11240 Negative spaces can lead to characters overlapping each other.
11241 Thus they can be used to enforce ligatures, what is e.
11242 \begin_inset Space \thinspace{}
11246 \begin_inset Space ~
11249 useful for summation operators:
11252 \begin_layout Standard
11254 \begin_inset Tabular
11255 <lyxtabular version="3" rows="3" columns="2">
11257 <column alignment="center" valignment="top" width="0">
11258 <column alignment="center" valignment="top" width="0">
11260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11263 \begin_layout Plain Layout
11269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11272 \begin_layout Plain Layout
11274 \begin_inset Note Note
11277 \begin_layout Plain Layout
11284 is only used as spacer.
11296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11308 \begin_layout Plain Layout
11322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11325 \begin_layout Plain Layout
11326 \begin_inset Formula $\raisebox {4.5mm}{}\sum\sum f_{kl}\raisebox {-2.5mm}{}$
11336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11339 \begin_layout Plain Layout
11350 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11367 \begin_layout Plain Layout
11368 \begin_inset Formula $\raisebox {4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox {-2.5mm}{}$
11384 \begin_layout Standard
11385 Relations like for example equal signs, are always surrounded by space.
11386 To suppress this, the equal sign is placed into a TeX-brace.
11387 The following example demonstrates this:
11390 \begin_layout Standard
11392 \begin_inset Tabular
11393 <lyxtabular version="3" rows="2" columns="2">
11395 <column alignment="center" valignment="top" width="0pt">
11396 <column alignment="center" valignment="top" width="0pt">
11398 <cell alignment="center" valignment="top" usebox="none">
11401 \begin_layout Plain Layout
11407 <cell alignment="center" valignment="top" usebox="none">
11410 \begin_layout Plain Layout
11411 \begin_inset Formula $A=B$
11421 <cell alignment="center" valignment="top" usebox="none">
11424 \begin_layout Plain Layout
11425 \begin_inset Note Note
11428 \begin_layout Plain Layout
11435 is only used as spacer.
11441 \begin_inset Formula $\raisebox {5mm}{}$
11444 equation without space
11449 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11452 \begin_layout Plain Layout
11453 \begin_inset Formula $A{=}B$
11469 \begin_layout Standard
11471 The command for the last formula is:
11476 \begin_inset Formula $\to$
11482 \begin_layout Standard
11483 \begin_inset VSpace bigskip
11486 Spaces are needed for physical units, because the space between the value
11487 and the unit is the smallest one and not a normal space.
11488 For units in text, the smallest space is inserted via the menu
11490 Insert\SpecialChar \menuseparator
11491 Formatting\SpecialChar \menuseparator
11493 \begin_inset Space ~
11505 \begin_layout Standard
11506 An example to visualize the difference:
11509 \begin_layout Standard
11510 \begin_inset Tabular
11511 <lyxtabular version="3" rows="2" columns="2">
11513 <column alignment="left" valignment="top" width="0">
11514 <column alignment="left" valignment="top" width="0">
11516 <cell alignment="center" valignment="top" usebox="none">
11519 \begin_layout Plain Layout
11521 \begin_inset Formula $\cdot$
11529 <cell alignment="center" valignment="top" usebox="none">
11532 \begin_layout Plain Layout
11533 space between value and unit
11540 <cell alignment="center" valignment="top" usebox="none">
11543 \begin_layout Plain Layout
11545 \begin_inset Space \thinspace{}
11549 \begin_inset Formula $\cdot$
11557 <cell alignment="center" valignment="top" usebox="none">
11560 \begin_layout Plain Layout
11561 smallest space between value and unit
11574 \begin_layout Subsection
11579 \begin_layout Plain Layout
11592 \begin_layout Plain Layout
11593 for vertical space in formulas see
11594 \begin_inset CommandInset ref
11596 reference "sub:Line-Separation"
11609 \begin_layout Plain Layout
11617 \begin_inset Note Note
11620 \begin_layout Plain Layout
11623 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11626 \begin_layout Plain Layout
11629 texorpdfstring is in section
11630 \begin_inset CommandInset ref
11632 reference "sub:Formulas-in-Section"
11642 \begin_inset CommandInset label
11644 name "sub:Variable-Space"
11652 \begin_layout Plain Layout
11653 Space ! horizontal ! variable
11661 \begin_layout Standard
11662 Space with a defined length can be inserted in LyX with the command
11663 \begin_inset Newline newline
11676 \begin_layout Plain Layout
11685 For the length all units listed in
11686 \begin_inset CommandInset ref
11688 reference "tab:Used-units"
11692 are allowed, except of the unit
11693 \begin_inset Quotes eld
11697 \begin_inset Quotes erd
11701 The length may also be negative.
11702 To insert so many space that the formula uses all available space, the
11713 \begin_layout Plain Layout
11724 \begin_layout Standard
11725 \begin_inset VSpace -1mm
11731 \begin_layout Standard
11733 \begin_inset Tabular
11734 <lyxtabular version="3" rows="4" columns="2">
11736 <column alignment="center" valignment="top" width="0">
11737 <column alignment="center" valignment="top" width="0">
11739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11742 \begin_layout Plain Layout
11748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11751 \begin_layout Plain Layout
11759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11762 \begin_layout Plain Layout
11766 \begin_inset Formula $\to$
11776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11779 \begin_layout Plain Layout
11780 \begin_inset Formula $A=B\hspace {3cm}A\not=C$
11790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11793 \begin_layout Plain Layout
11797 \begin_inset Formula $\to$
11807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11810 \begin_layout Plain Layout
11811 \begin_inset Formula $A\hspace {-1mm}A\not=A$
11821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11824 \begin_layout Plain Layout
11831 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Formula $A=A\hfill B=B$
11865 \begin_layout Standard
11866 In the last example the available space is given by the longest column entry
11868 In an inline formula the space depends on the length of the line in which
11876 Thus, when the line uses the full width, no space will be created.
11883 has only an effect on displayed formulas when the formula style
11888 (Formula styles are explained in
11889 \begin_inset CommandInset ref
11891 reference "sec:Formula-Styles"
11898 \begin_layout Standard
11911 can also be inserted in TeX-mode to use them for text:
11914 \begin_layout Standard
11915 This is a line with
11919 \begin_layout Plain Layout
11929 \begin_inset Space \thinspace{}
11935 \begin_layout Standard
11936 This is a line with
11937 \begin_inset Space \hfill{}
11943 \begin_layout Standard
11944 In the last example
11950 was inserted via the menu
11952 Insert\SpecialChar \menuseparator
11953 Formatting\SpecialChar \menuseparator
11955 \begin_inset Space ~
11960 , what is not possible in formulas.
11961 This has the advantage that one can directly see in LyX that this is a
11965 \begin_layout Standard
11966 When the commands are at the begin of a text line but not at the beginning
11967 of a paragraph, they will be ignored by LaTeX.
11968 To avoid that, the command
11981 To get the same with
11987 , a line break and an empty placeholder
11993 \begin_layout Plain Layout
11994 for placeholders see
11995 \begin_inset CommandInset ref
11997 reference "sub:Placeholders"
12008 is inserted in TeX-mode with the command
12024 \begin_layout Subsection
12025 Space besides inline Formulas
12029 \begin_layout Plain Layout
12030 Space ! besides inline formulas
12038 \begin_layout Standard
12039 The space that surrounds inline formulas can be adjusted with the length
12048 \begin_layout Plain Layout
12059 The value of a length is set with the command
12067 \begin_layout Plain Layout
12077 that has the following scheme:
12080 \begin_layout Standard
12085 setlength{length name}{value}
12088 \begin_layout Standard
12096 \begin_inset Space \thinspace{}
12102 \begin_layout Standard
12112 \begin_layout Standard
12113 is inserted in TeX-mode.
12115 \begin_inset Space \thinspace{}
12118 mm space will now be set around all inline formulas:
12122 \begin_layout Plain Layout
12136 \begin_layout Standard
12137 This is a line with an inline formula
12138 \begin_inset Formula $A=B$
12142 \begin_inset Space \thinspace{}
12145 mm surrounding space.
12149 \begin_layout Plain Layout
12163 \begin_layout Standard
12164 To return to the predefined value,
12170 is set to the value 0
12171 \begin_inset Space \thinspace{}
12177 \begin_layout Section
12182 \begin_layout Plain Layout
12192 \begin_layout Plain Layout
12197 \begin_layout Plain Layout
12208 \begin_layout Plain Layout
12223 \begin_layout Standard
12224 Boxes for text are described in chapter
12231 \begin_inset Space ~
12239 \begin_layout Subsection
12241 \begin_inset CommandInset label
12243 name "sub:Boxes-with-Frame"
12251 \begin_layout Plain Layout
12260 \begin_layout Standard
12261 It is possible to frame formulas or parts of it with the commands
12271 \begin_layout Plain Layout
12289 \begin_layout Plain Layout
12300 \begin_layout Standard
12301 When one of these commands is inserted to a formula, a blue box appears
12302 within a frame to enter formula parts.
12309 an additional formula has to be created by
12317 \begin_layout Plain Layout
12318 Due to a bug in LyX it is not possible to create a new formula with
12326 \begin_layout Plain Layout
12330 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12339 \begin_layout Plain Layout
12351 , because the box content will otherwise be treated as mathematical text.
12358 is used, a new formula is automatically created inside the frame.
12361 \begin_layout Standard
12368 is not suitable to frame displayed formulas, because the formula will always
12369 be set in the size of the text.
12376 is in contrary not suitable to frame inline formulas, because the formula
12377 will always be set in the size of a displayed formula.
12380 \begin_layout Standard
12387 there is the command
12397 \begin_layout Plain Layout
12405 where additionally the frame width and the alignment can be specified.
12412 is used in the following scheme:
12415 \begin_layout Standard
12420 framebox[frame width][position]{box content}
12423 \begin_layout Standard
12424 The position can either be
12441 right aligns the formula in the box.
12442 When no position is given, the formula will be centered.
12443 \begin_inset Newline newline
12446 Is no width given, also no position can be given.
12447 In this case the frame width is adjusted to the box content like for
12456 \begin_layout Standard
12463 is inserted, a box appears containing three blue boxes.
12464 The first two boxes are surrounded by brackets and denote the two optional
12466 The third box is for formula parts like for
12475 \begin_layout Standard
12477 \begin_inset Note Note
12480 \begin_layout Plain Layout
12481 The table has been set into a minipage to make the footnote appearing.
12482 Otherwise the footnote text would not be displayed.
12488 \begin_inset Box Frameless
12497 height_special "totalheight"
12500 \begin_layout Plain Layout
12502 \begin_inset Tabular
12503 <lyxtabular version="3" rows="5" columns="2">
12505 <column alignment="center" valignment="top" width="0">
12506 <column alignment="center" valignment="top" width="0">
12508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12511 \begin_layout Plain Layout
12516 \begin_layout Plain Layout
12517 Due to a bug in LyX it is not possible to create a new formula with
12525 \begin_layout Plain Layout
12529 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
12538 \begin_layout Plain Layout
12555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12558 \begin_layout Plain Layout
12560 \begin_inset Note Note
12563 \begin_layout Plain Layout
12570 is only used as spacer.
12582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12585 \begin_layout Plain Layout
12592 \begin_layout Plain Layout
12611 \begin_layout Plain Layout
12625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12628 \begin_layout Plain Layout
12629 \begin_inset Formula \raisebox {6mm}{}\fbox{$\int A=B$}\raisebox {-4mm}{}
12640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12643 \begin_layout Plain Layout
12650 \begin_layout Plain Layout
12665 \begin_layout Plain Layout
12679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12682 \begin_layout Plain Layout
12683 \begin_inset Formula $\raisebox {8.5mm}{}\boxed{\int A=B}\raisebox {-6.5mm}{}$
12693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12696 \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 $\raisebox {6mm}{}A+\fbox{B}\raisebox {-3mm}{}$
12731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12734 \begin_layout Plain Layout
12741 \begin_layout Plain Layout
12751 \begin_inset Formula $\to$
12755 \begin_inset Formula $\to$
12768 \begin_layout Plain Layout
12778 \begin_inset Formula $\downarrow$
12786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12789 \begin_layout Plain Layout
12790 \begin_inset Formula $\raisebox {6mm}{}$
12794 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12798 \begin_inset Formula $\raisebox {-4mm}{}$
12819 \begin_layout Standard
12820 The frame thickness can also be adjusted.
12821 To do this the following commands have to be inserted in TeX-mode before
12825 \begin_layout Standard
12835 \begin_inset Quotes eld
12839 \begin_inset Quotes erd
12853 \begin_inset Quotes eld
12857 \begin_inset Quotes erd
12863 \begin_layout Standard
12864 \begin_inset Quotes eld
12868 \begin_inset Quotes erd
12871 specifies the minimal distance between the frame and the first character
12873 An example for this is the following framed formula:
12877 \begin_layout Plain Layout
12889 \begin_inset Formula \[
12894 Before this formula the commands
12897 \begin_layout Standard
12919 \begin_layout Standard
12920 were inserted in TeX-mode.
12921 The given values are used for all following boxes.
12924 \begin_layout Standard
12925 To return to the standard frame size, the command
12928 \begin_layout Standard
12953 \begin_layout Plain Layout
12967 \begin_layout Standard
12968 is inserted in TeX-mode before the next formula.
12971 \begin_layout Subsection
12972 Boxes without Frame
12973 \begin_inset CommandInset label
12975 name "sub:Boxes-without-Frame"
12983 \begin_layout Plain Layout
12984 Boxes ! without frame
12992 \begin_layout Standard
12993 For boxes without a frame there are the following box commands:
13003 \begin_layout Plain Layout
13021 \begin_layout Plain Layout
13039 \begin_layout Plain Layout
13050 \begin_layout Standard
13057 a box can be super- or subscripted.
13058 But in contrary to normal super- and subscripting, the characters in the
13059 box keep their font size.
13066 is used in the following scheme:
13069 \begin_layout Standard
13074 raisebox{height}{box content}
13077 \begin_layout Standard
13078 When the box should contain a formula, an extra formula is needed like for
13088 \begin_layout Standard
13090 \begin_inset Tabular
13091 <lyxtabular version="3" rows="4" columns="2">
13093 <column alignment="center" valignment="top" width="0">
13094 <column alignment="center" valignment="top" width="0">
13096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13099 \begin_layout Plain Layout
13105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13108 \begin_layout Plain Layout
13116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13119 \begin_layout Plain Layout
13123 \begin_inset Formula $\to$
13129 \begin_inset Formula $\to$
13137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13140 \begin_layout Plain Layout
13141 \begin_inset Formula $H\raisebox {2mm}{al}lo$
13151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13154 \begin_layout Plain Layout
13158 \begin_inset Formula $\to$
13164 \begin_inset Formula $\to$
13172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13175 \begin_layout Plain Layout
13176 \begin_inset Formula $H\raisebox {-2mm}{al}lo$
13186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13189 \begin_layout Plain Layout
13193 \begin_inset Formula $\to$
13208 \begin_layout Plain Layout
13222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13225 \begin_layout Plain Layout
13229 \begin_layout Plain Layout
13253 \begin_layout Standard
13254 The last formula can currently only be created using TeX-mode because LyX
13255 inserts a box instead of the needed extra formula.
13259 \begin_layout Plain Layout
13264 \begin_layout Plain Layout
13268 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
13277 \begin_layout Plain Layout
13292 \begin_layout Standard
13317 , with the difference that there is no frame.
13320 \begin_layout Subsection
13322 \begin_inset CommandInset label
13324 name "sub:Colored-Boxes"
13332 \begin_layout Plain Layout
13341 \begin_layout Standard
13342 To be able to use all commands explained in this section, the LaTeX-package
13351 \begin_layout Plain Layout
13356 is part of every LaTeX standard installation.
13365 \begin_layout Plain Layout
13371 has to be loaded in the LaTeX-preamble with the line
13375 \begin_layout Plain Layout
13376 When text is colored somewhere in the document with a predefined color,
13377 LyX loads the LaTeX-package
13382 Thus it is possible that the package is loaded twice, but this doesn't
13389 \begin_inset Note Note
13392 \begin_layout Plain Layout
13393 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13402 \begin_layout Standard
13410 \begin_layout Standard
13411 \begin_inset VSpace medskip
13414 To color boxes, the command
13424 \begin_layout Plain Layout
13432 is used in the following scheme:
13435 \begin_layout Standard
13440 colorbox{color}{box content}
13443 \begin_layout Standard
13444 The box content can also be a box and a
13450 can also be part of another box (see the 2nd and 3rd example).
13451 When the box should contain a formula, an extra formula has to be created,
13462 \begin_layout Plain Layout
13463 This also applies for the command
13474 \begin_layout Plain Layout
13478 href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
13487 \begin_layout Plain Layout
13502 \begin_layout Standard
13503 One of the following predefined colors can be chosen:
13506 \begin_layout Standard
13540 \begin_layout Standard
13542 \begin_inset Tabular
13543 <lyxtabular version="3" rows="4" columns="2">
13545 <column alignment="center" valignment="top" width="0">
13546 <column alignment="center" valignment="top" width="0">
13548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13551 \begin_layout Plain Layout
13557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13560 \begin_layout Plain Layout
13562 \begin_inset Note Note
13565 \begin_layout Plain Layout
13572 is only used as spacer.
13584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13587 \begin_layout Plain Layout
13591 \begin_inset Formula $\to$
13601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13604 \begin_layout Plain Layout
13605 \begin_inset Formula $\raisebox {6mm}{}\colorbox {yellow}{A=B}\raisebox {-3mm}{}$
13615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13618 \begin_layout Plain Layout
13622 \begin_inset Formula $\to$
13633 \begin_layout Plain Layout
13647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13650 \begin_layout Plain Layout
13651 \begin_inset Formula $\raisebox {6mm}{}\colorbox {green}{\fbox{A=B}}\raisebox {-3mm}{}$
13661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13664 \begin_layout Plain Layout
13671 \begin_layout Plain Layout
13683 \begin_inset Formula $\to$
13693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13696 \begin_layout Plain Layout
13697 \begin_inset Formula $\raisebox {6mm}{}\fbox{\colorbox {green}{A=B}}\raisebox {-3mm}{}$
13713 \begin_layout Standard
13720 only colors the box but not the characters in the box.
13721 To color all characters, the whole formula is highlighted and the wanted
13722 color is chosen in the
13725 \begin_inset Space ~
13731 The dialog can be called with the toolbar button
13732 \begin_inset Graphics
13733 filename ../images/dialog-show_character.png
13741 Edit\SpecialChar \menuseparator
13743 \begin_inset Space ~
13746 Style\SpecialChar \menuseparator
13750 The formula number has then the same color as the formula.
13751 When the formula number should get another color than the formula characters,
13752 the color must be changed within the formula.
13755 \begin_layout Standard
13759 \begin_layout Standard
13762 \begin_inset Formula \begin{equation}
13763 \int A=B\label{eq:red}\end{equation}
13770 \begin_inset Formula \begin{equation}
13771 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13778 \begin_layout Standard
13780 \begin_inset CommandInset ref
13786 is completely colored red.
13787 \begin_inset Newline newline
13791 \begin_inset CommandInset ref
13793 reference "eq:redgreen"
13797 was first completely colored green to set the color for the formula number.
13798 Subsequently the formula characters were colored red.
13801 \begin_layout Standard
13802 \begin_inset VSpace bigskip
13805 To color the frame different than the rest of the box, the command
13815 \begin_layout Plain Layout
13823 is used in the following scheme:
13826 \begin_layout Standard
13831 fcolorbox{frame color}{color}{box content}
13834 \begin_layout Standard
13841 is an extension of the command
13848 The frame width is set, like for
13871 \begin_layout Plain Layout
13883 \begin_inset Formula \[
13884 \fcolorbox {cyan}{magenta}{A=B}\]
13892 \begin_layout Plain Layout
13906 \begin_layout Standard
13907 This formula was created with the command
13908 \begin_inset Newline newline
13916 \begin_inset Formula $\to$
13922 \begin_inset Formula $\to$
13932 \begin_layout Standard
13933 \begin_inset VSpace bigskip
13936 To use other colors than the predefined ones, they have to be defined first.
13939 \begin_layout Standard
13940 One can for example define the color
13941 \begin_inset Quotes eld
13949 \begin_inset Quotes erd
13952 with the LaTeX-preamble line:
13955 \begin_layout Standard
13960 definecolor{darkgreen}{cmyk}{0.5,
13978 \begin_layout Plain Layout
13989 \begin_layout Standard
13994 is the color space that denotes the colors
14011 The four comma separated numbers are the portion factor for the corresponding
14012 colors of the color space.
14013 The factors can be in the range of 0
14014 \begin_inset Space \thinspace{}
14018 \begin_inset Space \thinspace{}
14026 also the color space
14030 can be used for definitions.
14047 , so that there are in this case three portion factors for the corresponding
14049 Furthermore there is the color space
14053 with one portion factor for the gray value.
14056 \begin_layout Standard
14057 As example a framed box with the new defined color
14061 where the characters have been colored
14066 \begin_inset Formula \begin{equation}
14067 \colorbox {darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14074 \begin_layout Standard
14075 Self-defined colors can also be used for text with the help of the command
14086 \begin_layout Plain Layout
14095 \begin_layout Standard
14099 \begin_layout Plain Layout
14103 textcolor{darkgreen}{
14109 \begin_inset Quotes eld
14113 \begin_inset Quotes erd
14120 \begin_layout Plain Layout
14130 \begin_layout Standard
14141 \begin_layout Plain Layout
14149 is used in the scheme
14153 textcolor{color}{characters to color}
14158 \begin_layout Subsection
14160 \begin_inset CommandInset label
14162 name "sub:Paragraph-Boxes"
14170 \begin_layout Plain Layout
14171 Boxes ! as paragraph
14179 \begin_layout Standard
14180 A box that can contain several lines and paragraphs, a so called paragraph
14181 box (parbox), can be created with the menu
14183 Insert\SpecialChar \menuseparator
14186 or the toolbar button
14187 \begin_inset Graphics
14188 filename ../images/box-insert.png
14197 \begin_layout Standard
14198 The following example shows a framed parbox in a line:
14201 \begin_layout Standard
14202 \begin_inset VSpace medskip
14206 \begin_inset Box Boxed
14215 height_special "totalheight"
14218 \begin_layout Plain Layout
14219 This is a paragraph box.
14221 \begin_inset Space \thinspace{}
14224 cm long and can also contain formulas:
14225 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14236 \begin_layout Standard
14237 \begin_inset VSpace medskip
14243 \begin_layout Standard
14244 Such a box is created by right-clicking on the gray box inset.
14245 A dialog pops up showing the box properties.
14259 \begin_inset Space \thinspace{}
14264 Vertical Box Alignment
14269 \begin_layout Standard
14270 \begin_inset VSpace medskip
14273 In LaTeX a parbox is created with the command
14283 \begin_layout Plain Layout
14291 that has the following scheme:
14294 \begin_layout Standard
14299 parbox[position]{width}{box content}
14302 \begin_layout Standard
14316 for bottom means that the box is aligned within the surrounding text with
14322 for top this is done with the first line.
14323 When no position is given, the box will be vertically centered, see section
14331 \begin_inset Space ~
14336 manual for examples.
14339 \begin_layout Standard
14340 \begin_inset VSpace bigskip
14343 To frame formulas completely, including the formula number, the formula
14344 must be set into a parbox.
14345 To do this, the command
14359 is inserted in TeX-mode before the formula.
14368 \begin_layout Plain Layout
14378 is hereby the line width set for the document.
14379 Because the frame is outside the parbox, 2
14380 \begin_inset Space \thinspace{}
14383 times the frame separation and the frame thickness must be subtracted from
14385 As this is not automatically done by LyX due to a bug
14389 \begin_layout Plain Layout
14393 \begin_layout Plain Layout
14397 href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
14406 \begin_layout Plain Layout
14418 , TeX-mode has to be used.
14419 To be able to multiply and subtract in arguments, the LaTeX-package
14427 \begin_layout Plain Layout
14432 is part of every LaTeX standard installation.
14441 \begin_layout Plain Layout
14447 must be loaded in the LaTeX-preamble with the line
14450 \begin_layout Standard
14458 \begin_layout Standard
14459 Behind the formula both boxes are closed by entering
14464 Here is an example:
14468 \begin_layout Plain Layout
14482 \begin_layout Standard
14486 \begin_layout Plain Layout
14504 \begin_inset Formula \begin{equation}
14505 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14513 \begin_layout Plain Layout
14524 \begin_layout Plain Layout
14538 \begin_layout Standard
14539 \begin_inset VSpace medskip
14542 As a parbox is used as argument of
14548 , there is in this case no difference between
14563 \begin_layout Standard
14564 \begin_inset VSpace bigskip
14567 Paragraph boxes are very useful to comment formulas directly.
14574 is used in combination with the command
14588 \begin_inset CommandInset ref
14590 reference "sub:User-defined-Numbering"
14597 \begin_layout Standard
14598 An example of a formula commented with
14607 \begin_layout Standard
14611 \begin_layout Plain Layout
14624 This is a description.
14625 It is distinctly separated from the formula and multiline.
14629 \begin_layout Plain Layout
14641 \begin_layout Standard
14642 Such a formula must be inserted completely in TeX-mode because LyX does
14643 not yet support the command
14650 The formula is created with the following command sequence:
14653 \begin_layout Standard
14666 is inserted in TeX-mode.
14670 \begin_layout Plain Layout
14671 When the formula style
14683 can also be replaced by
14690 (formula styles see
14691 \begin_inset CommandInset ref
14693 reference "sec:Formula-Styles"
14702 Then the description follows as normal text, and finally
14708 is inserted in TeX-mode.
14721 hereby create a displayed formula.
14724 \begin_layout Standard
14731 can be seen in this example that was
14732 \begin_inset Quotes eld
14736 \begin_inset Quotes erd
14739 using the mathematical textmode:
14740 \begin_inset Formula \[
14741 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14748 \begin_layout Section
14753 \begin_layout Plain Layout
14762 \begin_layout Subsection
14764 \begin_inset CommandInset label
14766 name "sub:Big-Operators"
14774 \begin_layout Plain Layout
14784 \begin_layout Plain Layout
14794 \begin_layout Plain Layout
14803 \begin_layout Standard
14804 To be able to use all integral operators listed here, the option
14806 Use esint package automatically
14808 must be set in the document settings under
14811 \begin_inset Space ~
14819 \begin_layout Standard
14820 \begin_inset Space \hfill{}
14824 \begin_inset Tabular
14825 <lyxtabular version="3" rows="11" columns="2">
14827 <column alignment="center" valignment="top" width="0pt">
14828 <column alignment="center" valignment="top" width="0pt">
14830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14833 \begin_layout Plain Layout
14839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14842 \begin_layout Plain Layout
14850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14853 \begin_layout Plain Layout
14860 \begin_layout Plain Layout
14873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14876 \begin_layout Plain Layout
14877 \begin_inset Formula $\sum$
14887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14890 \begin_layout Plain Layout
14897 \begin_layout Plain Layout
14910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14913 \begin_layout Plain Layout
14914 \begin_inset Formula $\int$
14924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14927 \begin_layout Plain Layout
14935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14938 \begin_layout Plain Layout
14939 \begin_inset Formula $\intop$
14949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14952 \begin_layout Plain Layout
14960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14963 \begin_layout Plain Layout
14964 \begin_inset Formula $\oint$
14974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14977 \begin_layout Plain Layout
14985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14988 \begin_layout Plain Layout
14989 \begin_inset Formula $\ointop$
14999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15002 \begin_layout Plain Layout
15010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15013 \begin_layout Plain Layout
15014 \begin_inset Formula $\ointctrclockwise$
15024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15027 \begin_layout Plain Layout
15035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15038 \begin_layout Plain Layout
15039 \begin_inset Formula $\ointclockwise$
15049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15052 \begin_layout Plain Layout
15060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15063 \begin_layout Plain Layout
15064 \begin_inset Formula $\sqint$
15074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15077 \begin_layout Plain Layout
15085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15088 \begin_layout Plain Layout
15089 \begin_inset Formula $\bigcap$
15099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15113 \begin_layout Plain Layout
15114 \begin_inset Formula $\bigcup$
15128 \begin_inset Space \hfill{}
15132 \begin_inset Tabular
15133 <lyxtabular version="3" rows="10" columns="2">
15135 <column alignment="center" valignment="top" width="0pt">
15136 <column alignment="center" valignment="top" width="0pt">
15138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15141 \begin_layout Plain Layout
15147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15150 \begin_layout Plain Layout
15158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15161 \begin_layout Plain Layout
15168 \begin_layout Plain Layout
15181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15184 \begin_layout Plain Layout
15185 \begin_inset Formula $\prod$
15195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15198 \begin_layout Plain Layout
15206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15209 \begin_layout Plain Layout
15210 \begin_inset Formula $\coprod$
15220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15223 \begin_layout Plain Layout
15231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15234 \begin_layout Plain Layout
15235 \begin_inset Formula $\bigodot$
15245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15248 \begin_layout Plain Layout
15256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15259 \begin_layout Plain Layout
15260 \begin_inset Formula $\bigotimes$
15270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15273 \begin_layout Plain Layout
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15285 \begin_inset Formula $\bigoplus$
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15298 \begin_layout Plain Layout
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15309 \begin_layout Plain Layout
15310 \begin_inset Formula $\bigwedge$
15320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15323 \begin_layout Plain Layout
15331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15334 \begin_layout Plain Layout
15335 \begin_inset Formula $\bigvee$
15345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15348 \begin_layout Plain Layout
15356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15359 \begin_layout Plain Layout
15360 \begin_inset Formula $\bigsqcup$
15370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15373 \begin_layout Plain Layout
15381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15384 \begin_layout Plain Layout
15385 \begin_inset Formula $\biguplus$
15399 \begin_inset Space \hfill{}
15405 \begin_layout Standard
15406 All big operators can also be inserted via the math toolbar button
15407 \begin_inset Graphics
15408 filename ../images/math/intop.png
15417 \begin_layout Standard
15418 The operators are called big because they are bigger than the sometimes
15419 equal looking binary operators.
15420 All big operators can have limits as described in the next subsection.
15423 \begin_layout Standard
15449 \begin_inset Space ~
15452 in the style the operator limits are displayed, see
15453 \begin_inset CommandInset ref
15455 reference "sub:Operator-Limits"
15463 \begin_layout Subsubsection*
15464 Advices for Integrals
15467 \begin_layout Standard
15472 in an integral is an operator, that therefore has to be set upright.
15473 This is done by highlighting the
15477 and using the keyboard shortcut
15480 \begin_inset Space ~
15489 \begin_layout Plain Layout
15495 \begin_inset CommandInset ref
15497 reference "sub:Font-Styles"
15507 Finally the smallest space is inserted before the
15511 , as this is usual for operators.
15515 \begin_layout Standard
15517 \begin_inset Formula $\int A(x)dx$
15521 \begin_inset Newline newline
15528 \begin_layout Plain Layout
15538 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15544 \begin_layout Standard
15545 For multiple integrals there are the following commands:
15546 \begin_inset VSpace medskip
15552 \begin_layout Standard
15553 \begin_inset Space \hfill{}
15557 \begin_inset Tabular
15558 <lyxtabular version="3" rows="4" columns="2">
15560 <column alignment="center" valignment="top" width="0">
15561 <column alignment="center" valignment="top" width="0">
15563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15566 \begin_layout Plain Layout
15572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15575 \begin_layout Plain Layout
15577 \begin_inset Note Note
15580 \begin_layout Plain Layout
15587 is only used as spacer.
15599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15602 \begin_layout Plain Layout
15610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15613 \begin_layout Plain Layout
15614 \begin_inset Formula $\raisebox {4.5mm}{}\iint\raisebox {-2.5mm}{}$
15624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15627 \begin_layout Plain Layout
15635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15638 \begin_layout Plain Layout
15639 \begin_inset Formula $\raisebox {4.5mm}{}\oiint\raisebox {-2.5mm}{}$
15649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15652 \begin_layout Plain Layout
15660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15663 \begin_layout Plain Layout
15664 \begin_inset Formula $\raisebox {4.5mm}{}\sqiint\raisebox {-2.5mm}{}$
15678 \begin_inset Space \hfill{}
15682 \begin_inset Tabular
15683 <lyxtabular version="3" rows="4" columns="2">
15685 <column alignment="center" valignment="top" width="0">
15686 <column alignment="center" valignment="top" width="0">
15688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15691 \begin_layout Plain Layout
15697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15700 \begin_layout Plain Layout
15708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15711 \begin_layout Plain Layout
15719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15722 \begin_layout Plain Layout
15723 \begin_inset Formula $\raisebox {4.5mm}{}\iiint\raisebox {-2.5mm}{}$
15733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15736 \begin_layout Plain Layout
15744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15747 \begin_layout Plain Layout
15748 \begin_inset Formula $\raisebox {4.5mm}{}\iiiint\raisebox {-2.5mm}{}$
15758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15761 \begin_layout Plain Layout
15769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15772 \begin_layout Plain Layout
15773 \begin_inset Formula $\raisebox {4.5mm}{}\dotsint\raisebox {-2.5mm}{}$
15787 \begin_inset Space \hfill{}
15793 \begin_layout Subsection
15795 \begin_inset CommandInset label
15797 name "sub:Operator-Limits"
15805 \begin_layout Plain Layout
15814 \begin_layout Standard
15815 Limits are created by super- and subscripts:
15818 \begin_layout Standard
15820 \begin_inset Tabular
15821 <lyxtabular version="3" rows="2" columns="2">
15823 <column alignment="center" valignment="top" width="0pt">
15824 <column alignment="center" valignment="top" width="0pt">
15826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15829 \begin_layout Plain Layout
15835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15838 \begin_layout Plain Layout
15840 \begin_inset Note Note
15843 \begin_layout Plain Layout
15850 is only used as spacer.
15862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15865 \begin_layout Plain Layout
15874 \begin_layout Plain Layout
15884 \begin_inset Formula $\to$
15888 \begin_inset Formula $\to$
15896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15899 \begin_layout Plain Layout
15900 \begin_inset Formula $\raisebox {5mm}{}\prod_{0}^{\infty}A(x)\raisebox {-2.5mm}{}$
15916 \begin_layout Standard
15917 Limits of inline formulas are set right beside the operator.
15918 Limits in displayed formulas are set above or below the operator, except
15919 of integral limits.
15922 \begin_layout Standard
15923 To force that the limits are set beside the operator, the cursor is set
15924 directly behind the operator and the limits type is changed with the menu
15927 Edit\SpecialChar \menuseparator
15928 Math\SpecialChar \menuseparator
15940 \begin_inset Space ~
15949 \begin_layout Standard
15950 The default limits type is this:
15951 \begin_inset Formula \[
15952 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15956 This is how it looks when the limits type was changed to
15963 \begin_inset Formula \[
15964 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15968 For integrals, except of
15980 , the limits are by default set beside the operator.
15981 But for multiple integrals the limits are often set below the operator.
15982 In the following example the limits type was therefore set to
15986 and so set below the integrals:
15987 \begin_inset Formula \begin{equation}
15988 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15995 \begin_layout Standard
15996 \begin_inset VSpace medskip
15999 To specify conditions for limits, the commands
16009 \begin_layout Plain Layout
16027 \begin_layout Plain Layout
16036 To create for example this expression
16037 \begin_inset Formula \begin{equation}
16038 \sum_{\begin{subarray}{c}
16040 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16047 \begin_layout Standard
16048 the following has to be done:
16049 \begin_inset Newline newline
16064 \begin_layout Plain Layout
16076 One is now in a blue box under the summation operator and insert there
16085 \begin_layout Plain Layout
16097 The blue box is now within a purple box and now several lines can be written
16099 A new line is created by inserting a line break (
16105 \begin_inset Newline newline
16110 0<k<1000 Ctrl-Return
16111 \begin_inset Newline newline
16116 is typed in, a new box appears below for the new line.
16119 \begin_layout Standard
16120 The alignment of the lines can be changed to left aligned with the
16130 Edit\SpecialChar \menuseparator
16134 To get right alignment,
16142 \begin_layout Plain Layout
16153 is inserted at the beginning of the line.
16156 \begin_layout Standard
16169 with the difference that the lines are always centered.
16172 \begin_layout Standard
16173 \begin_inset VSpace bigskip
16177 \begin_inset CommandInset ref
16179 reference "eq:substack"
16183 there can be too much space beside an operator, because the characters
16184 following the operator are set beside the limits.
16187 \begin_layout Standard
16188 To avoid this, the following macro can be used in the LaTeX-preamble:
16191 \begin_layout Standard
16205 \begin_inset Newline newline
16217 \begin_inset Newline newline
16224 mathclapinternal #1#2{
16228 mathsurround =0pt #1{#2}$}}
16231 \begin_layout Standard
16232 This defines the command
16242 \begin_layout Plain Layout
16250 that sets the width of the limit to 0
16251 \begin_inset Space \thinspace{}
16255 The command scheme is
16258 \begin_layout Standard
16266 \begin_layout Standard
16267 where the limit can consist of several conditions.
16270 \begin_layout Standard
16272 \begin_inset CommandInset ref
16274 reference "eq:substack"
16278 , one uses the command
16281 \begin_layout Standard
16294 \begin_layout Plain Layout
16303 0<k<1000 Ctrl-Enter
16306 \begin_layout Standard
16307 to create the lower limit.
16308 The summand is now directly behind the summation operator:
16309 \begin_inset Formula \[
16310 \sum_{\mathclap {\substack{0<k<1000\\
16311 \\k\,\in\,\mathbb{N}}
16319 \begin_layout Standard
16320 \begin_inset VSpace bigskip
16323 How to use one limit for several operators is described in
16324 \begin_inset CommandInset ref
16326 reference "sub:Self-defined-Operators"
16333 \begin_layout Subsection
16335 \begin_inset CommandInset label
16337 name "sub:Binary-Operators"
16345 \begin_layout Plain Layout
16354 \begin_layout Standard
16355 Binary operators are surrounded by space when there is a character before
16357 \begin_inset VSpace medskip
16363 \begin_layout Standard
16364 \begin_inset Space \hfill{}
16368 \begin_inset Tabular
16369 <lyxtabular version="3" rows="13" columns="2">
16371 <column alignment="center" valignment="top" width="0pt">
16372 <column alignment="center" valignment="top" width="0pt">
16374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16377 \begin_layout Plain Layout
16379 \begin_inset Note Note
16382 \begin_layout Plain Layout
16389 is only used as spacer.
16399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16402 \begin_layout Plain Layout
16410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16413 \begin_layout Plain Layout
16419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16422 \begin_layout Plain Layout
16423 \begin_inset Formula $+$
16433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16436 \begin_layout Plain Layout
16442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16445 \begin_layout Plain Layout
16446 \begin_inset Formula $-$
16456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16459 \begin_layout Plain Layout
16467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16470 \begin_layout Plain Layout
16471 \begin_inset Formula $\pm$
16481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16484 \begin_layout Plain Layout
16492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16495 \begin_layout Plain Layout
16496 \begin_inset Formula $\mp$
16506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16509 \begin_layout Plain Layout
16517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16520 \begin_layout Plain Layout
16521 \begin_inset Formula $\cdot$
16531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16534 \begin_layout Plain Layout
16542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16545 \begin_layout Plain Layout
16546 \begin_inset Formula $\times$
16556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16559 \begin_layout Plain Layout
16567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16570 \begin_layout Plain Layout
16571 \begin_inset Formula $\div$
16581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16584 \begin_layout Plain Layout
16588 \begin_layout Plain Layout
16601 \begin_layout Plain Layout
16613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16616 \begin_layout Plain Layout
16617 \begin_inset Formula $*$
16627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16630 \begin_layout Plain Layout
16638 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16641 \begin_layout Plain Layout
16642 \begin_inset Formula $\star$
16652 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16655 \begin_layout Plain Layout
16663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16666 \begin_layout Plain Layout
16667 \begin_inset Formula $\circ$
16677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16680 \begin_layout Plain Layout
16688 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16691 \begin_layout Plain Layout
16692 \begin_inset Formula $\diamond$
16702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16705 \begin_layout Plain Layout
16713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16716 \begin_layout Plain Layout
16717 \begin_inset Formula $\bullet$
16731 \begin_inset Space \hfill{}
16735 \begin_inset Tabular
16736 <lyxtabular version="3" rows="13" columns="2">
16738 <column alignment="center" valignment="top" width="0pt">
16739 <column alignment="center" valignment="top" width="0pt">
16741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16744 \begin_layout Plain Layout
16750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16753 \begin_layout Plain Layout
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16764 \begin_layout Plain Layout
16772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16775 \begin_layout Plain Layout
16776 \begin_inset Formula $\nabla$
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16789 \begin_layout Plain Layout
16797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16800 \begin_layout Plain Layout
16801 \begin_inset Formula $\bigtriangledown$
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16814 \begin_layout Plain Layout
16822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16825 \begin_layout Plain Layout
16826 \begin_inset Formula $\bigtriangleup$
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16839 \begin_layout Plain Layout
16847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16850 \begin_layout Plain Layout
16851 \begin_inset Formula $\Box$
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16864 \begin_layout Plain Layout
16872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16875 \begin_layout Plain Layout
16876 \begin_inset Formula $\cap$
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16889 \begin_layout Plain Layout
16897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16900 \begin_layout Plain Layout
16901 \begin_inset Formula $\cup$
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16914 \begin_layout Plain Layout
16922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16925 \begin_layout Plain Layout
16926 \begin_inset Formula $\dagger$
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16939 \begin_layout Plain Layout
16947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16950 \begin_layout Plain Layout
16951 \begin_inset Formula $\ddagger$
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16964 \begin_layout Plain Layout
16972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16975 \begin_layout Plain Layout
16976 \begin_inset Formula $\wr$
16986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16989 \begin_layout Plain Layout
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17000 \begin_layout Plain Layout
17001 \begin_inset Formula $\bigcirc$
17011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17014 \begin_layout Plain Layout
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17025 \begin_layout Plain Layout
17026 \begin_inset Formula $\wedge$
17036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17039 \begin_layout Plain Layout
17047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17050 \begin_layout Plain Layout
17051 \begin_inset Formula $\vee$
17065 \begin_inset Space \hfill{}
17069 \begin_inset Tabular
17070 <lyxtabular version="3" rows="13" columns="2">
17072 <column alignment="center" valignment="top" width="0pt">
17073 <column alignment="center" valignment="top" width="0pt">
17075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17078 \begin_layout Plain Layout
17084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17087 \begin_layout Plain Layout
17095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17098 \begin_layout Plain Layout
17106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17109 \begin_layout Plain Layout
17110 \begin_inset Formula $\oplus$
17120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17123 \begin_layout Plain Layout
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17134 \begin_layout Plain Layout
17135 \begin_inset Formula $\ominus$
17145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17148 \begin_layout Plain Layout
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17159 \begin_layout Plain Layout
17160 \begin_inset Formula $\otimes$
17170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17173 \begin_layout Plain Layout
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17184 \begin_layout Plain Layout
17185 \begin_inset Formula $\oslash$
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17198 \begin_layout Plain Layout
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17209 \begin_layout Plain Layout
17210 \begin_inset Formula $\odot$
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17223 \begin_layout Plain Layout
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17234 \begin_layout Plain Layout
17235 \begin_inset Formula $\amalg$
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17248 \begin_layout Plain Layout
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17259 \begin_layout Plain Layout
17260 \begin_inset Formula $\uplus$
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17273 \begin_layout Plain Layout
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17284 \begin_layout Plain Layout
17285 \begin_inset Formula $\setminus$
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17298 \begin_layout Plain Layout
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17309 \begin_layout Plain Layout
17310 \begin_inset Formula $\sqcap$
17320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17323 \begin_layout Plain Layout
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17334 \begin_layout Plain Layout
17335 \begin_inset Formula $\sqcup$
17345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17348 \begin_layout Plain Layout
17356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17359 \begin_layout Plain Layout
17360 \begin_inset Formula $\triangleleft$
17370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17373 \begin_layout Plain Layout
17381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17384 \begin_layout Plain Layout
17385 \begin_inset Formula $\triangleright$
17399 \begin_inset Space \hfill{}
17405 \begin_layout Standard
17406 All binary operators can also be inserted via the math toolbar button
17407 \begin_inset Graphics
17408 filename ../images/math/pm.png
17417 \begin_layout Standard
17418 To typeset the Laplace operator also
17435 \begin_inset Formula $\nabla^{2}$
17438 ) can be used instead of
17447 \begin_layout Standard
17454 Insert\SpecialChar \menuseparator
17466 \begin_layout Subsection
17467 Self-defined Operators
17468 \begin_inset CommandInset label
17470 name "sub:Self-defined-Operators"
17478 \begin_layout Plain Layout
17479 Operators ! self-defined
17487 \begin_layout Standard
17488 With the help of the command
17492 DeclareMathOperator
17498 \begin_layout Plain Layout
17503 DeclareMathOperator
17508 custom operators can be defined in the LaTeX-preamble.
17509 Its command scheme is:
17512 \begin_layout Standard
17517 DeclareMathOperator{new command}{display}
17520 \begin_layout Standard
17521 Display can be characters or symbols that define how the operator looks
17523 To define a big operator a * is set behind the command.
17524 All self-defined big operators can have limits as described in
17525 \begin_inset CommandInset ref
17527 reference "sub:Operator-Limits"
17534 \begin_layout Standard
17535 For example the LaTeX-preamble line
17538 \begin_layout Standard
17543 DeclareMathOperator*{
17550 \begin_layout Standard
17551 defines the command
17557 , that inserts a big operator consisting of the lozenge symbol from
17558 \begin_inset CommandInset ref
17560 reference "sub:Miscellaneous-Symbols"
17565 \begin_inset Formula \[
17566 \Lozenge _{n=1}^{\infty}\]
17570 The command for this formula is:
17581 \begin_inset Formula $\to$
17587 \begin_layout Standard
17588 \begin_inset VSpace bigskip
17591 When self-defined operators are not used several times in the document,
17592 they can also be defined with the commands
17602 \begin_layout Plain Layout
17620 \begin_layout Plain Layout
17628 , which have the following scheme:
17631 \begin_layout Standard
17645 \begin_layout Standard
17652 defines big operators,
17661 \begin_layout Standard
17669 \begin_inset Space \thinspace{}
17673 \begin_inset Space ~
17676 be used to use one limit for several operators:
17679 \begin_layout Standard
17680 \begin_inset Formula \[
17681 \mathop {\sum\negmedspace\sum}_{i,j=1}^{N}\]
17688 \begin_layout Standard
17689 The command for the formula above is:
17690 \begin_inset Newline newline
17709 \begin_layout Plain Layout
17721 \begin_inset Formula $\to$
17730 \begin_layout Plain Layout
17744 \begin_layout Section
17749 \begin_layout Plain Layout
17758 \begin_layout Subsection
17760 \begin_inset CommandInset label
17762 name "sub:Font-Styles"
17770 \begin_layout Plain Layout
17779 \begin_layout Standard
17780 Latin letters in formulas can be set in one of the following font styles:
17781 \begin_inset VSpace -2mm
17787 \begin_layout Standard
17789 \begin_inset Tabular
17790 <lyxtabular version="3" rows="6" columns="3">
17792 <column alignment="center" valignment="top" width="0">
17793 <column alignment="center" valignment="top" width="0">
17794 <column alignment="center" valignment="top" width="0">
17796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17799 \begin_layout Plain Layout
17805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17808 \begin_layout Plain Layout
17814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17817 \begin_layout Plain Layout
17825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17828 \begin_layout Plain Layout
17837 \begin_layout Plain Layout
17853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17856 \begin_layout Plain Layout
17857 \begin_inset Formula $\mathbb{ABC}$
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17868 \begin_layout Plain Layout
17876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17879 \begin_layout Plain Layout
17888 \begin_layout Plain Layout
17904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17907 \begin_layout Plain Layout
17908 \begin_inset Formula $\mathbf{AbC}$
17916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17919 \begin_layout Plain Layout
17927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17930 \begin_layout Plain Layout
17939 \begin_layout Plain Layout
17955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17958 \begin_layout Plain Layout
17959 \begin_inset Formula $\boldsymbol{AbC}$
17967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17970 \begin_layout Plain Layout
17978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17981 \begin_layout Plain Layout
17990 \begin_layout Plain Layout
18006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18009 \begin_layout Plain Layout
18010 \begin_inset Formula $\mathcal{ABC}$
18018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18021 \begin_layout Plain Layout
18029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18032 \begin_layout Plain Layout
18041 \begin_layout Plain Layout
18057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18060 \begin_layout Plain Layout
18061 \begin_inset Formula $\mathfrak{AbC}$
18069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18072 \begin_layout Plain Layout
18086 \begin_layout Standard
18088 \begin_inset Tabular
18089 <lyxtabular version="3" rows="5" columns="3">
18091 <column alignment="center" valignment="top" width="0">
18092 <column alignment="center" valignment="top" width="0">
18093 <column alignment="center" valignment="top" width="0">
18095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18098 \begin_layout Plain Layout
18104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18107 \begin_layout Plain Layout
18113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18116 \begin_layout Plain Layout
18124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18127 \begin_layout Plain Layout
18136 \begin_layout Plain Layout
18152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18155 \begin_layout Plain Layout
18156 \begin_inset Formula $\mathit{AbC}$
18164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18167 \begin_layout Plain Layout
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18178 \begin_layout Plain Layout
18187 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18207 \begin_inset Formula $\mathrm{AbC}$
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18218 \begin_layout Plain Layout
18226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18229 \begin_layout Plain Layout
18238 \begin_layout Plain Layout
18254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18257 \begin_layout Plain Layout
18258 \begin_inset Formula $\mathsf{AbC}$
18266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18269 \begin_layout Plain Layout
18277 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18280 \begin_layout Plain Layout
18289 \begin_layout Plain Layout
18305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18308 \begin_layout Plain Layout
18309 \begin_inset Formula $\mathtt{AbC}$
18317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18320 \begin_layout Plain Layout
18334 \begin_layout Standard
18335 \begin_inset Note Greyedout
18338 \begin_layout Plain Layout
18355 can only be used for big letters.
18363 \begin_layout Standard
18364 Predefined is the style
18373 \begin_layout Standard
18374 The style commands work also for letters in mathematical constructs:
18375 \begin_inset Formula \[
18376 \mathfrak{A=\frac{b}{C}}\]
18383 \begin_layout Standard
18384 Characters in mathematical text don't appear in a math font style but in
18385 the text font style
18392 That their style can't be set correctly via the text style dialog is a
18397 \begin_layout Plain Layout
18402 \begin_layout Plain Layout
18406 href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
18415 \begin_layout Plain Layout
18430 \begin_layout Standard
18431 Instead of the style commands the dialog
18433 Edit\SpecialChar \menuseparator
18434 Math\SpecialChar \menuseparator
18437 or the toolbar button
18438 \begin_inset Graphics
18439 filename ../images/math/font.png
18448 \begin_layout Subsection
18450 \begin_inset CommandInset label
18452 name "sub:Bold-Formulas"
18460 \begin_layout Plain Layout
18469 \begin_layout Standard
18470 To make a complete formula bold, the command
18476 from the previous subsection cannot be used, because it doesn't work for
18477 small Greek letters.
18478 Furthermore it prints Latin letters always upright, like in the following
18482 \begin_layout Standard
18483 \begin_inset Formula \[
18484 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18491 \begin_layout Standard
18492 To display the formula correctly, the command
18499 \begin_inset Formula \[
18500 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18504 It is also possible to set the formula in a
18506 boldmath environment
18509 This environment is created by inserting the command
18517 \begin_layout Plain Layout
18528 To end the environment, the command
18536 \begin_layout Plain Layout
18546 is inserted in TeX-mode.
18550 \begin_layout Plain Layout
18560 \begin_inset Formula \[
18561 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18569 \begin_layout Plain Layout
18581 \begin_layout Subsection
18583 \begin_inset CommandInset label
18585 name "sub:Font-Sizes"
18593 \begin_layout Plain Layout
18602 \begin_layout Standard
18603 For characters in formulas there are, analog to characters in text, the
18604 following size commands:
18607 \begin_layout Standard
18651 \begin_inset Newline newline
18673 \begin_layout Standard
18674 The size produced by the commands depends on the document font size, that
18675 corresponds with the command
18682 The other commands produce smaller or larger sizes than
18689 The font size can however not exceed a certain value.
18690 Is for example the document font size 12
18691 \begin_inset Space \thinspace{}
18700 switches to the same size as
18710 \begin_layout Standard
18711 A size command is inserted in TeX-mode before the formula and sets the size
18712 for all following formula and text characters.
18713 To switch back to the initial size, the command
18719 is inserted behind the formula in TeX-mode.
18722 \begin_layout Standard
18723 Within a formula the size can only be changed for symbols or letters in
18725 To do this, the size command is inserted in mathematical text.
18726 All following characters until the end of the mathematical text or until
18727 another size command will have the selected size.
18729 \begin_inset VSpace -2mm
18735 \begin_layout Standard
18739 \begin_layout Plain Layout
18749 \begin_inset Formula \[
18750 A=\frac{B}{c}\cdot\maltese\]
18755 \begin_inset Formula \[
18756 \maltese A\textrm{\Large \maltese\textit{A}}\textrm{\tiny \maltese\textit{A}}\]
18764 \begin_layout Plain Layout
18776 \begin_layout Standard
18777 \begin_inset VSpace medskip
18780 Before both formulas the command
18787 The command for the second formula is:
18788 \begin_inset Newline newline
18799 \begin_layout Plain Layout
18814 \begin_layout Plain Layout
18829 \begin_layout Plain Layout
18844 \begin_layout Plain Layout
18854 \begin_inset Formula $\to$
18858 \begin_inset Formula $\to$
18862 \begin_inset Newline newline
18866 \begin_inset Space \hspace*{}
18880 \begin_layout Plain Layout
18895 \begin_layout Plain Layout
18910 \begin_layout Plain Layout
18922 \begin_layout Standard
18923 If a symbol cannot be displayed in different sizes, it will always be displayed
18924 in the default size.
18927 \begin_layout Section
18932 \begin_layout Plain Layout
18941 \begin_layout Standard
18942 All Greek letters can also be inserted via the toolbar button
18943 \begin_inset Graphics
18944 filename ../images/math/alpha.png
18953 \begin_layout Subsection
18955 \begin_inset CommandInset label
18957 name "sub:Small-Letters"
18965 \begin_layout Plain Layout
18966 Greek letters ! small
18974 \begin_layout Standard
18975 \begin_inset Space \hfill{}
18979 \begin_inset Tabular
18980 <lyxtabular version="3" rows="11" columns="2">
18982 <column alignment="center" valignment="top" width="0pt">
18983 <column alignment="center" valignment="top" width="0pt">
18985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18988 \begin_layout Plain Layout
18994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18997 \begin_layout Plain Layout
19005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19008 \begin_layout Plain Layout
19016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19019 \begin_layout Plain Layout
19020 \begin_inset Formula $\alpha$
19030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19033 \begin_layout Plain Layout
19041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19044 \begin_layout Plain Layout
19045 \begin_inset Formula $\beta$
19055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19058 \begin_layout Plain Layout
19066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19069 \begin_layout Plain Layout
19070 \begin_inset Formula $\gamma$
19080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19083 \begin_layout Plain Layout
19091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19094 \begin_layout Plain Layout
19095 \begin_inset Formula $\delta$
19105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19108 \begin_layout Plain Layout
19116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19119 \begin_layout Plain Layout
19120 \begin_inset Formula $\epsilon$
19130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19133 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19144 \begin_layout Plain Layout
19145 \begin_inset Formula $\varepsilon$
19155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19158 \begin_layout Plain Layout
19166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19169 \begin_layout Plain Layout
19170 \begin_inset Formula $\zeta$
19180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19183 \begin_layout Plain Layout
19191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19194 \begin_layout Plain Layout
19195 \begin_inset Formula $\eta$
19205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19208 \begin_layout Plain Layout
19216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19219 \begin_layout Plain Layout
19220 \begin_inset Formula $\theta$
19230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19233 \begin_layout Plain Layout
19241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19244 \begin_layout Plain Layout
19245 \begin_inset Formula $\vartheta$
19259 \begin_inset Space \hfill{}
19263 \begin_inset Tabular
19264 <lyxtabular version="3" rows="12" columns="2">
19266 <column alignment="center" valignment="top" width="0pt">
19267 <column alignment="center" valignment="top" width="0pt">
19269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19272 \begin_layout Plain Layout
19278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19281 \begin_layout Plain Layout
19289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19292 \begin_layout Plain Layout
19300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19303 \begin_layout Plain Layout
19304 \begin_inset Formula $\iota$
19314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19317 \begin_layout Plain Layout
19325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19328 \begin_layout Plain Layout
19329 \begin_inset Formula $\kappa$
19339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19342 \begin_layout Plain Layout
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19353 \begin_layout Plain Layout
19354 \begin_inset Formula $\varkappa$
19364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19367 \begin_layout Plain Layout
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19378 \begin_layout Plain Layout
19379 \begin_inset Formula $\lambda$
19389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19392 \begin_layout Plain Layout
19400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19403 \begin_layout Plain Layout
19404 \begin_inset Formula $\mu$
19414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19417 \begin_layout Plain Layout
19425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19428 \begin_layout Plain Layout
19429 \begin_inset Formula $\nu$
19439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19442 \begin_layout Plain Layout
19450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19453 \begin_layout Plain Layout
19454 \begin_inset Formula $\xi$
19464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19467 \begin_layout Plain Layout
19473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19476 \begin_layout Plain Layout
19477 \begin_inset Formula $o$
19487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19490 \begin_layout Plain Layout
19498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19501 \begin_layout Plain Layout
19502 \begin_inset Formula $\pi$
19512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19515 \begin_layout Plain Layout
19523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19526 \begin_layout Plain Layout
19527 \begin_inset Formula $\varpi$
19537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19540 \begin_layout Plain Layout
19548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19551 \begin_layout Plain Layout
19552 \begin_inset Formula $\rho$
19566 \begin_inset Space \hfill{}
19570 \begin_inset Tabular
19571 <lyxtabular version="3" rows="11" columns="2">
19573 <column alignment="center" valignment="top" width="0pt">
19574 <column alignment="center" valignment="top" width="0pt">
19576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19579 \begin_layout Plain Layout
19585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19588 \begin_layout Plain Layout
19596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19599 \begin_layout Plain Layout
19607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19610 \begin_layout Plain Layout
19611 \begin_inset Formula $\varrho$
19621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19624 \begin_layout Plain Layout
19632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19635 \begin_layout Plain Layout
19636 \begin_inset Formula $\sigma$
19646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19649 \begin_layout Plain Layout
19657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19660 \begin_layout Plain Layout
19661 \begin_inset Formula $\varsigma$
19671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19674 \begin_layout Plain Layout
19682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19685 \begin_layout Plain Layout
19686 \begin_inset Formula $\tau$
19696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19699 \begin_layout Plain Layout
19707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19710 \begin_layout Plain Layout
19711 \begin_inset Formula $\upsilon$
19721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19724 \begin_layout Plain Layout
19732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19735 \begin_layout Plain Layout
19736 \begin_inset Formula $\phi$
19746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19749 \begin_layout Plain Layout
19757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19760 \begin_layout Plain Layout
19761 \begin_inset Formula $\varphi$
19771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19785 \begin_layout Plain Layout
19786 \begin_inset Formula $\chi$
19796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19799 \begin_layout Plain Layout
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19810 \begin_layout Plain Layout
19811 \begin_inset Formula $\psi$
19821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19835 \begin_layout Plain Layout
19836 \begin_inset Formula $\omega$
19850 \begin_inset Space \hfill{}
19856 \begin_layout Standard
19857 \begin_inset VSpace medskip
19863 \begin_layout Standard
19864 How to create upright Greek letters is explained in
19865 \begin_inset CommandInset ref
19867 reference "sub:Upright-small-Greek"
19874 \begin_layout Subsection
19879 \begin_layout Plain Layout
19880 Greek letters ! big
19888 \begin_layout Standard
19889 \begin_inset Space \hfill{}
19893 \begin_inset Tabular
19894 <lyxtabular version="3" rows="7" columns="2">
19896 <column alignment="center" valignment="top" width="0pt">
19897 <column alignment="center" valignment="top" width="0pt">
19899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19902 \begin_layout Plain Layout
19908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19922 \begin_layout Plain Layout
19930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19933 \begin_layout Plain Layout
19934 \begin_inset Formula $\Gamma$
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19947 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19959 \begin_inset Formula $\Delta$
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19972 \begin_layout Plain Layout
19980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19983 \begin_layout Plain Layout
19984 \begin_inset Formula $\Theta$
19994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19997 \begin_layout Plain Layout
20005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20008 \begin_layout Plain Layout
20009 \begin_inset Formula $\Lambda$
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\Xi$
20044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\Pi$
20073 \begin_inset Space \hfill{}
20077 \begin_inset Tabular
20078 <lyxtabular version="3" rows="6" columns="2">
20080 <column alignment="center" valignment="top" width="0pt">
20081 <column alignment="center" valignment="top" width="0pt">
20083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20086 \begin_layout Plain Layout
20092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20106 \begin_layout Plain Layout
20114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20117 \begin_layout Plain Layout
20118 \begin_inset Formula $\Sigma$
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20131 \begin_layout Plain Layout
20139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20142 \begin_layout Plain Layout
20143 \begin_inset Formula $\Upsilon$
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20156 \begin_layout Plain Layout
20164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20167 \begin_layout Plain Layout
20168 \begin_inset Formula $\Phi$
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20181 \begin_layout Plain Layout
20189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20192 \begin_layout Plain Layout
20193 \begin_inset Formula $\Psi$
20203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20206 \begin_layout Plain Layout
20214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20217 \begin_layout Plain Layout
20218 \begin_inset Formula $\Omega$
20232 \begin_inset Space \hfill{}
20238 \begin_layout Standard
20239 \begin_inset VSpace medskip
20242 That the big Greek letters appear upright is caused by a design bug when
20244 To get correct italic big letters, begin every command with
20249 For example the command
20256 \begin_inset Formula $\varGamma $
20262 \begin_layout Subsection
20267 \begin_layout Plain Layout
20268 Greek letters ! bold
20276 \begin_layout Standard
20277 Greek letters cannot be set with different font styles like Latin letters.
20278 They can only be made bold with the command
20288 \begin_layout Plain Layout
20299 \begin_layout Standard
20301 \begin_inset Tabular
20302 <lyxtabular version="3" rows="3" columns="2">
20304 <column alignment="center" valignment="top" width="0">
20305 <column alignment="center" valignment="top" width="0">
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
20342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20345 \begin_layout Plain Layout
20346 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20359 \begin_layout Plain Layout
20371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20374 \begin_layout Plain Layout
20375 \begin_inset Formula $\theta\boldsymbol{\theta}$
20391 \begin_layout Section
20396 \begin_layout Plain Layout
20409 \begin_layout Plain Layout
20410 A list with all symbols of most of the LaTeX-packages can be found in
20411 \begin_inset CommandInset citation
20426 \begin_layout Plain Layout
20434 \begin_inset Note Note
20437 \begin_layout Plain Layout
20440 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20443 \begin_layout Plain Layout
20446 texorpdfstring is in section
20447 \begin_inset CommandInset ref
20449 reference "sub:Formulas-in-Section"
20462 \begin_layout Plain Layout
20471 \begin_layout Standard
20472 Many of the symbols listed in this section can also be inserted via the
20474 \begin_inset Graphics
20475 filename ../images/math/nabla.png
20482 \begin_inset Graphics
20483 filename ../images/math/digamma.png
20492 \begin_layout Subsection
20493 Mathematical Symbols
20494 \begin_inset CommandInset label
20496 name "sub:Mathematical-Symbols"
20504 \begin_layout Plain Layout
20505 Symbols ! mathematical
20513 \begin_layout Standard
20514 \begin_inset Space \hfill{}
20518 \begin_inset Tabular
20519 <lyxtabular version="3" rows="10" columns="2">
20521 <column alignment="center" valignment="top" width="0pt">
20522 <column alignment="center" valignment="top" width="0pt">
20524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20536 \begin_layout Plain Layout
20544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20547 \begin_layout Plain Layout
20555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20558 \begin_layout Plain Layout
20559 \begin_inset Formula $\neg$
20569 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20572 \begin_layout Plain Layout
20580 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20583 \begin_layout Plain Layout
20584 \begin_inset Formula $\Im$
20594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20597 \begin_layout Plain Layout
20605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20608 \begin_layout Plain Layout
20609 \begin_inset Formula $\Re$
20619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20622 \begin_layout Plain Layout
20630 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20633 \begin_layout Plain Layout
20634 \begin_inset Formula $\aleph$
20644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20658 \begin_layout Plain Layout
20659 \begin_inset Formula $\partial$
20669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20672 \begin_layout Plain Layout
20680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20683 \begin_layout Plain Layout
20684 \begin_inset Formula $\infty$
20694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20697 \begin_layout Plain Layout
20705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20708 \begin_layout Plain Layout
20709 \begin_inset Formula $\wp$
20719 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20722 \begin_layout Plain Layout
20730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20733 \begin_layout Plain Layout
20734 \begin_inset Formula $\imath$
20744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20747 \begin_layout Plain Layout
20755 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20758 \begin_layout Plain Layout
20759 \begin_inset Formula $\jmath$
20773 \begin_inset Space \hfill{}
20777 \begin_inset Tabular
20778 <lyxtabular version="3" rows="10" columns="2">
20780 <column alignment="center" valignment="top" width="0pt">
20781 <column alignment="center" valignment="top" width="0pt">
20783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20786 \begin_layout Plain Layout
20792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20795 \begin_layout Plain Layout
20797 \begin_inset Note Note
20800 \begin_layout Plain Layout
20807 is only used as spacer.
20819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20822 \begin_layout Plain Layout
20830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20833 \begin_layout Plain Layout
20834 \begin_inset Formula $\forall$
20844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20847 \begin_layout Plain Layout
20855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20858 \begin_layout Plain Layout
20859 \begin_inset Formula $\exists$
20869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20872 \begin_layout Plain Layout
20880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20883 \begin_layout Plain Layout
20884 \begin_inset Formula $\nexists$
20894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20897 \begin_layout Plain Layout
20905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20908 \begin_layout Plain Layout
20909 \begin_inset Formula $\emptyset$
20919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20922 \begin_layout Plain Layout
20930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20933 \begin_layout Plain Layout
20934 \begin_inset Formula $\varnothing$
20944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20947 \begin_layout Plain Layout
20955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20958 \begin_layout Plain Layout
20959 \begin_inset Formula $\dag $
20969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20972 \begin_layout Plain Layout
20980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20983 \begin_layout Plain Layout
20984 \begin_inset Formula $\ddag $
20994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20997 \begin_layout Plain Layout
21005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21008 \begin_layout Plain Layout
21012 \begin_layout Plain Layout
21022 \begin_inset Formula $\complement$
21029 \begin_layout Plain Layout
21043 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21046 \begin_layout Plain Layout
21054 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21057 \begin_layout Plain Layout
21058 \begin_inset Formula $\Bbbk$
21072 \begin_inset Space \hfill{}
21076 \begin_inset Tabular
21077 <lyxtabular version="3" rows="10" columns="2">
21079 <column alignment="center" valignment="top" width="0pt">
21080 <column alignment="center" valignment="top" width="0pt">
21082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21085 \begin_layout Plain Layout
21091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21094 \begin_layout Plain Layout
21102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21105 \begin_layout Plain Layout
21113 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21116 \begin_layout Plain Layout
21117 \begin_inset Formula $\prime$
21127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21130 \begin_layout Plain Layout
21138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21141 \begin_layout Plain Layout
21142 \begin_inset Formula $\backprime$
21152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21155 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21166 \begin_layout Plain Layout
21167 \begin_inset Formula $\mho$
21177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21180 \begin_layout Plain Layout
21188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21191 \begin_layout Plain Layout
21192 \begin_inset Formula $\triangle$
21202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21205 \begin_layout Plain Layout
21213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21216 \begin_layout Plain Layout
21217 \begin_inset Formula $\angle$
21227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21230 \begin_layout Plain Layout
21238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21241 \begin_layout Plain Layout
21242 \begin_inset Formula $\measuredangle$
21252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21255 \begin_layout Plain Layout
21263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21266 \begin_layout Plain Layout
21267 \begin_inset Formula $\sphericalangle$
21277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21280 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21291 \begin_layout Plain Layout
21292 \begin_inset Formula $\top$
21302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21305 \begin_layout Plain Layout
21313 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21316 \begin_layout Plain Layout
21317 \begin_inset Formula $\bot$
21331 \begin_inset Space \hfill{}
21337 \begin_layout Standard
21338 \begin_inset Newpage newpage
21344 \begin_layout Subsection
21345 Miscellaneous Symbols
21346 \begin_inset CommandInset label
21348 name "sub:Miscellaneous-Symbols"
21356 \begin_layout Plain Layout
21357 Symbols ! miscellaneous
21365 \begin_layout Standard
21368 \begin_inset Tabular
21369 <lyxtabular version="3" rows="10" columns="2">
21371 <column alignment="center" valignment="top" width="0pt">
21372 <column alignment="center" valignment="top" width="0pt">
21374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21377 \begin_layout Plain Layout
21383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21386 \begin_layout Plain Layout
21394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21397 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $\flat$
21419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21422 \begin_layout Plain Layout
21430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21433 \begin_layout Plain Layout
21434 \begin_inset Formula $\natural$
21444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21447 \begin_layout Plain Layout
21455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21458 \begin_layout Plain Layout
21459 \begin_inset Formula $\sharp$
21469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21472 \begin_layout Plain Layout
21480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21483 \begin_layout Plain Layout
21484 \begin_inset Formula $\surd$
21494 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21497 \begin_layout Plain Layout
21505 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21508 \begin_layout Plain Layout
21509 \begin_inset Formula $\checkmark$
21519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21522 \begin_layout Plain Layout
21530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21533 \begin_layout Plain Layout
21534 \begin_inset Formula $\yen$
21544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21547 \begin_layout Plain Layout
21555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21558 \begin_layout Plain Layout
21559 \begin_inset Formula $\pounds $
21569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21572 \begin_layout Plain Layout
21578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Plain Layout
21582 \begin_inset Formula $\$$
21592 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21595 \begin_layout Plain Layout
21601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21604 \begin_layout Plain Layout
21605 \begin_inset Formula $§$
21619 \begin_inset Tabular
21620 <lyxtabular version="3" rows="10" columns="2">
21622 <column alignment="center" valignment="top" width="0">
21623 <column alignment="center" valignment="top" width="0">
21625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21628 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21648 \begin_layout Plain Layout
21656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21659 \begin_layout Plain Layout
21660 \begin_inset Formula $\hbar$
21670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21673 \begin_layout Plain Layout
21681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21684 \begin_layout Plain Layout
21685 \begin_inset Formula $\hslash$
21695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21698 \begin_layout Plain Layout
21706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21709 \begin_layout Plain Layout
21710 \begin_inset Formula $\clubsuit$
21720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21723 \begin_layout Plain Layout
21731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21734 \begin_layout Plain Layout
21735 \begin_inset Formula $\spadesuit$
21745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21748 \begin_layout Plain Layout
21756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21759 \begin_layout Plain Layout
21760 \begin_inset Formula $\bigstar$
21770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21773 \begin_layout Plain Layout
21781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21784 \begin_layout Plain Layout
21785 \begin_inset Formula $\blacklozenge$
21795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21798 \begin_layout Plain Layout
21806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21809 \begin_layout Plain Layout
21810 \begin_inset Formula $\blacktriangle$
21820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21823 \begin_layout Plain Layout
21831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21834 \begin_layout Plain Layout
21835 \begin_inset Formula $\blacktriangledown$
21845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21848 \begin_layout Plain Layout
21856 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21859 \begin_layout Plain Layout
21860 \begin_inset Formula $\bullet$
21874 \begin_inset Tabular
21875 <lyxtabular version="3" rows="10" columns="2">
21877 <column alignment="center" valignment="top" width="0pt">
21878 <column alignment="center" valignment="top" width="0pt">
21880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21883 \begin_layout Plain Layout
21889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21892 \begin_layout Plain Layout
21900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21903 \begin_layout Plain Layout
21911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21914 \begin_layout Plain Layout
21915 \begin_inset Formula $\diamondsuit$
21925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21928 \begin_layout Plain Layout
21936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21939 \begin_layout Plain Layout
21940 \begin_inset Formula $\Diamond$
21950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21953 \begin_layout Plain Layout
21961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21964 \begin_layout Plain Layout
21965 \begin_inset Formula $\heartsuit$
21975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21978 \begin_layout Plain Layout
21986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21989 \begin_layout Plain Layout
21990 \begin_inset Formula $\P $
22000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22003 \begin_layout Plain Layout
22011 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22014 \begin_layout Plain Layout
22015 \begin_inset Formula $\copyright $
22025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22028 \begin_layout Plain Layout
22036 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22039 \begin_layout Plain Layout
22040 \begin_inset Formula $\circledR$
22050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22053 \begin_layout Plain Layout
22061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22064 \begin_layout Plain Layout
22065 \begin_inset Formula $\maltese$
22075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22078 \begin_layout Plain Layout
22086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22089 \begin_layout Plain Layout
22090 \begin_inset Formula $\diagup$
22100 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22103 \begin_layout Plain Layout
22111 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22114 \begin_layout Plain Layout
22115 \begin_inset Formula $\diagdown$
22131 \begin_layout Standard
22132 \begin_inset VSpace medskip
22135 More symbols are listed in
22136 \begin_inset CommandInset ref
22138 reference "sub:Miscellaneous-Special-Characters"
22145 \begin_layout Standard
22146 Some symbols can be displayed in different sizes, see
22147 \begin_inset CommandInset ref
22149 reference "sub:Font-Sizes"
22156 \begin_layout Subsection
22161 \begin_layout Plain Layout
22162 Symbols ! Euro-symbol
22171 \begin_layout Plain Layout
22175 \begin_layout Plain Layout
22192 \begin_layout Standard
22193 To use the Euro symbol in formulas, the LaTeX-package
22201 \begin_layout Plain Layout
22207 must be installed and loaded with the LaTeX-preamble line
22210 \begin_layout Standard
22215 usepackage[gennarrow]{eurosym}
22218 \begin_layout Standard
22219 The Euro symbol can now be inserted with the command
22229 \begin_layout Plain Layout
22240 \begin_layout Standard
22241 The Euro symbol can directly be inserted with the € key in mathematical
22242 text, without having
22257 can also be inserted in TeX-mode.
22258 The official currency symbol can then be inserted with the command
22268 \begin_layout Plain Layout
22276 , that is only available in TeX-mode.
22279 \begin_layout Standard
22283 \begin_layout Plain Layout
22293 \begin_inset Note Note
22296 \begin_layout Plain Layout
22297 The following table will only be displayed when the LaTeX-package
22309 \begin_layout Standard
22310 An overview about the different Euro symbols:
22313 \begin_layout Standard
22315 \begin_inset Tabular
22316 <lyxtabular version="3" rows="4" columns="3">
22318 <column alignment="center" valignment="top" width="0pt">
22319 <column alignment="center" valignment="top" width="0pt">
22320 <column alignment="center" valignment="top" width="0pt">
22322 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22325 \begin_layout Plain Layout
22331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22343 \begin_layout Plain Layout
22351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22354 \begin_layout Plain Layout
22360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22363 \begin_layout Plain Layout
22371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22374 \begin_layout Plain Layout
22375 \begin_inset Formula $\euro $
22385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22388 \begin_layout Plain Layout
22394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22397 \begin_layout Plain Layout
22403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22406 \begin_layout Plain Layout
22407 \begin_inset Formula $\mbox{€}$
22417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22420 \begin_layout Plain Layout
22426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22429 \begin_layout Plain Layout
22437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22440 \begin_layout Plain Layout
22444 \begin_layout Plain Layout
22466 \begin_layout Standard
22470 \begin_layout Plain Layout
22480 \begin_inset Note Note
22483 \begin_layout Plain Layout
22484 The following will be displayed when the LaTeX-package
22496 \begin_layout Standard
22497 You need to install the LaTeX-package
22501 to see the rest of this subsection in the output.
22504 \begin_layout Standard
22508 \begin_layout Plain Layout
22520 \begin_layout Section
22522 \begin_inset CommandInset label
22524 name "sec:Relations"
22532 \begin_layout Plain Layout
22542 \begin_layout Plain Layout
22547 \begin_layout Plain Layout
22558 \begin_layout Plain Layout
22573 \begin_layout Standard
22574 All relations can also be inserted via the toolbar button
22575 \begin_inset Graphics
22576 filename ../images/math/leq.png
22585 \begin_layout Standard
22586 \begin_inset Space \hfill{}
22590 \begin_inset Tabular
22591 <lyxtabular version="3" rows="17" columns="2">
22593 <column alignment="center" valignment="top" width="0pt">
22594 <column alignment="center" valignment="top" width="0pt">
22596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22599 \begin_layout Plain Layout
22605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22608 \begin_layout Plain Layout
22616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22619 \begin_layout Plain Layout
22625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22628 \begin_layout Plain Layout
22629 \begin_inset Formula $<$
22639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22642 \begin_layout Plain Layout
22650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22653 \begin_layout Plain Layout
22654 \begin_inset Formula $\le$
22664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22667 \begin_layout Plain Layout
22675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22678 \begin_layout Plain Layout
22679 \begin_inset Formula $\ll$
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22703 \begin_layout Plain Layout
22704 \begin_inset Formula $\prec$
22714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22728 \begin_layout Plain Layout
22729 \begin_inset Formula $\preceq$
22739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22742 \begin_layout Plain Layout
22750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22753 \begin_layout Plain Layout
22754 \begin_inset Formula $\subset$
22764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22767 \begin_layout Plain Layout
22775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22778 \begin_layout Plain Layout
22779 \begin_inset Formula $\subseteq$
22789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22792 \begin_layout Plain Layout
22800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22803 \begin_layout Plain Layout
22804 \begin_inset Formula $\sqsubseteq$
22814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22817 \begin_layout Plain Layout
22825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22828 \begin_layout Plain Layout
22829 \begin_inset Formula $\in$
22839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22842 \begin_layout Plain Layout
22850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22853 \begin_layout Plain Layout
22854 \begin_inset Formula $\vdash$
22864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22867 \begin_layout Plain Layout
22875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22878 \begin_layout Plain Layout
22879 \begin_inset Formula $\smile$
22889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22892 \begin_layout Plain Layout
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22903 \begin_layout Plain Layout
22904 \begin_inset Formula $\lhd$
22914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22917 \begin_layout Plain Layout
22925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22928 \begin_layout Plain Layout
22929 \begin_inset Formula $\unlhd$
22939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22942 \begin_layout Plain Layout
22950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22953 \begin_layout Plain Layout
22954 \begin_inset Formula $\gtrless$
22964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22967 \begin_layout Plain Layout
22975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22978 \begin_layout Plain Layout
22979 \begin_inset Formula $\mid$
22989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22992 \begin_layout Plain Layout
23000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23003 \begin_layout Plain Layout
23004 \begin_inset Formula $\nmid$
23018 \begin_inset Space \hfill{}
23022 \begin_inset Tabular
23023 <lyxtabular version="3" rows="17" columns="2">
23025 <column alignment="center" valignment="top" width="0pt">
23026 <column alignment="center" valignment="top" width="0pt">
23028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23031 \begin_layout Plain Layout
23037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23040 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23051 \begin_layout Plain Layout
23057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23060 \begin_layout Plain Layout
23061 \begin_inset Formula $=$
23071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23074 \begin_layout Plain Layout
23082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23085 \begin_layout Plain Layout
23086 \begin_inset Formula $\not=$
23096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23099 \begin_layout Plain Layout
23107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23110 \begin_layout Plain Layout
23111 \begin_inset Formula $\equiv$
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23135 \begin_layout Plain Layout
23136 \begin_inset Formula $\sim$
23146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23160 \begin_layout Plain Layout
23161 \begin_inset Formula $\simeq$
23171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23174 \begin_layout Plain Layout
23182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23185 \begin_layout Plain Layout
23186 \begin_inset Formula $\approx$
23196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23199 \begin_layout Plain Layout
23207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23210 \begin_layout Plain Layout
23211 \begin_inset Formula $\cong$
23221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23224 \begin_layout Plain Layout
23232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23235 \begin_layout Plain Layout
23236 \begin_inset Formula $\bowtie$
23246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23249 \begin_layout Plain Layout
23257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23260 \begin_layout Plain Layout
23261 \begin_inset Formula $\notin$
23271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23274 \begin_layout Plain Layout
23282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23285 \begin_layout Plain Layout
23286 \begin_inset Formula $\perp$
23296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23299 \begin_layout Plain Layout
23307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23310 \begin_layout Plain Layout
23311 \begin_inset Formula $\propto$
23321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23324 \begin_layout Plain Layout
23332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23335 \begin_layout Plain Layout
23336 \begin_inset Formula $\asymp$
23346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23349 \begin_layout Plain Layout
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23360 \begin_layout Plain Layout
23361 \begin_inset Formula $\doteq$
23371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23374 \begin_layout Plain Layout
23382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23385 \begin_layout Plain Layout
23386 \begin_inset Formula $\circeq$
23396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23399 \begin_layout Plain Layout
23407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23410 \begin_layout Plain Layout
23411 \begin_inset Formula $\models$
23421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23424 \begin_layout Plain Layout
23432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23435 \begin_layout Plain Layout
23436 \begin_inset Formula $\widehat{=}$
23450 \begin_inset Space \hfill{}
23454 \begin_inset Tabular
23455 <lyxtabular version="3" rows="17" columns="2">
23457 <column alignment="center" valignment="top" width="0pt">
23458 <column alignment="center" valignment="top" width="0pt">
23460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23463 \begin_layout Plain Layout
23469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23483 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $>$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\ge$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\gg$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\succ$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\succeq$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\supset$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\supseteq$
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\sqsupseteq$
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23693 \begin_inset Formula $\ni$
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23717 \begin_layout Plain Layout
23718 \begin_inset Formula $\dashv$
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23742 \begin_layout Plain Layout
23743 \begin_inset Formula $\frown$
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23756 \begin_layout Plain Layout
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23767 \begin_layout Plain Layout
23768 \begin_inset Formula $\rhd$
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23781 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23792 \begin_layout Plain Layout
23793 \begin_inset Formula $\unrhd$
23803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23806 \begin_layout Plain Layout
23814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23817 \begin_layout Plain Layout
23818 \begin_inset Formula $\lessgtr$
23828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23831 \begin_layout Plain Layout
23839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23842 \begin_layout Plain Layout
23843 \begin_inset Formula $\parallel$
23853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23856 \begin_layout Plain Layout
23864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23867 \begin_layout Plain Layout
23868 \begin_inset Formula $\nparallel$
23882 \begin_inset Space \hfill{}
23888 \begin_layout Standard
23889 \begin_inset VSpace medskip
23904 are bigger than the equal looking operators
23919 \begin_layout Standard
23920 Relations are, in contrary to symbols, always surrounded by space.
23923 \begin_layout Standard
23924 Relations with labels can be created with the command
23934 \begin_layout Plain Layout
23945 \begin_layout Standard
23947 \begin_inset Tabular
23948 <lyxtabular version="3" rows="2" columns="2">
23950 <column alignment="center" valignment="top" width="0">
23951 <column alignment="center" valignment="top" width="0">
23953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23956 \begin_layout Plain Layout
23962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23965 \begin_layout Plain Layout
23967 \begin_inset Note Note
23970 \begin_layout Plain Layout
23977 is only used as spacer.
23989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
23999 \begin_layout Plain Layout
24016 \begin_layout Plain Layout
24026 \begin_inset Formula $\downarrow$
24035 \begin_layout Plain Layout
24048 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24065 \begin_layout Plain Layout
24066 \begin_inset Formula $\raisebox {5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24082 \begin_layout Section
24086 \begin_layout Subsection
24087 Predefined Functions
24088 \begin_inset CommandInset label
24090 name "sub:Predefined-Functions"
24098 \begin_layout Plain Layout
24099 Functions ! predefined
24107 \begin_layout Standard
24108 In general, variables are set
24112 in mathematical expressions, but not function names, because
24113 \begin_inset Formula $sin$
24116 could be misunderstood as
24117 \begin_inset Formula $s\cdot i\cdot n$
24121 Therefore there are predefined functions, that are additionally a bit separated
24123 They are inserted as commands starting with a backslash before their name.
24126 \begin_layout Standard
24128 \begin_inset Tabular
24129 <lyxtabular version="3" rows="2" columns="4">
24131 <column alignment="center" valignment="top" width="0pt">
24132 <column alignment="center" valignment="top" width="0pt">
24133 <column alignment="center" valignment="top" width="0pt">
24134 <column alignment="center" valignment="top" width="0pt">
24136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24139 \begin_layout Plain Layout
24145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24148 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24166 \begin_layout Plain Layout
24174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24177 \begin_layout Plain Layout
24183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24186 \begin_layout Plain Layout
24187 \begin_inset Formula $Asin(x)+B$
24195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24209 \begin_layout Plain Layout
24210 \begin_inset Formula $A\sin(x)+B$
24227 \begin_layout Plain Layout
24239 \begin_layout Standard
24240 The following functions are predefined:
24243 \begin_layout Standard
24244 \begin_inset VSpace -2mm
24250 \begin_layout Standard
24252 \begin_inset Tabular
24253 <lyxtabular version="3" rows="9" columns="4">
24255 <column alignment="center" valignment="top" width="0pt">
24256 <column alignment="center" valignment="top" width="0pt">
24257 <column alignment="center" valignment="top" width="0pt">
24258 <column alignment="center" valignment="top" width="0pt">
24260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24263 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24272 \begin_layout Plain Layout
24278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24281 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24312 \begin_layout Plain Layout
24320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24334 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24369 \begin_layout Plain Layout
24377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24380 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24415 \begin_layout Plain Layout
24423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24426 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24461 \begin_layout Plain Layout
24469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24472 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24485 \begin_layout Plain Layout
24493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24496 \begin_layout Plain Layout
24504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24507 \begin_layout Plain Layout
24515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24518 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24531 \begin_layout Plain Layout
24539 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24542 \begin_layout Plain Layout
24550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24553 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24564 \begin_layout Plain Layout
24574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24577 \begin_layout Plain Layout
24585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24588 \begin_layout Plain Layout
24596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24599 \begin_layout Plain Layout
24607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24610 \begin_layout Plain Layout
24620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24623 \begin_layout Plain Layout
24631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24634 \begin_layout Plain Layout
24642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24645 \begin_layout Plain Layout
24653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24656 \begin_layout Plain Layout
24672 \begin_layout Standard
24673 They can also be inserted with the math toolbar button
24674 \begin_inset Graphics
24675 filename ../images/math/functions.png
24684 \begin_layout Subsection
24685 Self-defined Functions
24689 \begin_layout Plain Layout
24690 Functions ! self-defined
24698 \begin_layout Standard
24699 To use a function that is not predefined, like for example the sign function
24700 sgn(x), there are two possibilities:
24703 \begin_layout Itemize
24704 Define the function by inserting the following line to the LaTeX-preamble
24708 \begin_layout Plain Layout
24713 DeclareMathOperator
24716 \begin_inset CommandInset ref
24718 reference "sub:Self-defined-Operators"
24728 \begin_inset Newline newline
24732 \begin_inset VSpace -3mm
24736 \begin_inset Newline newline
24743 DeclareMathOperator{
24751 \begin_layout Plain Layout
24756 DeclareMathOperator
24762 \begin_inset Newline newline
24766 \begin_inset VSpace -2mm
24770 \begin_inset Newline newline
24773 Now the new defined function can be called with the command
24782 \begin_layout Itemize
24783 Write the the formula as usual, mark the formula name, in our example the
24788 , and change it to mathematical text.
24789 At last a space is inserted between prefactor and function.
24792 \begin_layout Standard
24793 The result is the same with both methods as with a predefined function
24797 \begin_layout Plain Layout
24798 In LyX self-defined functions are displayed red, predefined ones black.
24806 \begin_layout Standard
24808 \begin_inset Tabular
24809 <lyxtabular version="3" rows="3" columns="2">
24811 <column alignment="center" valignment="top" width="0pt">
24812 <column alignment="center" valignment="top" width="0pt">
24814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24817 \begin_layout Plain Layout
24823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24826 \begin_layout Plain Layout
24834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24849 \begin_inset Formula $A\sgn (x)+B$
24859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24862 \begin_layout Plain Layout
24866 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24877 \begin_layout Plain Layout
24878 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24894 \begin_layout Standard
24895 The first method is more suitable when the self-defined function should
24896 be used several times.
24899 \begin_layout Subsection
24904 \begin_layout Plain Layout
24913 \begin_layout Standard
24914 For limits there are defined besides
24924 \begin_layout Plain Layout
24944 furthermore the following functions:
24947 \begin_layout Standard
24949 \begin_inset Tabular
24950 <lyxtabular version="3" rows="5" columns="2">
24952 <column alignment="center" valignment="top" width="0">
24953 <column alignment="center" valignment="top" width="0">
24955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24958 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24967 \begin_layout Plain Layout
24969 \begin_inset Note Note
24972 \begin_layout Plain Layout
24979 is only used as spacer.
24991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24994 \begin_layout Plain Layout
25002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25005 \begin_layout Plain Layout
25006 \begin_inset Formula $\varliminf $
25016 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25019 \begin_layout Plain Layout
25027 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25030 \begin_layout Plain Layout
25031 \begin_inset Formula $\varlimsup $
25041 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25044 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25055 \begin_layout Plain Layout
25056 \begin_inset Formula $\varprojlim $
25066 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25069 \begin_layout Plain Layout
25077 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25080 \begin_layout Plain Layout
25081 \begin_inset Formula $\varinjlim $
25085 \begin_inset Formula $\raisebox {-2.5mm}{}$
25101 \begin_layout Standard
25102 \begin_inset VSpace medskip
25105 The limit is created by inserting a subscript.
25106 It is set right beside the function in an inline formula:
25109 \begin_layout Standard
25111 \begin_inset Tabular
25112 <lyxtabular version="3" rows="2" columns="2">
25114 <column alignment="center" valignment="top" width="0pt">
25115 <column alignment="center" valignment="top" width="0pt">
25117 <cell alignment="center" valignment="top" usebox="none">
25120 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" usebox="none">
25129 \begin_layout Plain Layout
25133 \begin_layout Plain Layout
25143 \begin_inset Note Note
25146 \begin_layout Plain Layout
25159 are used here as spacer.
25171 <cell alignment="center" valignment="top" usebox="none">
25174 \begin_layout Plain Layout
25183 \begin_layout Plain Layout
25196 \begin_layout Plain Layout
25210 <cell alignment="center" valignment="top" usebox="none">
25213 \begin_layout Plain Layout
25214 \begin_inset Formula $\hspace {1cm}\raisebox {5mm}{}\lim_{x\to A}x=B$
25230 \begin_layout Standard
25231 In a displayed formula the limit is set below the formula, as usual:
25232 \begin_inset Formula \[
25240 \begin_layout Subsection
25245 \begin_layout Plain Layout
25246 Functions ! modulo-
25254 \begin_layout Standard
25255 The modulo-function is special, because it exists in four variants.
25258 \begin_layout Standard
25259 The variants in a displayed formula:
25260 \begin_inset Formula \begin{align*}
25261 \underline{\textrm{Command}\raisebox {-0.9mm}{}} & & \underline{\textrm{Result}}\\
25262 \mathrm{a\backslash mod\textrm{\spce }b} & & a\mod b\\
25263 \mathrm{a\backslash pmod\textrm{\spce }b} & & a\pmod b\\
25264 \mathrm{a\backslash bmod\textrm{\spce }b} & & a\bmod b\\
25265 \mathrm{a\backslash pod\textrm{\spce }b} & & a\pod b\end{align*}
25272 \begin_layout Standard
25273 In an inline formula less space is set before the function names for all
25277 \begin_layout Section
25282 \begin_layout Plain Layout
25291 \begin_layout Subsection
25292 Special Characters in Mathematical Text
25295 \begin_layout Standard
25296 The following commands can only be used in mathematical text or in TeX-mode:
25299 \begin_layout Standard
25300 \begin_inset Space \hfill{}
25304 \begin_inset Tabular
25305 <lyxtabular version="3" rows="8" columns="2">
25307 <column alignment="block" valignment="top" width="0">
25308 <column alignment="block" valignment="top" width="0">
25310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25313 \begin_layout Plain Layout
25319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25322 \begin_layout Plain Layout
25330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25333 \begin_layout Plain Layout
25341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25344 \begin_layout Plain Layout
25345 \begin_inset Formula $\textrm{\oe }$
25355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25358 \begin_layout Plain Layout
25366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25369 \begin_layout Plain Layout
25370 \begin_inset Formula $\textrm{\OE }$
25380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25383 \begin_layout Plain Layout
25391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25394 \begin_layout Plain Layout
25395 \begin_inset Formula $\textrm{\ae }$
25405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25408 \begin_layout Plain Layout
25416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25419 \begin_layout Plain Layout
25420 \begin_inset Formula $\textrm{\AE }$
25430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25433 \begin_layout Plain Layout
25441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25444 \begin_layout Plain Layout
25445 \begin_inset Formula $\textrm{\aa }$
25455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25458 \begin_layout Plain Layout
25465 \begin_layout Plain Layout
25469 \begin_layout Plain Layout
25477 \begin_layout Plain Layout
25488 \begin_layout Plain Layout
25504 \begin_layout Plain Layout
25512 \begin_layout Plain Layout
25523 \begin_layout Plain Layout
25539 \begin_layout Plain Layout
25550 \begin_layout Plain Layout
25558 \begin_layout Plain Layout
25569 \begin_layout Plain Layout
25585 \begin_layout Plain Layout
25602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25605 \begin_layout Plain Layout
25606 \begin_inset Formula $\textrm{\AA}$
25616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25619 \begin_layout Plain Layout
25627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25630 \begin_layout Plain Layout
25631 \begin_inset Formula $\textrm{\i }$
25645 \begin_inset Space \hfill{}
25649 \begin_inset Tabular
25650 <lyxtabular version="3" rows="8" columns="2">
25652 <column alignment="block" valignment="top" width="0">
25653 <column alignment="center" valignment="top" width="0">
25655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25658 \begin_layout Plain Layout
25660 \begin_inset Note Note
25663 \begin_layout Plain Layout
25670 is used for separation, because otherwise the output will be ¡ and ¿ respective
25681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25684 \begin_layout Plain Layout
25692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25695 \begin_layout Plain Layout
25703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25706 \begin_layout Plain Layout
25707 \begin_inset Formula $\textrm{\o }$
25717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25720 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25731 \begin_layout Plain Layout
25732 \begin_inset Formula $\textrm{\O}$
25742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25745 \begin_layout Plain Layout
25753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25756 \begin_layout Plain Layout
25757 \begin_inset Formula $\textrm{\l }$
25767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25770 \begin_layout Plain Layout
25778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25781 \begin_layout Plain Layout
25782 \begin_inset Formula $\textrm{\L }$
25792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25795 \begin_layout Plain Layout
25800 \begin_layout Plain Layout
25813 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25830 \begin_layout Plain Layout
25831 \begin_inset Formula $\textrm{!`}$
25841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25844 \begin_layout Plain Layout
25849 \begin_layout Plain Layout
25862 \begin_layout Plain Layout
25876 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25879 \begin_layout Plain Layout
25880 \begin_inset Formula $\textrm{?`}$
25890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25893 \begin_layout Plain Layout
25901 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25904 \begin_layout Plain Layout
25905 \begin_inset Formula $\textrm{\j }$
25919 \begin_inset Space \hfill{}
25925 \begin_layout Standard
25927 \begin_inset Formula $\textrm{\textrm{Å}}$
25931 \begin_inset Formula $\textrm{\textrm{Ø}}$
25934 can also be inserted via the math toolbar button
25935 \begin_inset Graphics
25936 filename ../images/math/digamma.png
25945 \begin_layout Standard
25946 An exception are the commands
25952 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25980 , because they can be inserted in LyX directly to text.
25983 \begin_layout Subsection
25985 \begin_inset CommandInset label
25987 name "sub:Accents-in-Text"
25995 \begin_layout Plain Layout
26004 \begin_layout Standard
26005 With the following commands all letters can be accented.
26006 The commands must be inserted in TeX-mode.
26009 \begin_layout Standard
26010 \begin_inset Space \hfill{}
26014 \begin_inset Tabular
26015 <lyxtabular version="3" rows="8" columns="2">
26017 <column alignment="block" valignment="top" width="0">
26018 <column alignment="block" valignment="top" width="0">
26020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26023 \begin_layout Plain Layout
26029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26032 \begin_layout Plain Layout
26040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26043 \begin_layout Plain Layout
26047 \begin_inset Quotes grd
26055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26058 \begin_layout Plain Layout
26062 \begin_layout Plain Layout
26078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26081 \begin_layout Plain Layout
26089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26092 \begin_layout Plain Layout
26096 \begin_layout Plain Layout
26112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26115 \begin_layout Plain Layout
26122 \begin_layout Plain Layout
26136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26139 \begin_layout Plain Layout
26143 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26162 \begin_layout Plain Layout
26170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26173 \begin_layout Plain Layout
26177 \begin_layout Plain Layout
26193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26196 \begin_layout Plain Layout
26203 \begin_layout Plain Layout
26217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26220 \begin_layout Plain Layout
26224 \begin_layout Plain Layout
26240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26250 \begin_layout Plain Layout
26264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26267 \begin_layout Plain Layout
26271 \begin_layout Plain Layout
26287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26290 \begin_layout Plain Layout
26297 \begin_layout Plain Layout
26311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26314 \begin_layout Plain Layout
26318 \begin_layout Plain Layout
26338 \begin_inset Space \hfill{}
26342 \begin_inset Tabular
26343 <lyxtabular version="3" rows="8" columns="2">
26345 <column alignment="block" valignment="top" width="0">
26346 <column alignment="center" valignment="top" width="0">
26348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26351 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26360 \begin_layout Plain Layout
26368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26371 \begin_layout Plain Layout
26378 \begin_layout Plain Layout
26392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26395 \begin_layout Plain Layout
26399 \begin_layout Plain Layout
26415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26418 \begin_layout Plain Layout
26426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26429 \begin_layout Plain Layout
26433 \begin_layout Plain Layout
26449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26452 \begin_layout Plain Layout
26459 \begin_layout Plain Layout
26470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26473 \begin_layout Plain Layout
26477 \begin_layout Plain Layout
26493 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26496 \begin_layout Plain Layout
26504 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26507 \begin_layout Plain Layout
26511 \begin_layout Plain Layout
26527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26530 \begin_layout Plain Layout
26537 \begin_layout Plain Layout
26551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26554 \begin_layout Plain Layout
26558 \begin_layout Plain Layout
26574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26577 \begin_layout Plain Layout
26584 \begin_layout Plain Layout
26598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26601 \begin_layout Plain Layout
26605 \begin_layout Plain Layout
26621 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26624 \begin_layout Plain Layout
26631 \begin_layout Plain Layout
26645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26648 \begin_layout Plain Layout
26652 \begin_layout Plain Layout
26672 \begin_inset Space \hfill{}
26678 \begin_layout Standard
26679 \begin_inset VSpace medskip
26688 also two different characters can be accented.
26697 \begin_layout Plain Layout
26712 \begin_layout Plain Layout
26724 \begin_layout Standard
26737 can in combination with vowels directly be inserted with the keyboard without
26739 The same applies for the tilde
26743 \begin_layout Plain Layout
26744 This only applies for keyboards where the tilde is defined as accent.
26753 in combination with
26768 \begin_layout Standard
26811 , and accents inserted directly with the keyboard are also available in
26813 For the other accents there are special math commands to be used in formulas,
26815 \begin_inset CommandInset ref
26817 reference "sub:Accents-for-one"
26824 \begin_layout Standard
26825 \begin_inset VSpace bigskip
26828 Furthermore, with the command
26838 \begin_layout Plain Layout
26846 all numbers and letters can be set into a circle, quasi accented with a
26847 circle, similar to the the copyright symbol.
26850 \begin_layout Standard
26852 \begin_inset Tabular
26853 <lyxtabular version="3" rows="3" columns="2">
26855 <column alignment="center" valignment="top" width="0">
26856 <column alignment="center" valignment="top" width="0">
26858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26861 \begin_layout Plain Layout
26867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26870 \begin_layout Plain Layout
26872 \begin_inset Note Note
26875 \begin_layout Plain Layout
26882 is only used as spacer.
26894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26897 \begin_layout Plain Layout
26905 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26908 \begin_layout Plain Layout
26912 \begin_layout Plain Layout
26928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26931 \begin_layout Plain Layout
26942 raisebox{-1.5pt}{W}}
26947 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26950 \begin_layout Plain Layout
26951 \begin_inset Formula $\raisebox {4.5mm}{}$
26958 \begin_layout Plain Layout
26976 \begin_inset Formula $\raisebox {-2mm}{}$
26992 \begin_layout Standard
26993 One has to take care that the character fits in the circle.
27004 \begin_layout Plain Layout
27006 \begin_inset CommandInset ref
27008 reference "sub:Font-Sizes"
27017 specifies thereby the size of the circle.
27028 \begin_layout Plain Layout
27030 \begin_inset CommandInset ref
27032 reference "sub:Boxes-without-Frame"
27041 the character can be centered.
27044 \begin_layout Subsection
27049 \begin_layout Plain Layout
27058 \begin_layout Standard
27059 Minuscule numbers are created with the command
27069 \begin_layout Plain Layout
27078 The command can be used in formulas and in TeX-mode.
27079 The command scheme is:
27082 \begin_layout Standard
27087 oldstylenums{number}
27090 \begin_layout Standard
27095 oldstylenums{0123456789
27098 \begin_inset Formula $\oldstylenums {0123456789}$
27104 \begin_layout Subsection
27105 Miscellaneous Special Characters
27106 \begin_inset CommandInset label
27108 name "sub:Miscellaneous-Special-Characters"
27116 \begin_layout Plain Layout
27117 Special characters ! miscellaneous
27125 \begin_layout Standard
27126 The following characters can only be inserted to formulas by using commands:
27129 \begin_layout Standard
27131 \begin_inset Tabular
27132 <lyxtabular version="3" rows="4" columns="2">
27134 <column alignment="center" valignment="top" width="0">
27135 <column alignment="center" valignment="top" width="0">
27137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27140 \begin_layout Plain Layout
27146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27149 \begin_layout Plain Layout
27157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27160 \begin_layout Plain Layout
27167 \begin_layout Plain Layout
27181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27184 \begin_layout Plain Layout
27185 \begin_inset Formula $\mathcircumflex$
27195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27198 \begin_layout Plain Layout
27206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27209 \begin_layout Plain Layout
27210 \begin_inset Formula $\_{} {}{}{}{}{}{}{}$
27220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27223 \begin_layout Plain Layout
27228 \begin_layout Plain Layout
27243 \begin_layout Plain Layout
27254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27257 \begin_layout Plain Layout
27258 \begin_inset Formula $^{\circ}$
27274 \begin_layout Standard
27275 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27276 contains the following line
27280 \begin_layout Plain Layout
27281 More about this is described in
27282 \begin_inset CommandInset ref
27284 reference "sub:Text-Characters-in"
27296 \begin_layout Standard
27301 DeclareInputtext{176}{
27311 f\SpecialChar \textcompwordmark{}
27315 \begin_layout Standard
27316 \begin_inset VSpace bigskip
27323 \begin_layout Plain Layout
27329 is designed as accent, thus is looks alone a bit misplaced: ~
27330 \begin_inset Newline newline
27333 But for web addresses (URLs) sometimes a single tilde is needed.
27334 In this case the relation sign
27342 \begin_layout Plain Layout
27344 \begin_inset CommandInset ref
27346 reference "sec:Relations"
27357 is used in a formula.
27358 As a formula cannot be created in an URL-box (menu
27360 Insert\SpecialChar \menuseparator
27363 ), the URL is inserted as normal text with the font style '
27368 Should the URL be a hyperlink in the DVI- or PDF-output, the command
27378 \begin_layout Plain Layout
27385 can only be used together with the LaTeX-package
27393 \begin_layout Plain Layout
27394 Packages ! hyperref
27406 is written in the section
27413 \begin_inset Space ~
27427 \begin_layout Plain Layout
27438 \begin_layout Standard
27439 As example an URL with a tilde:
27442 \begin_layout Standard
27445 http://www.lyx.org/
27446 \begin_inset Formula $\sim$
27452 \begin_layout Standard
27463 \begin_layout Plain Layout
27467 href{http://www.lyx.org/~mustermann}{
27472 http://www.lyx.org/
27473 \begin_inset Formula $\sim$
27480 \begin_layout Plain Layout
27490 \begin_layout Section
27492 \begin_inset CommandInset label
27494 name "sec:Formula-Styles"
27502 \begin_layout Plain Layout
27511 \begin_layout Itemize
27512 There are two different alignment styles:
27516 \begin_layout Description
27517 Centered is the predefined standard
27520 \begin_layout Description
27521 Indented for this the option
27525 must be inserted in the menu
27527 Document\SpecialChar \menuseparator
27533 \begin_inset Space ~
27539 \begin_layout Standard
27544 is used, the indentation can be adjusted with the length
27554 \begin_layout Plain Layout
27563 Should the distance be 15
27564 \begin_inset Space \thinspace{}
27567 mm, the following command line is inserted in the LaTeX-preamble
27570 \begin_layout Standard
27580 \begin_layout Standard
27581 When no length is specified, the predefined value of 30
27582 \begin_inset Space \thinspace{}
27589 \begin_layout Itemize
27590 And two different numbering styles:
27594 \begin_layout Description
27595 Right is the predefined standard
27598 \begin_layout Description
27599 Left for this the option
27603 must be inserted in the menu
27605 Document\SpecialChar \menuseparator
27611 \begin_inset Space ~
27618 \begin_layout Standard
27627 can also be used together.
27628 In this case both options are inserted, separated by a comma.
27631 \begin_layout Standard
27632 The chosen styles are used for all displayed formulas of the document.
27633 When both, centered and indented formulas should be created in a document,
27639 The indented formulas are then set in a flalign environment, see
27640 \begin_inset CommandInset ref
27642 reference "sub:Flalign-Environment"
27649 \begin_layout Section
27651 \begin_inset CommandInset label
27653 name "sec:Multiline-Formulas"
27661 \begin_layout Plain Layout
27662 Formula ! multiline
27670 \begin_layout Subsection
27674 \begin_layout Standard
27675 In LyX multiline formulas are created by pressing
27686 that is described in
27687 \begin_inset CommandInset ref
27689 reference "sub:Standard-align-Environment"
27696 \begin_layout Standard
27697 There are other multiline formula environments that can be created via the
27700 Insert\SpecialChar \menuseparator
27704 These environments are described in the following sections.
27707 \begin_layout Standard
27708 In all multiline formula environments a new line is created by pressing
27714 To add or delete lines, the math toolbar buttons
27715 \begin_inset Graphics
27716 filename ../images/tabular-feature_append-row.png
27723 \begin_inset Graphics
27724 filename ../images/tabular-feature_delete-row.png
27730 , respectively, or the menu
27732 Edit\SpecialChar \menuseparator
27738 \begin_layout Subsubsection
27740 \begin_inset CommandInset label
27742 name "sub:Line-Separation"
27750 \begin_layout Plain Layout
27751 Formula ! multiline ! Line separation
27759 \begin_layout Standard
27760 There is sometimes not enough space in multiline formulas between the lines:
27761 \begin_inset Formula \begin{eqnarray*}
27762 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}\\
27763 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*}
27770 \begin_layout Standard
27771 In LaTeX additional line space is specified as optional argument of the
27773 This is not yet possible in LyX
27777 \begin_layout Plain Layout
27782 \begin_layout Plain Layout
27786 href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
27795 \begin_layout Plain Layout
27807 , therefore the whole formula must be inserted in TeX-mode.
27808 To add in our example space, the command
27816 is inserted at the end of the first line.
27821 \begin_layout Plain Layout
27828 \begin_layout Plain Layout
27830 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27833 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27840 \begin_layout Plain Layout
27844 left(B^{2}+x_{0}^{2}
27852 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27857 \begin_layout Plain Layout
27869 \begin_layout Standard
27870 \begin_inset VSpace bigskip
27873 To set the the line separation for all lines in a formula, the length
27883 \begin_layout Plain Layout
27893 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27904 \begin_inset Space \thinspace{}
27909 \begin_inset Space \thinspace{}
27912 mm additional line separation as in the previous example, the command
27915 \begin_layout Standard
27925 \begin_layout Standard
27926 is inserted in TeX-mode before the formula.
27927 This requires that the LaTeX-package
27935 \begin_layout Plain Layout
27940 is part of every LaTeX standard installation.
27949 \begin_layout Plain Layout
27955 was loaded in LaTeX-preamble with the line
27958 \begin_layout Standard
27966 \begin_layout Standard
27971 \begin_layout Plain Layout
27983 \begin_inset Formula \begin{eqnarray*}
27984 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}\\
27985 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*}
27992 \begin_layout Standard
27996 \begin_layout Plain Layout
28007 To get back to the predefined distance,
28013 is set to the value 3
28014 \begin_inset Space \thinspace{}
28020 \begin_layout Subsubsection
28022 \begin_inset CommandInset label
28024 name "sub:Column-Separation"
28032 \begin_layout Plain Layout
28033 Formula ! multiline ! Column separation
28041 \begin_layout Standard
28042 Multiline formulas form a matrix.
28043 A formula in the eqnarray environment is for example a matrix with three
28045 By changing the column separation in this environment, the space beside
28046 the relation sign can be changed.
28049 \begin_layout Standard
28050 The column separation is specified with the length
28060 \begin_layout Plain Layout
28069 \begin_inset Newline newline
28072 column separation = 2
28073 \begin_inset Space \thinspace{}
28083 \begin_inset Newline newline
28089 \begin_layout Standard
28099 \begin_layout Standard
28100 inserted in TeX-mode, sets for all following formulas a column separation
28102 \begin_inset Space \thinspace{}
28106 To get back to the predefined distance,
28113 \begin_inset Space \thinspace{}
28119 \begin_layout Standard
28121 \begin_inset Space \thinspace{}
28124 cm column separation:
28128 \begin_layout Plain Layout
28140 \begin_inset Formula \begin{eqnarray*}
28142 C & \ne & A\end{eqnarray*}
28146 A formula with the predefined column separation for matrices of 10
28147 \begin_inset Space \thinspace{}
28154 \begin_layout Plain Layout
28166 \begin_inset Formula \begin{eqnarray*}
28168 C & \ne & A\end{eqnarray*}
28175 \begin_layout Subsubsection
28180 \begin_layout Plain Layout
28189 \begin_layout Standard
28190 Long formulas can be typeset using these methods:
28193 \begin_layout Itemize
28194 When one side of the equation is much shorther than the line width, this
28195 one is chosen for the left side and the right side is typeset over two
28200 \begin_layout Plain Layout
28210 \begin_inset Formula \begin{eqnarray}
28211 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 \\
28212 & & -\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:kurzlang}\end{eqnarray}
28220 \begin_layout Plain Layout
28230 \begin_inset Newline newline
28233 The minus sign at the beginning of the second line does normally not appear
28234 as operator because it is the first character of the line.
28235 Thus it would not be surrounded by space and could not be distinguished
28236 from the fraction bar.
28237 To avoid this, space was inserted behind the minus sign with the command
28248 \begin_layout Plain Layout
28256 \begin_inset CommandInset ref
28258 reference "sub:Variable-Space"
28271 \begin_layout Plain Layout
28282 \begin_layout Itemize
28283 When both sides of the equation are too long, the command
28293 \begin_layout Plain Layout
28302 It is inserted to the first column of the first line and effects that all
28303 further insertions overwrite the following columns:
28307 \begin_layout Plain Layout
28317 \begin_inset Formula \begin{eqnarray}
28318 \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 \\
28319 & & -\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 \\
28320 & & =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}
28328 \begin_layout Plain Layout
28338 \begin_inset Newline newline
28341 After the insertion of
28347 , the cursor is in a purple box that is a bit shifted to the left from the
28349 In this the formula is inserted.
28353 \begin_layout Plain Layout
28363 \begin_inset Newline newline
28366 The content of the further lines is inserted to the second or another formula
28368 The greater the column number where it was inserted, the larger the indentation.
28372 \begin_layout Plain Layout
28382 \begin_inset Newline newline
28386 \begin_inset Note Greyedout
28389 \begin_layout Plain Layout
28390 Note the following when using
28399 \begin_layout Itemize
28400 The formula doesn't use the full page width.
28402 \begin_inset Space \thinspace{}
28406 \begin_inset Space ~
28410 \begin_inset Formula $-B^{2}$
28413 is added to the first line in the above example, it would have been outside
28415 To better use the width, negative space can be inserted at the beginning
28419 \begin_layout Itemize
28420 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28425 \begin_layout Plain Layout
28429 \begin_layout Plain Layout
28433 href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
28442 \begin_layout Plain Layout
28454 One can only set the cursor at the beginning of the line and move it with
28463 \begin_layout Itemize
28464 Other methods to set long formulas are offered by the environments described
28466 \begin_inset CommandInset ref
28468 reference "sub:Multline-Environment"
28473 \begin_inset CommandInset ref
28475 reference "sub:Multiline-Formula-Parts"
28482 \begin_layout Subsubsection
28484 \begin_inset CommandInset label
28486 name "sub:Multiline-Brackets"
28494 \begin_layout Plain Layout
28495 Brackets ! for multiline expressions
28503 \begin_layout Standard
28504 For brackets spanning multiple lines the following problem occurs:
28505 \begin_inset Formula \begin{eqnarray*}
28506 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28507 & & \left.\cdots+B-D\right]\end{eqnarray*}
28514 \begin_layout Standard
28515 The closing bracket is smaller than the opening bracket because brackets
28516 with variable size may not span multiple lines.
28519 \begin_layout Standard
28520 To set the bracket size for the second line correctly, the first line is
28531 \begin_layout Plain Layout
28539 and the second line with
28547 \begin_layout Plain Layout
28561 \begin_inset CommandInset ref
28563 reference "sub:Automatic-Bracket-Size"
28578 \begin_layout Plain Layout
28604 \begin_layout Plain Layout
28623 \begin_layout Plain Layout
28642 \begin_layout Plain Layout
28654 \begin_inset Formula $\downarrow$
28663 \begin_layout Plain Layout
28671 is inserted, because the multiplication operator with its limits is the
28672 largest symbol in the first line and this should be the size for the bracket
28673 in the second line.
28676 \begin_layout Standard
28677 The result is this:
28678 \begin_inset Formula \begin{eqnarray*}
28679 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28680 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28687 \begin_layout Subsection
28691 \begin_layout Standard
28692 Align environments can be used for every kind of multiline formulas.
28693 They are specially useful to set several formulas side by side.
28696 \begin_layout Standard
28697 Align environments consist of columns.
28698 The odd columns are right aligned, the even ones left aligned.
28699 Every line in an Align environment can be numbered.
28702 \begin_layout Standard
28703 Align environments are created via the menu
28705 Insert\SpecialChar \menuseparator
28711 Edit\SpecialChar \menuseparator
28712 Math\SpecialChar \menuseparator
28713 Change Formula Type
28715 already existing formulas can be converted to Align environments.
28718 \begin_layout Standard
28719 To add or delete columns, the math toolbar buttons
28720 \begin_inset Graphics
28721 filename ../images/tabular-feature_append-column.png
28728 \begin_inset Graphics
28729 filename ../images/tabular-feature_delete-column.png
28735 , respectively, or the menu
28737 Edit\SpecialChar \menuseparator
28743 \begin_layout Subsubsection
28744 Standard align Environment
28745 \begin_inset CommandInset label
28747 name "sub:Standard-align-Environment"
28755 \begin_layout Plain Layout
28756 Formula ! multiline ! align environment
28764 \begin_layout Standard
28765 This Align environment is created by presssing
28769 in a formula or by the menu
28771 Insert\SpecialChar \menuseparator
28772 Math\SpecialChar \menuseparator
28773 AMS align Environment
28778 \begin_layout Standard
28779 An example for two formulas set side by side, that are created with a four
28780 column align environment:
28781 \begin_inset Formula \begin{align*}
28782 A & =\sin(B) & C & =D\\
28783 C & \ne A & B & \ne D\end{align*}
28787 As it can be seen, the formulas in this environment are placed so as if
28796 \begin_layout Plain Layout
28804 \begin_inset CommandInset ref
28806 reference "sub:Variable-Space"
28817 before the first and after every even column.
28818 When the formula style
28824 \begin_layout Plain Layout
28826 \begin_inset CommandInset ref
28828 reference "sec:Formula-Styles"
28839 is used, the formula is set without the
28845 before the first column.
28848 \begin_layout Subsubsection
28849 Alignat Environment
28853 \begin_layout Plain Layout
28854 Formula ! multiline ! alignat environment
28862 \begin_layout Standard
28863 The alignat environment has no predefined column separation.
28864 It can be inserted manually with the spaces that are described
28865 \begin_inset CommandInset ref
28867 reference "sub:Space"
28874 \begin_layout Standard
28875 The above example in the alignat environment where 1
28876 \begin_inset Space \thinspace{}
28879 cm space was inserted at the beginning of the second formula:
28880 \begin_inset Formula \begin{alignat*}{2}
28881 A & =\sin(B) & \hspace {1cm}C & =D\\
28882 C & \ne A & B & \ne D\end{alignat*}
28886 Because the column separation can be set separately for every column, this
28887 environment is especially suitable to set three and more formulas side
28891 \begin_layout Subsubsection
28892 Flalign Environment
28893 \begin_inset CommandInset label
28895 name "sub:Flalign-Environment"
28903 \begin_layout Plain Layout
28904 Formula ! multiline ! flalign environment
28912 \begin_layout Standard
28913 In this environment the first two columns are always set as much as possible
28914 to the left and the last two ones to the right.
28916 \begin_inset Formula \begin{flalign*}
28917 A & =1 & B & =2 & C & =3\\
28918 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28925 \begin_layout Standard
28926 By creating a flalign environment with an odd number of columns where an
28927 empty TeX-brace is inserted to the last column, several formulas in a document
28928 can be set to the left, although the formula style
28933 As example the indented formula
28934 \begin_inset CommandInset ref
28936 reference "eq:VolInt"
28941 \begin_inset Formula \begin{flalign}
28942 \hspace {30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28946 The first two columns contain the formula.
28947 To indent it as with the formula style
28952 \begin_inset Space \thinspace{}
28955 pt space was inserted at the beginning of the first column.
28958 \begin_layout Subsection
28959 Eqnarray Environment
28963 \begin_layout Plain Layout
28964 Formula ! multiline ! eqnarray environment
28972 \begin_layout Standard
28973 When this environment has been created, three blue boxes appear.
28974 The content of the first box is right aligned, the content of the last
28976 The content of the middle box appears centered and a bit smaller, because
28977 it is designed to insert there only relation characters.
28978 \begin_inset Formula \begin{eqnarray*}
28979 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28981 A & = & A\end{eqnarray*}
28988 \begin_layout Subsection
28993 \begin_layout Plain Layout
28994 Formula ! multiline ! gather environment
29002 \begin_layout Standard
29003 This environment consists of only one centered column.
29004 Every line can be numbered.
29005 \begin_inset Formula \begin{gather}
29007 X=\textrm{-}1\end{gather}
29014 \begin_layout Subsection
29015 Multline Environment
29016 \begin_inset CommandInset label
29018 name "sub:Multline-Environment"
29026 \begin_layout Plain Layout
29027 Formula ! multiline ! multline environment
29035 \begin_layout Standard
29036 The multline environment consists, like the gather environment, of only
29038 But the first line is left aligned, the last one right aligned.
29039 All other lines are centered.
29040 Therefore this environment is suitable for long formulas.
29042 \begin_inset CommandInset ref
29044 reference "eq:lefteqn"
29048 in the multline environment:
29049 \begin_inset Formula \begin{multline}
29050 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}\\
29051 -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}\\
29052 =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}
29059 \begin_layout Standard
29060 In the output only the last (first) line of a multline environment appears
29061 numbered when the document numbering is right (left).
29065 \begin_layout Plain Layout
29066 numbering styles see
29067 \begin_inset CommandInset ref
29069 reference "sec:Formula-Styles"
29078 This is also the case when there is a formula number displayed after every
29083 \begin_layout Plain Layout
29088 \begin_layout Plain Layout
29092 href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
29101 \begin_layout Plain Layout
29116 \begin_layout Standard
29125 \begin_layout Plain Layout
29143 \begin_layout Plain Layout
29153 a centered line can be right or left aligned, respectively.
29154 The commands are used as follows:
29157 \begin_layout Standard
29162 shoveright{line content}
29168 shoveleft{line content}
29171 \begin_layout Standard
29172 \begin_inset VSpace medskip
29183 \begin_layout Plain Layout
29193 specifies the distance of the first line from the left page margin.
29194 Predefined is the length 0
29195 \begin_inset Space \thinspace{}
29201 \begin_layout Standard
29202 As example the above formula where the command
29205 \begin_layout Standard
29215 \begin_layout Standard
29216 was inserted in TeX-mode before:
29220 \begin_layout Plain Layout
29232 \begin_inset Formula \begin{multline}
29233 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}\\
29234 \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}}\\
29235 =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}
29243 \begin_layout Plain Layout
29254 The second line was left aligned using
29263 \begin_layout Subsection
29264 Multiline Formula Parts
29265 \begin_inset CommandInset label
29267 name "sub:Multiline-Formula-Parts"
29275 \begin_layout Plain Layout
29276 Formula ! multiline ! formula parts
29284 \begin_layout Standard
29285 To display only parts of a formula with multiple lines, one of the following
29286 environments are used:
29303 They can be inserted via the menu
29305 Insert\SpecialChar \menuseparator
29308 or by using the commands described in this section.
29311 \begin_layout Standard
29312 The first three have the same properties as the corresponding multiline
29313 formula environments, but it is possible to set further formula parts beside
29316 \begin_inset Formula \[
29317 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29318 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29319 \right\} \textrm{Uncertainty relations}\]
29326 \begin_layout Standard
29327 To get this formula, a displayed formula is created where the command
29335 \begin_layout Plain Layout
29346 A purple box appears around the blue formula box where now columns and
29347 lines can be added.
29348 Outside the multiline environment other formula parts can be set, like
29352 \begin_layout Standard
29353 The aligned environment is also suitable for long formulas whose lines are
29354 horizontally aligned.
29355 Using aligned in a displayed formula has the advantage that the formula
29356 number is vertically centered behind the lines.
29358 \begin_inset CommandInset ref
29360 reference "eq:kurzlang"
29364 in the aligned environment:
29365 \begin_inset Formula \begin{equation}
29366 \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}|}\\
29367 & -\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}
29375 \begin_layout Standard
29376 To use the environments
29398 \begin_layout Plain Layout
29416 \begin_layout Plain Layout
29434 \begin_layout Plain Layout
29442 are inserted, respectively.
29443 The split environment has the same properties as the aligned environment
29444 but it can only have two columns.
29447 \begin_layout Subsection
29448 Text in multiline Formulas
29449 \begin_inset CommandInset label
29451 name "sub:Text-in-multiline"
29459 \begin_layout Plain Layout
29469 \begin_layout Plain Layout
29470 Formula ! multiline ! text
29478 \begin_layout Standard
29479 In the Align environments, and the multline and gather environment, text
29480 can be inserted that will appear in a separate line and doesn't affect
29481 the column alignment.
29482 To do this, the command
29490 \begin_layout Plain Layout
29500 is used in the following scheme:
29503 \begin_layout Standard
29511 \begin_layout Standard
29512 The text should not be longer than a line because it cannot be hyphenated.
29513 As LyX doesn't yet support
29519 directly, the text is written as mathematical text.
29526 must hereby be at the beginning of a line and appears in the output above
29528 An example where the text was inserted at the beginning of the second line:
29529 \begin_inset Formula \begin{align}
29530 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29531 \intertext {\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29538 \begin_layout Section
29543 \begin_layout Plain Layout
29553 \begin_layout Plain Layout
29554 Formula ! numbering|see
29558 \begin_layout Plain Layout
29569 \begin_layout Plain Layout
29584 \begin_layout Subsection
29588 \begin_layout Standard
29589 Numbered formulas can be created with the menu
29591 Insert\SpecialChar \menuseparator
29592 Math\SpecialChar \menuseparator
29594 \begin_inset Space ~
29602 \begin_inset Space ~
29608 Existing formulas can be numbered with the menu
29610 Edit\SpecialChar \menuseparator
29611 Math\SpecialChar \menuseparator
29613 \begin_inset Space ~
29621 \begin_inset Space ~
29627 The formula number is displayed in LyX behind the formula as number sign
29629 The number sign is replaced in the output by the formula number.
29632 \begin_layout Standard
29633 When numbering is turned on in multiline formulas, all lines will be numbered.
29634 But the numbering can be controlled with the menu
29636 Edit\SpecialChar \menuseparator
29637 Math\SpecialChar \menuseparator
29639 \begin_inset Space ~
29643 \begin_inset Space ~
29647 \begin_inset Space ~
29655 \begin_inset Space ~
29663 \begin_layout Standard
29664 Except of inline formulas, all formulas can be numbered with two different
29666 \begin_inset CommandInset ref
29668 reference "sec:Formula-Styles"
29675 \begin_layout Subsection
29677 \begin_inset CommandInset label
29679 name "sub:Cross-References"
29687 \begin_layout Plain Layout
29688 Cross-references ! to formulas
29696 \begin_layout Standard
29697 All labeled formulas can be cross-referenced.
29698 A label is added by the menu
29700 Insert\SpecialChar \menuseparator
29703 or the toolbar button
29704 \begin_inset Graphics
29705 filename ../images/label-insert.png
29712 The cursor must hereby be inside a displayed formula.
29713 A dialog pops up displaying the prefix
29718 The label is inserted there behind the prefix.
29719 The predefined prefix means
29720 \begin_inset Quotes eld
29724 \begin_inset Quotes erd
29727 and makes it easier to find labels in large documents because it marks
29728 it as formula label to divide it from e.
29729 \begin_inset Space \thinspace{}
29733 \begin_inset Space ~
29737 To change a label, the menu
29739 Insert\SpecialChar \menuseparator
29745 \begin_layout Standard
29746 The name of the label is displayed in LyX within two parentheses behind
29748 A formula with a label is always numbered.
29751 \begin_layout Standard
29752 Cross-references are inserted via the menu
29754 Insert\SpecialChar \menuseparator
29757 or with the toolbar button
29758 \begin_inset Graphics
29759 filename ../images/dialog-show-new-inset_ref.png
29766 A formula cross-reference appears in the output as formula number.
29767 When in the cross-reference dialog window the format
29771 is chosen, the cross-reference appears in the output as formula number
29773 \begin_inset Newline newline
29776 By right-clicking on a cross-reference in LyX, one jumps to the formula
29777 that is referenced.
29780 \begin_layout Standard
29781 Here are as examples cross-references to formulas of the following subsections:
29782 \begin_inset Note Note
29785 \begin_layout Plain Layout
29786 Note the different cross-reference types.
29794 \begin_layout Standard
29796 \begin_inset CommandInset ref
29803 \begin_inset CommandInset ref
29811 \begin_inset CommandInset ref
29817 ) big Latin letters are used for the numbering in contrary to (
29818 \begin_inset CommandInset ref
29827 \begin_layout Standard
29828 \begin_inset VSpace medskip
29831 When the argument of
29839 \begin_layout Plain Layout
29847 \begin_inset CommandInset ref
29849 reference "sub:User-defined-Numbering"
29860 contains a box like in
29861 \begin_inset CommandInset ref
29863 reference "sub:Paragraph-Boxes"
29867 , the formula cannot be referenced.
29870 \begin_layout Subsection
29875 \begin_layout Plain Layout
29876 Formula numbering ! subnumbering
29884 \begin_layout Standard
29885 With the help of the commands
29889 begin{subequations}
29897 formulas can be subnumbered.
29898 Both commands are inserted in TeX-mode.
29901 \begin_layout Standard
29903 \begin_inset Formula \begin{equation}
29904 A=C-B\label{eq:a}\end{equation}
29912 \begin_layout Plain Layout
29916 addtocounter{equation}{-1}
29925 \begin_layout Plain Layout
29929 begin{subequations}
29935 \begin_inset VSpace -5mm
29939 \begin_inset Formula \begin{equation}
29940 B=C-A\label{eq:b}\end{equation}
29945 \begin_inset Formula \begin{equation}
29946 C=A+B\label{eq:c}\end{equation}
29953 \begin_layout Standard
29957 \begin_layout Plain Layout
29969 \begin_layout Standard
29970 To create the example, the following is done:
29973 \begin_layout Enumerate
29974 first formula is inserted
29977 \begin_layout Enumerate
29982 addtocounter{equation}{-1}
29984 begin{subequations}
29988 \begin_layout Plain Layout
29997 \begin_inset Newline newline
30002 is inserted after the first formula
30005 \begin_layout Enumerate
30006 second formula is inserted
30009 \begin_layout Enumerate
30010 third formula is inserted
30013 \begin_layout Enumerate
30020 is inserted after the third formula
30023 \begin_layout Standard
30024 Every formula between the commands
30036 is subnumbered as a, b,
30040 \begin_layout Plain Layout
30049 c, \SpecialChar \ldots{}
30050 For multiline formulas every line will be subnumbered.
30051 All subnumbered formulas are treated as
30056 But as every numbered formula increases the counter
30060 by one, the command
30066 is needed to decrease it.
30067 Otherwise the formulas
30068 \begin_inset CommandInset ref
30075 \begin_inset CommandInset ref
30082 \begin_inset CommandInset ref
30088 would be numbered as
30089 \begin_inset CommandInset ref
30096 \begin_inset CommandInset ref
30103 \begin_inset CommandInset ref
30112 \begin_layout Standard
30113 By inserting the commands in TeX-mode, a space is created between the first
30116 \begin_inset Space \thinspace{}
30119 mm vertical space is inserted after the command
30123 begin{subequations}
30126 When the formula style
30132 \begin_layout Plain Layout
30134 \begin_inset CommandInset ref
30136 reference "sec:Formula-Styles"
30148 \begin_inset Space \thinspace{}
30151 mm space is inserted instead.
30154 \begin_layout Standard
30155 Here is an example for a multiline formula where the numbering was turned
30156 off for the second line:
30160 \begin_layout Plain Layout
30164 begin{subequations}
30170 \begin_inset Formula \begin{eqnarray}
30171 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30172 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
30173 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
30181 \begin_layout Plain Layout
30193 \begin_layout Subsection
30194 User-defined Numbering
30195 \begin_inset CommandInset label
30197 name "sub:User-defined-Numbering"
30205 \begin_layout Plain Layout
30206 Formula numbering ! user-defined
30214 \begin_layout Standard
30218 \begin_layout Plain Layout
30219 Formula numbering ! self-defined delimiters
30224 With the standard numbering parentheses are set around the formula number.
30225 To replace the parentheses for example by vertical bars, the following
30226 line is added to the LaTeX-preamble:
30229 \begin_layout Standard
30241 \begin_inset Note Note
30244 \begin_layout Plain Layout
30245 This macro is already declared in the LaTeX-preamble for testing.
30246 To activate it, remove the percent sign at the beginning.
30254 \begin_layout Standard
30255 To use other characters, the vertical bars besides the
30259 are replaced by one ore more characters.
30260 To get only the formula number the vertical bars are omitted.
30263 \begin_layout Standard
30264 \begin_inset VSpace bigskip
30267 When there should be an expression of your choice instead of the consecutive
30268 formula number in parentheses behind the formula, the command
30278 \begin_layout Plain Layout
30287 \begin_inset Formula \begin{equation}
30288 A+B=C\tag{something}\label{eq:tag}\end{equation}
30292 In this example the command
30300 \begin_layout Plain Layout
30311 was inserted to the formula.
30314 \begin_layout Standard
30323 \begin_layout Plain Layout
30334 is inserted instead, the star prevents the parentheses around the expression:
30335 \begin_inset Formula \[
30336 A+B=C\tag*{something}\]
30343 \begin_layout Standard
30344 \begin_inset VSpace bigskip
30347 To restart the formula numbering with new document parts or sections, the
30348 following command is used:
30351 \begin_layout Standard
30356 @addtoreset{equation}{part}
30362 \begin_layout Plain Layout
30367 \begin_layout Plain Layout
30378 \begin_layout Plain Layout
30391 \begin_layout Plain Layout
30402 \begin_layout Plain Layout
30415 \begin_inset Newline newline
30419 \begin_inset Newline newline
30426 @addtoreset{equation}{section}
30429 \begin_layout Standard
30430 To be able to use these commands in TeX-mode, the
30431 \begin_inset Quotes eld
30435 \begin_inset Quotes erd
30438 character has to be made
30439 \begin_inset Quotes eld
30443 \begin_inset Quotes erd
30446 for LaTeX using the command
30460 So the command sequence in TeX-mode is:
30463 \begin_layout Standard
30469 \begin_inset Newline newline
30474 @addtoreset{equation}{section}
30475 \begin_inset Newline newline
30483 \begin_layout Standard
30484 In the LaTeX-preamble
30496 can be omitted as they are automatically internally inserted by LyX.
30499 \begin_layout Standard
30514 \begin_layout Plain Layout
30519 is part of the LaTeX-package
30527 \begin_layout Plain Layout
30528 Packages ! carlisle
30533 that is part of every LaTeX standard installation.
30542 \begin_layout Plain Layout
30543 Packages ! remreset
30548 has to be loaded in the LaTeX-preamble with the line
30551 \begin_layout Standard
30556 usepackage{remreset}
30559 \begin_layout Standard
30570 \begin_layout Plain Layout
30575 \begin_layout Plain Layout
30586 \begin_layout Plain Layout
30599 \begin_layout Plain Layout
30610 \begin_layout Plain Layout
30622 can be used with the same scheme as
30631 \begin_layout Standard
30632 \begin_inset VSpace bigskip
30635 Sometimes formulas should be numbered in the following form:
30638 \begin_layout Standard
30641 (section number.formula number)
30644 \begin_layout Standard
30645 The formula number should start with every section with
30646 \begin_inset Quotes eld
30650 \begin_inset Quotes erd
30656 \begin_layout Standard
30657 For this case there is the command
30667 \begin_layout Plain Layout
30675 , which is used with the following scheme:
30678 \begin_layout Standard
30683 numberwithin{counter}{sectioning}
30686 \begin_layout Standard
30687 Counter denotes what kind of numbering is affected, sectioning denotes what
30688 number is before the dot.
30691 \begin_layout Standard
30692 Thus in our case the following LaTeX-preamble or ERT line is used:
30695 \begin_layout Standard
30700 numberwithin{equation}{section}
30703 \begin_layout Standard
30704 This is the result:
30708 \begin_layout Plain Layout
30712 numberwithin{equation}{section}
30718 \begin_inset Formula \begin{equation}
30719 A+B=C\end{equation}
30726 \begin_layout Standard
30728 \begin_inset Space \thinspace{}
30732 \begin_inset Space ~
30735 tables so that the number of the part is the sectioning,
30736 \begin_inset Newline newline
30743 numberwithin{table}{part}
30748 \begin_layout Standard
30749 To go back to the standard numbering or to prevent this kind of numbering
30750 when it is defined by the document class, the following command is inserted
30751 as ERT or to the LaTeX-preamble:
30754 \begin_layout Standard
30767 \begin_layout Plain Layout
30781 \begin_layout Plain Layout
30797 \begin_inset Newline newline
30805 \begin_inset Newline newline
30817 \begin_layout Standard
30824 uses internally the command
30830 , described above, that also needs to be reverted.
30834 \begin_layout Plain Layout
30841 \begin_layout Plain Layout
30845 @removefromreset{equation}{section}
30848 \begin_layout Plain Layout
30860 \begin_layout Subsection
30861 Numbering with Roman Numbers and Letters
30862 \begin_inset CommandInset label
30864 name "sub:Numbering-with-Roman"
30872 \begin_layout Plain Layout
30873 Formula numbering ! with letters
30882 \begin_layout Plain Layout
30883 Formula numbering ! with Roman numbers
30891 \begin_layout Standard
30892 Formulas can also be numbered with Roman numbers and Latin letters.
30893 To number for example with small Roman numbers, the command
30896 \begin_layout Standard
30908 \begin_layout Standard
30909 is inserted before the formula in TeX-mode.
30920 \begin_layout Plain Layout
30928 redefines the predefined command
30944 \begin_layout Plain Layout
30951 has the same scheme like the command
30957 that is described in
30958 \begin_inset CommandInset ref
30960 reference "sec:User-defined-commands"
30974 is the formula counter.
30981 is used as prefix for a counter, the value of the counter is output as
30983 When a formula is numbered, LaTeX sets internally the command
30989 behind the formula.
30998 \begin_layout Plain Layout
31008 outputs the counter as small Roman number.
31011 \begin_layout Standard
31012 All formulas behind the command
31022 are now numbered Roman.
31023 To switch to numbering with big Roman numbers, the command is inserted
31040 \begin_layout Plain Layout
31052 \begin_inset Quotes eld
31056 \begin_inset Quotes erd
31059 with small Latin letters there is the command
31069 \begin_layout Plain Layout
31077 , for big ones there is the command
31087 \begin_layout Plain Layout
31100 \begin_layout Standard
31101 \begin_inset Note Greyedout
31104 \begin_layout Plain Layout
31109 Only maximal 26 formulas can be numbered with Latin letters in one document.
31117 \begin_layout Standard
31121 \begin_layout Plain Layout
31137 \begin_layout Standard
31138 \begin_inset Formula \begin{equation}
31139 A=\textrm{small roman}\label{eq:rom}\end{equation}
31147 \begin_layout Plain Layout
31161 \begin_inset Formula \begin{equation}
31162 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31170 \begin_layout Plain Layout
31184 \begin_inset Formula \begin{equation}
31185 C=\textrm{small Latin}\label{eq:lat}\end{equation}
31193 \begin_layout Plain Layout
31207 \begin_inset Formula \begin{equation}
31208 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31215 \begin_layout Standard
31216 To switch back to the default numbering, insert the command:
31219 \begin_layout Standard
31232 \begin_layout Plain Layout
31243 \begin_layout Standard
31247 \begin_layout Plain Layout
31261 \begin_inset Formula \begin{equation}
31262 E=\textrm{Arabic}\label{eq:arab}\end{equation}
31269 \begin_layout Standard
31270 \begin_inset VSpace medskip
31273 As you see, formulas are numbered serially independent from the numbering
31275 When then numbering should start with
31276 \begin_inset Quotes eld
31280 \begin_inset Quotes erd
31283 when the style is changed, new equation counters have to be defined.
31284 A description about this can be found in the file
31288 \begin_layout Plain Layout
31292 href{Formula-numbering.lyx}{
31297 Formula-numbering.lyx
31301 \begin_layout Plain Layout
31311 \begin_layout Section
31312 User-defined commands
31313 \begin_inset CommandInset label
31315 name "sec:User-defined-commands"
31323 \begin_layout Plain Layout
31324 User-defined commands
31332 \begin_layout Standard
31333 Many LaTeX-commands are too long to be used frequently.
31334 But it is possible to define with the command
31344 \begin_layout Plain Layout
31352 new shorter commands.
31355 \begin_layout Standard
31356 The command scheme of
31365 \begin_layout Standard
31370 newcommand{new command name}[number of arguments][optional
31375 \begin_inset Newline newline
31382 \begin_layout Plain Layout
31397 \begin_layout Plain Layout
31404 {command definition}
31407 \begin_layout Standard
31408 \begin_inset Note Greyedout
31411 \begin_layout Plain Layout
31416 Assure that the name of the new command is not already used in your document
31417 or by LaTeX-packages that you use.
31418 When you for example define the command
31430 , you get an error message because
31436 is already defined as command for
31437 \begin_inset Quotes eld
31441 \begin_inset Formula $\le$
31445 \begin_inset Quotes erd
31456 \begin_layout Standard
31457 \begin_inset Note Greyedout
31460 \begin_layout Plain Layout
31465 The names of user-defined commands may only consist of Latin letters.
31473 \begin_layout Standard
31474 The number of arguments is an integer in the range 0
31475 \begin_inset Space \thinspace{}
31479 \begin_inset Space \thinspace{}
31482 9 and specifies how many arguments the new command should have.
31483 With the optional value a value for an optional argument can be predefined.
31484 When this is done, the
31492 rgument of the new command is automatically an optional one.
31495 \begin_layout Standard
31496 Here are some examples:
31499 \begin_layout Itemize
31500 To define the command
31512 , the LaTeX-preamble line is:
31516 \begin_layout Plain Layout
31528 \begin_inset Newline newline
31540 \begin_layout Itemize
31541 To define the command
31553 , the argument (that should be underlined) must be taken into account.
31554 For this the preamble line is:
31558 \begin_layout Plain Layout
31570 \begin_inset Newline newline
31585 \begin_layout Plain Layout
31597 \begin_inset Newline newline
31606 acts as argument placeholder, the
31610 behind it denotes that it is the placeholder for the first argument.
31613 \begin_layout Itemize
31621 \begin_inset Space \thinspace{}
31625 \begin_inset Space ~
31638 \begin_layout Plain Layout
31650 \begin_inset Newline newline
31659 framebox#1#2{$#3$}}
31665 \begin_layout Plain Layout
31677 \begin_inset Newline newline
31682 The two Dollar signs creates the extra formula needed for
31689 \begin_inset CommandInset ref
31691 reference "sub:Boxes-with-Frame"
31698 \begin_layout Itemize
31699 To create a new command for
31705 where the color for the box needn't to be specified, the argument for the
31706 color is defined optional:
31710 \begin_layout Plain Layout
31722 \begin_inset Newline newline
31731 fcolorbox{#2}{#1}{$#3$}}
31737 \begin_layout Plain Layout
31747 \begin_inset Newline newline
31750 When the color is not specified when using
31756 , the predefined color
31763 \begin_layout Standard
31764 A test of the new defined commands:
31767 \begin_layout Standard
31769 \begin_inset Tabular
31770 <lyxtabular version="3" rows="6" columns="2">
31772 <column alignment="center" valignment="top" width="0">
31773 <column alignment="center" valignment="top" width="0">
31775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31778 \begin_layout Plain Layout
31784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31787 \begin_layout Plain Layout
31789 \begin_inset Note Note
31792 \begin_layout Plain Layout
31799 is only used as spacer.
31811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31814 \begin_layout Plain Layout
31821 \begin_layout Plain Layout
31835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31838 \begin_layout Plain Layout
31839 \begin_inset Formula $A\gr B$
31849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31852 \begin_layout Plain Layout
31860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31863 \begin_layout Plain Layout
31864 \begin_inset Formula $\raisebox {4.5mm}{}\us {ABcd}\raisebox {-2mm}{}$
31874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31877 \begin_layout Plain Layout
31881 \begin_inset Formula $\to$
31887 \begin_inset Formula $\to$
31898 \begin_layout Plain Layout
31912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31915 \begin_layout Plain Layout
31916 \begin_inset Formula $\raisebox {6mm}{}\fb {[2cm]}{}{\int A=B}\raisebox {-4mm}{}$
31926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31929 \begin_layout Plain Layout
31933 \begin_inset Formula $\to$
31944 \begin_layout Plain Layout
31958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31961 \begin_layout Plain Layout
31962 \begin_inset Formula $\raisebox {6mm}{}\cb {red}{\int A=B}\raisebox {-4mm}{}$
31972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31975 \begin_layout Plain Layout
31981 \begin_inset Formula $\to$
31992 \begin_layout Plain Layout
32006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32009 \begin_layout Plain Layout
32010 \begin_inset Formula $\raisebox {6mm}{}\cb [green]{red}{\int A=B}\raisebox {-4mm}{}$
32026 \begin_layout Section
32031 \begin_layout Plain Layout
32040 \begin_layout Standard
32041 To create diagrams, the LaTeX-package
32047 \begin_layout Plain Layout
32052 is part of every LaTeX standard installation.
32063 \begin_layout Plain Layout
32070 It is loaded in the LaTeX-preamble with the line
32073 \begin_layout Standard
32081 \begin_layout Standard
32082 Diagrams visualize relations and look like this:
32083 \begin_inset Formula \[
32084 \begin{CD}A@>>>B@>>>C\\
32086 F@<<<E@<<<D\end{CD}\]
32093 \begin_layout Standard
32094 To get them, the command
32102 \begin_layout Plain Layout
32112 is inserted to a formula.
32113 A blue box appears with two dashed lines where further commands can be
32119 a new line is created.
32120 Horizontal relations are inserted in odd, vertical in even formula lines.
32123 \begin_layout Standard
32124 To create the relations there are the following commands:
32127 \begin_layout Itemize
32132 creates a left arrow,
32143 \begin_layout Itemize
32148 creates an up arrow,
32156 a vertical equal sign
32159 \begin_layout Itemize
32165 is a placeholder for non-existent relations
32168 \begin_layout Standard
32169 All arrows can be labeled as follows:
32172 \begin_layout Itemize
32173 Is text inserted between the first and second < or >, resp., it is placed
32175 When it is inserted between the second and third one, it appears under
32179 \begin_layout Itemize
32180 When text for vertical arrows is inserted between the first and second A
32181 or V, resp., it is placed left beside the arrow.
32182 When it is inserted between the second and third one, it appears right
32184 If the text contains an A or V, these letters must be set into a TeX-brace.
32187 \begin_layout Standard
32188 As example a diagram with all possible relations:
32191 \begin_layout Standard
32192 \begin_inset Formula \[
32193 \begin{CD}A@>j>>B@>>k>C@=F\\
32195 D@<<j<E@>k>>F@=C\end{CD}\]
32202 \begin_layout Standard
32203 The command for this is:
32204 \begin_inset Newline newline
32215 \begin_layout Plain Layout
32224 A@>j>>B@>>k>C@=F Ctrl-Enter
32225 \begin_inset Newline newline
32232 \begin_layout Plain Layout
32247 \begin_layout Plain Layout
32260 \begin_layout Plain Layout
32272 \begin_inset Formula $\to$
32278 \begin_inset Newline newline
32285 \begin_layout Plain Layout
32300 \begin_layout Plain Layout
32313 \begin_layout Plain Layout
32323 \begin_layout Standard
32324 \begin_inset Newpage newpage
32330 \begin_layout Section
32335 \begin_layout Plain Layout
32348 \begin_layout Plain Layout
32349 Other useful math tips can be found in
32350 \begin_inset CommandInset citation
32365 \begin_layout Plain Layout
32373 \begin_inset Note Note
32376 \begin_layout Plain Layout
32379 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32382 \begin_layout Plain Layout
32385 texorpdfstring is in section
32386 \begin_inset CommandInset ref
32388 reference "sub:Formulas-in-Section"
32401 \begin_layout Plain Layout
32411 \begin_layout Plain Layout
32416 \begin_layout Plain Layout
32423 Chemical characters
32427 \begin_layout Plain Layout
32442 \begin_layout Subsection
32443 Chemical Symbols and Equations
32444 \begin_inset CommandInset label
32446 name "sub:Chemical-Symbols-and"
32454 \begin_layout Plain Layout
32455 Chemical characters ! Symbols
32464 \begin_layout Plain Layout
32474 \begin_layout Plain Layout
32483 \begin_layout Standard
32484 An example text from chemistry:
32487 \begin_layout Quote
32489 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32492 -ion reacts with two
32493 \begin_inset Formula $\mathrm{Na^{+}}$
32496 -ions to sodium sulfate
32497 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32501 The chemical equation for this is:
32502 \begin_inset Formula \[
32503 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32510 \begin_layout Standard
32511 This chemical equation can directly be created as formula.
32512 To avoid that the symbols appear italic, everything is highlighted and
32513 changed by the shortcut
32516 \begin_inset Space ~
32521 to the upright font style.
32525 \begin_layout Plain Layout
32531 \begin_inset CommandInset ref
32533 reference "sub:Font-Styles"
32545 \begin_layout Subsection
32550 \begin_layout Plain Layout
32559 \begin_layout Standard
32560 Negative numbers often look ugly in formulas because the minus sign before
32561 the number is set with the same length as the minus operator sign.
32562 When writing the negative number in normal text, the minus sign appears
32566 \begin_layout Standard
32567 Thus, the problem disappears when converting the minus sign to mathematical
32571 \begin_layout Standard
32572 An example to visualize the problem:
32575 \begin_layout Standard
32577 \begin_inset Tabular
32578 <lyxtabular version="3" rows="3" columns="2">
32580 <column alignment="right" valignment="top" width="0">
32581 <column alignment="left" valignment="top" width="0">
32583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32586 \begin_layout Plain Layout
32592 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32595 \begin_layout Plain Layout
32603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32606 \begin_layout Plain Layout
32612 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32615 \begin_layout Plain Layout
32616 \begin_inset Formula $x=-2$
32626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32629 \begin_layout Plain Layout
32635 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32638 \begin_layout Plain Layout
32639 \begin_inset Formula $x=\textrm{-}2$
32655 \begin_layout Subsection
32656 Comma as Decimal Separator
32660 \begin_layout Plain Layout
32669 \begin_layout Standard
32670 In LaTeX a comma inside a formula is used, according to the English convention,
32671 as number group separator.
32672 So there will be space added behind all commas in formulas.
32675 \begin_layout Standard
32676 To avoid this, the comma is highlighted and changed to mathematical text
32680 \begin_inset Space ~
32688 \begin_layout Standard
32689 To use all formula commas in the document as decimal separator, the file
32698 \begin_layout Plain Layout
32703 is part of the LaTeX-package
32711 \begin_layout Plain Layout
32713 \begin_inset VSpace 4mm
32730 \begin_layout Plain Layout
32736 is loaded with the LaTeX-preamble line
32739 \begin_layout Standard
32747 \begin_layout Subsection
32749 \begin_inset CommandInset label
32751 name "sub:Physical-Vectors"
32759 \begin_layout Plain Layout
32768 \begin_layout Standard
32769 Predefined vectors are offered by the LaTeX-package
32777 \begin_layout Plain Layout
32782 should be part of every LaTeX standard installation.
32791 \begin_layout Plain Layout
32797 that is loaded with the LaTeX-preamble line
32800 \begin_layout Standard
32808 \begin_layout Standard
32812 \begin_layout Plain Layout
32822 \begin_inset Note Note
32825 \begin_layout Plain Layout
32826 The following table will only be displayed when the LaTeX-package
32835 The following commands are defined:
32838 \begin_layout Standard
32840 \begin_inset Tabular
32841 <lyxtabular version="3" rows="4" columns="2">
32843 <column alignment="center" valignment="top" width="0">
32844 <column alignment="center" valignment="top" width="0">
32846 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32849 \begin_layout Plain Layout
32855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32858 \begin_layout Plain Layout
32866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32869 \begin_layout Plain Layout
32879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32882 \begin_layout Plain Layout
32883 \begin_inset Formula $\Bra {\psi}$
32893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32896 \begin_layout Plain Layout
32906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32909 \begin_layout Plain Layout
32910 \begin_inset Formula $\Ket {\psi}$
32920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32923 \begin_layout Plain Layout
32935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32938 \begin_layout Plain Layout
32939 \begin_inset Formula $\Braket {\psi|\phi}$
32955 \begin_layout Standard
32962 assures that all vertical bars are set in the size of the surrounding brackets:
32963 \begin_inset Formula \[
32964 \Braket {\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32972 \begin_layout Plain Layout
32982 \begin_inset Note Note
32985 \begin_layout Plain Layout
32986 The following will be displayed when the LaTeX-package
32998 \begin_layout Standard
32999 You need to install the LaTeX-package
33003 to see the rest of this subsection in the output.
33006 \begin_layout Standard
33010 \begin_layout Plain Layout
33022 \begin_layout Standard
33029 can also be achieved using the command
33035 , that is described in
33036 \begin_inset CommandInset ref
33038 reference "sub:Automatic-Bracket-Size"
33045 \begin_layout Subsection
33046 Self-defined Fractions
33047 \begin_inset CommandInset label
33049 name "sub:Self-defined-Fractions"
33057 \begin_layout Plain Layout
33058 Fractions ! self-defined
33066 \begin_layout Standard
33067 To define custom commands for fractions, the command
33077 \begin_layout Plain Layout
33085 is used in the following scheme:
33088 \begin_layout Standard
33101 bracket}{fraction bar thickness}{style}
33102 \begin_inset Newline newline
33109 \begin_layout Plain Layout
33124 \begin_layout Plain Layout
33131 {numerator}{denominator}
33134 \begin_layout Standard
33135 The style is a number in the range of 0
33136 \begin_inset Space \thinspace{}
33140 \begin_inset Space \thinspace{}
33146 \begin_layout Standard
33148 \begin_inset Tabular
33149 <lyxtabular version="3" rows="5" columns="2">
33151 <column alignment="center" valignment="top" width="0">
33152 <column alignment="center" valignment="top" width="0">
33154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33157 \begin_layout Plain Layout
33163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33166 \begin_layout Plain Layout
33174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33177 \begin_layout Plain Layout
33183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33186 \begin_layout Plain Layout
33187 display style formula
33194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33197 \begin_layout Plain Layout
33203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33206 \begin_layout Plain Layout
33214 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33217 \begin_layout Plain Layout
33223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33226 \begin_layout Plain Layout
33234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33237 \begin_layout Plain Layout
33243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33246 \begin_layout Plain Layout
33260 \begin_layout Standard
33261 When no style is given, the size is adjusted to the surrounding environment
33262 like for the command
33271 \begin_layout Standard
33272 When no fraction bar thickness is given, the predefined value of 0.4
33273 \begin_inset Space \thinspace{}
33279 \begin_layout Standard
33280 \begin_inset VSpace medskip
33283 For example, the commands
33296 \begin_inset CommandInset ref
33298 reference "sub:Fractions"
33302 are defined with the commands
33305 \begin_layout Standard
33314 genfrac{}{}{}{0}{#1}{#2}}
33317 \begin_layout Standard
33321 \begin_layout Standard
33330 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33333 \begin_layout Standard
33334 \begin_inset VSpace medskip
33337 To define a fraction where the fraction bar thickness can be given as optional
33338 argument, the following line is inserted to the LaTeX-preamble:
33341 \begin_layout Standard
33350 genfrac{}{}{#1}{}{#2}{#3}}
33353 \begin_layout Standard
33355 \begin_inset Formula \begin{align*}
33356 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33357 \text{Result} & & \fracS [1mm]{A}{B} & & \fracS [5mm]{A}{B}\end{align*}
33361 As one can see, the distance of the numerator and the denominator to the
33362 fraction bar is round about three times the bar thickness.
33365 \begin_layout Subsection
33367 \begin_inset CommandInset label
33369 name "sub:Canceled-Formulas"
33377 \begin_layout Plain Layout
33386 \begin_layout Standard
33387 To cancel formulas or formula parts, the LaTeX-package
33395 \begin_layout Plain Layout
33400 is part of every LaTeX standard installation.
33409 \begin_layout Plain Layout
33415 has to be loaded with the LaTeX-preamble line
33418 \begin_layout Standard
33423 usepackage[samesize]{cancel}
33426 \begin_layout Standard
33427 There are four ways to cancel formulas:
33430 \begin_layout Standard
33432 \begin_inset Tabular
33433 <lyxtabular version="3" rows="5" columns="2">
33435 <column alignment="center" valignment="top" width="0">
33436 <column alignment="center" valignment="top" width="0">
33438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33441 \begin_layout Plain Layout
33447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33450 \begin_layout Plain Layout
33452 \begin_inset Note Note
33455 \begin_layout Plain Layout
33468 are used here as spacer.
33480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33483 \begin_layout Plain Layout
33492 \begin_layout Plain Layout
33506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33509 \begin_layout Plain Layout
33510 \begin_inset Formula $\raisebox {4.5mm}{}\cancel {\int A=B}\raisebox {-2.5mm}{}$
33520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33523 \begin_layout Plain Layout
33532 \begin_layout Plain Layout
33546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33549 \begin_layout Plain Layout
33550 \begin_inset Formula $\raisebox {4.5mm}{}\bcancel {\int A=B}\raisebox {-2.5mm}{}$
33560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33563 \begin_layout Plain Layout
33572 \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
33590 \begin_inset Formula $\raisebox {4.5mm}{}\xcancel {\int A=B}\raisebox {-2.5mm}{}$
33600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33603 \begin_layout Plain Layout
33607 \begin_inset Formula $\to$
33618 \begin_layout Plain Layout
33632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33635 \begin_layout Plain Layout
33636 \begin_inset Formula $\raisebox {7mm}{}\cancelto {1}{\int A=B}\raisebox {-2.5mm}{}\hspace {3mm}$
33652 \begin_layout Standard
33659 is especially suitable to visualize the reduction of fractions within formulas:
33660 \begin_inset Formula \[
33661 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto {2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel {1+b^{2}}}\]
33668 \begin_layout Subsection
33669 Formulas in Section Headings
33670 \begin_inset CommandInset label
33672 name "sub:Formulas-in-Section"
33680 \begin_layout Plain Layout
33681 Formula ! in section headings
33689 \begin_layout Standard
33690 When formulas are used in section headings, the following has to be taken
33694 \begin_layout Standard
33695 \begin_inset Note Greyedout
33698 \begin_layout Plain Layout
33699 When the LaTeX-package
33707 \begin_layout Plain Layout
33708 Packages ! hyperref
33713 is used, PDF-bookmarks are automatically created for every section heading
33714 in the table of contents.
33715 If a section heading contains formulas, they are incorrectly displayed
33716 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33725 \begin_layout Standard
33726 Both problems can be solved by inserting at the end of the section heading
33727 a short title with the menu
33729 Insert\SpecialChar \menuseparator
33731 \begin_inset Space ~
33737 Short titles are used as alternative for multiline section headings to
33738 keep the table of contents clearly arranged.
33739 Only the short title appears in the table of contents and therefore also
33740 in the PDF-bookmark.
33743 \begin_layout Standard
33744 When formulas should be used in the table of contents but
33748 is used, one can use the following command in TeX-mode:
33751 \begin_layout Standard
33756 texorpdfstring{part}{alternative}
33760 \begin_layout Plain Layout
33771 \begin_layout Standard
33772 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33773 This can be characters, formulas, footnotes, but also cross-references.
33774 The alternative is used instead of the part for the bookmark.
33777 \begin_layout Standard
33778 Here are two example headings:
33779 \begin_inset VSpace -3mm
33786 \begin_layout Plain Layout
33798 \begin_layout Subsubsection
33799 Heading without formula in table of contents
33800 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33804 \begin_inset OptArg
33807 \begin_layout Plain Layout
33808 Heading without formula in table of contents
33816 \begin_layout Subsubsection
33817 Heading with formula in table of contents
33821 \begin_layout Plain Layout
33831 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33838 \begin_layout Plain Layout
33848 \begin_layout Standard
33852 \begin_layout Plain Layout
33861 In the first heading a short title was used, in the second one
33870 \begin_layout Standard
33871 To get the same formatting as for the other headings, the complete heading
33874 boldmath environment
33880 \begin_layout Plain Layout
33882 \begin_inset CommandInset ref
33884 reference "sub:Bold-Formulas"
33896 \begin_layout Subsection
33897 Formulas in multi-column Text
33901 \begin_layout Plain Layout
33902 Formula ! in multi-column text
33910 \begin_layout Standard
33911 Formulas in multi-column text are often too wide to fit into a column and
33912 thus need to be set over the whole page width.
33913 This is done by using the LaTeX-package
33921 \begin_layout Plain Layout
33926 is part of every LaTeX standard installation.
33935 \begin_layout Plain Layout
33936 Packages ! multicol
33941 , that is loaded with the LaTeX-preamble line
33944 \begin_layout Standard
33949 usepackage{multicol}
33952 \begin_layout Standard
33953 \begin_inset Note Greyedout
33956 \begin_layout Plain Layout
33957 Note herby that the setting
33960 \begin_inset Space ~
33967 Document\SpecialChar \menuseparator
33973 \begin_inset Space ~
33993 \begin_layout Standard
33994 Before the multi-column text the command
33997 \begin_layout Standard
34002 begin{multicols}{column number}
34005 \begin_layout Standard
34006 is written in TeX-mode.
34007 The column number is a number in the range of 2
34008 \begin_inset Space \thinspace{}
34012 \begin_inset Space \thinspace{}
34016 Before the formula the multi-column text is ended by inserting the command
34019 \begin_layout Standard
34027 \begin_layout Standard
34031 \begin_layout Standard
34032 Due to the command some space is automatically added before the formula.
34034 \begin_inset Space \thinspace{}
34037 mm vertical space is inserted before the formula.
34038 When the formula style
34044 \begin_layout Plain Layout
34046 \begin_inset CommandInset ref
34048 reference "sec:Formula-Styles"
34060 \begin_inset Space \thinspace{}
34063 mm space is inserted instead.
34066 \begin_layout Standard
34067 As example a multi-column text with a displayed formula:
34070 \begin_layout Standard
34074 \begin_layout Plain Layout
34078 begin{multicols}{2}
34083 Das Spektrum wird fouriertransformiert.
34084 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
34085 , Lösungsmittel) zu trennen.
34086 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
34087 nun das Aussehen des Ausgangssignals.
34088 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
34089 über alle Phasen integrieren muss.
34091 \begin_inset Formula $S$
34094 unser normiertes Ausgangssignal and
34095 \begin_inset Formula $P$
34098 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
34102 \begin_layout Plain Layout
34112 \begin_inset VSpace -6mm
34116 \begin_inset Formula \begin{equation}
34117 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
34125 \begin_layout Plain Layout
34129 begin{multicols}{2}
34135 \begin_inset Formula $S_{0}$
34138 das Signal ohne Gradient ist and the Normierungsbedingung
34139 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
34143 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
34145 \begin_inset Formula $\nicefrac{\pi}{2}$
34149 \begin_inset Space \thinspace{}
34152 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
34153 das Signal zusätzlich abschwächt.
34154 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
34156 \begin_inset Formula $T_{2}$
34162 \begin_layout Standard
34166 \begin_layout Plain Layout
34178 \begin_layout Subsection
34179 Formulas with Description of Variables
34183 \begin_layout Plain Layout
34184 Formula ! with description of variables
34192 \begin_layout Standard
34193 To describe variables within a formula, like in formula
34194 \begin_inset CommandInset ref
34196 reference "eq:within"
34205 \begin_inset Formula $n$
34209 \begin_inset Space ~
34212 matrix is used with left aligned columns for the
34213 \begin_inset Formula $n$
34220 \begin_layout Plain Layout
34222 \begin_inset CommandInset ref
34224 reference "sec:Matrices"
34233 To set the description in a smaller size, before the matrix e.
34234 \begin_inset Space \thinspace{}
34238 \begin_inset Space ~
34251 \begin_layout Plain Layout
34253 \begin_inset CommandInset ref
34255 reference "sub:Font-Sizes"
34267 \begin_layout Standard
34268 When the formula style
34274 \begin_layout Plain Layout
34276 \begin_inset CommandInset ref
34278 reference "sec:Formula-Styles"
34299 \begin_layout Plain Layout
34306 only works in formulas with the style
34311 \begin_inset CommandInset ref
34313 reference "sub:Variable-Space"
34322 is inserted before and after the matrix to have the same separation of
34323 the matrix from the equation and the side margin.
34326 \begin_layout Standard
34327 When the formula style
34331 is used, the method described in
34332 \begin_inset CommandInset ref
34334 reference "sub:Flalign-Environment"
34338 is used to indent formulas.
34340 \begin_inset CommandInset ref
34342 reference "eq:within"
34346 consists of five columns whereas in the first two columns contain the equation,
34347 the third the matrix, and the last one an empty TeX-brace.
34348 \begin_inset Formula \begin{flalign}
34349 \hspace {30pt}F_{A} & =\rho·V·g & \footnotesize \begin{array}{ll}
34350 \rho & \textrm{density}\\
34351 V & \textrm{volume}\\
34352 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34359 \begin_layout Subsection
34360 Upright small Greek Letters
34361 \begin_inset CommandInset label
34363 name "sub:Upright-small-Greek"
34371 \begin_layout Plain Layout
34372 Greek letters ! upright
34380 \begin_layout Standard
34381 Most of the math fonts only provide italic small Greek letters.
34382 But for symbols of elementary particles like pions and neutrinos, upright
34383 Greek letters are needed.
34392 \begin_layout Plain Layout
34397 is part of the LaTeX-package
34405 \begin_layout Plain Layout
34407 \begin_inset VSpace 4mm
34424 \begin_layout Plain Layout
34430 that is loaded with the LaTeX-preamble line
34433 \begin_layout Standard
34438 usepackage{upgreek}
34441 \begin_layout Standard
34447 \begin_layout Plain Layout
34457 \begin_inset Note Note
34460 \begin_layout Plain Layout
34461 The following table will only be displayed when the LaTeX-package
34470 They are created when the command for a small Greek letters is started
34476 For example the command
34483 \begin_inset Formula $\uptau $
34489 \begin_layout Standard
34490 With these commands reactions of elementary particles can be typeset:
34491 \begin_inset Formula \[
34492 \uppi ^{+}\to\upmu ^{+}+\upnu _{\upmu }\]
34499 \begin_layout Standard
34500 The upright letters are more bold and wider than the italic ones.
34501 They should therefore not be used for units like
34502 \begin_inset Quotes eld
34506 \begin_inset Quotes erd
34512 \begin_layout Standard
34516 \begin_layout Plain Layout
34526 \begin_inset Note Note
34529 \begin_layout Plain Layout
34530 The following will be displayed when the LaTeX-package
34542 \begin_layout Standard
34543 You need to install the LaTeX-package
34547 to see the rest of this subsection in the output.
34550 \begin_layout Standard
34554 \begin_layout Plain Layout
34566 \begin_layout Subsection
34567 Text Characters in Formulas
34568 \begin_inset CommandInset label
34570 name "sub:Text-Characters-in"
34578 \begin_layout Plain Layout
34587 \begin_layout Standard
34588 In some cases you might want to insert text characters directly into formulas.
34589 When for example the centered dot · is often used in formulas like
34590 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34593 , one would have to insert the command
34603 \begin_layout Plain Layout
34605 \begin_inset CommandInset ref
34607 reference "sub:Binary-Operators"
34616 all the time, because this character is defined in all encodings as text
34618 But the encoding can be changed by this LaTeX-preamble line:
34621 \begin_layout Standard
34626 Declare Inputtext{183}{
34636 f\SpecialChar \textcompwordmark{}
34640 \begin_layout Standard
34641 The character encoding (menu
34643 Document\SpecialChar \menuseparator
34644 Settings\SpecialChar \menuseparator
34647 ) specifies what character appears when a keyboard key is pressed.
34648 When the key for the character '·' is pressed, internally the command
34655 But this command is not available in a formula so that you would get LaTeX-erro
34657 With the changed encoding the right command is chosen automatically, depending
34658 on if the character was inserted into a formula or not.
34661 \begin_layout Standard
34662 The encoding of several characters is saved in definition files.
34663 Fore example the encoding
34667 is defined in the file
34671 that is in the installation folder of LaTeX.
34672 Encodings should only be changed via the LaTeX-preamble and not in the
34674 Otherwise own documents could not be edited by other LyX users working
34675 on other computers.
34678 \begin_layout Standard
34679 \begin_inset VSpace medskip
34682 Besides the centered dot, in this document the degree sign ° is defined
34683 with the following LaTeX-preamble line so that it can directly be inserted
34687 \begin_layout Standard
34692 DeclareInputtext{176}{
34702 f\SpecialChar \textcompwordmark{}
34706 \begin_layout Standard
34707 \begin_inset Newpage newpage
34713 \begin_layout Section
34715 Typographic Advises
34719 \begin_layout Plain Layout
34720 Typographic Advises
34728 \begin_layout Standard
34729 This section is a summary of the most important typographic rules, listed
34734 \begin_layout Plain Layout
34735 This collection was partly taken from the German semi-official dictionary
34737 \begin_inset Quotes eld
34741 \begin_inset Quotes erd
34745 \begin_inset CommandInset citation
34751 that lists some of the ISO rules.
34759 \begin_layout Itemize
34768 \begin_layout Plain Layout
34769 done with font styles, see
34770 \begin_inset CommandInset ref
34772 reference "sub:Font-Styles"
34782 \begin_inset Space \thinspace{}
34786 \begin_inset Newline newline
34789 Between the value and the unit is the smallest space, see
34790 \begin_inset CommandInset ref
34792 reference "sub:Predefined-Space"
34799 \begin_layout Itemize
34800 Percent and perthousand signs are set like physical units:
34801 \begin_inset Newline newline
34805 \begin_inset Space \thinspace{}
34812 \begin_layout Plain Layout
34822 \begin_inset Space ~
34828 \begin_layout Itemize
34829 The degree sign follows directly on the value: 15°, but not when it is used
34831 \begin_inset Space \thinspace{}
34837 \begin_layout Itemize
34838 In numbers with more than four digits the smallest space is inserted before
34839 every third digit to group them:
34849 \begin_inset Space \thinspace{}
34853 \begin_inset Space \thinspace{}
34859 \begin_layout Itemize
34860 For dimensionings like 120×90×40
34861 \begin_inset Space \thinspace{}
34864 cm the multiplication sign
34865 \begin_inset Quotes eld
34869 \begin_inset Quotes erd
34873 It is available with the LaTeX-command
34879 , but can also directly be inserted with some keyboard definitions.
34882 \begin_layout Itemize
34883 Functions with names consisting of several letters are set upright to avoid
34885 \begin_inset CommandInset ref
34887 reference "sub:Predefined-Functions"
34894 \begin_layout Itemize
34895 Indices consisting of several letters, are set upright:
34896 \begin_inset Formula $E_{\mathrm{kin}}$
34900 \begin_inset Newline newline
34903 Components of matrices are set italic:
34904 \begin_inset Formula $\hat{H}_{kl}$
34910 \begin_layout Itemize
34911 The differentiation/integration operator 'd', the Euler's number 'e', and
34912 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34916 \begin_layout Standard
34917 \begin_inset Newpage newpage
34923 \begin_layout Section
34928 \begin_layout Plain Layout
34937 \begin_layout Standard
34938 Some characters and symbols can be created with several commands.
34939 Here is a list of the synonym commands:
34942 \begin_layout Standard
34943 \begin_inset VSpace bigskip
34947 \begin_inset Space \hfill{}
34951 \begin_inset Tabular
34952 <lyxtabular version="3" rows="12" columns="2">
34954 <column alignment="center" valignment="top" width="0pt">
34955 <column alignment="center" valignment="top" width="0pt">
34957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34960 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34969 \begin_layout Plain Layout
34971 \begin_inset Note Note
34974 \begin_layout Plain Layout
34981 is only used as spacer.
34993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34996 \begin_layout Plain Layout
35004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35007 \begin_layout Plain Layout
35011 \begin_layout Plain Layout
35024 \begin_layout Plain Layout
35038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35041 \begin_layout Plain Layout
35049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35052 \begin_layout Plain Layout
35062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35065 \begin_layout Plain Layout
35073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35076 \begin_layout Plain Layout
35086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35089 \begin_layout Plain Layout
35097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35100 \begin_layout Plain Layout
35108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35111 \begin_layout Plain Layout
35119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35122 \begin_layout Plain Layout
35130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35133 \begin_layout Plain Layout
35141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35144 \begin_layout Plain Layout
35154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35157 \begin_layout Plain Layout
35165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35168 \begin_layout Plain Layout
35178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35181 \begin_layout Plain Layout
35189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35192 \begin_layout Plain Layout
35202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35205 \begin_layout Plain Layout
35213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35216 \begin_layout Plain Layout
35226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35229 \begin_layout Plain Layout
35237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35240 \begin_layout Plain Layout
35248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35251 \begin_layout Plain Layout
35259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35262 \begin_layout Plain Layout
35274 \begin_inset Space \hfill{}
35278 \begin_inset Tabular
35279 <lyxtabular version="3" rows="12" columns="2">
35281 <column alignment="center" valignment="top" width="0pt">
35282 <column alignment="center" valignment="top" width="0pt">
35284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35287 \begin_layout Plain Layout
35293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35296 \begin_layout Plain Layout
35304 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35307 \begin_layout Plain Layout
35315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35318 \begin_layout Plain Layout
35330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35333 \begin_layout Plain Layout
35341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35344 \begin_layout Plain Layout
35354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35357 \begin_layout Plain Layout
35365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35368 \begin_layout Plain Layout
35378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35381 \begin_layout Plain Layout
35389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35392 \begin_layout Plain Layout
35400 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35403 \begin_layout Plain Layout
35411 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35414 \begin_layout Plain Layout
35422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35425 \begin_layout Plain Layout
35433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35436 \begin_layout Plain Layout
35446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35449 \begin_layout Plain Layout
35457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35460 \begin_layout Plain Layout
35470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35473 \begin_layout Plain Layout
35481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35484 \begin_layout Plain Layout
35494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35497 \begin_layout Plain Layout
35505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35508 \begin_layout Plain Layout
35518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35521 \begin_layout Plain Layout
35529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35532 \begin_layout Plain Layout
35542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35545 \begin_layout Plain Layout
35553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35556 \begin_layout Plain Layout
35570 \begin_inset Space \hfill{}
35576 \begin_layout Standard
35577 \begin_inset Newpage newpage
35583 \begin_layout Bibliography
35584 \begin_inset CommandInset bibitem
35585 LatexCommand bibitem
35597 The LaTeX Companion
35600 Addison Wesley, 2004
35603 \begin_layout Bibliography
35604 \begin_inset CommandInset bibitem
35605 LatexCommand bibitem
35614 \begin_layout Plain Layout
35618 href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
35627 \begin_layout Plain Layout
35634 of LaTeX's math abilities
35637 \begin_layout Bibliography
35638 \begin_inset CommandInset bibitem
35639 LatexCommand bibitem
35644 LaTeX tips and tricks-
35648 \begin_layout Plain Layout
35652 href{http://tug.org/TeXnik/}{
35661 \begin_layout Plain Layout
35671 \begin_layout Bibliography
35672 \begin_inset CommandInset bibitem
35673 LatexCommand bibitem
35682 \begin_layout Plain Layout
35686 href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
35695 \begin_layout Plain Layout
35706 \begin_layout Plain Layout
35718 \begin_layout Bibliography
35719 \begin_inset CommandInset bibitem
35720 LatexCommand bibitem
35729 \begin_layout Plain Layout
35733 href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
35742 \begin_layout Plain Layout
35749 of all symbols available with LaTeX-packages
35752 \begin_layout Bibliography
35753 \begin_inset CommandInset bibitem
35754 LatexCommand bibitem
35763 \begin_layout Plain Layout
35767 href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
35776 \begin_layout Plain Layout
35783 of the LaTeX-package
35791 \begin_layout Plain Layout
35792 Packages ! hyperref
35800 \begin_layout Bibliography
35801 \begin_inset CommandInset bibitem
35802 LatexCommand bibitem
35811 \begin_layout Plain Layout
35815 href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
35824 \begin_layout Plain Layout
35838 \begin_inset CommandInset ref
35840 reference "sub:Operator-Limits"
35848 \begin_layout Plain Layout
35859 \begin_layout Bibliography
35860 \begin_inset CommandInset bibitem
35861 LatexCommand bibitem
35872 Auflage, Duden 2001
35875 \begin_layout Subsubsection*
35876 \begin_inset CommandInset index_print
35877 LatexCommand printindex