1 #LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
74 \usepackage[samesize]{cancel}
76 % enables calculation of values,
79 % for multiple table row and column cells
86 % center multirows (e.g. in sec. 13.3)
87 \renewcommand{\multirowsetup}{\centering}
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
113 % redefine the greyed out note
114 \renewenvironment{lyxgreyedout}
115 {\textcolor{blue}\bgroup}{\egroup}
117 % ------------------------------------
118 % used to check for needed LaTeX packages
121 % check for package eurosym
122 % used for the Euro symbol
124 \IfFileExists{eurosym.sty}
125 {\usepackage[gennarrow]{eurosym}
126 \setboolean{eurosym}{true}}
127 {\setboolean{eurosym}{false}}
129 % needed in sec. 22.4
130 % check for package braket
132 \IfFileExists{braket.sty}
134 \setboolean{braket}{true}}
135 {\setboolean{braket}{false}}
137 % needed in sec. 22.10
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
146 \use_default_options false
151 \font_typewriter default
152 \font_default_family default
162 \pdf_title "LyX's Math Manual"
163 \pdf_author "LyX Team, Uwe Stöhr"
164 \pdf_subject "LyX-documentation about math"
165 \pdf_keywords "LyX, Mathed"
167 \pdf_bookmarksnumbered true
168 \pdf_bookmarksopen true
169 \pdf_bookmarksopenlevel 1
170 \pdf_breaklinks false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
182 \paperorientation portrait
185 \paragraph_separation skip
187 \quotes_language english
190 \paperpagestyle plain
194 \tracking_changes false
195 \output_changes false
203 LyX's detailed Math manual
211 \begin_layout Plain Layout
213 If you have comments or error corrections, please send them to the LyX Documenta
217 \begin_inset CommandInset href
219 name "lyx-docs@lists.lyx.org"
220 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
231 \begin_inset Note Note
234 \begin_layout Plain Layout
241 \begin_inset Newline newline
245 \begin_inset Newline newline
253 \begin_layout Standard
254 \begin_inset CommandInset toc
255 LatexCommand tableofcontents
262 \begin_layout Standard
263 \begin_inset Note Note
266 \begin_layout Plain Layout
267 To export this document to PDF, PS, or DVI the LaTeX-packages
280 If they are not installed you can export the document anyway but the sections
281 where the packages are required won't appear in the output.
284 \begin_layout Plain Layout
285 The latest PDF-version of this document can be found here:
286 \begin_inset Newline newline
291 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
299 \begin_layout Standard
300 \begin_inset Newpage newpage
306 \begin_layout Section
310 \begin_layout Standard
311 This document explains LyX's math features and is furthermore a collection
312 of LaTeX-commands used for mathematical characters and constructs.
313 The explanations are designed for the usage of commands.
314 It is therefore required that you have read the section
325 \begin_layout Standard
326 Most of the characters and many constructs explained in this manual are
327 also accessible via the menu
331 \SpecialChar \menuseparator
347 But everybody who has to write lots of formulas will notice that it is
348 much faster to use commands instead of the math toolbar.
349 Therefore this manual is focused on commands but also mentions the correspondin
350 g toolbar buttons when available.
353 \begin_layout Standard
354 If not specially mentioned the commands are only available within formulas.
355 To be able to use all commands explained in this document, the option
359 must be used in the document settings (menu
361 Document\SpecialChar \menuseparator
362 Settings\SpecialChar \menuseparator
373 \begin_layout Plain Layout
376 Use AMS math package automatically
382 \begin_layout Plain Layout
391 -math when math constructs are found that are supported by LyX.
399 \begin_layout Standard
400 This document doesn't list all
404 \begin_layout Plain Layout
417 \begin_layout Plain Layout
422 \begin_layout Plain Layout
431 -math commands is in the file
434 \begin_inset CommandInset href
437 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
443 , which is part of every LaTeX standard installation.
448 for lucidity reasons.
451 \begin_layout Section
455 \begin_layout Standard
456 To create an inline formula
460 \begin_layout Plain Layout
466 that is embedded into a text line, use one of the shortcuts
472 or the toolbar button
473 \begin_inset Graphics
474 filename ../images/math-mode.png
480 \begin_inset Newline newline
483 To create a display style formula
487 \begin_layout Plain Layout
488 Formula ! display style
493 that will appear bigger and in an own paragraph, use one of these shortcuts:
503 \begin_layout Standard
504 To change a display style formula to an inline formula, set the cursor into
505 the formula and use one of the shortcuts
513 Edit\SpecialChar \menuseparator
514 Math\SpecialChar \menuseparator
518 The same way is used to change an inline formula to a display style formula.
521 \begin_layout Standard
522 To display parts of an inline formula in the size of a display style formula,
531 \begin_layout Plain Layout
542 Then a new blue box appears in which the desired formula part is inserted.
545 \begin_layout Standard
546 Only inline formulas are allowed inside tables.
549 \begin_layout Standard
554 can be turned on in the menu
556 View\SpecialChar \menuseparator
560 When you click there on
561 \begin_inset Quotes eld
565 \begin_inset Quotes erd
568 the toolbar will be shown permanently at the bottom; this state is visualized
573 menu with a checkmark.
574 When you click in this state again on
575 \begin_inset Quotes eld
579 \begin_inset Quotes erd
590 is only shown when the cursor is within a formula; this state is visualized
591 by the renaming of the menu entry from
592 \begin_inset Quotes eld
596 \begin_inset Quotes erd
600 \begin_inset Quotes eld
608 \begin_inset Quotes erd
614 \begin_layout Standard
619 \begin_layout Plain Layout
625 is invoked by pressing the toolbar button
626 \begin_inset Graphics
627 filename ../images/ert-insert.png
634 Insert\SpecialChar \menuseparator
639 \begin_layout Plain Layout
655 \begin_inset Note Note
658 \begin_layout Plain Layout
659 In LyX there are three
660 \begin_inset Quotes eld
664 \begin_inset Quotes erd
667 that appear in the output with sub- and superscript letters: TeX, LaTeX,
671 \begin_layout Plain Layout
672 To avoid that these names are recognized as proper names, a TeX-brace pair
681 \begin_layout Standard
682 To change the LaTeX-preamble
686 \begin_layout Plain Layout
694 Document\SpecialChar \menuseparator
695 Settings\SpecialChar \menuseparator
700 \begin_layout Plain Layout
716 \begin_layout Standard
717 To edit matrices, case differentiations, and multiline formulas subsequently,
720 Edit\SpecialChar \menuseparator
725 Edit\SpecialChar \menuseparator
727 \begin_inset space \thinspace{}
731 \begin_inset space \thinspace{}
741 When lines and columns are swapped via the menu, the column or line where
742 the cursor is in is exchanged with the column to the right or the line
744 Is the cursor in the last column or row, the exchange is done with the
745 column to the left or the line above.
748 \begin_layout Standard
749 To write text in formulas
753 \begin_layout Plain Layout
754 For multiline formulas the command
761 \begin_inset CommandInset ref
763 reference "sub:Text-in-multiline"
780 \begin_layout Plain Layout
790 \begin_layout Plain Layout
797 This mode is invoked with the the shortcut
803 or by the insertion of the command
811 \begin_layout Plain Layout
822 The text appears black in LyX and can therefore be distinguished from the
823 other formula parts that appear blue.
824 In the output mathematical text is set upright, in contrary to other formula
828 \begin_layout Subsection*
832 \begin_layout Standard
833 Most of the LaTeX-commands for math constructs have the following scheme:
836 \begin_layout Standard
852 \begin_layout Standard
853 A command starts always with a backslash
854 \begin_inset Quotes gld
864 \begin_inset Quotes grd
868 To omit optional arguments, also omit the associated brackets.
869 The braces around the required arguments are named in this document as
874 \begin_layout Plain Layout
881 If you add in a formula a left brace to a command name, LyX creates automatical
883 In all other cases TeX-braces are created in formulas with the command
891 TeX-braces appear red in LyX, in contrary to normal braces that appear
893 In TeX-mode no command is needed to get TeX-braces.
894 TeX-braces don't appear in the output.
897 \begin_layout Standard
898 When commands without arguments, like commands for symbols are entered in
899 TeX-mode, a space character must
903 be behind the command to end it.
904 This space doesn't appear in the output.
905 When the space should appear in the output, the space must be followed
906 by a protected space in normal text.
909 \begin_layout Standard
910 A protected space is inserted with
917 \begin_layout Subsection*
918 \begin_inset Newpage newpage
924 \begin_layout Itemize
929 \begin_layout Plain Layout
930 This visible space character can be created with the command
940 \begin_layout Plain Layout
948 , inserted in TeX-mode.
957 \begin_layout Plain Layout
970 denotes a space character to be input.
973 \begin_layout Itemize
975 \begin_inset Formula $\to$
978 denotes the usage of the corresponding arrow key on the keyboard.
981 \begin_layout Subsection*
985 \begin_layout Standard
987 \begin_inset Float table
993 \begin_layout Plain Layout
997 \begin_layout Plain Layout
998 \begin_inset CommandInset label
1000 name "tab:Available-units"
1012 \begin_layout Plain Layout
1014 \begin_inset Tabular
1015 <lyxtabular version="3" rows="13" columns="2">
1017 <column alignment="center" valignment="top" width="0">
1018 <column alignment="center" valignment="top" width="0">
1020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1023 \begin_layout Plain Layout
1029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1032 \begin_layout Plain Layout
1040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1043 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1052 \begin_layout Plain Layout
1060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1063 \begin_layout Plain Layout
1069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1072 \begin_layout Plain Layout
1080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1083 \begin_layout Plain Layout
1089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1092 \begin_layout Plain Layout
1094 \begin_inset space \thinspace{}
1098 \begin_inset space \thinspace{}
1108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1111 \begin_layout Plain Layout
1117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1120 \begin_layout Plain Layout
1122 \begin_inset space \thinspace{}
1126 \begin_inset space \thinspace{}
1136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1139 \begin_layout Plain Layout
1145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1148 \begin_layout Plain Layout
1150 \begin_inset space \thinspace{}
1154 \begin_inset space \thinspace{}
1164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1167 \begin_layout Plain Layout
1173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1176 \begin_layout Plain Layout
1178 \begin_inset space \thinspace{}
1182 \begin_inset space \thinspace{}
1192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1195 \begin_layout Plain Layout
1201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1204 \begin_layout Plain Layout
1206 \begin_inset space \thinspace{}
1210 \begin_inset space \thinspace{}
1220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1223 \begin_layout Plain Layout
1229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1232 \begin_layout Plain Layout
1234 \begin_inset space \thinspace{}
1238 \begin_inset Formula $\approx$
1242 \begin_inset space \thinspace{}
1252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1255 \begin_layout Plain Layout
1261 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1264 \begin_layout Plain Layout
1266 \begin_inset space \thinspace{}
1270 \begin_inset space \thinspace{}
1280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1283 \begin_layout Plain Layout
1289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1292 \begin_layout Plain Layout
1296 \begin_inset Quotes eld
1302 \begin_inset Quotes erd
1312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1315 \begin_layout Plain Layout
1321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1324 \begin_layout Plain Layout
1326 \begin_inset Quotes eld
1334 \begin_inset Quotes erd
1344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1347 \begin_layout Plain Layout
1353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1356 \begin_layout Plain Layout
1358 \begin_inset space \thinspace{}
1362 \begin_inset Formula $\nicefrac{1}{18}$
1366 \begin_inset space \thinspace{}
1387 \begin_layout Standard
1388 \begin_inset Newpage newpage
1394 \begin_layout Section
1398 \begin_layout Subsection
1403 \begin_layout Plain Layout
1413 \begin_layout Plain Layout
1423 \begin_layout Plain Layout
1428 \begin_layout Plain Layout
1439 \begin_layout Plain Layout
1455 \begin_layout Plain Layout
1460 \begin_layout Plain Layout
1471 \begin_layout Plain Layout
1486 \begin_layout Standard
1487 Indices are created with an underscore
1488 \begin_inset Quotes eld
1492 \begin_inset Quotes erd
1495 or via the math toolbar button
1496 \begin_inset Graphics
1497 filename ../images/math-subscript.png
1502 , exponents with a caret
1503 \begin_inset Quotes eld
1507 \begin_inset Quotes erd
1510 or via the math toolbar button
1511 \begin_inset Graphics
1512 filename ../images/math-superscript.png
1520 \begin_layout Standard
1522 \begin_inset Tabular
1523 <lyxtabular version="3" rows="4" columns="2">
1525 <column alignment="center" valignment="top" width="0pt">
1526 <column alignment="center" valignment="top" width="0pt">
1528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1531 \begin_layout Plain Layout
1537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1540 \begin_layout Plain Layout
1542 \begin_inset Note Note
1545 \begin_layout Plain Layout
1552 is only used as spacer.
1564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1567 \begin_layout Plain Layout
1573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1576 \begin_layout Plain Layout
1577 \begin_inset Formula $B_{V}$
1587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1590 \begin_layout Plain Layout
1596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1599 \begin_layout Plain Layout
1600 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1613 \begin_layout Plain Layout
1618 \begin_layout Plain Layout
1632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1635 \begin_layout Plain Layout
1636 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1652 \begin_layout Standard
1653 As the caret is in some languages an accent, vowels will be accentuated
1654 in this case and not set as exponents
1658 \begin_layout Plain Layout
1659 Depending on the used keyboard settings this can also happen for other character
1666 To get in this case exponents, press
1670 after the caret as in the last example.
1673 \begin_layout Subsection
1675 \begin_inset CommandInset label
1677 name "sub:Fractions"
1685 \begin_layout Plain Layout
1694 \begin_layout Standard
1695 Fractions are generated with the command
1705 \begin_layout Plain Layout
1713 or via the math toolbar button
1714 \begin_inset Graphics
1715 filename ../images/math/frac.png
1721 The font size is adjusted automatically, depending on whether the fraction
1722 is in an inline or display style formula.
1723 With the math toolbar button
1724 \begin_inset Graphics
1725 filename ../images/math/frac-square.png
1730 you can select different fraction types.
1733 \begin_layout Standard
1742 \begin_layout Plain Layout
1752 a fraction can be created that has in any case the size of a display style
1762 \begin_layout Plain Layout
1772 the fraction appears always with the size of an inline formula.
1776 \begin_layout Standard
1777 A line with the fraction
1778 \begin_inset Formula $\frac{1}{2}$
1781 that was created with the command
1790 \begin_layout Standard
1791 A line with the fraction
1792 \begin_inset Formula $\dfrac{1}{2}$
1795 that was created with the command
1804 \begin_layout Standard
1806 \begin_inset Tabular
1807 <lyxtabular version="3" rows="4" columns="2">
1809 <column alignment="center" valignment="top" width="0pt">
1810 <column alignment="center" valignment="top" width="0pt">
1812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1815 \begin_layout Plain Layout
1821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1824 \begin_layout Plain Layout
1826 \begin_inset Note Note
1829 \begin_layout Plain Layout
1836 is only used as spacer.
1848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1851 \begin_layout Plain Layout
1858 \begin_layout Plain Layout
1868 \begin_inset Formula $\downarrow$
1876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1879 \begin_layout Plain Layout
1880 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1893 \begin_layout Plain Layout
1900 \begin_layout Plain Layout
1910 \begin_inset Formula $\downarrow$
1918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1921 \begin_layout Plain Layout
1922 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1935 \begin_layout Plain Layout
1942 \begin_layout Plain Layout
1955 \begin_layout Plain Layout
1970 \begin_layout Plain Layout
1980 \begin_inset Formula $\downarrow$
1984 \begin_inset Formula $\downarrow\downarrow$
1992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1995 \begin_layout Plain Layout
1996 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2012 \begin_layout Standard
2013 \begin_inset VSpace bigskip
2017 \begin_inset Newpage newpage
2020 For nested fractions the command
2030 \begin_layout Plain Layout
2040 \begin_inset VSpace -3mm
2046 \begin_layout Standard
2047 \begin_inset Formula \begin{align*}
2048 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2049 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2056 \begin_layout Standard
2057 The command for the example above is:
2060 \begin_layout Standard
2066 \begin_inset Formula $\to$
2076 \begin_inset Formula $\to$
2082 \begin_inset Formula $\to\to$
2090 \begin_layout Standard
2091 \begin_inset VSpace medskip
2097 \begin_layout Standard
2104 sets the fraction always in the size of a displayed formula, also when
2105 it is part of another fraction.
2112 has the following command scheme:
2115 \begin_layout Standard
2120 cfrac[numerator position]{numerator}{denominator}
2123 \begin_layout Standard
2124 The numerator position can be
2137 l or r aligns the numerator to the left or right, resp.
2138 \begin_inset space ~
2141 with the fraction stroke.
2146 or no position is given, the numerator appears centered.
2147 These fractions demonstrate the different alignments:
2148 \begin_inset Newline newline
2154 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2158 \begin_inset Formula $\cfrac{A}{B+C}$
2162 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2168 \begin_layout Standard
2169 \begin_inset VSpace medskip
2172 It is often advantageous to combine
2185 \begin_inset Formula \[
2186 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2193 \begin_layout Standard
2194 For inline fractions with a sloped fraction stroke you can use the command
2205 \begin_layout Plain Layout
2214 \begin_inset Formula $\nicefrac{5}{31}$
2227 \begin_layout Plain Layout
2236 \begin_inset Formula $\unitfrac{5}{31}$
2239 There is furthermore the command
2245 that offers to write a fraction in combination with a number:
2246 \begin_inset Formula $\unitfrac[2]{1}{3}$
2250 \begin_inset Newline newline
2259 is not a real LaTeX command but the command
2260 \begin_inset Newline newline
2267 unitfrac[number]{numerator}{denominator}
2269 , therefore you cannot use it in TeX code.
2272 \begin_layout Standard
2273 How to define own fractions where the fraction stroke can be changed, is
2275 \begin_inset CommandInset ref
2277 reference "sub:Self-defined-Fractions"
2284 \begin_layout Subsection
2289 \begin_layout Plain Layout
2298 \begin_layout Standard
2299 Square roots are created with
2309 \begin_layout Plain Layout
2317 or the math toolbar button
2318 \begin_inset Graphics
2319 filename ../images/math/sqrt.png
2324 , all other roots with the command
2334 \begin_layout Plain Layout
2342 or with the math toolbar button
2343 \begin_inset Graphics
2344 filename ../images/math/root.png
2352 \begin_layout Standard
2354 \begin_inset Tabular
2355 <lyxtabular version="3" rows="3" columns="2">
2357 <column alignment="center" valignment="top" width="0pt">
2358 <column alignment="center" valignment="top" width="0pt">
2360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2363 \begin_layout Plain Layout
2369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2372 \begin_layout Plain Layout
2374 \begin_inset Note Note
2377 \begin_layout Plain Layout
2384 is only used as spacer.
2396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2399 \begin_layout Plain Layout
2406 \begin_layout Plain Layout
2420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2423 \begin_layout Plain Layout
2424 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2437 \begin_layout Plain Layout
2444 \begin_layout Plain Layout
2454 \begin_inset Formula $\downarrow$
2462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2465 \begin_layout Plain Layout
2466 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2482 \begin_layout Standard
2483 A square root can also be created with
2489 when the root index field is left empty.
2492 \begin_layout Standard
2493 With certain indices the distance to the root is too small, like in this
2495 \begin_inset Formula $\sqrt[\beta]{B}$
2499 \begin_inset Newline newline
2503 \begin_inset Formula $\beta$
2507 To avoid this, the commands
2517 \begin_layout Plain Layout
2535 \begin_layout Plain Layout
2543 are used with the following scheme:
2546 \begin_layout Standard
2560 \begin_layout Standard
2561 Distance is the number of Big Points (unit bp;
2562 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2565 ), that the index should be moved to the left or top, resp..
2566 The commands are written to the index.
2567 This way the command
2568 \begin_inset Newline newline
2578 \begin_inset Formula $\to$
2584 \begin_inset Formula $\to$
2593 \begin_layout Plain Layout
2603 \begin_inset Formula $\to$
2607 \begin_inset Newline newline
2612 produces a correct typeset formula:
2613 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2619 \begin_layout Subsection
2620 Binomial Coefficients
2624 \begin_layout Plain Layout
2625 Binomial coefficients
2633 \begin_layout Standard
2634 Binomial coefficients are inserted with the command
2644 \begin_layout Plain Layout
2652 or with the submenu of the math toolbar button
2653 \begin_inset Graphics
2654 filename ../images/math/frac-square.png
2660 Analog to fractions (
2680 \begin_layout Plain Layout
2700 \begin_layout Plain Layout
2709 For other brackets around binomial coeficients there are the commands
2719 \begin_layout Plain Layout
2737 \begin_layout Plain Layout
2748 \begin_layout Standard
2750 \begin_inset Tabular
2751 <lyxtabular version="3" rows="6" columns="2">
2753 <column alignment="center" valignment="top" width="0pt">
2754 <column alignment="center" valignment="top" width="0pt">
2756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2759 \begin_layout Plain Layout
2765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2768 \begin_layout Plain Layout
2770 \begin_inset Note Note
2773 \begin_layout Plain Layout
2780 is only used as spacer.
2792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2795 \begin_layout Plain Layout
2802 \begin_layout Plain Layout
2812 \begin_inset Formula $\downarrow$
2820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2823 \begin_layout Plain Layout
2824 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2837 \begin_layout Plain Layout
2844 \begin_layout Plain Layout
2854 \begin_inset Formula $\downarrow$
2862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2865 \begin_layout Plain Layout
2866 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2879 \begin_layout Plain Layout
2886 \begin_layout Plain Layout
2896 \begin_inset Formula $\downarrow$
2904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2907 \begin_layout Plain Layout
2908 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2921 \begin_layout Plain Layout
2928 \begin_layout Plain Layout
2938 \begin_inset Formula $\downarrow$
2946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2949 \begin_layout Plain Layout
2950 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2963 \begin_layout Plain Layout
2970 \begin_layout Plain Layout
2980 \begin_inset Formula $\downarrow$
2988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2991 \begin_layout Plain Layout
2992 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3008 \begin_layout Subsection
3009 Case Differentiations
3013 \begin_layout Plain Layout
3014 Case differentiations
3022 \begin_layout Standard
3024 \begin_inset Tabular
3025 <lyxtabular version="3" rows="3" columns="2">
3027 <column alignment="center" valignment="top" width="0pt">
3028 <column alignment="center" valignment="top" width="0pt">
3030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3033 \begin_layout Plain Layout
3039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3042 \begin_layout Plain Layout
3050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3053 \begin_layout Plain Layout
3060 \begin_layout Plain Layout
3070 \begin_inset Formula $\to$
3077 \begin_layout Plain Layout
3090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3093 \begin_layout Plain Layout
3094 \begin_inset Formula $\begin{cases}
3105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3108 \begin_layout Plain Layout
3115 \begin_layout Plain Layout
3127 arg "newline-insert newline"
3135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3138 \begin_layout Plain Layout
3139 \begin_inset Formula $\begin{cases}
3140 A & \textrm{for }x>0\\
3141 B & \textrm{for }x=0\end{cases}$
3157 \begin_layout Standard
3164 or the usage of the math toolbar button
3165 \begin_inset Graphics
3166 filename ../images/math/cases.png
3171 you can create new lines with the shortcut
3174 arg "newline-insert newline"
3177 or the table toolbar button
3178 \begin_inset Graphics
3179 filename ../images/tabular-feature_append-row.png
3187 \begin_layout Standard
3194 is also available via the menu
3196 Insert\SpecialChar \menuseparator
3197 Math\SpecialChar \menuseparator
3203 \begin_layout Subsection
3208 \begin_layout Plain Layout
3217 \begin_layout Standard
3228 \begin_layout Plain Layout
3236 every character can be displayed canceled.
3237 The characters are quasi accentuated by a slash.
3240 \begin_layout Standard
3242 \begin_inset Tabular
3243 <lyxtabular version="3" rows="4" columns="2">
3245 <column alignment="center" valignment="top" width="0pt">
3246 <column alignment="center" valignment="top" width="0pt">
3248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3251 \begin_layout Plain Layout
3257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3260 \begin_layout Plain Layout
3268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3271 \begin_layout Plain Layout
3279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3282 \begin_layout Plain Layout
3283 \begin_inset Formula $\not=$
3293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3296 \begin_layout Plain Layout
3306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3309 \begin_layout Plain Layout
3310 \begin_inset Formula $\not\le$
3320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3323 \begin_layout Plain Layout
3333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3336 \begin_layout Plain Layout
3337 \begin_inset Formula $\not\parallel$
3353 \begin_layout Standard
3354 The last example shows, that not all negations look good.
3355 Therefore there are for some negations special commands (see
3356 \begin_inset CommandInset ref
3358 reference "sub:Mathematical-Symbols"
3363 \begin_inset CommandInset ref
3365 reference "sec:Relations"
3372 \begin_layout Subsection
3374 \begin_inset CommandInset label
3376 name "sub:Placeholders"
3384 \begin_layout Plain Layout
3394 \begin_layout Plain Layout
3395 Chemical characters ! Isotopes
3404 \begin_layout Plain Layout
3409 \begin_layout Plain Layout
3420 \begin_layout Plain Layout
3435 \begin_layout Standard
3436 When displaying e.g.
3437 \begin_inset space \space{}
3444 \begin_layout Plain Layout
3445 More about chemical symbols is written in
3446 \begin_inset CommandInset ref
3448 reference "sub:Chemical-Symbols-and"
3457 the following problem occurs:
3460 \begin_layout Standard
3462 \begin_inset Tabular
3463 <lyxtabular version="3" rows="2" columns="2">
3465 <column alignment="center" valignment="top" width="0pt">
3466 <column alignment="center" valignment="top" width="0pt">
3468 <cell alignment="center" valignment="top" usebox="none">
3471 \begin_layout Plain Layout
3472 Indices created with sub- and superscripts:
3477 <cell alignment="center" valignment="top" usebox="none">
3480 \begin_layout Plain Layout
3481 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3491 <cell alignment="center" valignment="top" usebox="none">
3494 \begin_layout Plain Layout
3500 <cell alignment="center" valignment="top" usebox="none">
3503 \begin_layout Plain Layout
3504 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3518 \begin_inset Note Note
3521 \begin_layout Plain Layout
3528 is only used as spacer.
3536 \begin_layout Standard
3537 The shorter index is by default placed below or above the first character
3538 of the longer index.
3539 To avoid this there is the command
3549 \begin_layout Plain Layout
3557 or the math toolbar button
3558 \begin_inset space \thinspace{}
3565 \begin_layout Plain Layout
3566 can be found in the submenu of the toolbar button
3567 \begin_inset Graphics
3568 filename ../images/math/space.png
3579 \begin_inset Graphics
3580 filename ../images/math/phantom.png
3585 that creates one or more phantom characters.
3592 a small blue box appears that is superposed with two red arrows.
3593 The arrows indicate that the complete width and height of the box content
3594 will be created as placeholder.
3595 Phantom characters are accordingly placeholders with the size of the characters.
3598 \begin_layout Standard
3600 \begin_inset Tabular
3601 <lyxtabular version="3" rows="4" columns="2">
3603 <column alignment="center" valignment="top" width="0">
3604 <column alignment="center" valignment="top" width="0">
3606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3609 \begin_layout Plain Layout
3615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3618 \begin_layout Plain Layout
3620 \begin_inset Note Note
3623 \begin_layout Plain Layout
3630 is only used as spacer.
3642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3645 \begin_layout Plain Layout
3650 \begin_layout Plain Layout
3665 \begin_layout Plain Layout
3675 \begin_inset Formula $\to$
3682 \begin_layout Plain Layout
3696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3699 \begin_layout Plain Layout
3700 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3713 \begin_layout Plain Layout
3718 \begin_layout Plain Layout
3733 \begin_layout Plain Layout
3743 \begin_inset Formula $\to$
3750 \begin_layout Plain Layout
3764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3767 \begin_layout Plain Layout
3768 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3781 \begin_layout Plain Layout
3788 \begin_layout Plain Layout
3803 \begin_layout Plain Layout
3813 \begin_inset Formula $\to$
3820 \begin_layout Plain Layout
3834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3837 \begin_layout Plain Layout
3838 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3854 \begin_layout Standard
3855 Furthermore there are the commands
3865 \begin_layout Plain Layout
3874 \begin_inset space ~
3878 \begin_inset Graphics
3879 filename ../images/math/vphantom.png
3894 \begin_layout Plain Layout
3903 \begin_inset space ~
3907 \begin_inset Graphics
3908 filename ../images/math/hphantom.png
3920 creates only space for the maximal height of the characters in the box
3921 but not for its width.
3928 creates only space for the width of the box content.
3929 Therefore the boxes of both commands have only one red arrow.
3932 \begin_layout Standard
3943 \begin_layout Plain Layout
3958 space for the height of the integral sign,
3962 \begin_layout Plain Layout
3969 creates an integral sign, see
3970 \begin_inset CommandInset ref
3972 reference "sub:Big-Operators"
3981 because this is the larger character.
3982 An example application is in
3983 \begin_inset CommandInset ref
3985 reference "sub:Multiline-Brackets"
3992 \begin_layout Subsection
3997 \begin_layout Plain Layout
4007 \begin_layout Plain Layout
4008 Formula ! underlined
4016 \begin_layout Standard
4018 \begin_inset Tabular
4019 <lyxtabular version="3" rows="4" columns="2">
4021 <column alignment="center" valignment="top" width="0pt">
4022 <column alignment="center" valignment="top" width="0pt">
4024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4027 \begin_layout Plain Layout
4033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4036 \begin_layout Plain Layout
4038 \begin_inset Note Note
4041 \begin_layout Plain Layout
4048 is only used as spacer.
4060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4063 \begin_layout Plain Layout
4070 \begin_layout Plain Layout
4083 \begin_layout Plain Layout
4096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4099 \begin_layout Plain Layout
4100 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4113 \begin_layout Plain Layout
4120 \begin_layout Plain Layout
4133 \begin_layout Plain Layout
4146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4149 \begin_layout Plain Layout
4150 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4163 \begin_layout Plain Layout
4170 \begin_layout Plain Layout
4185 \begin_layout Plain Layout
4199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4202 \begin_layout Plain Layout
4203 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4219 \begin_layout Standard
4220 In the last example it doesn't matter if first
4235 \begin_layout Standard
4236 To double underline e.g.
4237 \begin_inset space \space{}
4249 \begin_layout Standard
4250 It is possible to place up to 6 lines above or below characters.
4253 \begin_layout Standard
4254 \begin_inset VSpace bigskip
4257 Custom lines can be created using the command
4267 \begin_layout Plain Layout
4275 which has the following scheme:
4278 \begin_layout Standard
4283 rule[vertical offset]{length}{thickness}
4286 \begin_layout Standard
4287 The optional vertical offset shifts the line upwards (or downwards, when
4288 the value is negative).
4290 \begin_inset CommandInset ref
4292 reference "tab:Available-units"
4296 can be used for the values.
4297 Here are two example lines created with the commands
4298 \begin_inset Newline newline
4305 rule[-2ex]{3cm}{2pt}
4316 \begin_layout Standard
4318 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4324 \begin_layout Standard
4331 can also be used for text when it is inserted in TeX-mode.
4334 \begin_layout Subsection
4336 \begin_inset CommandInset label
4346 \begin_layout Plain Layout
4355 \begin_layout Standard
4356 There are different types of ellipses available.
4360 \begin_layout Plain Layout
4361 In the math toolbar in the submenu of the button
4362 \begin_inset Graphics
4363 filename ../images/math/ldots.png
4373 For listings dots at the baseline are used (
4383 \begin_layout Plain Layout
4391 ), while for operations dots are needed that are on the same height as the
4402 \begin_layout Plain Layout
4411 When using the command
4421 \begin_layout Plain Layout
4429 , LaTeX decides on the basis of the next character what type is used.
4432 \begin_layout Standard
4434 \begin_inset Tabular
4435 <lyxtabular version="3" rows="8" columns="2">
4437 <column alignment="center" valignment="top" width="0pt">
4438 <column alignment="center" valignment="top" width="0pt">
4440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4443 \begin_layout Plain Layout
4449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4452 \begin_layout Plain Layout
4460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4463 \begin_layout Plain Layout
4468 \begin_layout Plain Layout
4483 \begin_layout Plain Layout
4497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4500 \begin_layout Plain Layout
4501 \begin_inset Formula $A_{1},\dots,A_{n}$
4511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4514 \begin_layout Plain Layout
4519 \begin_layout Plain Layout
4534 \begin_layout Plain Layout
4548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4551 \begin_layout Plain Layout
4552 \begin_inset Formula $A_{1}+\dots+A_{n}$
4562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4565 \begin_layout Plain Layout
4570 \begin_layout Plain Layout
4585 \begin_layout Plain Layout
4599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4602 \begin_layout Plain Layout
4603 \begin_inset Formula $A_{1},\ldots,A_{n}$
4613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4616 \begin_layout Plain Layout
4621 \begin_layout Plain Layout
4636 \begin_layout Plain Layout
4650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4653 \begin_layout Plain Layout
4654 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4667 \begin_layout Plain Layout
4675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4678 \begin_layout Plain Layout
4679 \begin_inset Formula $\vdots$
4689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4692 \begin_layout Plain Layout
4700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4703 \begin_layout Plain Layout
4704 \begin_inset Formula $\ddots$
4714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4717 \begin_layout Plain Layout
4719 \begin_inset space \thinspace{}
4722 matrix with the different dots
4727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4730 \begin_layout Plain Layout
4731 \begin_inset Formula $\begin{array}{ccc}
4732 A_{11} & \cdots & A_{1m}\\
4733 \vdots & \ddots & \vdots\\
4734 A_{n1} & \cdots & A_{nm}\end{array}$
4750 \begin_layout Standard
4751 The ellipses available in menu
4753 Insert\SpecialChar \menuseparator
4755 \begin_inset space ~
4769 \begin_layout Standard
4770 \begin_inset VSpace medskip
4773 Specially for matrices there are ellipses that span over several columns.
4774 They are created with the command
4784 \begin_layout Plain Layout
4792 , that has the following scheme:
4795 \begin_layout Standard
4800 hdotsfor[distance]{number of columns}
4803 \begin_layout Standard
4804 The number of columns specifies how many columns should be spanned.
4805 Distance is a factor for the distance between the dots.
4808 \begin_layout Standard
4809 In the following matrix the command
4815 was inserted in the first box of the second line, to get an ellipsis with
4816 a dot distance twice as long as with the command
4823 \begin_inset Formula \[
4824 \left(\begin{array}{cccc}
4827 q & w & e & r\end{array}\right)\]
4831 Note that the matrix fields that should be spanned must be empty, otherwise
4832 you get LaTeX-errors.
4835 \begin_layout Standard
4836 \begin_inset VSpace bigskip
4839 Furthermore you can fill with the command
4849 \begin_layout Plain Layout
4857 the rest of a line with dots.
4858 The effect of these commands is the same like with
4865 \begin_inset CommandInset ref
4867 reference "sub:Variable-Space"
4874 \begin_layout Standard
4875 For example the command
4883 \begin_layout Plain Layout
4897 \begin_layout Standard
4898 \begin_inset Formula $A\dotfill B$
4904 \begin_layout Standard
4911 there is for a line the command
4921 \begin_layout Plain Layout
4932 \begin_layout Standard
4933 \begin_inset Formula $A\hrulefill B$
4939 \begin_layout Standard
4940 To use the commands for text, they have to be inserted in TeX-mode.
4943 \begin_layout Section
4945 \begin_inset CommandInset label
4955 \begin_layout Plain Layout
4964 \begin_layout Standard
4965 Matrices can be inserted via the math toolbar button
4966 \begin_inset Graphics
4967 filename ../images/dialog-show_mathmatrix.png
4974 Insert\SpecialChar \menuseparator
4975 Math\SpecialChar \menuseparator
4979 You will be asked for the number of matrix columns and rows, and the alignment.
4980 The vertical alignment is hereby only of importance for matrices in inline
4984 \begin_layout Standard
4985 The first matrix is top
4986 \begin_inset Formula $\begin{array}[t]{cccc}
4989 C & F & I & L\end{array}$
4993 \begin_inset Formula $\begin{array}{cccc}
4996 C & F & I & L\end{array}$
4999 , and the third bottom
5000 \begin_inset Formula $\begin{array}[b]{cccc}
5003 C & F & I & L\end{array}$
5009 \begin_layout Standard
5010 The horizontal alignment specifies how the column entries should be aligned.
5011 It is set by entering a letter for every column.
5016 denotes left aligned,
5025 To create for example a 4
5030 \begin_inset space ~
5033 matrix where the first column is left aligned, the second and third are
5034 centered, and the last one is right aligned, one enters for the horizontal
5040 Normally are in a matrix all columns centered, therefore the default is
5041 for every column is a
5048 \begin_layout Standard
5049 Horizontal alignment:
5052 \begin_layout Standard
5058 \begin_inset Formula $\begin{array}{lll}
5061 C & F & 10000\end{array}$
5069 \begin_inset Formula $\begin{array}{ccc}
5072 C & F & 10000\end{array}$
5080 \begin_inset Formula $\begin{array}{rrr}
5083 C & F & 10000\end{array}$
5089 \begin_layout Standard
5090 To add or delete rows and columns subsequently, the math toolbar buttons
5092 \begin_inset Graphics
5093 filename ../images/tabular-feature_append-row.png
5099 \begin_inset Graphics
5100 filename ../images/tabular-feature_delete-row.png
5106 \begin_inset space \thinspace{}
5111 Edit\SpecialChar \menuseparator
5115 New rows can also be created with
5118 arg "newline-insert newline"
5124 \begin_layout Standard
5125 \begin_inset VSpace bigskip
5128 Parentheses around a matrix can can either be created with the commands
5139 \begin_layout Plain Layout
5157 \begin_layout Plain Layout
5168 \begin_inset space ~
5174 \begin_inset CommandInset ref
5176 reference "sub:Automatic-Bracket-Size"
5180 , or by using the following commands:
5181 \begin_inset VSpace medskip
5187 \begin_layout Standard
5188 \begin_inset space \hfill{}
5192 \begin_inset Tabular
5193 <lyxtabular version="3" rows="4" columns="2">
5195 <column alignment="center" valignment="top" width="0">
5196 <column alignment="center" valignment="top" width="0">
5198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5201 \begin_layout Plain Layout
5207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5210 \begin_layout Plain Layout
5212 \begin_inset Note Note
5215 \begin_layout Plain Layout
5222 is only used as spacer.
5234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5237 \begin_layout Plain Layout
5244 \begin_layout Plain Layout
5258 \begin_inset space \thinspace{}
5266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5269 \begin_layout Plain Layout
5270 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5271 0 & \textrm{-}\mathrm{i}\\
5272 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5285 \begin_layout Plain Layout
5292 \begin_layout Plain Layout
5306 \begin_inset space \thinspace{}
5314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5317 \begin_layout Plain Layout
5318 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5319 0 & \textrm{-}\mathrm{i}\\
5320 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5333 \begin_layout Plain Layout
5340 \begin_layout Plain Layout
5354 \begin_inset space \thinspace{}
5362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5365 \begin_layout Plain Layout
5366 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5367 0 & \textrm{-}\mathrm{i}\\
5368 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5382 \begin_inset space \hfill{}
5386 \begin_inset Tabular
5387 <lyxtabular version="3" rows="4" columns="2">
5389 <column alignment="center" valignment="top" width="0">
5390 <column alignment="center" valignment="top" width="0">
5392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5395 \begin_layout Plain Layout
5401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5404 \begin_layout Plain Layout
5412 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5415 \begin_layout Plain Layout
5422 \begin_layout Plain Layout
5436 \begin_inset space \thinspace{}
5444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5447 \begin_layout Plain Layout
5448 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5449 0 & \textrm{-}\mathrm{i}\\
5450 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5463 \begin_layout Plain Layout
5470 \begin_layout Plain Layout
5484 \begin_inset space \thinspace{}
5492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5495 \begin_layout Plain Layout
5496 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5497 0 & \textrm{-}\mathrm{i}\\
5498 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5511 \begin_layout Plain Layout
5518 \begin_layout Plain Layout
5532 \begin_inset space \thinspace{}
5540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5543 \begin_layout Plain Layout
5544 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5545 0 & \textrm{-}\mathrm{i}\\
5546 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5560 \begin_inset space \hfill{}
5566 \begin_layout Standard
5567 \begin_inset VSpace medskip
5571 \begin_inset space \space{}
5580 is inserted, a blue box appears between two vertical lines where the matrix
5584 \begin_layout Standard
5585 \begin_inset VSpace bigskip
5588 As all multiline formulas are matrices, the length
5598 \begin_layout Plain Layout
5606 that is described in
5607 \begin_inset CommandInset ref
5609 reference "sub:Column-Separation"
5613 can also be used to change the column separation of matrices.
5616 \begin_layout Standard
5617 To change the row separation, the command
5627 \begin_layout Plain Layout
5636 It is used as follows:
5639 \begin_layout Standard
5646 arraystretch}{stretch factor}
5650 \begin_layout Plain Layout
5661 \begin_layout Standard
5668 assigns the stretch factor to the predefined command
5676 \begin_inset space \space{}
5679 the row separation, use the factor 2.
5680 This is then used for all following matrices.
5681 To go back to the original separation, assign the factor 1 to
5690 \begin_layout Standard
5691 To set matrices into a text line, the command
5701 \begin_layout Plain Layout
5710 When it is inserted a blue box with two dashed lines appears.
5711 In this box the matrix is inserted.
5714 \begin_layout Standard
5716 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5717 C & D\end{smallmatrix}\right)$
5723 \begin_layout Section
5724 Brackets and Delimiters
5728 \begin_layout Plain Layout
5738 \begin_layout Plain Layout
5747 \begin_layout Subsection
5748 Vertical Brackets and Delimiters
5752 \begin_layout Plain Layout
5761 \begin_layout Standard
5762 \begin_inset space \hfill{}
5766 \begin_inset Tabular
5767 <lyxtabular version="3" rows="9" columns="2">
5769 <column alignment="center" valignment="top" width="0pt">
5770 <column alignment="center" valignment="top" width="0pt">
5772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5775 \begin_layout Plain Layout
5781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5784 \begin_layout Plain Layout
5792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5795 \begin_layout Plain Layout
5801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5804 \begin_layout Plain Layout
5805 \begin_inset Formula $($
5815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5818 \begin_layout Plain Layout
5824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5827 \begin_layout Plain Layout
5828 \begin_inset Formula $\{$
5838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5841 \begin_layout Plain Layout
5847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5850 \begin_layout Plain Layout
5851 \begin_inset Formula $[$
5861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5864 \begin_layout Plain Layout
5872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5875 \begin_layout Plain Layout
5876 \begin_inset Formula $\langle$
5886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5889 \begin_layout Plain Layout
5897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5900 \begin_layout Plain Layout
5901 \begin_inset Formula $\lceil$
5911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5914 \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 $\lfloor$
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" bottomline="true" leftline="true" usebox="none">
5962 \begin_layout Plain Layout
5968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5971 \begin_layout Plain Layout
5972 \begin_inset Formula $|$
5986 \begin_inset space \hfill{}
5990 \begin_inset Tabular
5991 <lyxtabular version="3" rows="9" columns="2">
5993 <column alignment="center" valignment="top" width="0pt">
5994 <column alignment="center" valignment="top" width="0pt">
5996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5999 \begin_layout Plain Layout
6005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6008 \begin_layout Plain Layout
6016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6019 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6028 \begin_layout Plain Layout
6029 \begin_inset Formula $)$
6039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6042 \begin_layout Plain Layout
6048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6051 \begin_layout Plain Layout
6052 \begin_inset Formula $\}$
6062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6065 \begin_layout Plain Layout
6071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6074 \begin_layout Plain Layout
6075 \begin_inset Formula $]$
6085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6088 \begin_layout Plain Layout
6096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6099 \begin_layout Plain Layout
6100 \begin_inset Formula $\rangle$
6110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6113 \begin_layout Plain Layout
6121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6124 \begin_layout Plain Layout
6125 \begin_inset Formula $\rceil$
6135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6138 \begin_layout Plain Layout
6146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6149 \begin_layout Plain Layout
6150 \begin_inset Formula $\rfloor$
6160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6163 \begin_layout Plain Layout
6173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6176 \begin_layout Plain Layout
6177 \begin_inset Formula $\backslash$
6187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6190 \begin_layout Plain Layout
6198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6201 \begin_layout Plain Layout
6202 \begin_inset Formula $\|$
6216 \begin_inset space \hfill{}
6222 \begin_layout Standard
6225 \begin_inset Note Greyedout
6228 \begin_layout Plain Layout
6233 In TeX-mode the command
6243 \begin_layout Plain Layout
6251 must be used for the backslash, because the command
6259 produces there a line break.
6267 \begin_layout Standard
6268 For all characters listed above the size can be adjusted with the commands
6269 described in the following two subsections.
6270 When using these commands, the characters < and > can directly be used
6271 instead of the commands
6286 \begin_layout Subsubsection
6288 \begin_inset CommandInset label
6290 name "sub:Manual-Bracket-Size"
6298 \begin_layout Plain Layout
6299 Bracket size ! manual
6307 \begin_layout Standard
6308 The bracket size can be specified manually by the LaTeX-commands
6318 \begin_layout Plain Layout
6351 denotes the smallest and
6357 the largest bracket size.
6360 \begin_layout Standard
6361 These commands are used to emphasize levels of brackets:
6364 \begin_layout Standard
6366 \begin_inset Tabular
6367 <lyxtabular version="3" rows="2" columns="2">
6369 <column alignment="center" valignment="top" width="0pt">
6370 <column alignment="center" valignment="top" width="0pt">
6372 <cell alignment="center" valignment="top" usebox="none">
6375 \begin_layout Plain Layout
6376 all brackets in the same size:
6381 <cell alignment="center" valignment="top" usebox="none">
6384 \begin_layout Plain Layout
6385 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6395 <cell alignment="center" valignment="top" usebox="none">
6398 \begin_layout Plain Layout
6404 <cell alignment="center" valignment="top" usebox="none">
6407 \begin_layout Plain Layout
6408 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6422 \begin_inset Note Note
6425 \begin_layout Plain Layout
6432 is only used as spacer.
6440 \begin_layout Standard
6441 For the second formula the command
6451 \begin_layout Plain Layout
6465 \begin_layout Standard
6466 Here is an overview about all bracket sizes:
6469 \begin_layout Standard
6489 \begin_layout Plain Layout
6506 \begin_layout Plain Layout
6519 \begin_layout Plain Layout
6535 \begin_layout Standard
6537 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6543 \begin_layout Standard
6550 -commands there is the variant
6560 \begin_layout Plain Layout
6568 that adds a bit more space between the bracket and its content, and the
6585 \begin_layout Plain Layout
6595 , that don't add additional space.
6600 at the end of the command
6606 is for a left bracket; for a right bracket this will be replaced by an
6612 A left or right bracket can each be an opening or closing bracket.
6615 \begin_layout Standard
6616 In the following table is a comparison of the variants:
6619 \begin_layout Standard
6621 \begin_inset Tabular
6622 <lyxtabular version="3" rows="5" columns="2">
6624 <column alignment="center" valignment="middle" width="0">
6625 <column alignment="center" valignment="middle" width="0">
6627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6630 \begin_layout Plain Layout
6636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6639 \begin_layout Plain Layout
6641 \begin_inset Note Note
6644 \begin_layout Plain Layout
6651 is only used as spacer.
6663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6666 \begin_layout Plain Layout
6681 \begin_layout Plain Layout
6699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6702 \begin_layout Plain Layout
6703 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6716 \begin_layout Plain Layout
6731 \begin_layout Plain Layout
6749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6752 \begin_layout Plain Layout
6753 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6763 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6766 \begin_layout Plain Layout
6781 \begin_layout Plain Layout
6799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6802 \begin_layout Plain Layout
6803 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6816 \begin_layout Plain Layout
6828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6831 \begin_layout Plain Layout
6832 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6848 \begin_layout Subsubsection
6849 Automatic Bracket Size
6850 \begin_inset CommandInset label
6852 name "sub:Automatic-Bracket-Size"
6860 \begin_layout Plain Layout
6861 Bracket size ! automatic
6869 \begin_layout Standard
6870 Brackets with variable size can be inserted with the commands
6880 \begin_layout Plain Layout
6898 \begin_layout Plain Layout
6906 or via the math toolbar button
6907 \begin_inset Graphics
6908 filename ../images/dialog-show_mathdelimiter.png
6926 the wanted bracket must be inserted.
6927 The bracket size will then automatically be calculated for the output.
6930 \begin_layout Standard
6932 normal bracket: The command
6942 \begin_layout Plain Layout
6952 \begin_inset Formula $\downarrow$
6959 \begin_layout Plain Layout
6971 \begin_inset Formula \[
6979 \begin_layout Standard
6981 multiline bracket: The command
6993 \begin_layout Plain Layout
7003 \begin_inset Formula $\downarrow$
7010 \begin_layout Plain Layout
7024 \begin_inset Formula \[
7025 \ln\left(\frac{A}{C}\right)\]
7032 \begin_layout Standard
7048 \begin_inset space ~
7054 This has the advantage that you can see in LyX immediately the real bracket
7055 size and that the matching right bracket will be created too.
7056 \begin_inset Newline newline
7059 The command for the last example would then be:
7073 \begin_layout Plain Layout
7083 \begin_inset Formula $\downarrow$
7089 \begin_layout Standard
7090 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7091 For example the command
7101 \begin_layout Plain Layout
7111 \begin_inset Formula $\downarrow$
7118 \begin_layout Plain Layout
7134 \begin_inset Formula \[
7135 \left.\frac{A}{B}\right\} \]
7153 will be converted by LyX to brackets in the right size when the document
7154 is reloaded and an omitted bracket will appear as dashed line.
7157 \begin_layout Standard
7158 \begin_inset VSpace bigskip
7161 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7172 \begin_layout Plain Layout
7180 is additionally available for all brackets and limits.
7181 With this command the height of the following character is adapted to the
7182 one of the surrounding brackets, what is e.g.
7183 \begin_inset space \space{}
7186 needed for physical vectors:
7187 \begin_inset Formula \[
7188 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7192 For physical vectors there is a special LaTeX-package, described in
7193 \begin_inset CommandInset ref
7195 reference "sub:Physical-Vectors"
7202 \begin_layout Subsection
7207 \begin_layout Plain Layout
7208 Brackets ! horizontal
7216 \begin_layout Standard
7218 \begin_inset Tabular
7219 <lyxtabular version="3" rows="4" columns="2">
7221 <column alignment="center" valignment="top" width="0pt">
7222 <column alignment="center" valignment="top" width="0pt">
7224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7227 \begin_layout Plain Layout
7229 \begin_inset Note Note
7232 \begin_layout Plain Layout
7239 is only used as spacer.
7249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7252 \begin_layout Plain Layout
7260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7263 \begin_layout Plain Layout
7267 \begin_layout Plain Layout
7282 \begin_layout Plain Layout
7295 \begin_layout Plain Layout
7308 \begin_layout Plain Layout
7321 \begin_layout Plain Layout
7332 \begin_layout Plain Layout
7345 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7348 \begin_layout Plain Layout
7349 \begin_inset Formula $\overbrace{A+B}^{3}$
7359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7362 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7381 \begin_layout Plain Layout
7394 \begin_layout Plain Layout
7407 \begin_layout Plain Layout
7418 \begin_layout Plain Layout
7431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7434 \begin_layout Plain Layout
7435 \begin_inset Formula $\underbrace{A+B}_{5}$
7445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7448 \begin_layout Plain Layout
7455 \begin_layout Plain Layout
7470 \begin_layout Plain Layout
7483 \begin_layout Plain Layout
7496 \begin_layout Plain Layout
7509 \begin_layout Plain Layout
7522 \begin_layout Plain Layout
7535 \begin_layout Plain Layout
7549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7552 \begin_layout Plain Layout
7553 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7569 \begin_layout Standard
7570 In the last example it doesn't matter if
7582 is inserted at first.
7585 \begin_layout Standard
7586 \begin_inset VSpace bigskip
7589 When brackets are needed that overlap each other, multiline formulas, as
7591 \begin_inset CommandInset ref
7593 reference "sec:Multiline-Formulas"
7598 \begin_inset Formula \begin{eqnarray*}
7599 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7600 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7604 In the first row the formula is inserted together with the first brace.
7605 It is hereby important that the space command
7609 \begin_layout Plain Layout
7610 Space commands are explained in
7611 \begin_inset CommandInset ref
7613 reference "sub:Predefined-Space"
7628 is inserted before the first
7629 \begin_inset Formula $d$
7632 , because the brace that ends behind the
7633 \begin_inset Formula $q$
7636 prevents that the following
7637 \begin_inset Quotes eld
7641 \begin_inset Quotes erd
7644 is surrounded by space.
7648 \begin_layout Plain Layout
7649 because a bracket is not handled as character, see
7650 \begin_inset CommandInset ref
7652 reference "sub:Binary-Operators"
7661 In the second row the second brace is inserted.
7662 As it should begin before the
7663 \begin_inset Formula $b$
7678 \begin_layout Plain Layout
7686 \begin_inset CommandInset ref
7688 reference "sub:Placeholders"
7697 This space is needed because the
7698 \begin_inset Quotes eld
7702 \begin_inset Quotes erd
7705 is also surrounded by space in the formula.
7706 The brace is placed under the command
7715 \begin_layout Standard
7716 It gets more complicated when brackets overlap each other, like in the following
7721 \begin_layout Plain Layout
7733 \begin_inset Formula \begin{eqnarray*}
7734 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7735 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7743 \begin_layout Plain Layout
7754 The first formula row is the same as the second row of the previous example,
7755 with the difference that the brace is above.
7756 The second row contains the formula together with the second brace.
7757 To avoid that there is space between the upper brace in the first row and
7758 the formula, the row spacing need to be reduced.
7759 This is not easily possible due to a bug in LyX
7763 \begin_layout Plain Layout
7764 \begin_inset CommandInset href
7766 name "LyX-bug #1505"
7767 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7777 As solution for the problem, the global formula row separation
7787 \begin_layout Plain Layout
7795 must be changed to -6
7796 \begin_inset space \thinspace{}
7799 pt before the formula with the command
7814 is set back after the formula to the standard value of 3
7815 \begin_inset space \thinspace{}
7818 pt using the same command.
7819 More about the row separation in formulas is explained in
7820 \begin_inset CommandInset ref
7822 reference "sub:Line-Separation"
7829 \begin_layout Section
7834 \begin_layout Plain Layout
7843 \begin_layout Standard
7844 Arrows can be inserted via the math toolbar button
7845 \begin_inset Graphics
7846 filename ../images/math/leftarrow.png
7851 or the commands listed in the following subsections.
7854 \begin_layout Standard
7855 \begin_inset Newpage newpage
7861 \begin_layout Subsection
7866 \begin_layout Plain Layout
7875 \begin_layout Standard
7876 \begin_inset space \hfill{}
7880 \begin_inset Tabular
7881 <lyxtabular version="3" rows="8" columns="2">
7883 <column alignment="center" valignment="top" width="0pt">
7884 <column alignment="center" valignment="top" width="0pt">
7886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7889 \begin_layout Plain Layout
7895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7898 \begin_layout Plain Layout
7906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7920 \begin_layout Plain Layout
7921 \begin_inset Formula $\gets$
7931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7934 \begin_layout Plain Layout
7942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7945 \begin_layout Plain Layout
7946 \begin_inset Formula $\Leftarrow$
7956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7959 \begin_layout Plain Layout
7967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7970 \begin_layout Plain Layout
7971 \begin_inset Formula $\longleftarrow$
7981 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7984 \begin_layout Plain Layout
7992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7995 \begin_layout Plain Layout
7996 \begin_inset Formula $\Longleftarrow$
8006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8009 \begin_layout Plain Layout
8017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8020 \begin_layout Plain Layout
8021 \begin_inset Formula $\leftharpoonup$
8031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8034 \begin_layout Plain Layout
8042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8045 \begin_layout Plain Layout
8046 \begin_inset Formula $\leftharpoondown$
8056 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8059 \begin_layout Plain Layout
8067 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8070 \begin_layout Plain Layout
8071 \begin_inset Formula $\hookleftarrow$
8085 \begin_inset space \hfill{}
8089 \begin_inset Tabular
8090 <lyxtabular version="3" rows="8" columns="2">
8092 <column alignment="center" valignment="top" width="0pt">
8093 <column alignment="center" valignment="top" width="0pt">
8095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8098 \begin_layout Plain Layout
8104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8107 \begin_layout Plain Layout
8115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8129 \begin_layout Plain Layout
8130 \begin_inset Formula $\to$
8140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8143 \begin_layout Plain Layout
8151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8154 \begin_layout Plain Layout
8155 \begin_inset Formula $\Rightarrow$
8165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8168 \begin_layout Plain Layout
8176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8179 \begin_layout Plain Layout
8180 \begin_inset Formula $\longrightarrow$
8190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8193 \begin_layout Plain Layout
8201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8204 \begin_layout Plain Layout
8205 \begin_inset Formula $\Longrightarrow$
8215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8218 \begin_layout Plain Layout
8226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8229 \begin_layout Plain Layout
8230 \begin_inset Formula $\rightharpoonup$
8240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8243 \begin_layout Plain Layout
8251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8254 \begin_layout Plain Layout
8255 \begin_inset Formula $\rightharpoondown$
8265 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8268 \begin_layout Plain Layout
8276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8279 \begin_layout Plain Layout
8280 \begin_inset Formula $\hookrightarrow$
8294 \begin_inset space \hfill{}
8300 \begin_layout Standard
8301 \begin_inset space \hfill{}
8305 \begin_inset Tabular
8306 <lyxtabular version="3" rows="6" columns="2">
8308 <column alignment="center" valignment="top" width="0pt">
8309 <column alignment="center" valignment="top" width="0pt">
8311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8314 \begin_layout Plain Layout
8320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8323 \begin_layout Plain Layout
8331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8334 \begin_layout Plain Layout
8342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8345 \begin_layout Plain Layout
8346 \begin_inset Formula $\leftrightarrow$
8356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8359 \begin_layout Plain Layout
8367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8370 \begin_layout Plain Layout
8371 \begin_inset Formula $\Leftrightarrow$
8381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8384 \begin_layout Plain Layout
8392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8395 \begin_layout Plain Layout
8396 \begin_inset Formula $\longleftrightarrow$
8406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8409 \begin_layout Plain Layout
8417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8420 \begin_layout Plain Layout
8421 \begin_inset Formula $\Longleftrightarrow$
8431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8434 \begin_layout Plain Layout
8442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8445 \begin_layout Plain Layout
8446 \begin_inset Formula $\rightleftharpoons$
8460 \begin_inset space \hspace{}
8465 \begin_inset space \hfill{}
8469 \begin_inset Tabular
8470 <lyxtabular version="3" rows="5" columns="2">
8472 <column alignment="center" valignment="top" width="0pt">
8473 <column alignment="center" valignment="top" width="0pt">
8475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8478 \begin_layout Plain Layout
8484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8498 \begin_layout Plain Layout
8506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8509 \begin_layout Plain Layout
8510 \begin_inset Formula $\mapsto$
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8523 \begin_layout Plain Layout
8531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8534 \begin_layout Plain Layout
8535 \begin_inset Formula $\longmapsto$
8545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8548 \begin_layout Plain Layout
8556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8559 \begin_layout Plain Layout
8560 \begin_inset Formula $\leadsto$
8570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8573 \begin_layout Plain Layout
8581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8584 \begin_layout Plain Layout
8585 \begin_inset Formula $\dasharrow$
8599 \begin_inset space \hfill{}
8605 \begin_layout Standard
8606 \begin_inset VSpace medskip
8609 Arrows used as accent like e.g.
8610 \begin_inset space \space{}
8613 vector arrows are listed in
8614 \begin_inset CommandInset ref
8616 reference "sec:Accents"
8623 \begin_layout Standard
8624 \begin_inset VSpace bigskip
8627 Furthermore there are the labeled arrows
8631 \begin_layout Plain Layout
8647 \begin_layout Plain Layout
8665 \begin_layout Plain Layout
8672 \begin_layout Plain Layout
8687 When inserting one of these commands in a formula, an arrow with two blue
8688 boxes appear where the label can be inserted.
8689 The length of the arrow adapts to the label width.
8692 \begin_layout Standard
8694 \begin_inset Tabular
8695 <lyxtabular version="3" rows="3" columns="2">
8697 <column alignment="center" valignment="top" width="0pt">
8698 <column alignment="center" valignment="top" width="0pt">
8700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8703 \begin_layout Plain Layout
8709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8712 \begin_layout Plain Layout
8714 \begin_inset Note Note
8717 \begin_layout Plain Layout
8724 is only used as spacer.
8736 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8739 \begin_layout Plain Layout
8746 \begin_layout Plain Layout
8756 \begin_inset Formula $\downarrow$
8760 \begin_inset Formula $\to$
8768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8771 \begin_layout Plain Layout
8772 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8785 \begin_layout Plain Layout
8792 \begin_layout Plain Layout
8802 \begin_inset Formula $\downarrow$
8806 \begin_inset Formula $\to$
8814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8817 \begin_layout Plain Layout
8818 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8834 \begin_layout Subsection
8835 Vertical and diagonal Arrows
8839 \begin_layout Plain Layout
8849 \begin_layout Plain Layout
8858 \begin_layout Standard
8859 \begin_inset space \hfill{}
8863 \begin_inset Tabular
8864 <lyxtabular version="3" rows="7" columns="2">
8866 <column alignment="center" valignment="top" width="0pt">
8867 <column alignment="center" valignment="top" width="0pt">
8869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8872 \begin_layout Plain Layout
8878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8881 \begin_layout Plain Layout
8889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8892 \begin_layout Plain Layout
8900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8903 \begin_layout Plain Layout
8904 \begin_inset Formula $\uparrow$
8914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8917 \begin_layout Plain Layout
8925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8928 \begin_layout Plain Layout
8929 \begin_inset Formula $\Uparrow$
8939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8942 \begin_layout Plain Layout
8950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8953 \begin_layout Plain Layout
8954 \begin_inset Formula $\updownarrow$
8964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8967 \begin_layout Plain Layout
8975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8978 \begin_layout Plain Layout
8979 \begin_inset Formula $\Updownarrow$
8989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8992 \begin_layout Plain Layout
9000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9003 \begin_layout Plain Layout
9004 \begin_inset Formula $\Downarrow$
9014 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9017 \begin_layout Plain Layout
9025 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9028 \begin_layout Plain Layout
9029 \begin_inset Formula $\downarrow$
9043 \begin_inset space \hfill{}
9047 \begin_inset Tabular
9048 <lyxtabular version="3" rows="5" columns="2">
9050 <column alignment="center" valignment="top" width="0pt">
9051 <column alignment="center" valignment="top" width="0pt">
9053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9056 \begin_layout Plain Layout
9062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9065 \begin_layout Plain Layout
9073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9076 \begin_layout Plain Layout
9084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9087 \begin_layout Plain Layout
9088 \begin_inset Formula $\nearrow$
9098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9101 \begin_layout Plain Layout
9109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9112 \begin_layout Plain Layout
9113 \begin_inset Formula $\searrow$
9123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9126 \begin_layout Plain Layout
9134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9137 \begin_layout Plain Layout
9138 \begin_inset Formula $\swarrow$
9148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9151 \begin_layout Plain Layout
9159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9162 \begin_layout Plain Layout
9163 \begin_inset Formula $\nwarrow$
9177 \begin_inset space \hfill{}
9183 \begin_layout Standard
9184 \begin_inset VSpace medskip
9187 Vertical arrows can be used also as delimiter together with the commands
9189 \begin_inset CommandInset ref
9191 reference "sub:Manual-Bracket-Size"
9196 \begin_inset CommandInset ref
9198 reference "sub:Automatic-Bracket-Size"
9205 \begin_layout Standard
9206 \begin_inset Newpage newpage
9212 \begin_layout Section
9214 \begin_inset CommandInset label
9224 \begin_layout Plain Layout
9233 \begin_layout Standard
9234 Accents can be inserted via the math toolbar button
9235 \begin_inset Graphics
9236 filename ../images/math/hat.png
9241 or the commands listed in the following subsections.
9244 \begin_layout Subsection
9245 Accents for one Character
9249 \begin_layout Plain Layout
9262 \begin_layout Plain Layout
9264 \begin_inset CommandInset ref
9266 reference "sub:Accents-in-Text"
9279 \begin_layout Plain Layout
9287 \begin_inset Note Note
9290 \begin_layout Plain Layout
9293 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9296 \begin_layout Plain Layout
9299 texorpdfstring is in section
9300 \begin_inset CommandInset ref
9302 reference "sub:Formulas-in-Section"
9312 \begin_inset CommandInset label
9314 name "sub:Accents-for-one"
9322 \begin_layout Plain Layout
9323 Accents ! for one character
9331 \begin_layout Standard
9332 \begin_inset space \hfill{}
9336 \begin_inset Tabular
9337 <lyxtabular version="3" rows="8" columns="2">
9339 <column alignment="center" valignment="top" width="0pt">
9340 <column alignment="center" valignment="top" width="0pt">
9342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9345 \begin_layout Plain Layout
9351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9354 \begin_layout Plain Layout
9356 \begin_inset Note Note
9359 \begin_layout Plain Layout
9366 is only used as spacer.
9378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9381 \begin_layout Plain Layout
9388 \begin_layout Plain Layout
9402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9405 \begin_layout Plain Layout
9406 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9419 \begin_layout Plain Layout
9426 \begin_layout Plain Layout
9440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9443 \begin_layout Plain Layout
9444 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9457 \begin_layout Plain Layout
9464 \begin_layout Plain Layout
9478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9481 \begin_layout Plain Layout
9482 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9495 \begin_layout Plain Layout
9503 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9506 \begin_layout Plain Layout
9507 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9520 \begin_layout Plain Layout
9527 \begin_layout Plain Layout
9540 \begin_layout Plain Layout
9551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9554 \begin_layout Plain Layout
9555 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9568 \begin_layout Plain Layout
9575 \begin_layout Plain Layout
9589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9592 \begin_layout Plain Layout
9593 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9603 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9606 \begin_layout Plain Layout
9613 \begin_layout Plain Layout
9627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9630 \begin_layout Plain Layout
9631 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9645 \begin_inset space \hfill{}
9649 \begin_inset Tabular
9650 <lyxtabular version="3" rows="7" columns="2">
9652 <column alignment="center" valignment="top" width="0pt">
9653 <column alignment="center" valignment="top" width="0pt">
9655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9658 \begin_layout Plain Layout
9664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9667 \begin_layout Plain Layout
9675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9678 \begin_layout Plain Layout
9685 \begin_layout Plain Layout
9699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9702 \begin_layout Plain Layout
9703 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9716 \begin_layout Plain Layout
9723 \begin_layout Plain Layout
9737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9740 \begin_layout Plain Layout
9741 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9754 \begin_layout Plain Layout
9761 \begin_layout Plain Layout
9775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9778 \begin_layout Plain Layout
9779 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9792 \begin_layout Plain Layout
9799 \begin_layout Plain Layout
9813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9816 \begin_layout Plain Layout
9817 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9830 \begin_layout Plain Layout
9837 \begin_layout Plain Layout
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9854 \begin_layout Plain Layout
9855 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9868 \begin_layout Plain Layout
9875 \begin_layout Plain Layout
9889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9892 \begin_layout Plain Layout
9893 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9907 \begin_inset space \hfill{}
9913 \begin_layout Standard
9914 \begin_inset VSpace bigskip
9920 \begin_layout Standard
9921 You can directly insert accents like é to formulas.
9922 LyX will transform them to the corresponding accent command.
9927 \begin_layout Plain Layout
9933 it is better to insert a quotation mark before the vowel.
9934 These two characters are then treated by LaTeX as
9938 character when the formula part with the umlaut is marked as German.
9946 \begin_inset Quotes eld
9950 \begin_inset Quotes erd
9953 umlauts are created as demonstrated in the following example:
9956 \begin_layout Standard
9957 \begin_inset VSpace -2mm
9963 \begin_layout Standard
9965 \begin_inset Tabular
9966 <lyxtabular version="3" rows="3" columns="2">
9968 <column alignment="center" valignment="top" width="0">
9969 <column alignment="center" valignment="top" width="0">
9971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9974 \begin_layout Plain Layout
9980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9983 \begin_layout Plain Layout
9985 \begin_inset Note Note
9988 \begin_layout Plain Layout
9996 \begin_inset space \thinspace{}
9999 pt space are only used as spacer.
10011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10014 \begin_layout Plain Layout
10017 \begin_inset Quotes grd
10025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10028 \begin_layout Plain Layout
10029 \begin_inset space \hspace{}
10036 \begin_inset Formula $"i$
10046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10049 \begin_layout Plain Layout
10056 \begin_layout Plain Layout
10070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10073 \begin_layout Plain Layout
10074 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10090 \begin_layout Standard
10091 Another advantage to
10097 is that umlauts can directly be converted to mathematical text because
10098 the accent commands above are
10104 in mathematical text
10107 To convert an accented character to mathematical text, only the character
10108 under the accent may be converted.
10109 This applies also for all other conversions, e.g.
10110 \begin_inset space \space{}
10116 \begin_layout Standard
10117 In mathematical text, umlauts and other accented characters can directly
10121 \begin_layout Subsection
10122 Accents for Operators
10126 \begin_layout Plain Layout
10127 Accents ! for operators
10135 \begin_layout Standard
10146 \begin_layout Plain Layout
10164 \begin_layout Plain Layout
10172 characters can be placed above or below an operator, respectively, to accent
10184 \begin_layout Plain Layout
10192 characters can be set before and behind an operator.
10193 The command scheme is:
10196 \begin_layout Standard
10212 \begin_layout Standard
10219 must always be before the operator that should be accented.
10220 You can accent with several characters and even with other operators and
10228 for example only characters behind an operator, write nothing between the
10229 first braces but don't omit the braces.
10232 \begin_layout Standard
10233 For example the command
10238 \begin_inset Formula $\to$
10248 \begin_inset Formula $\to$
10257 \begin_layout Plain Layout
10273 \begin_inset Formula \[
10274 \sideset{}{'}\sum_{k=1}^{n}\]
10281 \begin_layout Standard
10290 \begin_layout Plain Layout
10305 \begin_layout Plain Layout
10317 \begin_inset Formula $\uparrow$
10325 \begin_inset Formula \[
10326 \overset{a}{\maltese}\]
10330 As seen in the last example, with
10342 also symbols and characters can be accented; with
10348 this is not possible.
10351 \begin_layout Subsection
10352 Accents for several Characters
10356 \begin_layout Plain Layout
10357 Accents ! for several characters
10365 \begin_layout Standard
10366 \begin_inset space \hfill{}
10370 \begin_inset Tabular
10371 <lyxtabular version="3" rows="5" columns="2">
10373 <column alignment="center" valignment="top" width="0pt">
10374 <column alignment="center" valignment="top" width="0pt">
10376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10379 \begin_layout Plain Layout
10385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10388 \begin_layout Plain Layout
10390 \begin_inset Note Note
10393 \begin_layout Plain Layout
10400 is only used as spacer.
10412 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10415 \begin_layout Plain Layout
10422 \begin_layout Plain Layout
10436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10439 \begin_layout Plain Layout
10440 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10453 \begin_layout Plain Layout
10460 \begin_layout Plain Layout
10474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10477 \begin_layout Plain Layout
10478 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10491 \begin_layout Plain Layout
10498 \begin_layout Plain Layout
10512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10515 \begin_layout Plain Layout
10516 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10526 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10529 \begin_layout Plain Layout
10532 underleftrightarrow
10536 \begin_layout Plain Layout
10550 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10553 \begin_layout Plain Layout
10554 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10568 \begin_inset space \hfill{}
10572 \begin_inset Tabular
10573 <lyxtabular version="3" rows="5" columns="2">
10575 <column alignment="center" valignment="top" width="0pt">
10576 <column alignment="center" valignment="top" width="0pt">
10578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10581 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10590 \begin_layout Plain Layout
10598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10601 \begin_layout Plain Layout
10608 \begin_layout Plain Layout
10622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10625 \begin_layout Plain Layout
10626 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10639 \begin_layout Plain Layout
10646 \begin_layout Plain Layout
10660 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10663 \begin_layout Plain Layout
10664 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10677 \begin_layout Plain Layout
10684 \begin_layout Plain Layout
10698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10701 \begin_layout Plain Layout
10702 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10715 \begin_layout Plain Layout
10722 \begin_layout Plain Layout
10736 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10739 \begin_layout Plain Layout
10740 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10754 \begin_inset space \hfill{}
10760 \begin_layout Standard
10761 \begin_inset VSpace medskip
10764 With these commands as many characters as you like can be accented.
10777 will only be set in the output with a length of three characters, as shown
10778 in the following example:
10779 \begin_inset Formula \[
10780 \widetilde{A+B=C-D}\]
10787 \begin_layout Standard
10798 \begin_layout Plain Layout
10816 \begin_layout Plain Layout
10824 described in the previous subsection it is also possible to accent several
10834 \begin_layout Plain Layout
10844 \begin_inset Formula $\downarrow$
10850 \begin_inset Formula \[
10851 \underset{***}{A=B}\]
10858 \begin_layout Section
10860 \begin_inset CommandInset label
10870 \begin_layout Plain Layout
10879 \begin_layout Subsection
10881 \begin_inset CommandInset label
10883 name "sub:Predefined-Space"
10891 \begin_layout Plain Layout
10892 Space ! horizontal ! predefined
10900 \begin_layout Standard
10901 Sometimes it is necessary to insert horizontal space to a formula.
10902 This is done by inserting a protected space (shortcut
10908 \begin_inset Quotes eld
10918 \begin_layout Plain Layout
10931 \begin_inset Quotes erd
10934 appears and by pressing
10938 several times one can select one of eight different space sizes.
10939 The spaces can also be inserted using the math toolbar button
10940 \begin_inset Graphics
10941 filename ../images/math/space.png
10946 or special commands.
10947 Independent from the inserted command, one can select the size again by
10955 \begin_layout Standard
10958 \begin_inset VSpace -5mm
10962 \begin_inset Tabular
10963 <lyxtabular version="3" rows="3" columns="7">
10965 <column alignment="center" valignment="middle" width="6.8cm">
10966 <column alignment="center" valignment="top" width="0">
10967 <column alignment="center" valignment="top" width="0">
10968 <column alignment="center" valignment="top" width="0">
10969 <column alignment="center" valignment="top" width="0">
10970 <column alignment="center" valignment="top" width="0">
10971 <column alignment="center" valignment="top" width="0">
10973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10976 \begin_layout Plain Layout
10982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10985 \begin_layout Plain Layout
10993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10996 \begin_layout Plain Layout
11004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11007 \begin_layout Plain Layout
11015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11018 \begin_layout Plain Layout
11026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11029 \begin_layout Plain Layout
11037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11040 \begin_layout Plain Layout
11050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11053 \begin_layout Plain Layout
11058 keystrokes after inserting the protected space
11063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11075 \begin_layout Plain Layout
11081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11084 \begin_layout Plain Layout
11090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11093 \begin_layout Plain Layout
11099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11102 \begin_layout Plain Layout
11108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11111 \begin_layout Plain Layout
11119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11122 \begin_layout Plain Layout
11128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11132 \begin_inset Formula $A\, B$
11140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11143 \begin_layout Plain Layout
11144 \begin_inset Formula $A\: B$
11152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11155 \begin_layout Plain Layout
11156 \begin_inset Formula $A\; B$
11164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11167 \begin_layout Plain Layout
11168 \begin_inset Formula $A\quad B$
11176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11179 \begin_layout Plain Layout
11180 \begin_inset Formula $A\qquad B$
11188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11191 \begin_layout Plain Layout
11192 \begin_inset Formula $A\! B$
11208 \begin_layout Standard
11209 The last size seem to produce no space.
11210 It is displayed red in LyX contrary to the other sizes, because it is a
11212 There are two more negative spaces:
11215 \begin_layout Standard
11217 \begin_inset Tabular
11218 <lyxtabular version="3" rows="3" columns="3">
11220 <column alignment="center" valignment="middle" width="6.8cm">
11221 <column alignment="center" valignment="top" width="0pt">
11222 <column alignment="center" valignment="top" width="0pt">
11224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11227 \begin_layout Plain Layout
11233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11236 \begin_layout Plain Layout
11244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11247 \begin_layout Plain Layout
11257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11260 \begin_layout Plain Layout
11265 keystrokes after inserting the protected space
11270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11279 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11282 \begin_layout Plain Layout
11290 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11293 \begin_layout Plain Layout
11299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11302 \begin_layout Plain Layout
11303 \begin_inset Formula $A\negmedspace B$
11311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11314 \begin_layout Plain Layout
11315 \begin_inset Formula $A\negthickspace B$
11331 \begin_layout Standard
11332 Negative spaces can lead to characters overlapping each other.
11333 Thus they can be used to enforce ligatures, what is e.g.
11334 \begin_inset space \space{}
11337 useful for summation operators:
11340 \begin_layout Standard
11342 \begin_inset Tabular
11343 <lyxtabular version="3" rows="3" columns="2">
11345 <column alignment="center" valignment="top" width="0">
11346 <column alignment="center" valignment="top" width="0">
11348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11351 \begin_layout Plain Layout
11357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11360 \begin_layout Plain Layout
11362 \begin_inset Note Note
11365 \begin_layout Plain Layout
11372 is only used as spacer.
11384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11387 \begin_layout Plain Layout
11396 \begin_layout Plain Layout
11410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11413 \begin_layout Plain Layout
11414 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11427 \begin_layout Plain Layout
11438 \begin_layout Plain Layout
11452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11455 \begin_layout Plain Layout
11456 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11472 \begin_layout Standard
11473 Relations like for example equal signs, are always surrounded by space.
11474 To suppress this, the equal sign is placed into a TeX-brace.
11475 The following example demonstrates this:
11478 \begin_layout Standard
11480 \begin_inset Tabular
11481 <lyxtabular version="3" rows="2" columns="2">
11483 <column alignment="center" valignment="top" width="0pt">
11484 <column alignment="center" valignment="top" width="0pt">
11486 <cell alignment="center" valignment="top" usebox="none">
11489 \begin_layout Plain Layout
11495 <cell alignment="center" valignment="top" usebox="none">
11498 \begin_layout Plain Layout
11499 \begin_inset Formula $A=B$
11509 <cell alignment="center" valignment="top" usebox="none">
11512 \begin_layout Plain Layout
11513 \begin_inset Note Note
11516 \begin_layout Plain Layout
11523 is only used as spacer.
11529 \begin_inset Formula $\raisebox{5mm}{}$
11532 equation without space
11537 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11540 \begin_layout Plain Layout
11541 \begin_inset Formula $A{=}B$
11557 \begin_layout Standard
11559 The command for the last formula is:
11564 \begin_inset Formula $\to$
11570 \begin_layout Standard
11571 \begin_inset VSpace bigskip
11574 Spaces are needed for physical units, because the space between the value
11575 and the unit is the smallest one and not a normal space.
11576 For units in text, the smallest space is inserted via the menu
11578 Insert\SpecialChar \menuseparator
11579 Formatting\SpecialChar \menuseparator
11581 \begin_inset space ~
11589 arg "space-insert thin"
11595 \begin_layout Standard
11596 An example to visualize the difference:
11599 \begin_layout Standard
11600 \begin_inset Tabular
11601 <lyxtabular version="3" rows="2" columns="2">
11603 <column alignment="left" valignment="top" width="0">
11604 <column alignment="left" valignment="top" width="0">
11606 <cell alignment="center" valignment="top" usebox="none">
11609 \begin_layout Plain Layout
11611 \begin_inset Formula $\cdot$
11619 <cell alignment="center" valignment="top" usebox="none">
11622 \begin_layout Plain Layout
11623 space between value and unit
11630 <cell alignment="center" valignment="top" usebox="none">
11633 \begin_layout Plain Layout
11635 \begin_inset space \thinspace{}
11639 \begin_inset Formula $\cdot$
11647 <cell alignment="center" valignment="top" usebox="none">
11650 \begin_layout Plain Layout
11651 smallest space between value and unit
11664 \begin_layout Subsection
11669 \begin_layout Plain Layout
11682 \begin_layout Plain Layout
11683 for vertical space in formulas see
11684 \begin_inset CommandInset ref
11686 reference "sub:Line-Separation"
11699 \begin_layout Plain Layout
11707 \begin_inset Note Note
11710 \begin_layout Plain Layout
11713 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11716 \begin_layout Plain Layout
11719 texorpdfstring is in section
11720 \begin_inset CommandInset ref
11722 reference "sub:Formulas-in-Section"
11732 \begin_inset CommandInset label
11734 name "sub:Variable-Space"
11742 \begin_layout Plain Layout
11743 Space ! horizontal ! variable
11751 \begin_layout Standard
11752 Space with a defined length can be inserted in LyX with the command
11753 \begin_inset Newline newline
11766 \begin_layout Plain Layout
11775 For the length all units listed in
11776 \begin_inset CommandInset ref
11778 reference "tab:Available-units"
11782 are allowed, except of the unit
11783 \begin_inset Quotes eld
11787 \begin_inset Quotes erd
11791 The length may also be negative.
11792 To insert so many space that the formula uses all available space, the
11803 \begin_layout Plain Layout
11814 \begin_layout Standard
11815 \begin_inset VSpace -1mm
11821 \begin_layout Standard
11823 \begin_inset Tabular
11824 <lyxtabular version="3" rows="4" columns="2">
11826 <column alignment="center" valignment="top" width="0">
11827 <column alignment="center" valignment="top" width="0">
11829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11832 \begin_layout Plain Layout
11838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11841 \begin_layout Plain Layout
11849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11852 \begin_layout Plain Layout
11856 \begin_inset Formula $\to$
11866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11869 \begin_layout Plain Layout
11870 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11883 \begin_layout Plain Layout
11887 \begin_inset Formula $\to$
11897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11900 \begin_layout Plain Layout
11901 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11914 \begin_layout Plain Layout
11921 \begin_layout Plain Layout
11935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11938 \begin_layout Plain Layout
11939 \begin_inset Formula $A=A\hfill B=B$
11955 \begin_layout Standard
11956 In the last example the available space is given by the longest column entry
11958 In an inline formula the space depends on the length of the line in which
11966 Thus, when the line uses the full width, no space will be created.
11973 only has an effect on displayed formulas when the formula style
11978 (Formula styles are explained in
11979 \begin_inset CommandInset ref
11981 reference "sec:Formula-Styles"
11988 \begin_layout Standard
11995 , there are the commands
12007 that fill the space with a pattern, see
12008 \begin_inset CommandInset ref
12010 reference "sub:Ellipses"
12017 \begin_layout Standard
12018 For text, variable space can be inserted via the menu
12020 Insert\SpecialChar \menuseparator
12021 Formatting\SpecialChar \menuseparator
12023 \begin_inset space ~
12028 , what is not possible in formulas:
12031 \begin_layout Standard
12032 This is a line with
12033 \begin_inset space \hspace{}
12038 \begin_inset space \thinspace{}
12044 \begin_layout Standard
12045 This is a line with
12046 \begin_inset space \hfill{}
12052 \begin_layout Subsection
12053 Space besides inline Formulas
12057 \begin_layout Plain Layout
12058 Space ! besides inline formulas
12066 \begin_layout Standard
12067 The space that surrounds inline formulas can be adjusted with the length
12076 \begin_layout Plain Layout
12087 The value of a length is set with the command
12095 \begin_layout Plain Layout
12105 that has the following scheme:
12108 \begin_layout Standard
12113 setlength{length name}{value}
12116 \begin_layout Standard
12124 \begin_inset space \thinspace{}
12130 \begin_layout Standard
12140 \begin_layout Standard
12141 is inserted in TeX-mode.
12143 \begin_inset space \thinspace{}
12146 mm space will now be set around all inline formulas:
12150 \begin_layout Plain Layout
12164 \begin_layout Standard
12165 This is a line with an inline formula
12166 \begin_inset Formula $A=B$
12170 \begin_inset space \thinspace{}
12173 mm surrounding space.
12177 \begin_layout Plain Layout
12191 \begin_layout Standard
12192 To return to the predefined value,
12198 is set to the value 0
12199 \begin_inset space \thinspace{}
12205 \begin_layout Section
12210 \begin_layout Plain Layout
12220 \begin_layout Plain Layout
12225 \begin_layout Plain Layout
12236 \begin_layout Plain Layout
12251 \begin_layout Standard
12252 Boxes for text are described in chapter
12259 \begin_inset space ~
12267 \begin_layout Subsection
12269 \begin_inset CommandInset label
12271 name "sub:Boxes-with-Frame"
12279 \begin_layout Plain Layout
12288 \begin_layout Standard
12289 It is possible to frame formulas or parts of it with the commands
12299 \begin_layout Plain Layout
12317 \begin_layout Plain Layout
12328 \begin_layout Standard
12329 When one of these commands is inserted to a formula, a blue box appears
12330 within a frame to enter formula parts.
12337 an additional formula has to be created by
12345 \begin_layout Plain Layout
12346 Due to a bug in LyX it is not possible to create a new formula with
12351 \begin_inset CommandInset href
12353 name "LyX-bug #1435"
12354 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12363 , because the box content will otherwise be treated as mathematical text.
12370 is used, a new formula is automatically created inside the frame.
12373 \begin_layout Standard
12380 is not suitable to frame displayed formulas, because the formula will always
12381 be set in the size of the text.
12388 is in contrary not suitable to frame inline formulas, because the formula
12389 will always be set in the size of a displayed formula.
12392 \begin_layout Standard
12399 there is the command
12409 \begin_layout Plain Layout
12417 where additionally the frame width and the alignment can be specified.
12424 is used in the following scheme:
12427 \begin_layout Standard
12432 framebox[frame width][position]{box content}
12435 \begin_layout Standard
12436 The position can either be
12453 right aligns the formula in the box.
12454 When no position is given, the formula will be centered.
12455 \begin_inset Newline newline
12458 Is no width given, also no position can be given.
12459 In this case the frame width is adjusted to the box content like for
12468 \begin_layout Standard
12475 is inserted, a box appears containing three blue boxes.
12476 The first two boxes are surrounded by brackets and denote the two optional
12478 The third box is for formula parts like for
12487 \begin_layout Standard
12489 \begin_inset Note Note
12492 \begin_layout Plain Layout
12493 The table has been set into a minipage to make the footnote appearing.
12494 Otherwise the footnote text would not be displayed.
12500 \begin_inset Box Frameless
12509 height_special "totalheight"
12512 \begin_layout Plain Layout
12514 \begin_inset Tabular
12515 <lyxtabular version="3" rows="5" columns="2">
12517 <column alignment="center" valignment="top" width="0">
12518 <column alignment="center" valignment="top" width="0">
12520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12523 \begin_layout Plain Layout
12528 \begin_layout Plain Layout
12529 Due to a bug in LyX it is not possible to create a new formula with
12534 \begin_inset CommandInset href
12536 name "LyX-bug #1435"
12537 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12554 \begin_layout Plain Layout
12556 \begin_inset Note Note
12559 \begin_layout Plain Layout
12566 is only used as spacer.
12578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12581 \begin_layout Plain Layout
12588 \begin_layout Plain Layout
12607 \begin_layout Plain Layout
12621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12624 \begin_layout Plain Layout
12625 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12638 \begin_layout Plain Layout
12645 \begin_layout Plain Layout
12660 \begin_layout Plain Layout
12674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12677 \begin_layout Plain Layout
12678 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12691 \begin_layout Plain Layout
12698 \begin_layout Plain Layout
12712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12715 \begin_layout Plain Layout
12716 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12729 \begin_layout Plain Layout
12736 \begin_layout Plain Layout
12746 \begin_inset Formula $\to$
12750 \begin_inset Formula $\to$
12763 \begin_layout Plain Layout
12773 \begin_inset Formula $\downarrow$
12781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12784 \begin_layout Plain Layout
12785 \begin_inset Formula $\raisebox{6mm}{}$
12789 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12793 \begin_inset Formula $\raisebox{-4mm}{}$
12814 \begin_layout Standard
12815 The frame thickness can also be adjusted.
12816 To do this the following commands have to be inserted in TeX-mode before
12820 \begin_layout Standard
12830 \begin_inset Quotes eld
12834 \begin_inset Quotes erd
12848 \begin_inset Quotes eld
12852 \begin_inset Quotes erd
12858 \begin_layout Standard
12859 \begin_inset Quotes eld
12863 \begin_inset Quotes erd
12866 specifies the minimal distance between the frame and the first character
12868 An example for this is the following framed formula:
12872 \begin_layout Plain Layout
12884 \begin_inset Formula \[
12889 Before this formula the commands
12892 \begin_layout Standard
12914 \begin_layout Standard
12915 were inserted in TeX-mode.
12916 The given values are used for all following boxes.
12919 \begin_layout Standard
12920 To return to the standard frame size, the command
12923 \begin_layout Standard
12948 \begin_layout Plain Layout
12962 \begin_layout Standard
12963 is inserted in TeX-mode before the next formula.
12966 \begin_layout Subsection
12967 Boxes without Frame
12968 \begin_inset CommandInset label
12970 name "sub:Boxes-without-Frame"
12978 \begin_layout Plain Layout
12979 Boxes ! without frame
12987 \begin_layout Standard
12988 For boxes without a frame there are the following box commands:
12998 \begin_layout Plain Layout
13016 \begin_layout Plain Layout
13034 \begin_layout Plain Layout
13045 \begin_layout Standard
13052 a box can be super- or subscripted.
13053 But in contrary to normal super- and subscripting, the characters in the
13054 box keep their font size.
13061 is used in the following scheme:
13064 \begin_layout Standard
13069 raisebox{height}{box content}
13072 \begin_layout Standard
13073 When the box should contain a formula, an extra formula is needed like for
13083 \begin_layout Standard
13085 \begin_inset Tabular
13086 <lyxtabular version="3" rows="4" columns="2">
13088 <column alignment="center" valignment="top" width="0">
13089 <column alignment="center" valignment="top" width="0">
13091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13094 \begin_layout Plain Layout
13100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13103 \begin_layout Plain Layout
13111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13114 \begin_layout Plain Layout
13118 \begin_inset Formula $\to$
13124 \begin_inset Formula $\to$
13132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13135 \begin_layout Plain Layout
13136 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13149 \begin_layout Plain Layout
13153 \begin_inset Formula $\to$
13159 \begin_inset Formula $\to$
13167 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13170 \begin_layout Plain Layout
13171 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13181 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13184 \begin_layout Plain Layout
13188 \begin_inset Formula $\to$
13203 \begin_layout Plain Layout
13217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13220 \begin_layout Plain Layout
13224 \begin_layout Plain Layout
13248 \begin_layout Standard
13249 The last formula can currently only be created using TeX-mode because LyX
13250 inserts a box instead of the needed extra formula.
13254 \begin_layout Plain Layout
13256 \begin_inset CommandInset href
13258 name "LyX-bug #1435"
13259 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13271 \begin_layout Standard
13296 , with the difference that there is no frame.
13299 \begin_layout Subsection
13301 \begin_inset CommandInset label
13303 name "sub:Colored-Boxes"
13311 \begin_layout Plain Layout
13320 \begin_layout Standard
13321 To be able to use all commands explained in this section, the LaTeX-package
13330 \begin_layout Plain Layout
13335 is part of every LaTeX standard installation.
13344 \begin_layout Plain Layout
13350 has to be loaded in the LaTeX-preamble with the line
13354 \begin_layout Plain Layout
13355 When text is colored somewhere in the document with a predefined color,
13356 LyX loads the LaTeX-package
13361 Thus it is possible that the package is loaded twice, but this doesn't
13368 \begin_inset Note Note
13371 \begin_layout Plain Layout
13372 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13381 \begin_layout Standard
13389 \begin_layout Standard
13390 \begin_inset VSpace medskip
13393 To color boxes, the command
13403 \begin_layout Plain Layout
13411 is used in the following scheme:
13414 \begin_layout Standard
13419 colorbox{color}{box content}
13422 \begin_layout Standard
13423 The box content can also be a box and a
13429 can also be part of another box (see the 2nd and 3rd example).
13430 When the box should contain a formula, an extra formula has to be created,
13441 \begin_layout Plain Layout
13442 This also applies for the command
13450 \begin_inset CommandInset href
13452 name "LyX-bug #1435"
13453 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13465 \begin_layout Standard
13466 One of the following predefined colors can be chosen:
13469 \begin_layout Standard
13503 \begin_layout Standard
13505 \begin_inset Tabular
13506 <lyxtabular version="3" rows="4" columns="2">
13508 <column alignment="center" valignment="top" width="0">
13509 <column alignment="center" valignment="top" width="0">
13511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13514 \begin_layout Plain Layout
13520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13523 \begin_layout Plain Layout
13525 \begin_inset Note Note
13528 \begin_layout Plain Layout
13535 is only used as spacer.
13547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13550 \begin_layout Plain Layout
13554 \begin_inset Formula $\to$
13564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13567 \begin_layout Plain Layout
13568 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13581 \begin_layout Plain Layout
13585 \begin_inset Formula $\to$
13596 \begin_layout Plain Layout
13610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13613 \begin_layout Plain Layout
13614 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13627 \begin_layout Plain Layout
13634 \begin_layout Plain Layout
13646 \begin_inset Formula $\to$
13656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13659 \begin_layout Plain Layout
13660 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13676 \begin_layout Standard
13683 only colors the box but not the characters in the box.
13684 To color all characters, the whole formula is highlighted and the wanted
13685 color is chosen in the
13688 \begin_inset space ~
13694 The dialog can be called with the toolbar button
13695 \begin_inset Graphics
13696 filename ../images/dialog-show_character.png
13703 Edit\SpecialChar \menuseparator
13705 \begin_inset space ~
13708 Style\SpecialChar \menuseparator
13712 The formula number has then the same color as the formula.
13713 When the formula number should get another color than the formula characters,
13714 the color must be changed within the formula.
13717 \begin_layout Standard
13721 \begin_layout Standard
13724 \begin_inset Formula \begin{equation}
13725 \int A=B\label{eq:red}\end{equation}
13732 \begin_inset Formula \begin{equation}
13733 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13740 \begin_layout Standard
13742 \begin_inset CommandInset ref
13748 is completely colored red.
13749 \begin_inset Newline newline
13753 \begin_inset CommandInset ref
13755 reference "eq:redgreen"
13759 was first completely colored green to set the color for the formula number.
13760 Subsequently the formula characters were colored red.
13763 \begin_layout Standard
13764 \begin_inset VSpace bigskip
13767 To color the frame different than the rest of the box, the command
13777 \begin_layout Plain Layout
13785 is used in the following scheme:
13788 \begin_layout Standard
13793 fcolorbox{frame color}{color}{box content}
13796 \begin_layout Standard
13803 is an extension of the command
13810 The frame width is set, like for
13833 \begin_layout Plain Layout
13845 \begin_inset Formula \[
13846 \fcolorbox{cyan}{magenta}{A=B}\]
13854 \begin_layout Plain Layout
13868 \begin_layout Standard
13869 This formula was created with the command
13870 \begin_inset Newline newline
13878 \begin_inset Formula $\to$
13884 \begin_inset Formula $\to$
13894 \begin_layout Standard
13895 \begin_inset VSpace bigskip
13898 To use other colors than the predefined ones, they have to be defined first.
13901 \begin_layout Standard
13902 One can for example define the color
13903 \begin_inset Quotes eld
13911 \begin_inset Quotes erd
13914 with the LaTeX-preamble line:
13917 \begin_layout Standard
13922 definecolor{darkgreen}{cmyk}{0.5,
13940 \begin_layout Plain Layout
13951 \begin_layout Standard
13956 is the color space that denotes the colors
13973 The four comma separated numbers are the portion factor for the corresponding
13974 colors of the color space.
13975 The factors can be in the range of 0
13976 \begin_inset space \thinspace{}
13980 \begin_inset space \thinspace{}
13988 also the color space
13992 can be used for definitions.
14009 , so that there are in this case three portion factors for the corresponding
14011 Furthermore there is the color space
14015 with one portion factor for the gray value.
14018 \begin_layout Standard
14019 As example a framed box with the new defined color
14023 where the characters have been colored
14028 \begin_inset Formula \begin{equation}
14029 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14036 \begin_layout Standard
14037 Self-defined colors can also be used for text with the help of the command
14048 \begin_layout Plain Layout
14057 \begin_layout Standard
14061 \begin_layout Plain Layout
14065 textcolor{darkgreen}{
14071 \begin_inset Quotes eld
14075 \begin_inset Quotes erd
14082 \begin_layout Plain Layout
14092 \begin_layout Standard
14103 \begin_layout Plain Layout
14111 is used in the scheme
14115 textcolor{color}{characters to color}
14120 \begin_layout Subsection
14122 \begin_inset CommandInset label
14124 name "sub:Paragraph-Boxes"
14132 \begin_layout Plain Layout
14133 Boxes ! as paragraph
14141 \begin_layout Standard
14142 A box that can contain several lines and paragraphs, a so called paragraph
14143 box (parbox), can be created with the menu
14145 Insert\SpecialChar \menuseparator
14148 or the toolbar button
14149 \begin_inset Graphics
14150 filename ../images/box-insert.png
14158 \begin_layout Standard
14159 The following example shows a framed parbox in a line:
14162 \begin_layout Standard
14163 \begin_inset VSpace medskip
14167 \begin_inset Box Boxed
14176 height_special "totalheight"
14179 \begin_layout Plain Layout
14180 This is a paragraph box.
14182 \begin_inset space \thinspace{}
14185 cm long and can also contain formulas:
14186 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14197 \begin_layout Standard
14198 \begin_inset VSpace medskip
14204 \begin_layout Standard
14205 Such a box is created by right-clicking on the gray box inset.
14206 A dialog pops up showing the box properties.
14220 \begin_inset space \thinspace{}
14225 Vertical Box Alignment
14230 \begin_layout Standard
14231 \begin_inset VSpace medskip
14234 In LaTeX a parbox is created with the command
14244 \begin_layout Plain Layout
14252 that has the following scheme:
14255 \begin_layout Standard
14260 parbox[position]{width}{box content}
14263 \begin_layout Standard
14277 for bottom means that the box is aligned within the surrounding text with
14283 for top this is done with the first line.
14284 When no position is given, the box will be vertically centered, see section
14292 \begin_inset space ~
14297 manual for examples.
14300 \begin_layout Standard
14301 \begin_inset VSpace bigskip
14304 To frame formulas completely, including the formula number, the formula
14305 must be set into a parbox.
14306 To do this, the command
14320 is inserted in TeX-mode before the formula.
14329 \begin_layout Plain Layout
14339 is hereby the line width set for the document.
14340 Because the frame is outside the parbox, 2
14341 \begin_inset space \thinspace{}
14344 times the frame separation and the frame thickness must be subtracted from
14346 As this is not automatically done by LyX due to a bug
14350 \begin_layout Plain Layout
14351 \begin_inset CommandInset href
14353 name "LyX-bug #4483"
14354 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14363 , TeX-mode has to be used.
14364 To be able to multiply and subtract in arguments, the LaTeX-package
14372 \begin_layout Plain Layout
14377 is part of every LaTeX standard installation.
14386 \begin_layout Plain Layout
14392 must be loaded in the LaTeX-preamble with the line
14395 \begin_layout Standard
14403 \begin_layout Standard
14404 Behind the formula both boxes are closed by entering
14409 Here is an example:
14413 \begin_layout Plain Layout
14427 \begin_layout Standard
14431 \begin_layout Plain Layout
14449 \begin_inset Formula \begin{equation}
14450 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14458 \begin_layout Plain Layout
14469 \begin_layout Plain Layout
14483 \begin_layout Standard
14484 \begin_inset VSpace medskip
14487 As a parbox is used as argument of
14493 , there is in this case no difference between
14508 \begin_layout Standard
14509 \begin_inset VSpace bigskip
14512 Paragraph boxes are very useful to comment formulas directly.
14519 is used in combination with the command
14533 \begin_inset CommandInset ref
14535 reference "sub:User-defined-Numbering"
14542 \begin_layout Standard
14543 An example of a formula commented with
14552 \begin_layout Standard
14556 \begin_layout Plain Layout
14569 This is a description.
14570 It is distinctly separated from the formula and multiline.
14574 \begin_layout Plain Layout
14586 \begin_layout Standard
14587 Such a formula must be inserted completely in TeX-mode because LyX does
14588 not yet support the command
14595 The formula is created with the following command sequence:
14598 \begin_layout Standard
14611 is inserted in TeX-mode.
14615 \begin_layout Plain Layout
14616 When the formula style
14628 can also be replaced by
14635 (formula styles see
14636 \begin_inset CommandInset ref
14638 reference "sec:Formula-Styles"
14647 Then the description follows as normal text, and finally
14653 is inserted in TeX-mode.
14666 hereby create a displayed formula.
14669 \begin_layout Standard
14676 can be seen in this example that was
14677 \begin_inset Quotes eld
14681 \begin_inset Quotes erd
14684 using the mathematical textmode:
14685 \begin_inset Formula \[
14686 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14693 \begin_layout Section
14698 \begin_layout Plain Layout
14707 \begin_layout Subsection
14709 \begin_inset CommandInset label
14711 name "sub:Big-Operators"
14719 \begin_layout Plain Layout
14729 \begin_layout Plain Layout
14739 \begin_layout Plain Layout
14748 \begin_layout Standard
14749 To be able to use all integral operators listed here, the option
14751 Use esint package automatically
14753 must be set in the document settings under
14756 \begin_inset space ~
14764 \begin_layout Standard
14765 \begin_inset space \hfill{}
14769 \begin_inset Tabular
14770 <lyxtabular version="3" rows="11" columns="2">
14772 <column alignment="center" valignment="top" width="0pt">
14773 <column alignment="center" valignment="top" width="0pt">
14775 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14778 \begin_layout Plain Layout
14784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14787 \begin_layout Plain Layout
14795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14798 \begin_layout Plain Layout
14805 \begin_layout Plain Layout
14818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14821 \begin_layout Plain Layout
14822 \begin_inset Formula $\sum$
14832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14835 \begin_layout Plain Layout
14842 \begin_layout Plain Layout
14855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14858 \begin_layout Plain Layout
14859 \begin_inset Formula $\int$
14869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14872 \begin_layout Plain Layout
14880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14883 \begin_layout Plain Layout
14884 \begin_inset Formula $\intop$
14894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14897 \begin_layout Plain Layout
14905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14908 \begin_layout Plain Layout
14909 \begin_inset Formula $\oint$
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14922 \begin_layout Plain Layout
14930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14933 \begin_layout Plain Layout
14934 \begin_inset Formula $\ointop$
14944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14947 \begin_layout Plain Layout
14955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14958 \begin_layout Plain Layout
14959 \begin_inset Formula $\ointctrclockwise$
14969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14972 \begin_layout Plain Layout
14980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14983 \begin_layout Plain Layout
14984 \begin_inset Formula $\ointclockwise$
14994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14997 \begin_layout Plain Layout
15005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15008 \begin_layout Plain Layout
15009 \begin_inset Formula $\sqint$
15019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15022 \begin_layout Plain Layout
15030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15033 \begin_layout Plain Layout
15034 \begin_inset Formula $\bigcap$
15044 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15047 \begin_layout Plain Layout
15055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15058 \begin_layout Plain Layout
15059 \begin_inset Formula $\bigcup$
15073 \begin_inset space \hfill{}
15077 \begin_inset Tabular
15078 <lyxtabular version="3" rows="10" columns="2">
15080 <column alignment="center" valignment="top" width="0pt">
15081 <column alignment="center" valignment="top" width="0pt">
15083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15086 \begin_layout Plain Layout
15092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15095 \begin_layout Plain Layout
15103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15106 \begin_layout Plain Layout
15113 \begin_layout Plain Layout
15126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15129 \begin_layout Plain Layout
15130 \begin_inset Formula $\prod$
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15143 \begin_layout Plain Layout
15151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15154 \begin_layout Plain Layout
15155 \begin_inset Formula $\coprod$
15165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15168 \begin_layout Plain Layout
15176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15179 \begin_layout Plain Layout
15180 \begin_inset Formula $\bigodot$
15190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15193 \begin_layout Plain Layout
15201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15204 \begin_layout Plain Layout
15205 \begin_inset Formula $\bigotimes$
15215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15218 \begin_layout Plain Layout
15226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15229 \begin_layout Plain Layout
15230 \begin_inset Formula $\bigoplus$
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15243 \begin_layout Plain Layout
15251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15254 \begin_layout Plain Layout
15255 \begin_inset Formula $\bigwedge$
15265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15268 \begin_layout Plain Layout
15276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15279 \begin_layout Plain Layout
15280 \begin_inset Formula $\bigvee$
15290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15293 \begin_layout Plain Layout
15301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15304 \begin_layout Plain Layout
15305 \begin_inset Formula $\bigsqcup$
15315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15318 \begin_layout Plain Layout
15326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15329 \begin_layout Plain Layout
15330 \begin_inset Formula $\biguplus$
15344 \begin_inset space \hfill{}
15350 \begin_layout Standard
15351 All big operators can also be inserted via the math toolbar button
15352 \begin_inset Graphics
15353 filename ../images/math/intop.png
15361 \begin_layout Standard
15362 The operators are called big because they are bigger than the sometimes
15363 equal looking binary operators.
15364 All big operators can have limits as described in the next subsection.
15367 \begin_layout Standard
15393 \begin_inset space ~
15396 in the style the operator limits are displayed, see
15397 \begin_inset CommandInset ref
15399 reference "sub:Operator-Limits"
15407 \begin_layout Subsubsection*
15408 Advices for Integrals
15411 \begin_layout Standard
15416 in an integral is an operator, that therefore has to be set upright.
15417 This is done by highlighting the
15421 and using the keyboard shortcut
15431 \begin_layout Plain Layout
15437 \begin_inset CommandInset ref
15439 reference "sub:Font-Styles"
15449 Finally the smallest space is inserted before the
15453 , as this is usual for operators.
15457 \begin_layout Standard
15459 \begin_inset Formula $\int A(x)dx$
15463 \begin_inset Newline newline
15470 \begin_layout Plain Layout
15480 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15486 \begin_layout Standard
15487 For multiple integrals there are the following commands:
15488 \begin_inset VSpace medskip
15494 \begin_layout Standard
15495 \begin_inset space \hfill{}
15499 \begin_inset Tabular
15500 <lyxtabular version="3" rows="4" columns="2">
15502 <column alignment="center" valignment="top" width="0">
15503 <column alignment="center" valignment="top" width="0">
15505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15508 \begin_layout Plain Layout
15514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15517 \begin_layout Plain Layout
15519 \begin_inset Note Note
15522 \begin_layout Plain Layout
15529 is only used as spacer.
15541 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15544 \begin_layout Plain Layout
15552 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15555 \begin_layout Plain Layout
15556 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15569 \begin_layout Plain Layout
15577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15580 \begin_layout Plain Layout
15581 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15594 \begin_layout Plain Layout
15602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15605 \begin_layout Plain Layout
15606 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15620 \begin_inset space \hfill{}
15624 \begin_inset Tabular
15625 <lyxtabular version="3" rows="4" columns="2">
15627 <column alignment="center" valignment="top" width="0">
15628 <column alignment="center" valignment="top" width="0">
15630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15633 \begin_layout Plain Layout
15639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15642 \begin_layout Plain Layout
15650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15653 \begin_layout Plain Layout
15661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15664 \begin_layout Plain Layout
15665 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15678 \begin_layout Plain Layout
15686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15689 \begin_layout Plain Layout
15690 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15700 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15703 \begin_layout Plain Layout
15711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15714 \begin_layout Plain Layout
15715 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15729 \begin_inset space \hfill{}
15735 \begin_layout Subsection
15737 \begin_inset CommandInset label
15739 name "sub:Operator-Limits"
15747 \begin_layout Plain Layout
15756 \begin_layout Standard
15757 Limits are created by super- and subscripts:
15760 \begin_layout Standard
15762 \begin_inset Tabular
15763 <lyxtabular version="3" rows="2" columns="2">
15765 <column alignment="center" valignment="top" width="0pt">
15766 <column alignment="center" valignment="top" width="0pt">
15768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15771 \begin_layout Plain Layout
15777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15780 \begin_layout Plain Layout
15782 \begin_inset Note Note
15785 \begin_layout Plain Layout
15792 is only used as spacer.
15804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15807 \begin_layout Plain Layout
15816 \begin_layout Plain Layout
15826 \begin_inset Formula $\to$
15830 \begin_inset Formula $\to$
15838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15841 \begin_layout Plain Layout
15842 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15858 \begin_layout Standard
15859 Limits of inline formulas are set right beside the operator.
15860 Limits in displayed formulas are set above or below the operator, except
15861 of integral limits.
15864 \begin_layout Standard
15865 To force that the limits are set beside the operator, the cursor is set
15866 directly behind the operator and the limits type is changed with the menu
15869 Edit\SpecialChar \menuseparator
15870 Math\SpecialChar \menuseparator
15889 \begin_layout Standard
15890 The default limits type is this:
15891 \begin_inset Formula \[
15892 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15896 This is how it looks when the limits type was changed to
15903 \begin_inset Formula \[
15904 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15908 For integrals, except of
15920 , the limits are by default set beside the operator.
15921 But for multiple integrals the limits are often set below the operator.
15922 In the following example the limits type was therefore set to
15926 and so set below the integrals:
15927 \begin_inset Formula \begin{equation}
15928 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15935 \begin_layout Standard
15936 \begin_inset VSpace medskip
15939 To specify conditions for limits, the commands
15949 \begin_layout Plain Layout
15967 \begin_layout Plain Layout
15976 To create for example this expression
15977 \begin_inset Formula \begin{equation}
15978 \sum_{\begin{subarray}{c}
15980 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15987 \begin_layout Standard
15988 the following has to be done:
15989 \begin_inset Newline newline
16004 \begin_layout Plain Layout
16016 One is now in a blue box under the summation operator and insert there
16025 \begin_layout Plain Layout
16037 The blue box is now within a purple box and now several lines can be written
16039 A new line is created by inserting a line break (
16042 arg "newline-insert newline"
16047 \begin_inset Newline newline
16052 0<k<1000 Ctrl+Return
16053 \begin_inset Newline newline
16058 is typed in, a new box appears below for the new line.
16061 \begin_layout Standard
16062 The alignment of the lines can be changed to left aligned with the
16072 Edit\SpecialChar \menuseparator
16076 To get right alignment,
16084 \begin_layout Plain Layout
16095 is inserted at the beginning of the line.
16098 \begin_layout Standard
16111 with the difference that the lines are always centered.
16114 \begin_layout Standard
16115 \begin_inset VSpace bigskip
16119 \begin_inset CommandInset ref
16121 reference "eq:substack"
16125 there can be too much space beside an operator, because the characters
16126 following the operator are set beside the limits.
16129 \begin_layout Standard
16130 To avoid this, the following macro can be used in the LaTeX-preamble:
16133 \begin_layout Standard
16147 \begin_inset Newline newline
16159 \begin_inset Newline newline
16166 mathclapinternal #1#2{
16170 mathsurround =0pt #1{#2}$}}
16173 \begin_layout Standard
16174 This defines the command
16184 \begin_layout Plain Layout
16192 that sets the width of the limit to 0
16193 \begin_inset space \thinspace{}
16197 The command scheme is
16200 \begin_layout Standard
16208 \begin_layout Standard
16209 where the limit can consist of several conditions.
16212 \begin_layout Standard
16214 \begin_inset CommandInset ref
16216 reference "eq:substack"
16220 , one uses the command
16223 \begin_layout Standard
16236 \begin_layout Plain Layout
16245 0<k<1000 Ctrl+Return
16248 \begin_layout Standard
16249 to create the lower limit.
16250 The summand is now directly behind the summation operator:
16251 \begin_inset Formula \[
16252 \sum_{\mathclap{\substack{0<k<1000\\
16253 \\k\,\in\,\mathbb{N}}
16261 \begin_layout Standard
16262 \begin_inset VSpace bigskip
16265 How to use one limit for several operators is described in
16266 \begin_inset CommandInset ref
16268 reference "sub:Self-defined-Operators"
16275 \begin_layout Standard
16276 \begin_inset Newpage newpage
16282 \begin_layout Subsection
16284 \begin_inset CommandInset label
16286 name "sub:Binary-Operators"
16294 \begin_layout Plain Layout
16303 \begin_layout Standard
16304 Binary operators are surrounded by space when there is a character before
16306 \begin_inset VSpace medskip
16312 \begin_layout Standard
16313 \begin_inset space \hfill{}
16317 \begin_inset Tabular
16318 <lyxtabular version="3" rows="13" columns="2">
16320 <column alignment="center" valignment="top" width="0pt">
16321 <column alignment="center" valignment="top" width="0pt">
16323 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16326 \begin_layout Plain Layout
16328 \begin_inset Note Note
16331 \begin_layout Plain Layout
16338 is only used as spacer.
16348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16351 \begin_layout Plain Layout
16359 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16362 \begin_layout Plain Layout
16368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16371 \begin_layout Plain Layout
16372 \begin_inset Formula $+$
16382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16385 \begin_layout Plain Layout
16391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16394 \begin_layout Plain Layout
16395 \begin_inset Formula $-$
16405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16408 \begin_layout Plain Layout
16416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16419 \begin_layout Plain Layout
16420 \begin_inset Formula $\pm$
16430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16433 \begin_layout Plain Layout
16441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16444 \begin_layout Plain Layout
16445 \begin_inset Formula $\mp$
16455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16458 \begin_layout Plain Layout
16466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16469 \begin_layout Plain Layout
16470 \begin_inset Formula $\cdot$
16480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16483 \begin_layout Plain Layout
16491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16494 \begin_layout Plain Layout
16495 \begin_inset Formula $\times$
16505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16508 \begin_layout Plain Layout
16516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16519 \begin_layout Plain Layout
16520 \begin_inset Formula $\div$
16530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16533 \begin_layout Plain Layout
16537 \begin_layout Plain Layout
16550 \begin_layout Plain Layout
16562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16565 \begin_layout Plain Layout
16566 \begin_inset Formula $*$
16576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16579 \begin_layout Plain Layout
16587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16590 \begin_layout Plain Layout
16591 \begin_inset Formula $\star$
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16604 \begin_layout Plain Layout
16612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16615 \begin_layout Plain Layout
16616 \begin_inset Formula $\circ$
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16629 \begin_layout Plain Layout
16637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16640 \begin_layout Plain Layout
16641 \begin_inset Formula $\diamond$
16651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16654 \begin_layout Plain Layout
16662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16665 \begin_layout Plain Layout
16666 \begin_inset Formula $\bullet$
16680 \begin_inset space \hfill{}
16684 \begin_inset Tabular
16685 <lyxtabular version="3" rows="13" columns="2">
16687 <column alignment="center" valignment="top" width="0pt">
16688 <column alignment="center" valignment="top" width="0pt">
16690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16693 \begin_layout Plain Layout
16699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16702 \begin_layout Plain Layout
16710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16713 \begin_layout Plain Layout
16721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16724 \begin_layout Plain Layout
16725 \begin_inset Formula $\nabla$
16735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16738 \begin_layout Plain Layout
16746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16749 \begin_layout Plain Layout
16750 \begin_inset Formula $\bigtriangledown$
16760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16763 \begin_layout Plain Layout
16771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16774 \begin_layout Plain Layout
16775 \begin_inset Formula $\bigtriangleup$
16785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16788 \begin_layout Plain Layout
16796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16799 \begin_layout Plain Layout
16800 \begin_inset Formula $\Box$
16810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16813 \begin_layout Plain Layout
16821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16824 \begin_layout Plain Layout
16825 \begin_inset Formula $\cap$
16835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16838 \begin_layout Plain Layout
16846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16849 \begin_layout Plain Layout
16850 \begin_inset Formula $\cup$
16860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16863 \begin_layout Plain Layout
16871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16874 \begin_layout Plain Layout
16875 \begin_inset Formula $\dagger$
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16888 \begin_layout Plain Layout
16896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16899 \begin_layout Plain Layout
16900 \begin_inset Formula $\ddagger$
16910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16913 \begin_layout Plain Layout
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16924 \begin_layout Plain Layout
16925 \begin_inset Formula $\wr$
16935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16938 \begin_layout Plain Layout
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16949 \begin_layout Plain Layout
16950 \begin_inset Formula $\bigcirc$
16960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16963 \begin_layout Plain Layout
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16974 \begin_layout Plain Layout
16975 \begin_inset Formula $\wedge$
16985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16988 \begin_layout Plain Layout
16996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16999 \begin_layout Plain Layout
17000 \begin_inset Formula $\vee$
17014 \begin_inset space \hfill{}
17018 \begin_inset Tabular
17019 <lyxtabular version="3" rows="13" columns="2">
17021 <column alignment="center" valignment="top" width="0pt">
17022 <column alignment="center" valignment="top" width="0pt">
17024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17027 \begin_layout Plain Layout
17033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17036 \begin_layout Plain Layout
17044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17047 \begin_layout Plain Layout
17055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17058 \begin_layout Plain Layout
17059 \begin_inset Formula $\oplus$
17069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17072 \begin_layout Plain Layout
17080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17083 \begin_layout Plain Layout
17084 \begin_inset Formula $\ominus$
17094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17097 \begin_layout Plain Layout
17105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17108 \begin_layout Plain Layout
17109 \begin_inset Formula $\otimes$
17119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17122 \begin_layout Plain Layout
17130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17133 \begin_layout Plain Layout
17134 \begin_inset Formula $\oslash$
17144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17147 \begin_layout Plain Layout
17155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17158 \begin_layout Plain Layout
17159 \begin_inset Formula $\odot$
17169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17172 \begin_layout Plain Layout
17180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17183 \begin_layout Plain Layout
17184 \begin_inset Formula $\amalg$
17194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17197 \begin_layout Plain Layout
17205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17208 \begin_layout Plain Layout
17209 \begin_inset Formula $\uplus$
17219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17222 \begin_layout Plain Layout
17230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17233 \begin_layout Plain Layout
17234 \begin_inset Formula $\setminus$
17244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17247 \begin_layout Plain Layout
17255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17258 \begin_layout Plain Layout
17259 \begin_inset Formula $\sqcap$
17269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17272 \begin_layout Plain Layout
17280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17283 \begin_layout Plain Layout
17284 \begin_inset Formula $\sqcup$
17294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17297 \begin_layout Plain Layout
17305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17308 \begin_layout Plain Layout
17309 \begin_inset Formula $\triangleleft$
17319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17322 \begin_layout Plain Layout
17330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17333 \begin_layout Plain Layout
17334 \begin_inset Formula $\triangleright$
17348 \begin_inset space \hfill{}
17354 \begin_layout Standard
17355 All binary operators can also be inserted via the math toolbar button
17356 \begin_inset Graphics
17357 filename ../images/math/pm.png
17365 \begin_layout Standard
17366 To typeset the Laplace operator also
17383 \begin_inset Formula $\nabla^{2}$
17386 ) can be used instead of
17395 \begin_layout Standard
17402 Insert\SpecialChar \menuseparator
17414 \begin_layout Subsection
17415 Self-defined Operators
17416 \begin_inset CommandInset label
17418 name "sub:Self-defined-Operators"
17426 \begin_layout Plain Layout
17427 Operators ! self-defined
17435 \begin_layout Standard
17436 With the help of the command
17440 DeclareMathOperator
17446 \begin_layout Plain Layout
17451 DeclareMathOperator
17456 custom operators can be defined in the LaTeX-preamble.
17457 Its command scheme is:
17460 \begin_layout Standard
17465 DeclareMathOperator{new command}{display}
17468 \begin_layout Standard
17469 Display can be characters or symbols that define how the operator looks
17471 To define a big operator a * is set behind the command.
17472 All self-defined big operators can have limits as described in
17473 \begin_inset CommandInset ref
17475 reference "sub:Operator-Limits"
17482 \begin_layout Standard
17483 For example the LaTeX-preamble line
17486 \begin_layout Standard
17491 DeclareMathOperator*{
17498 \begin_layout Standard
17499 defines the command
17505 , that inserts a big operator consisting of the lozenge symbol from
17506 \begin_inset CommandInset ref
17508 reference "sub:Miscellaneous-Symbols"
17513 \begin_inset Formula \[
17514 \Lozenge_{n=1}^{\infty}\]
17518 The command for this formula is:
17529 \begin_inset Formula $\to$
17535 \begin_layout Standard
17536 \begin_inset VSpace bigskip
17539 When self-defined operators are not used several times in the document,
17540 they can also be defined with the commands
17550 \begin_layout Plain Layout
17568 \begin_layout Plain Layout
17576 , which have the following scheme:
17579 \begin_layout Standard
17593 \begin_layout Standard
17600 defines big operators,
17609 \begin_layout Standard
17617 \begin_inset space \space{}
17620 be used to use one limit for several operators:
17623 \begin_layout Standard
17624 \begin_inset Formula \[
17625 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17632 \begin_layout Standard
17633 The command for the formula above is:
17634 \begin_inset Newline newline
17653 \begin_layout Plain Layout
17665 \begin_inset Formula $\to$
17674 \begin_layout Plain Layout
17688 \begin_layout Section
17693 \begin_layout Plain Layout
17702 \begin_layout Subsection
17704 \begin_inset CommandInset label
17706 name "sub:Font-Styles"
17714 \begin_layout Plain Layout
17723 \begin_layout Standard
17724 Latin letters in formulas can be set in one of the following font styles:
17725 \begin_inset VSpace -2mm
17731 \begin_layout Standard
17733 \begin_inset Tabular
17734 <lyxtabular version="3" rows="6" columns="3">
17736 <column alignment="center" valignment="top" width="0">
17737 <column alignment="center" valignment="top" width="0">
17738 <column alignment="center" valignment="top" width="0">
17740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17743 \begin_layout Plain Layout
17749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17752 \begin_layout Plain Layout
17758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17761 \begin_layout Plain Layout
17769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17772 \begin_layout Plain Layout
17781 \begin_layout Plain Layout
17797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17800 \begin_layout Plain Layout
17801 \begin_inset Formula $\mathbb{ABC}$
17809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17812 \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 $\mathbf{AbC}$
17865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17868 \begin_layout Plain Layout
17881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17884 \begin_layout Plain Layout
17893 \begin_layout Plain Layout
17909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17912 \begin_layout Plain Layout
17913 \begin_inset Formula $\boldsymbol{AbC}$
17921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17924 \begin_layout Plain Layout
17927 arg "font-boldsymbol"
17937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17940 \begin_layout Plain Layout
17949 \begin_layout Plain Layout
17965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17968 \begin_layout Plain Layout
17969 \begin_inset Formula $\mathcal{ABC}$
17977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17980 \begin_layout Plain Layout
17993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17996 \begin_layout Plain Layout
18005 \begin_layout Plain Layout
18021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18024 \begin_layout Plain Layout
18025 \begin_inset Formula $\mathfrak{AbC}$
18033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18036 \begin_layout Plain Layout
18050 \begin_layout Standard
18052 \begin_inset Tabular
18053 <lyxtabular version="3" rows="5" columns="3">
18055 <column alignment="center" valignment="top" width="0">
18056 <column alignment="center" valignment="top" width="0">
18057 <column alignment="center" valignment="top" width="0">
18059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18062 \begin_layout Plain Layout
18068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18071 \begin_layout Plain Layout
18077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18080 \begin_layout Plain Layout
18088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18091 \begin_layout Plain Layout
18100 \begin_layout Plain Layout
18116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18119 \begin_layout Plain Layout
18120 \begin_inset Formula $\mathit{AbC}$
18128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18131 \begin_layout Plain Layout
18139 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18142 \begin_layout Plain Layout
18151 \begin_layout Plain Layout
18167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18170 \begin_layout Plain Layout
18171 \begin_inset Formula $\mathrm{AbC}$
18179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18182 \begin_layout Plain Layout
18195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18198 \begin_layout Plain Layout
18207 \begin_layout Plain Layout
18223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18226 \begin_layout Plain Layout
18227 \begin_inset Formula $\mathsf{AbC}$
18235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18238 \begin_layout Plain Layout
18251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18254 \begin_layout Plain Layout
18263 \begin_layout Plain Layout
18279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18282 \begin_layout Plain Layout
18283 \begin_inset Formula $\mathtt{AbC}$
18291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18294 \begin_layout Plain Layout
18297 arg "font-typewriter"
18313 \begin_layout Standard
18314 \begin_inset Note Greyedout
18317 \begin_layout Plain Layout
18334 can only be used for big letters.
18342 \begin_layout Standard
18343 Predefined is the style
18352 \begin_layout Standard
18353 The style commands work also for letters in mathematical constructs:
18354 \begin_inset Formula \[
18355 \mathfrak{A=\frac{b}{C}}\]
18362 \begin_layout Standard
18363 Characters in mathematical text don't appear in a math font style but in
18364 the text font style
18371 That their style can't be set correctly via the text style dialog is a
18376 \begin_layout Plain Layout
18377 \begin_inset CommandInset href
18379 name "LyX-bug #4091"
18380 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18392 \begin_layout Standard
18393 Instead of the style commands the dialog
18395 Edit\SpecialChar \menuseparator
18396 Math\SpecialChar \menuseparator
18399 or the toolbar button
18400 \begin_inset Graphics
18401 filename ../images/math/font.png
18409 \begin_layout Subsection
18411 \begin_inset CommandInset label
18413 name "sub:Bold-Formulas"
18421 \begin_layout Plain Layout
18430 \begin_layout Standard
18431 To make a complete formula bold, the command
18437 from the previous subsection cannot be used, because it doesn't work for
18438 small Greek letters.
18439 Furthermore it prints Latin letters always upright, like in the following
18443 \begin_layout Standard
18444 \begin_inset Formula \[
18445 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18452 \begin_layout Standard
18453 To display the formula correctly, the command
18460 \begin_inset Formula \[
18461 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18465 It is also possible to set the formula in a
18467 boldmath environment
18470 This environment is created by inserting the command
18478 \begin_layout Plain Layout
18489 To end the environment, the command
18497 \begin_layout Plain Layout
18507 is inserted in TeX-mode.
18511 \begin_layout Plain Layout
18521 \begin_inset Formula \[
18522 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18530 \begin_layout Plain Layout
18542 \begin_layout Subsection
18547 \begin_layout Plain Layout
18556 \begin_layout Standard
18557 Formulas can be colored like normal text: Highlight a formula or a formula
18563 Here is a formula in magenta:
18564 \begin_inset Formula \[
18565 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18572 \begin_layout Standard
18573 You can also define your own colors as described in
18574 \begin_inset CommandInset ref
18576 reference "sub:Colored-Boxes"
18581 They can be used with the TeX code command
18591 \begin_layout Plain Layout
18602 \begin_layout Standard
18607 textcolor{color}{characters or formula}
18610 \begin_layout Standard
18611 The following example was colored completely dark green and partly red:
18614 \begin_layout Standard
18618 \begin_layout Plain Layout
18622 textcolor{darkgreen}{
18628 \begin_inset Formula \[
18629 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18637 \begin_layout Plain Layout
18647 \begin_layout Standard
18648 Due to a bug in LyX only complete formulas can be colored with self-defined
18653 \begin_layout Plain Layout
18654 \begin_inset CommandInset href
18656 name "LyX-bug #5269"
18657 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18669 \begin_layout Subsection
18671 \begin_inset CommandInset label
18673 name "sub:Font-Sizes"
18681 \begin_layout Plain Layout
18690 \begin_layout Standard
18691 For characters in formulas there are, analog to characters in text, the
18692 following size commands:
18695 \begin_layout Standard
18739 \begin_inset Newline newline
18761 \begin_layout Standard
18762 The size produced by the commands depends on the document font size, that
18763 corresponds with the command
18770 The other commands produce smaller or larger sizes than
18777 The font size can however not exceed a certain value.
18778 Is for example the document font size 12
18779 \begin_inset space \thinspace{}
18788 switches to the same size as
18798 \begin_layout Standard
18799 A size command is inserted in TeX-mode before the formula and sets the size
18800 for all following formula and text characters.
18801 To switch back to the initial size, the command
18807 is inserted behind the formula in TeX-mode.
18810 \begin_layout Standard
18811 Within a formula the size can only be changed for symbols or letters in
18813 To do this, the size command is inserted in mathematical text.
18814 All following characters until the end of the mathematical text or until
18815 another size command will have the selected size.
18817 \begin_inset VSpace -2mm
18823 \begin_layout Standard
18827 \begin_layout Plain Layout
18837 \begin_inset Formula \[
18838 A=\frac{B}{c}\cdot\maltese\]
18843 \begin_inset Formula \[
18844 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18852 \begin_layout Plain Layout
18864 \begin_layout Standard
18865 \begin_inset VSpace medskip
18868 Before both formulas the command
18875 The command for the second formula is:
18876 \begin_inset Newline newline
18887 \begin_layout Plain Layout
18902 \begin_layout Plain Layout
18917 \begin_layout Plain Layout
18932 \begin_layout Plain Layout
18942 \begin_inset Formula $\to$
18946 \begin_inset Formula $\to$
18950 \begin_inset Newline newline
18954 \begin_inset space \hspace*{}
18968 \begin_layout Plain Layout
18983 \begin_layout Plain Layout
18998 \begin_layout Plain Layout
19010 \begin_layout Standard
19011 If a symbol cannot be displayed in different sizes, it will always be displayed
19012 in the default size.
19015 \begin_layout Section
19020 \begin_layout Plain Layout
19029 \begin_layout Standard
19030 All Greek letters can also be inserted via the toolbar button
19031 \begin_inset Graphics
19032 filename ../images/math/alpha.png
19040 \begin_layout Subsection
19045 \begin_layout Plain Layout
19046 Greek letters ! small
19054 \begin_layout Standard
19055 \begin_inset space \hfill{}
19059 \begin_inset Tabular
19060 <lyxtabular version="3" rows="11" columns="2">
19062 <column alignment="center" valignment="top" width="0pt">
19063 <column alignment="center" valignment="top" width="0pt">
19065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19068 \begin_layout Plain Layout
19074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19077 \begin_layout Plain Layout
19085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19088 \begin_layout Plain Layout
19096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19099 \begin_layout Plain Layout
19100 \begin_inset Formula $\alpha$
19110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19113 \begin_layout Plain Layout
19121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19124 \begin_layout Plain Layout
19125 \begin_inset Formula $\beta$
19135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19138 \begin_layout Plain Layout
19146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19149 \begin_layout Plain Layout
19150 \begin_inset Formula $\gamma$
19160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19163 \begin_layout Plain Layout
19171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19174 \begin_layout Plain Layout
19175 \begin_inset Formula $\delta$
19185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19188 \begin_layout Plain Layout
19196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19199 \begin_layout Plain Layout
19200 \begin_inset Formula $\epsilon$
19210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19213 \begin_layout Plain Layout
19221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19224 \begin_layout Plain Layout
19225 \begin_inset Formula $\varepsilon$
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19238 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula $\zeta$
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula $\eta$
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\theta$
19310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $\vartheta$
19339 \begin_inset space \hfill{}
19343 \begin_inset Tabular
19344 <lyxtabular version="3" rows="12" columns="2">
19346 <column alignment="center" valignment="top" width="0pt">
19347 <column alignment="center" valignment="top" width="0pt">
19349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19352 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19372 \begin_layout Plain Layout
19380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19383 \begin_layout Plain Layout
19384 \begin_inset Formula $\iota$
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19397 \begin_layout Plain Layout
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19408 \begin_layout Plain Layout
19409 \begin_inset Formula $\kappa$
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19422 \begin_layout Plain Layout
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19433 \begin_layout Plain Layout
19434 \begin_inset Formula $\varkappa$
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19447 \begin_layout Plain Layout
19455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19458 \begin_layout Plain Layout
19459 \begin_inset Formula $\lambda$
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19472 \begin_layout Plain Layout
19480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19483 \begin_layout Plain Layout
19484 \begin_inset Formula $\mu$
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19497 \begin_layout Plain Layout
19505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19508 \begin_layout Plain Layout
19509 \begin_inset Formula $\nu$
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19522 \begin_layout Plain Layout
19530 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19533 \begin_layout Plain Layout
19534 \begin_inset Formula $\xi$
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19547 \begin_layout Plain Layout
19553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19556 \begin_layout Plain Layout
19557 \begin_inset Formula $o$
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19570 \begin_layout Plain Layout
19578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19581 \begin_layout Plain Layout
19582 \begin_inset Formula $\pi$
19592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19595 \begin_layout Plain Layout
19603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19606 \begin_layout Plain Layout
19607 \begin_inset Formula $\varpi$
19617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19620 \begin_layout Plain Layout
19628 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19631 \begin_layout Plain Layout
19632 \begin_inset Formula $\rho$
19646 \begin_inset space \hfill{}
19650 \begin_inset Tabular
19651 <lyxtabular version="3" rows="11" columns="2">
19653 <column alignment="center" valignment="top" width="0pt">
19654 <column alignment="center" valignment="top" width="0pt">
19656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19659 \begin_layout Plain Layout
19665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19668 \begin_layout Plain Layout
19676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19679 \begin_layout Plain Layout
19687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19690 \begin_layout Plain Layout
19691 \begin_inset Formula $\varrho$
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19704 \begin_layout Plain Layout
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19715 \begin_layout Plain Layout
19716 \begin_inset Formula $\sigma$
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19729 \begin_layout Plain Layout
19737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19740 \begin_layout Plain Layout
19741 \begin_inset Formula $\varsigma$
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19754 \begin_layout Plain Layout
19762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19765 \begin_layout Plain Layout
19766 \begin_inset Formula $\tau$
19776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19779 \begin_layout Plain Layout
19787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19790 \begin_layout Plain Layout
19791 \begin_inset Formula $\upsilon$
19801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19804 \begin_layout Plain Layout
19812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19815 \begin_layout Plain Layout
19816 \begin_inset Formula $\phi$
19826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19829 \begin_layout Plain Layout
19837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19840 \begin_layout Plain Layout
19841 \begin_inset Formula $\varphi$
19851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19854 \begin_layout Plain Layout
19862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19865 \begin_layout Plain Layout
19866 \begin_inset Formula $\chi$
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19879 \begin_layout Plain Layout
19887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19890 \begin_layout Plain Layout
19891 \begin_inset Formula $\psi$
19901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19904 \begin_layout Plain Layout
19912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19915 \begin_layout Plain Layout
19916 \begin_inset Formula $\omega$
19930 \begin_inset space \hfill{}
19936 \begin_layout Standard
19937 \begin_inset VSpace medskip
19943 \begin_layout Standard
19944 How to create upright Greek letters is explained in
19945 \begin_inset CommandInset ref
19947 reference "sub:Upright-small-Greek"
19954 \begin_layout Subsection
19959 \begin_layout Plain Layout
19960 Greek letters ! big
19968 \begin_layout Standard
19969 \begin_inset space \hfill{}
19973 \begin_inset Tabular
19974 <lyxtabular version="3" rows="7" columns="2">
19976 <column alignment="center" valignment="top" width="0pt">
19977 <column alignment="center" valignment="top" width="0pt">
19979 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19982 \begin_layout Plain Layout
19988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20013 \begin_layout Plain Layout
20014 \begin_inset Formula $\Gamma$
20024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20038 \begin_layout Plain Layout
20039 \begin_inset Formula $\Delta$
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\Theta$
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20077 \begin_layout Plain Layout
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20088 \begin_layout Plain Layout
20089 \begin_inset Formula $\Lambda$
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20102 \begin_layout Plain Layout
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20113 \begin_layout Plain Layout
20114 \begin_inset Formula $\Xi$
20124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20127 \begin_layout Plain Layout
20135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20138 \begin_layout Plain Layout
20139 \begin_inset Formula $\Pi$
20153 \begin_inset space \hfill{}
20157 \begin_inset Tabular
20158 <lyxtabular version="3" rows="6" columns="2">
20160 <column alignment="center" valignment="top" width="0pt">
20161 <column alignment="center" valignment="top" width="0pt">
20163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20166 \begin_layout Plain Layout
20172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20175 \begin_layout Plain Layout
20183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20186 \begin_layout Plain Layout
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20197 \begin_layout Plain Layout
20198 \begin_inset Formula $\Sigma$
20208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20211 \begin_layout Plain Layout
20219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20222 \begin_layout Plain Layout
20223 \begin_inset Formula $\Upsilon$
20233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20236 \begin_layout Plain Layout
20244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20247 \begin_layout Plain Layout
20248 \begin_inset Formula $\Phi$
20258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20261 \begin_layout Plain Layout
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20272 \begin_layout Plain Layout
20273 \begin_inset Formula $\Psi$
20283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20286 \begin_layout Plain Layout
20294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20297 \begin_layout Plain Layout
20298 \begin_inset Formula $\Omega$
20312 \begin_inset space \hfill{}
20318 \begin_layout Standard
20319 \begin_inset VSpace medskip
20322 That the big Greek letters appear upright is caused by a design bug when
20324 To get correct italic big letters, begin every command with
20329 For example the command
20336 \begin_inset Formula $\varGamma$
20342 \begin_layout Subsection
20347 \begin_layout Plain Layout
20348 Greek letters ! bold
20356 \begin_layout Standard
20357 Greek letters cannot be set with different font styles like Latin letters.
20358 They can only be made bold with the command
20368 \begin_layout Plain Layout
20379 \begin_layout Standard
20381 \begin_inset Tabular
20382 <lyxtabular version="3" rows="3" columns="2">
20384 <column alignment="center" valignment="top" width="0">
20385 <column alignment="center" valignment="top" width="0">
20387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20390 \begin_layout Plain Layout
20396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20399 \begin_layout Plain Layout
20407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20410 \begin_layout Plain Layout
20422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20425 \begin_layout Plain Layout
20426 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20439 \begin_layout Plain Layout
20451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20454 \begin_layout Plain Layout
20455 \begin_inset Formula $\theta\boldsymbol{\theta}$
20471 \begin_layout Section
20476 \begin_layout Plain Layout
20489 \begin_layout Plain Layout
20490 A list with all symbols of most of the LaTeX-packages can be found in
20491 \begin_inset CommandInset citation
20506 \begin_layout Plain Layout
20514 \begin_inset Note Note
20517 \begin_layout Plain Layout
20520 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20523 \begin_layout Plain Layout
20526 texorpdfstring is in section
20527 \begin_inset CommandInset ref
20529 reference "sub:Formulas-in-Section"
20542 \begin_layout Plain Layout
20551 \begin_layout Standard
20552 Many of the symbols listed in this section can also be inserted via the
20554 \begin_inset Graphics
20555 filename ../images/math/nabla.png
20561 \begin_inset Graphics
20562 filename ../images/math/digamma.png
20570 \begin_layout Subsection
20571 Mathematical Symbols
20572 \begin_inset CommandInset label
20574 name "sub:Mathematical-Symbols"
20582 \begin_layout Plain Layout
20583 Symbols ! mathematical
20591 \begin_layout Standard
20592 \begin_inset space \hfill{}
20596 \begin_inset Tabular
20597 <lyxtabular version="3" rows="10" columns="2">
20599 <column alignment="center" valignment="top" width="0pt">
20600 <column alignment="center" valignment="top" width="0pt">
20602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20605 \begin_layout Plain Layout
20611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20614 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20625 \begin_layout Plain Layout
20633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20636 \begin_layout Plain Layout
20637 \begin_inset Formula $\neg$
20647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20661 \begin_layout Plain Layout
20662 \begin_inset Formula $\Im$
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Re$
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\aleph$
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\partial$
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\infty$
20772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\wp$
20797 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20800 \begin_layout Plain Layout
20808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20811 \begin_layout Plain Layout
20812 \begin_inset Formula $\imath$
20822 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20825 \begin_layout Plain Layout
20833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20836 \begin_layout Plain Layout
20837 \begin_inset Formula $\jmath$
20851 \begin_inset space \hfill{}
20855 \begin_inset Tabular
20856 <lyxtabular version="3" rows="10" columns="2">
20858 <column alignment="center" valignment="top" width="0pt">
20859 <column alignment="center" valignment="top" width="0pt">
20861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20873 \begin_layout Plain Layout
20875 \begin_inset Note Note
20878 \begin_layout Plain Layout
20885 is only used as spacer.
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20911 \begin_layout Plain Layout
20912 \begin_inset Formula $\forall$
20922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20925 \begin_layout Plain Layout
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20936 \begin_layout Plain Layout
20937 \begin_inset Formula $\exists$
20947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20950 \begin_layout Plain Layout
20958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20961 \begin_layout Plain Layout
20962 \begin_inset Formula $\nexists$
20972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20975 \begin_layout Plain Layout
20983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20986 \begin_layout Plain Layout
20987 \begin_inset Formula $\emptyset$
20997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21000 \begin_layout Plain Layout
21008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21011 \begin_layout Plain Layout
21012 \begin_inset Formula $\varnothing$
21022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21025 \begin_layout Plain Layout
21033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21036 \begin_layout Plain Layout
21037 \begin_inset Formula $\dag$
21047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21050 \begin_layout Plain Layout
21058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21061 \begin_layout Plain Layout
21062 \begin_inset Formula $\ddag$
21072 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21075 \begin_layout Plain Layout
21083 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21086 \begin_layout Plain Layout
21090 \begin_layout Plain Layout
21100 \begin_inset Formula $\complement$
21107 \begin_layout Plain Layout
21121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21124 \begin_layout Plain Layout
21132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21135 \begin_layout Plain Layout
21136 \begin_inset Formula $\Bbbk$
21150 \begin_inset space \hfill{}
21154 \begin_inset Tabular
21155 <lyxtabular version="3" rows="10" columns="2">
21157 <column alignment="center" valignment="top" width="0pt">
21158 <column alignment="center" valignment="top" width="0pt">
21160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21163 \begin_layout Plain Layout
21169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21183 \begin_layout Plain Layout
21191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21194 \begin_layout Plain Layout
21195 \begin_inset Formula $\prime$
21205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21208 \begin_layout Plain Layout
21216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21219 \begin_layout Plain Layout
21220 \begin_inset Formula $\backprime$
21230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21233 \begin_layout Plain Layout
21241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21244 \begin_layout Plain Layout
21245 \begin_inset Formula $\mho$
21255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21258 \begin_layout Plain Layout
21266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21269 \begin_layout Plain Layout
21270 \begin_inset Formula $\triangle$
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21283 \begin_layout Plain Layout
21291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21294 \begin_layout Plain Layout
21295 \begin_inset Formula $\angle$
21305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21308 \begin_layout Plain Layout
21316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21319 \begin_layout Plain Layout
21320 \begin_inset Formula $\measuredangle$
21330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21333 \begin_layout Plain Layout
21341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21344 \begin_layout Plain Layout
21345 \begin_inset Formula $\sphericalangle$
21355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21358 \begin_layout Plain Layout
21366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21369 \begin_layout Plain Layout
21370 \begin_inset Formula $\top$
21380 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21383 \begin_layout Plain Layout
21391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21394 \begin_layout Plain Layout
21395 \begin_inset Formula $\bot$
21409 \begin_inset space \hfill{}
21415 \begin_layout Subsection
21416 Miscellaneous Symbols
21417 \begin_inset CommandInset label
21419 name "sub:Miscellaneous-Symbols"
21427 \begin_layout Plain Layout
21428 Symbols ! miscellaneous
21436 \begin_layout Standard
21439 \begin_inset Tabular
21440 <lyxtabular version="3" rows="10" columns="2">
21442 <column alignment="center" valignment="top" width="0pt">
21443 <column alignment="center" valignment="top" width="0pt">
21445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21448 \begin_layout Plain Layout
21454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21457 \begin_layout Plain Layout
21465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21468 \begin_layout Plain Layout
21476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21479 \begin_layout Plain Layout
21480 \begin_inset Formula $\flat$
21490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21504 \begin_layout Plain Layout
21505 \begin_inset Formula $\natural$
21515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21518 \begin_layout Plain Layout
21526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21529 \begin_layout Plain Layout
21530 \begin_inset Formula $\sharp$
21540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21543 \begin_layout Plain Layout
21551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21554 \begin_layout Plain Layout
21555 \begin_inset Formula $\surd$
21565 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21568 \begin_layout Plain Layout
21576 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21579 \begin_layout Plain Layout
21580 \begin_inset Formula $\checkmark$
21590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21593 \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 $\yen$
21615 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21618 \begin_layout Plain Layout
21626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21629 \begin_layout Plain Layout
21630 \begin_inset Formula $\pounds$
21640 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21643 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21653 \begin_inset Formula $\$$
21663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21666 \begin_layout Plain Layout
21672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21675 \begin_layout Plain Layout
21676 \begin_inset Formula $§$
21690 \begin_inset Tabular
21691 <lyxtabular version="3" rows="10" columns="2">
21693 <column alignment="center" valignment="top" width="0">
21694 <column alignment="center" valignment="top" width="0">
21696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21708 \begin_layout Plain Layout
21716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21719 \begin_layout Plain Layout
21727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21730 \begin_layout Plain Layout
21731 \begin_inset Formula $\hbar$
21741 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21744 \begin_layout Plain Layout
21752 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21755 \begin_layout Plain Layout
21756 \begin_inset Formula $\hslash$
21766 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21769 \begin_layout Plain Layout
21777 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21780 \begin_layout Plain Layout
21781 \begin_inset Formula $\clubsuit$
21791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21794 \begin_layout Plain Layout
21802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21805 \begin_layout Plain Layout
21806 \begin_inset Formula $\spadesuit$
21816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21819 \begin_layout Plain Layout
21827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21830 \begin_layout Plain Layout
21831 \begin_inset Formula $\bigstar$
21841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21844 \begin_layout Plain Layout
21852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21855 \begin_layout Plain Layout
21856 \begin_inset Formula $\blacklozenge$
21866 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21869 \begin_layout Plain Layout
21877 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21880 \begin_layout Plain Layout
21881 \begin_inset Formula $\blacktriangle$
21891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21894 \begin_layout Plain Layout
21902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21905 \begin_layout Plain Layout
21906 \begin_inset Formula $\blacktriangledown$
21916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21919 \begin_layout Plain Layout
21927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21930 \begin_layout Plain Layout
21931 \begin_inset Formula $\bullet$
21945 \begin_inset Tabular
21946 <lyxtabular version="3" rows="10" columns="2">
21948 <column alignment="center" valignment="top" width="0pt">
21949 <column alignment="center" valignment="top" width="0pt">
21951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21954 \begin_layout Plain Layout
21960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21963 \begin_layout Plain Layout
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\diamondsuit$
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\Diamond$
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\heartsuit$
22046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22049 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22061 \begin_inset Formula $\P$
22071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22074 \begin_layout Plain Layout
22082 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22085 \begin_layout Plain Layout
22086 \begin_inset Formula $\copyright$
22096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22099 \begin_layout Plain Layout
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22110 \begin_layout Plain Layout
22111 \begin_inset Formula $\circledR$
22121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22124 \begin_layout Plain Layout
22132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22135 \begin_layout Plain Layout
22136 \begin_inset Formula $\maltese$
22146 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22149 \begin_layout Plain Layout
22157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22160 \begin_layout Plain Layout
22161 \begin_inset Formula $\diagup$
22171 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22174 \begin_layout Plain Layout
22182 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22185 \begin_layout Plain Layout
22186 \begin_inset Formula $\diagdown$
22202 \begin_layout Standard
22203 \begin_inset VSpace medskip
22206 More symbols are listed in
22207 \begin_inset CommandInset ref
22209 reference "sub:Miscellaneous-special-Characters"
22216 \begin_layout Standard
22217 Some symbols can be displayed in different sizes, see
22218 \begin_inset CommandInset ref
22220 reference "sub:Font-Sizes"
22227 \begin_layout Subsection
22232 \begin_layout Plain Layout
22233 Symbols ! Euro-symbol
22242 \begin_layout Plain Layout
22249 \begin_layout Plain Layout
22266 \begin_layout Standard
22267 To use the Euro symbol in formulas, the LaTeX-package
22275 \begin_layout Plain Layout
22281 must be installed and loaded with the LaTeX-preamble line
22284 \begin_layout Standard
22289 usepackage[gennarrow]{eurosym}
22292 \begin_layout Standard
22293 The Euro symbol can now be inserted with the command
22303 \begin_layout Plain Layout
22314 \begin_layout Standard
22315 The Euro symbol can directly be inserted with the € key in mathematical
22316 text, without having
22331 can also be inserted in TeX-mode.
22332 The official currency symbol can then be inserted with the command
22342 \begin_layout Plain Layout
22350 , that is only available in TeX-mode.
22353 \begin_layout Standard
22357 \begin_layout Plain Layout
22367 \begin_inset Note Note
22370 \begin_layout Plain Layout
22371 The following table will only be displayed when the LaTeX-package
22383 \begin_layout Standard
22384 An overview about the different Euro symbols:
22387 \begin_layout Standard
22389 \begin_inset Tabular
22390 <lyxtabular version="3" rows="4" columns="3">
22392 <column alignment="center" valignment="top" width="0pt">
22393 <column alignment="center" valignment="top" width="0pt">
22394 <column alignment="center" valignment="top" width="0pt">
22396 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22399 \begin_layout Plain Layout
22405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22408 \begin_layout Plain Layout
22414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22417 \begin_layout Plain Layout
22425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22428 \begin_layout Plain Layout
22434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22437 \begin_layout Plain Layout
22445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22448 \begin_layout Plain Layout
22449 \begin_inset Formula $\euro$
22459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22462 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22471 \begin_layout Plain Layout
22477 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22480 \begin_layout Plain Layout
22481 \begin_inset Formula $\mbox{€}$
22491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22494 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22503 \begin_layout Plain Layout
22511 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22514 \begin_layout Plain Layout
22518 \begin_layout Plain Layout
22540 \begin_layout Standard
22544 \begin_layout Plain Layout
22554 \begin_inset Note Note
22557 \begin_layout Plain Layout
22558 The following will be displayed when the LaTeX-package
22570 \begin_layout Standard
22571 You need to install the LaTeX-package
22575 to see the rest of this subsection in the output.
22578 \begin_layout Standard
22582 \begin_layout Plain Layout
22594 \begin_layout Section
22596 \begin_inset CommandInset label
22598 name "sec:Relations"
22606 \begin_layout Plain Layout
22616 \begin_layout Plain Layout
22621 \begin_layout Plain Layout
22632 \begin_layout Plain Layout
22647 \begin_layout Standard
22648 All relations can also be inserted via the toolbar button
22649 \begin_inset Graphics
22650 filename ../images/math/leq.png
22658 \begin_layout Standard
22659 \begin_inset space \hfill{}
22663 \begin_inset Tabular
22664 <lyxtabular version="3" rows="17" columns="2">
22666 <column alignment="center" valignment="top" width="0pt">
22667 <column alignment="center" valignment="top" width="0pt">
22669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22672 \begin_layout Plain Layout
22678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22681 \begin_layout Plain Layout
22689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22692 \begin_layout Plain Layout
22698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22701 \begin_layout Plain Layout
22702 \begin_inset Formula $<$
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\le$
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\ll$
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\prec$
22787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\preceq$
22812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\subset$
22837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22840 \begin_layout Plain Layout
22848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22851 \begin_layout Plain Layout
22852 \begin_inset Formula $\subseteq$
22862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22865 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22876 \begin_layout Plain Layout
22877 \begin_inset Formula $\sqsubseteq$
22887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22901 \begin_layout Plain Layout
22902 \begin_inset Formula $\in$
22912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22926 \begin_layout Plain Layout
22927 \begin_inset Formula $\vdash$
22937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22940 \begin_layout Plain Layout
22948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22951 \begin_layout Plain Layout
22952 \begin_inset Formula $\smile$
22962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22965 \begin_layout Plain Layout
22973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22976 \begin_layout Plain Layout
22977 \begin_inset Formula $\lhd$
22987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22990 \begin_layout Plain Layout
22998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23001 \begin_layout Plain Layout
23002 \begin_inset Formula $\unlhd$
23012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23015 \begin_layout Plain Layout
23023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23026 \begin_layout Plain Layout
23027 \begin_inset Formula $\gtrless$
23037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23040 \begin_layout Plain Layout
23048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23051 \begin_layout Plain Layout
23052 \begin_inset Formula $\mid$
23062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23065 \begin_layout Plain Layout
23073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23076 \begin_layout Plain Layout
23077 \begin_inset Formula $\nmid$
23091 \begin_inset space \hfill{}
23095 \begin_inset Tabular
23096 <lyxtabular version="3" rows="17" columns="2">
23098 <column alignment="center" valignment="top" width="0pt">
23099 <column alignment="center" valignment="top" width="0pt">
23101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23104 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23124 \begin_layout Plain Layout
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23133 \begin_layout Plain Layout
23134 \begin_inset Formula $=$
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23147 \begin_layout Plain Layout
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23158 \begin_layout Plain Layout
23159 \begin_inset Formula $\not=$
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23172 \begin_layout Plain Layout
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23183 \begin_layout Plain Layout
23184 \begin_inset Formula $\equiv$
23194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23197 \begin_layout Plain Layout
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23208 \begin_layout Plain Layout
23209 \begin_inset Formula $\sim$
23219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23222 \begin_layout Plain Layout
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23233 \begin_layout Plain Layout
23234 \begin_inset Formula $\simeq$
23244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23247 \begin_layout Plain Layout
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23258 \begin_layout Plain Layout
23259 \begin_inset Formula $\approx$
23269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23272 \begin_layout Plain Layout
23280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23283 \begin_layout Plain Layout
23284 \begin_inset Formula $\cong$
23294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23297 \begin_layout Plain Layout
23305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23308 \begin_layout Plain Layout
23309 \begin_inset Formula $\bowtie$
23319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23322 \begin_layout Plain Layout
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23333 \begin_layout Plain Layout
23334 \begin_inset Formula $\notin$
23344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23347 \begin_layout Plain Layout
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23358 \begin_layout Plain Layout
23359 \begin_inset Formula $\perp$
23369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23372 \begin_layout Plain Layout
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23383 \begin_layout Plain Layout
23384 \begin_inset Formula $\propto$
23394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23397 \begin_layout Plain Layout
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23408 \begin_layout Plain Layout
23409 \begin_inset Formula $\asymp$
23419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23433 \begin_layout Plain Layout
23434 \begin_inset Formula $\doteq$
23444 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23458 \begin_layout Plain Layout
23459 \begin_inset Formula $\circeq$
23469 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23472 \begin_layout Plain Layout
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23483 \begin_layout Plain Layout
23484 \begin_inset Formula $\models$
23494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23497 \begin_layout Plain Layout
23505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23508 \begin_layout Plain Layout
23509 \begin_inset Formula $\widehat{=}$
23523 \begin_inset space \hfill{}
23527 \begin_inset Tabular
23528 <lyxtabular version="3" rows="17" columns="2">
23530 <column alignment="center" valignment="top" width="0pt">
23531 <column alignment="center" valignment="top" width="0pt">
23533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23536 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23565 \begin_layout Plain Layout
23566 \begin_inset Formula $>$
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23579 \begin_layout Plain Layout
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23590 \begin_layout Plain Layout
23591 \begin_inset Formula $\ge$
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23604 \begin_layout Plain Layout
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23615 \begin_layout Plain Layout
23616 \begin_inset Formula $\gg$
23626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23629 \begin_layout Plain Layout
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23640 \begin_layout Plain Layout
23641 \begin_inset Formula $\succ$
23651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23654 \begin_layout Plain Layout
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23665 \begin_layout Plain Layout
23666 \begin_inset Formula $\succeq$
23676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23679 \begin_layout Plain Layout
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23690 \begin_layout Plain Layout
23691 \begin_inset Formula $\supset$
23701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23704 \begin_layout Plain Layout
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23715 \begin_layout Plain Layout
23716 \begin_inset Formula $\supseteq$
23726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23729 \begin_layout Plain Layout
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23740 \begin_layout Plain Layout
23741 \begin_inset Formula $\sqsupseteq$
23751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23765 \begin_layout Plain Layout
23766 \begin_inset Formula $\ni$
23776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23779 \begin_layout Plain Layout
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23790 \begin_layout Plain Layout
23791 \begin_inset Formula $\dashv$
23801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23804 \begin_layout Plain Layout
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23815 \begin_layout Plain Layout
23816 \begin_inset Formula $\frown$
23826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23829 \begin_layout Plain Layout
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23840 \begin_layout Plain Layout
23841 \begin_inset Formula $\rhd$
23851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23865 \begin_layout Plain Layout
23866 \begin_inset Formula $\unrhd$
23876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23890 \begin_layout Plain Layout
23891 \begin_inset Formula $\lessgtr$
23901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23904 \begin_layout Plain Layout
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23915 \begin_layout Plain Layout
23916 \begin_inset Formula $\parallel$
23926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23929 \begin_layout Plain Layout
23937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23940 \begin_layout Plain Layout
23941 \begin_inset Formula $\nparallel$
23955 \begin_inset space \hfill{}
23961 \begin_layout Standard
23962 \begin_inset VSpace medskip
23977 are bigger than the equal looking operators
23992 \begin_layout Standard
23993 Relations are, in contrary to symbols, always surrounded by space.
23996 \begin_layout Standard
23997 Relations with labels can be created with the command
24007 \begin_layout Plain Layout
24018 \begin_layout Standard
24020 \begin_inset Tabular
24021 <lyxtabular version="3" rows="2" columns="2">
24023 <column alignment="center" valignment="top" width="0">
24024 <column alignment="center" valignment="top" width="0">
24026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24029 \begin_layout Plain Layout
24035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24038 \begin_layout Plain Layout
24040 \begin_inset Note Note
24043 \begin_layout Plain Layout
24050 is only used as spacer.
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24072 \begin_layout Plain Layout
24089 \begin_layout Plain Layout
24099 \begin_inset Formula $\downarrow$
24108 \begin_layout Plain Layout
24121 \begin_layout Plain Layout
24135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24138 \begin_layout Plain Layout
24139 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24155 \begin_layout Section
24159 \begin_layout Subsection
24160 Predefined Functions
24161 \begin_inset CommandInset label
24163 name "sub:Predefined-Functions"
24171 \begin_layout Plain Layout
24172 Functions ! predefined
24180 \begin_layout Standard
24181 In general, variables are set
24185 in mathematical expressions, but not function names, because
24186 \begin_inset Formula $sin$
24189 could be misunderstood as
24190 \begin_inset Formula $s\cdot i\cdot n$
24194 Therefore there are predefined functions, that are additionally a bit separated
24196 They are inserted as commands starting with a backslash before their name.
24199 \begin_layout Standard
24201 \begin_inset Tabular
24202 <lyxtabular version="3" rows="2" columns="4">
24204 <column alignment="center" valignment="top" width="0pt">
24205 <column alignment="center" valignment="top" width="0pt">
24206 <column alignment="center" valignment="top" width="0pt">
24207 <column alignment="center" valignment="top" width="0pt">
24209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24212 \begin_layout Plain Layout
24218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24221 \begin_layout Plain Layout
24227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24230 \begin_layout Plain Layout
24236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24239 \begin_layout Plain Layout
24247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24250 \begin_layout Plain Layout
24256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24259 \begin_layout Plain Layout
24260 \begin_inset Formula $Asin(x)+B$
24268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24271 \begin_layout Plain Layout
24279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24282 \begin_layout Plain Layout
24283 \begin_inset Formula $A\sin(x)+B$
24299 \begin_layout Standard
24300 The following functions are predefined:
24303 \begin_layout Standard
24304 \begin_inset VSpace -2mm
24310 \begin_layout Standard
24312 \begin_inset Tabular
24313 <lyxtabular version="3" rows="9" columns="4">
24315 <column alignment="center" valignment="top" width="0pt">
24316 <column alignment="center" valignment="top" width="0pt">
24317 <column alignment="center" valignment="top" width="0pt">
24318 <column alignment="center" valignment="top" width="0pt">
24320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24323 \begin_layout Plain Layout
24329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24332 \begin_layout Plain Layout
24338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24361 \begin_layout Plain Layout
24369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24394 \begin_layout Plain Layout
24404 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24407 \begin_layout Plain Layout
24415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24418 \begin_layout Plain Layout
24426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24429 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24440 \begin_layout Plain Layout
24450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24453 \begin_layout Plain Layout
24461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24464 \begin_layout Plain Layout
24472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24475 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24486 \begin_layout Plain Layout
24496 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24499 \begin_layout Plain Layout
24507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24510 \begin_layout Plain Layout
24518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24521 \begin_layout Plain Layout
24529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24532 \begin_layout Plain Layout
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24545 \begin_layout Plain Layout
24553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24556 \begin_layout Plain Layout
24564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24567 \begin_layout Plain Layout
24575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24578 \begin_layout Plain Layout
24588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24591 \begin_layout Plain Layout
24599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24602 \begin_layout Plain Layout
24610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24613 \begin_layout Plain Layout
24621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24624 \begin_layout Plain Layout
24634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24637 \begin_layout Plain Layout
24645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24648 \begin_layout Plain Layout
24656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24659 \begin_layout Plain Layout
24667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24670 \begin_layout Plain Layout
24680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24683 \begin_layout Plain Layout
24691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24694 \begin_layout Plain Layout
24702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24705 \begin_layout Plain Layout
24713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24716 \begin_layout Plain Layout
24732 \begin_layout Standard
24733 They can also be inserted with the math toolbar button
24734 \begin_inset Graphics
24735 filename ../images/math/functions.png
24743 \begin_layout Subsection
24744 Self-defined Functions
24748 \begin_layout Plain Layout
24749 Functions ! self-defined
24757 \begin_layout Standard
24758 To use a function that is not predefined, like for example the sign function
24759 sgn(x), there are two possibilities:
24762 \begin_layout Itemize
24763 Define the function by inserting the following line to the LaTeX-preamble
24767 \begin_layout Plain Layout
24772 DeclareMathOperator
24775 \begin_inset CommandInset ref
24777 reference "sub:Self-defined-Operators"
24787 \begin_inset Newline newline
24791 \begin_inset VSpace -3mm
24795 \begin_inset Newline newline
24802 DeclareMathOperator{
24810 \begin_layout Plain Layout
24815 DeclareMathOperator
24821 \begin_inset Newline newline
24825 \begin_inset VSpace -2mm
24829 \begin_inset Newline newline
24832 Now the new defined function can be called with the command
24841 \begin_layout Itemize
24842 Write the the formula as usual, mark the formula name, in our example the
24847 , and change it to mathematical text.
24848 At last a space is inserted between prefactor and function.
24851 \begin_layout Standard
24852 The result is the same with both methods as with a predefined function
24856 \begin_layout Plain Layout
24857 In LyX self-defined functions are displayed red, predefined ones black.
24865 \begin_layout Standard
24867 \begin_inset Tabular
24868 <lyxtabular version="3" rows="3" columns="2">
24870 <column alignment="center" valignment="top" width="0pt">
24871 <column alignment="center" valignment="top" width="0pt">
24873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24876 \begin_layout Plain Layout
24882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24885 \begin_layout Plain Layout
24893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24896 \begin_layout Plain Layout
24904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24907 \begin_layout Plain Layout
24908 \begin_inset Formula $A\sgn(x)+B$
24918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24921 \begin_layout Plain Layout
24925 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24936 \begin_layout Plain Layout
24937 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24953 \begin_layout Standard
24954 The first method is more suitable when the self-defined function should
24955 be used several times.
24958 \begin_layout Subsection
24963 \begin_layout Plain Layout
24972 \begin_layout Standard
24973 For limits there are defined besides
24983 \begin_layout Plain Layout
25003 furthermore the following functions:
25006 \begin_layout Standard
25008 \begin_inset Tabular
25009 <lyxtabular version="3" rows="5" columns="2">
25011 <column alignment="center" valignment="top" width="0">
25012 <column alignment="center" valignment="top" width="0">
25014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25017 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25026 \begin_layout Plain Layout
25028 \begin_inset Note Note
25031 \begin_layout Plain Layout
25038 is only used as spacer.
25050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25053 \begin_layout Plain Layout
25061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25064 \begin_layout Plain Layout
25065 \begin_inset Formula $\varliminf$
25075 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25089 \begin_layout Plain Layout
25090 \begin_inset Formula $\varlimsup$
25100 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25111 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25114 \begin_layout Plain Layout
25115 \begin_inset Formula $\varprojlim$
25125 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25128 \begin_layout Plain Layout
25136 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25139 \begin_layout Plain Layout
25140 \begin_inset Formula $\varinjlim$
25144 \begin_inset Formula $\raisebox{-2.5mm}{}$
25160 \begin_layout Standard
25161 \begin_inset VSpace medskip
25164 The limit is created by inserting a subscript.
25165 It is set right beside the function in an inline formula:
25168 \begin_layout Standard
25170 \begin_inset Tabular
25171 <lyxtabular version="3" rows="2" columns="2">
25173 <column alignment="center" valignment="top" width="0pt">
25174 <column alignment="center" valignment="top" width="0pt">
25176 <cell alignment="center" valignment="top" usebox="none">
25179 \begin_layout Plain Layout
25185 <cell alignment="center" valignment="top" usebox="none">
25188 \begin_layout Plain Layout
25189 \begin_inset space \hspace{}
25194 \begin_inset Note Note
25197 \begin_layout Plain Layout
25210 are used here as spacer.
25222 <cell alignment="center" valignment="top" usebox="none">
25225 \begin_layout Plain Layout
25234 \begin_layout Plain Layout
25247 \begin_layout Plain Layout
25261 <cell alignment="center" valignment="top" usebox="none">
25264 \begin_layout Plain Layout
25265 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25281 \begin_layout Standard
25282 In a displayed formula the limit is set below the formula, as usual:
25283 \begin_inset Formula \[
25291 \begin_layout Subsection
25296 \begin_layout Plain Layout
25297 Functions ! modulo-
25305 \begin_layout Standard
25306 The modulo-function is special, because it exists in four variants.
25309 \begin_layout Standard
25310 The variants in a displayed formula:
25311 \begin_inset Formula \begin{align*}
25312 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25313 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25314 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25315 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25316 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25323 \begin_layout Standard
25324 In an inline formula less space is set before the function names for all
25328 \begin_layout Section
25333 \begin_layout Plain Layout
25342 \begin_layout Subsection
25343 Special Characters in Mathematical Text
25346 \begin_layout Standard
25347 The following commands can only be used in mathematical text or in TeX-mode:
25350 \begin_layout Standard
25351 \begin_inset space \hfill{}
25355 \begin_inset Tabular
25356 <lyxtabular version="3" rows="8" columns="2">
25358 <column alignment="block" valignment="top" width="0">
25359 <column alignment="block" valignment="top" width="0">
25361 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25373 \begin_layout Plain Layout
25381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25395 \begin_layout Plain Layout
25396 \begin_inset Formula $\textrm{œ}$
25406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25409 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25420 \begin_layout Plain Layout
25421 \begin_inset Formula $\textrm{Œ}$
25431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25434 \begin_layout Plain Layout
25442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25445 \begin_layout Plain Layout
25446 \begin_inset Formula $\textrm{æ}$
25456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25459 \begin_layout Plain Layout
25467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25470 \begin_layout Plain Layout
25471 \begin_inset Formula $\textrm{Æ}$
25481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25484 \begin_layout Plain Layout
25492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25495 \begin_layout Plain Layout
25496 \begin_inset Formula $\textrm{\aa}$
25506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25509 \begin_layout Plain Layout
25516 \begin_layout Plain Layout
25523 \begin_layout Plain Layout
25544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25547 \begin_layout Plain Layout
25548 \begin_inset Formula $\textrm{Å}$
25558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25561 \begin_layout Plain Layout
25569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25572 \begin_layout Plain Layout
25573 \begin_inset Formula $\textrm{ı}$
25587 \begin_inset space \hfill{}
25591 \begin_inset Tabular
25592 <lyxtabular version="3" rows="8" columns="2">
25594 <column alignment="block" valignment="top" width="0">
25595 <column alignment="center" valignment="top" width="0">
25597 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25600 \begin_layout Plain Layout
25602 \begin_inset Note Note
25605 \begin_layout Plain Layout
25612 is used for separation, because otherwise the output will be ¡ and ¿ respective
25623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25626 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25637 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25648 \begin_layout Plain Layout
25649 \begin_inset Formula $\textrm{ø}$
25659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25662 \begin_layout Plain Layout
25670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25673 \begin_layout Plain Layout
25674 \begin_inset Formula $\textrm{Ø}$
25684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25687 \begin_layout Plain Layout
25695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25698 \begin_layout Plain Layout
25699 \begin_inset Formula $\textrm{ł}$
25709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25712 \begin_layout Plain Layout
25720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25723 \begin_layout Plain Layout
25724 \begin_inset Formula $\textrm{Ł}$
25734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25737 \begin_layout Plain Layout
25739 \begin_inset space \hspace{}
25747 \begin_layout Plain Layout
25761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25764 \begin_layout Plain Layout
25765 \begin_inset Formula $\textrm{!`}$
25775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25778 \begin_layout Plain Layout
25780 \begin_inset space \hspace{}
25788 \begin_layout Plain Layout
25802 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25805 \begin_layout Plain Layout
25806 \begin_inset Formula $\textrm{?`}$
25816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25819 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25830 \begin_layout Plain Layout
25831 \begin_inset Formula $\textrm{ȷ}$
25845 \begin_inset space \hfill{}
25851 \begin_layout Standard
25853 \begin_inset Formula $\textrm{\textrm{Å}}$
25857 \begin_inset Formula $\textrm{\textrm{Ø}}$
25860 can also be inserted via the math toolbar button
25861 \begin_inset Graphics
25862 filename ../images/math/digamma.png
25870 \begin_layout Standard
25871 An exception are the commands
25874 \begin_inset space \hspace{}
25883 \begin_inset space \hspace{}
25889 , because they can be inserted in LyX directly to text.
25892 \begin_layout Subsection
25894 \begin_inset CommandInset label
25896 name "sub:Accents-in-Text"
25904 \begin_layout Plain Layout
25913 \begin_layout Standard
25914 With the following commands all letters can be accented.
25915 The commands must be inserted in TeX-mode.
25918 \begin_layout Standard
25919 \begin_inset space \hfill{}
25923 \begin_inset Tabular
25924 <lyxtabular version="3" rows="8" columns="2">
25926 <column alignment="block" valignment="top" width="0">
25927 <column alignment="block" valignment="top" width="0">
25929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25932 \begin_layout Plain Layout
25938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25941 \begin_layout Plain Layout
25949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25952 \begin_layout Plain Layout
25956 \begin_inset Quotes grd
25964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25971 \begin_layout Plain Layout
25987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25990 \begin_layout Plain Layout
25998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26001 \begin_layout Plain Layout
26005 \begin_layout Plain Layout
26021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26024 \begin_layout Plain Layout
26031 \begin_layout Plain Layout
26045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26048 \begin_layout Plain Layout
26052 \begin_layout Plain Layout
26068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26071 \begin_layout Plain Layout
26079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26082 \begin_layout Plain Layout
26086 \begin_layout Plain Layout
26102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26105 \begin_layout Plain Layout
26112 \begin_layout Plain Layout
26126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26133 \begin_layout Plain Layout
26149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26159 \begin_layout Plain Layout
26173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26176 \begin_layout Plain Layout
26180 \begin_layout Plain Layout
26196 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26199 \begin_layout Plain Layout
26206 \begin_layout Plain Layout
26220 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26223 \begin_layout Plain Layout
26227 \begin_layout Plain Layout
26247 \begin_inset space \hfill{}
26251 \begin_inset Tabular
26252 <lyxtabular version="3" rows="8" columns="2">
26254 <column alignment="block" valignment="top" width="0">
26255 <column alignment="center" valignment="top" width="0">
26257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26260 \begin_layout Plain Layout
26266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26269 \begin_layout Plain Layout
26277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26280 \begin_layout Plain Layout
26287 \begin_layout Plain Layout
26301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26304 \begin_layout Plain Layout
26308 \begin_layout Plain Layout
26324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26327 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26342 \begin_layout Plain Layout
26358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26361 \begin_layout Plain Layout
26368 \begin_layout Plain Layout
26379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26382 \begin_layout Plain Layout
26386 \begin_layout Plain Layout
26402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26405 \begin_layout Plain Layout
26413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26416 \begin_layout Plain Layout
26420 \begin_layout Plain Layout
26436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26439 \begin_layout Plain Layout
26446 \begin_layout Plain Layout
26460 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26463 \begin_layout Plain Layout
26467 \begin_layout Plain Layout
26483 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26486 \begin_layout Plain Layout
26493 \begin_layout Plain Layout
26507 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26510 \begin_layout Plain Layout
26514 \begin_layout Plain Layout
26530 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26533 \begin_layout Plain Layout
26540 \begin_layout Plain Layout
26554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26557 \begin_layout Plain Layout
26561 \begin_layout Plain Layout
26581 \begin_inset space \hfill{}
26587 \begin_layout Standard
26588 \begin_inset VSpace medskip
26597 also two different characters can be accented.
26606 \begin_layout Plain Layout
26621 \begin_layout Plain Layout
26633 \begin_layout Standard
26646 can in combination with vowels directly be inserted with the keyboard without
26648 The same applies for the tilde
26652 \begin_layout Plain Layout
26653 This only applies for keyboards where the tilde is defined as accent.
26662 in combination with
26677 \begin_layout Standard
26720 , and accents inserted directly with the keyboard are also available in
26722 For the other accents there are special math commands to be used in formulas,
26724 \begin_inset CommandInset ref
26726 reference "sub:Accents-for-one"
26733 \begin_layout Standard
26734 \begin_inset VSpace bigskip
26737 Furthermore, with the command
26747 \begin_layout Plain Layout
26755 all numbers and letters can be set into a circle, quasi accented with a
26756 circle, similar to the the copyright symbol.
26759 \begin_layout Standard
26761 \begin_inset Tabular
26762 <lyxtabular version="3" rows="3" columns="2">
26764 <column alignment="center" valignment="top" width="0">
26765 <column alignment="center" valignment="top" width="0">
26767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26770 \begin_layout Plain Layout
26776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26779 \begin_layout Plain Layout
26781 \begin_inset Note Note
26784 \begin_layout Plain Layout
26791 is only used as spacer.
26803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26806 \begin_layout Plain Layout
26814 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26817 \begin_layout Plain Layout
26821 \begin_layout Plain Layout
26837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26840 \begin_layout Plain Layout
26851 raisebox{-1.5pt}{W}}
26856 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26859 \begin_layout Plain Layout
26860 \begin_inset Formula $\raisebox{4.5mm}{}$
26867 \begin_layout Plain Layout
26885 \begin_inset Formula $\raisebox{-2mm}{}$
26901 \begin_layout Standard
26902 One has to take care that the character fits in the circle.
26913 \begin_layout Plain Layout
26915 \begin_inset CommandInset ref
26917 reference "sub:Font-Sizes"
26926 specifies thereby the size of the circle.
26937 \begin_layout Plain Layout
26939 \begin_inset CommandInset ref
26941 reference "sub:Boxes-without-Frame"
26950 the character can be centered.
26953 \begin_layout Subsection
26958 \begin_layout Plain Layout
26967 \begin_layout Standard
26968 Minuscule numbers are created with the command
26978 \begin_layout Plain Layout
26987 The command can be used in formulas and in TeX-mode.
26988 The command scheme is:
26991 \begin_layout Standard
26996 oldstylenums{number}
26999 \begin_layout Standard
27004 oldstylenums{0123456789
27007 \begin_inset Formula $\oldstylenums{0123456789}$
27013 \begin_layout Subsection
27014 Miscellaneous special Characters
27015 \begin_inset CommandInset label
27017 name "sub:Miscellaneous-special-Characters"
27025 \begin_layout Plain Layout
27026 Special characters ! miscellaneous
27034 \begin_layout Standard
27035 The following characters can only be inserted to formulas by using commands:
27038 \begin_layout Standard
27040 \begin_inset Tabular
27041 <lyxtabular version="3" rows="4" columns="2">
27043 <column alignment="center" valignment="top" width="0">
27044 <column alignment="center" valignment="top" width="0">
27046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27049 \begin_layout Plain Layout
27055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27058 \begin_layout Plain Layout
27066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27069 \begin_layout Plain Layout
27076 \begin_layout Plain Layout
27090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27093 \begin_layout Plain Layout
27094 \begin_inset Formula $\mathcircumflex$
27104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27107 \begin_layout Plain Layout
27115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27118 \begin_layout Plain Layout
27119 \begin_inset Formula $\_$
27129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27132 \begin_layout Plain Layout
27137 \begin_layout Plain Layout
27152 \begin_layout Plain Layout
27165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27168 \begin_layout Plain Layout
27169 \begin_inset Formula $^{\circ}$
27185 \begin_layout Standard
27186 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27187 contains the following line
27191 \begin_layout Plain Layout
27192 More about this is described in
27193 \begin_inset CommandInset ref
27195 reference "sub:Text-Characters-in"
27207 \begin_layout Standard
27212 DeclareInputtext{176}{
27225 \begin_layout Section
27227 \begin_inset CommandInset label
27229 name "sec:Formula-Styles"
27237 \begin_layout Plain Layout
27246 \begin_layout Itemize
27247 There are two different alignment styles:
27251 \begin_layout Description
27252 Centered is the predefined standard
27255 \begin_layout Description
27256 Indented for this the option
27260 must be inserted in the menu
27262 Document\SpecialChar \menuseparator
27268 \begin_inset space ~
27274 \begin_layout Standard
27279 is used, the indentation can be adjusted with the length
27289 \begin_layout Plain Layout
27298 Should the distance be 15
27299 \begin_inset space \thinspace{}
27302 mm, the following command line is inserted in the LaTeX-preamble
27305 \begin_layout Standard
27315 \begin_layout Standard
27316 When no length is specified, the predefined value of 30
27317 \begin_inset space \thinspace{}
27324 \begin_layout Itemize
27325 And two different numbering styles:
27329 \begin_layout Description
27330 Right is the predefined standard
27333 \begin_layout Description
27334 Left for this the option
27338 must be inserted in the menu
27340 Document\SpecialChar \menuseparator
27346 \begin_inset space ~
27353 \begin_layout Standard
27362 can also be used together.
27363 In this case both options are inserted, separated by a comma.
27366 \begin_layout Standard
27367 The chosen styles are used for all displayed formulas of the document.
27368 When both, centered and indented formulas should be created in a document,
27374 The indented formulas are then set in a flalign environment, see
27375 \begin_inset CommandInset ref
27377 reference "sub:Flalign-Environment"
27384 \begin_layout Section
27386 \begin_inset CommandInset label
27388 name "sec:Multiline-Formulas"
27396 \begin_layout Plain Layout
27397 Formula ! multiline
27405 \begin_layout Subsection
27409 \begin_layout Standard
27410 In LyX multiline formulas are created by pressing
27415 arg "newline-insert newline"
27421 This creates either an
27423 eqnarray environment
27425 that is described in
27426 \begin_inset CommandInset ref
27428 reference "sub:Eqnarray-Environment"
27432 or, when the option
27434 Use AMS math package
27436 in the document settings is selected, an
27440 that is described in
27441 \begin_inset CommandInset ref
27443 reference "sub:Standard-align-Environment"
27450 \begin_layout Standard
27451 There are other multiline formula environments that can be created via the
27454 Insert\SpecialChar \menuseparator
27458 These environments are described in the following sections.
27461 \begin_layout Standard
27462 In all multiline formula environments a new line is created by pressing
27466 arg "newline-insert newline"
27470 To add or delete lines, the math toolbar buttons
27471 \begin_inset Graphics
27472 filename ../images/tabular-feature_append-row.png
27478 \begin_inset Graphics
27479 filename ../images/tabular-feature_delete-row.png
27484 , respectively, or the menu
27486 Edit\SpecialChar \menuseparator
27492 \begin_layout Subsubsection
27494 \begin_inset CommandInset label
27496 name "sub:Line-Separation"
27504 \begin_layout Plain Layout
27505 Formula ! multiline ! Line separation
27513 \begin_layout Standard
27514 There is sometimes not enough space in multiline formulas between the lines:
27515 \begin_inset Formula \begin{eqnarray*}
27516 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}\\
27517 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*}
27524 \begin_layout Standard
27525 In LaTeX additional line space is specified as optional argument of the
27527 This is not yet possible in LyX
27531 \begin_layout Plain Layout
27533 \begin_inset CommandInset href
27535 name "LyX-bug #1505"
27536 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27545 , therefore the whole formula must be inserted in TeX-mode.
27546 To add in our example space, the command
27554 is inserted at the end of the first line.
27559 \begin_layout Plain Layout
27566 \begin_layout Plain Layout
27568 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27571 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27578 \begin_layout Plain Layout
27582 left(B^{2}+x_{0}^{2}
27590 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27595 \begin_layout Plain Layout
27607 \begin_layout Standard
27608 \begin_inset VSpace bigskip
27611 To set the the line separation for all lines in a formula, the length
27621 \begin_layout Plain Layout
27631 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27642 \begin_inset space \thinspace{}
27647 \begin_inset space \thinspace{}
27650 mm additional line separation as in the previous example, the command
27653 \begin_layout Standard
27663 \begin_layout Standard
27664 is inserted in TeX-mode before the formula.
27665 This requires that the LaTeX-package
27673 \begin_layout Plain Layout
27678 is part of every LaTeX standard installation.
27687 \begin_layout Plain Layout
27693 was loaded in LaTeX-preamble with the line
27696 \begin_layout Standard
27704 \begin_layout Standard
27709 \begin_layout Plain Layout
27721 \begin_inset Formula \begin{eqnarray*}
27722 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}\\
27723 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*}
27730 \begin_layout Standard
27734 \begin_layout Plain Layout
27745 To get back to the predefined distance,
27751 is set to the value 3
27752 \begin_inset space \thinspace{}
27758 \begin_layout Subsubsection
27760 \begin_inset CommandInset label
27762 name "sub:Column-Separation"
27770 \begin_layout Plain Layout
27771 Formula ! multiline ! Column separation
27779 \begin_layout Standard
27780 Multiline formulas form a matrix.
27781 A formula in the eqnarray environment is for example a matrix with three
27783 By changing the column separation in this environment, the space beside
27784 the relation sign can be changed.
27787 \begin_layout Standard
27788 The column separation is specified with the length
27798 \begin_layout Plain Layout
27807 \begin_inset Newline newline
27810 column separation = 2
27811 \begin_inset space \thinspace{}
27821 \begin_inset Newline newline
27827 \begin_layout Standard
27837 \begin_layout Standard
27838 inserted in TeX-mode, sets for all following formulas a column separation
27840 \begin_inset space \thinspace{}
27844 To get back to the predefined distance,
27851 \begin_inset space \thinspace{}
27857 \begin_layout Standard
27859 \begin_inset space \thinspace{}
27862 cm column separation:
27866 \begin_layout Plain Layout
27878 \begin_inset Formula \begin{eqnarray*}
27880 C & \ne & A\end{eqnarray*}
27884 A formula with the predefined column separation for matrices of 10
27885 \begin_inset space \thinspace{}
27892 \begin_layout Plain Layout
27904 \begin_inset Formula \begin{eqnarray*}
27906 C & \ne & A\end{eqnarray*}
27913 \begin_layout Subsubsection
27918 \begin_layout Plain Layout
27927 \begin_layout Standard
27928 Long formulas can be typeset using these methods:
27931 \begin_layout Itemize
27932 When one side of the equation is much shorther than the line width, this
27933 one is chosen for the left side and the right side is typeset over two
27938 \begin_layout Plain Layout
27948 \begin_inset Formula \begin{eqnarray}
27949 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 \\
27950 & & -\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}
27958 \begin_layout Plain Layout
27968 \begin_inset Newline newline
27971 The minus sign at the beginning of the second line does normally not appear
27972 as operator because it is the first character of the line.
27973 Thus it would not be surrounded by space and could not be distinguished
27974 from the fraction bar.
27975 To avoid this, space was inserted behind the minus sign with the command
27986 \begin_layout Plain Layout
27994 \begin_inset CommandInset ref
27996 reference "sub:Variable-Space"
28009 \begin_layout Plain Layout
28020 \begin_layout Itemize
28021 When both sides of the equation are too long, the command
28031 \begin_layout Plain Layout
28040 It is inserted to the first column of the first line and effects that all
28041 further insertions overwrite the following columns:
28045 \begin_layout Plain Layout
28055 \begin_inset Formula \begin{eqnarray}
28056 \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 \\
28057 & & -\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 \\
28058 & & =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}
28066 \begin_layout Plain Layout
28076 \begin_inset Newline newline
28079 After the insertion of
28085 , the cursor is in a purple box that is a bit shifted to the left from the
28087 In this the formula is inserted.
28091 \begin_layout Plain Layout
28101 \begin_inset Newline newline
28104 The content of the further lines is inserted to the second or another formula
28106 The greater the column number where it was inserted, the larger the indentation.
28110 \begin_layout Plain Layout
28120 \begin_inset Newline newline
28124 \begin_inset Note Greyedout
28127 \begin_layout Plain Layout
28128 Note the following when using
28137 \begin_layout Itemize
28138 The formula doesn't use the full page width.
28140 \begin_inset space \space{}
28144 \begin_inset Formula $-B^{2}$
28147 is added to the first line in the above example, it would have been outside
28149 To better use the width, negative space can be inserted at the beginning
28153 \begin_layout Itemize
28154 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28159 \begin_layout Plain Layout
28160 \begin_inset CommandInset href
28162 name "LyX-bug #1429"
28163 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28172 One can only set the cursor at the beginning of the line and move it with
28181 \begin_layout Itemize
28182 Other methods to set long formulas are offered by the environments described
28184 \begin_inset CommandInset ref
28186 reference "sub:Multline-Environment"
28191 \begin_inset CommandInset ref
28193 reference "sub:Multiline-Formula-Parts"
28200 \begin_layout Subsubsection
28202 \begin_inset CommandInset label
28204 name "sub:Multiline-Brackets"
28212 \begin_layout Plain Layout
28213 Brackets ! for multiline expressions
28221 \begin_layout Standard
28222 For brackets spanning multiple lines the following problem occurs:
28223 \begin_inset Formula \begin{eqnarray*}
28224 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28225 & & \left.\cdots+B-D\right]\end{eqnarray*}
28232 \begin_layout Standard
28233 The closing bracket is smaller than the opening bracket because brackets
28234 with variable size may not span multiple lines.
28237 \begin_layout Standard
28238 To set the bracket size for the second line correctly, the first line is
28249 \begin_layout Plain Layout
28257 and the second line with
28265 \begin_layout Plain Layout
28279 \begin_inset CommandInset ref
28281 reference "sub:Automatic-Bracket-Size"
28296 \begin_layout Plain Layout
28322 \begin_layout Plain Layout
28341 \begin_layout Plain Layout
28360 \begin_layout Plain Layout
28372 \begin_inset Formula $\downarrow$
28381 \begin_layout Plain Layout
28389 is inserted, because the multiplication operator with its limits is the
28390 largest symbol in the first line and this should be the size for the bracket
28391 in the second line.
28394 \begin_layout Standard
28395 The result is this:
28396 \begin_inset Formula \begin{eqnarray*}
28397 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28398 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28405 \begin_layout Subsection
28409 \begin_layout Standard
28410 Align environments can be used for every kind of multiline formulas.
28411 They are specially useful to set several formulas side by side.
28414 \begin_layout Standard
28415 Align environments consist of columns.
28416 The odd columns are right aligned, the even ones left aligned.
28417 Every line in an Align environment can be numbered.
28420 \begin_layout Standard
28421 Align environments are created via the menu
28423 Insert\SpecialChar \menuseparator
28429 Edit\SpecialChar \menuseparator
28430 Math\SpecialChar \menuseparator
28431 Change Formula Type
28433 already existing formulas can be converted to Align environments.
28436 \begin_layout Standard
28437 To add or delete columns, the math toolbar buttons
28438 \begin_inset Graphics
28439 filename ../images/tabular-feature_append-column.png
28445 \begin_inset Graphics
28446 filename ../images/tabular-feature_delete-column.png
28451 , respectively, or the menu
28453 Edit\SpecialChar \menuseparator
28459 \begin_layout Subsubsection
28460 Standard align Environment
28461 \begin_inset CommandInset label
28463 name "sub:Standard-align-Environment"
28471 \begin_layout Plain Layout
28472 Formula ! multiline ! align environment
28480 \begin_layout Standard
28481 This Align environment is created by presssing
28484 arg "newline-insert newline"
28487 in a formula or by the menu
28489 Insert\SpecialChar \menuseparator
28490 Math\SpecialChar \menuseparator
28491 AMS align Environment
28496 \begin_layout Standard
28497 An example for two formulas set side by side, that are created with a four
28498 column align environment:
28499 \begin_inset Formula \begin{align*}
28500 A & =\sin(B) & C & =D\\
28501 C & \ne A & B & \ne D\end{align*}
28505 As it can be seen, the formulas in this environment are placed so as if
28514 \begin_layout Plain Layout
28522 \begin_inset CommandInset ref
28524 reference "sub:Variable-Space"
28535 before the first and after every even column.
28536 When the formula style
28542 \begin_layout Plain Layout
28544 \begin_inset CommandInset ref
28546 reference "sec:Formula-Styles"
28557 is used, the formula is set without the
28563 before the first column.
28566 \begin_layout Subsubsection
28567 Alignat Environment
28571 \begin_layout Plain Layout
28572 Formula ! multiline ! alignat environment
28580 \begin_layout Standard
28581 The alignat environment has no predefined column separation.
28582 It can be inserted manually with the spaces that are described
28583 \begin_inset CommandInset ref
28585 reference "sub:Space"
28592 \begin_layout Standard
28593 The above example in the alignat environment where 1
28594 \begin_inset space \thinspace{}
28597 cm space was inserted at the beginning of the second formula:
28598 \begin_inset Formula \begin{alignat*}{2}
28599 A & =\sin(B) & \hspace{1cm}C & =D\\
28600 C & \ne A & B & \ne D\end{alignat*}
28604 Because the column separation can be set separately for every column, this
28605 environment is especially suitable to set three and more formulas side
28609 \begin_layout Subsubsection
28610 Flalign Environment
28611 \begin_inset CommandInset label
28613 name "sub:Flalign-Environment"
28621 \begin_layout Plain Layout
28622 Formula ! multiline ! flalign environment
28630 \begin_layout Standard
28631 In this environment the first two columns are always set as much as possible
28632 to the left and the last two ones to the right.
28634 \begin_inset Formula \begin{flalign*}
28635 A & =1 & B & =2 & C & =3\\
28636 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28643 \begin_layout Standard
28644 By creating a flalign environment with an odd number of columns where an
28645 empty TeX-brace is inserted to the last column, several formulas in a document
28646 can be set to the left, although the formula style
28651 As example the indented formula
28652 \begin_inset CommandInset ref
28654 reference "eq:VolInt"
28659 \begin_inset Formula \begin{flalign}
28660 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28664 The first two columns contain the formula.
28665 To indent it as with the formula style
28670 \begin_inset space \thinspace{}
28673 pt space was inserted at the beginning of the first column.
28676 \begin_layout Subsection
28677 Eqnarray Environment
28678 \begin_inset CommandInset label
28680 name "sub:Eqnarray-Environment"
28688 \begin_layout Plain Layout
28689 Formula ! multiline ! eqnarray environment
28697 \begin_layout Standard
28698 When this environment has been created, three blue boxes appear.
28699 The content of the first box is right aligned, the content of the last
28701 The content of the middle box appears centered and a bit smaller, because
28702 it is designed to insert there only relation characters.
28703 \begin_inset Formula \begin{eqnarray*}
28704 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28706 A & = & A\end{eqnarray*}
28713 \begin_layout Subsection
28718 \begin_layout Plain Layout
28719 Formula ! multiline ! gather environment
28727 \begin_layout Standard
28728 This environment consists of only one centered column.
28729 Every line can be numbered.
28730 \begin_inset Formula \begin{gather}
28732 X=\textrm{-}1\end{gather}
28739 \begin_layout Subsection
28740 Multline Environment
28741 \begin_inset CommandInset label
28743 name "sub:Multline-Environment"
28751 \begin_layout Plain Layout
28752 Formula ! multiline ! multline environment
28760 \begin_layout Standard
28761 The multline environment consists, like the gather environment, of only
28763 But the first line is left aligned, the last one right aligned.
28764 All other lines are centered.
28765 Therefore this environment is suitable for long formulas.
28767 \begin_inset CommandInset ref
28769 reference "eq:lefteqn"
28773 in the multline environment:
28774 \begin_inset Formula \begin{multline}
28775 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}\\
28776 -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}\\
28777 =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}
28784 \begin_layout Standard
28785 In the output only the last (first) line of a multline environment appears
28786 numbered when the document numbering is right (left).
28790 \begin_layout Plain Layout
28791 numbering styles see
28792 \begin_inset CommandInset ref
28794 reference "sec:Formula-Styles"
28806 \begin_layout Standard
28815 \begin_layout Plain Layout
28833 \begin_layout Plain Layout
28843 a centered line can be right or left aligned, respectively.
28844 The commands are used as follows:
28847 \begin_layout Standard
28852 shoveright{line content}
28858 shoveleft{line content}
28861 \begin_layout Standard
28862 \begin_inset VSpace medskip
28873 \begin_layout Plain Layout
28883 specifies the distance of the first line from the left page margin.
28884 Predefined is the length 0
28885 \begin_inset space \thinspace{}
28891 \begin_layout Standard
28892 As example the above formula where the command
28895 \begin_layout Standard
28905 \begin_layout Standard
28906 was inserted in TeX-mode before:
28910 \begin_layout Plain Layout
28922 \begin_inset Formula \begin{multline}
28923 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}\\
28924 \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}}\\
28925 =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}
28933 \begin_layout Plain Layout
28944 The second line was left aligned using
28953 \begin_layout Subsection
28954 Multiline Formula Parts
28955 \begin_inset CommandInset label
28957 name "sub:Multiline-Formula-Parts"
28965 \begin_layout Plain Layout
28966 Formula ! multiline ! formula parts
28974 \begin_layout Standard
28975 To display only parts of a formula with multiple lines, one of the following
28976 environments are used:
28993 They can be inserted via the menu
28995 Insert\SpecialChar \menuseparator
28998 or by using the commands described in this section.
29001 \begin_layout Standard
29002 The first three have the same properties as the corresponding multiline
29003 formula environments, but it is possible to set further formula parts beside
29006 \begin_inset Formula \[
29007 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29008 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29009 \right\} \textrm{Uncertainty relations}\]
29016 \begin_layout Standard
29017 To get this formula, a displayed formula is created where the command
29025 \begin_layout Plain Layout
29036 A purple box appears around the blue formula box where now columns and
29037 lines can be added.
29038 Outside the multiline environment other formula parts can be set, like
29042 \begin_layout Standard
29043 The aligned environment is also suitable for long formulas whose lines are
29044 horizontally aligned.
29045 Using aligned in a displayed formula has the advantage that the formula
29046 number is vertically centered behind the lines.
29048 \begin_inset CommandInset ref
29050 reference "eq:kurzlang"
29054 in the aligned environment:
29055 \begin_inset Formula \begin{equation}
29056 \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}|}\\
29057 & -\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}
29065 \begin_layout Standard
29066 To use the environments
29088 \begin_layout Plain Layout
29106 \begin_layout Plain Layout
29124 \begin_layout Plain Layout
29132 are inserted, respectively.
29133 The split environment has the same properties as the aligned environment
29134 but it can only have two columns.
29137 \begin_layout Subsection
29138 Text in multiline Formulas
29139 \begin_inset CommandInset label
29141 name "sub:Text-in-multiline"
29149 \begin_layout Plain Layout
29159 \begin_layout Plain Layout
29160 Formula ! multiline ! text
29168 \begin_layout Standard
29169 In the Align environments, and the multline and gather environment, text
29170 can be inserted that will appear in a separate line and doesn't affect
29171 the column alignment.
29172 To do this, the command
29180 \begin_layout Plain Layout
29190 is used in the following scheme:
29193 \begin_layout Standard
29201 \begin_layout Standard
29202 The text should not be longer than a line because it cannot be hyphenated.
29203 As LyX doesn't yet support
29209 directly, the text is written as mathematical text.
29216 must hereby be at the beginning of a line and appears in the output above
29218 An example where the text was inserted at the beginning of the second line:
29219 \begin_inset Formula \begin{align}
29220 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29221 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29228 \begin_layout Section
29233 \begin_layout Plain Layout
29243 \begin_layout Plain Layout
29244 Formula ! numbering|see
29248 \begin_layout Plain Layout
29259 \begin_layout Plain Layout
29274 \begin_layout Subsection
29278 \begin_layout Standard
29279 Numbered formulas can be created with the menu
29281 Insert\SpecialChar \menuseparator
29282 Math\SpecialChar \menuseparator
29284 \begin_inset space ~
29292 \begin_inset space ~
29298 Existing formulas can be numbered with the menu
29300 Edit\SpecialChar \menuseparator
29301 Math\SpecialChar \menuseparator
29303 \begin_inset space ~
29311 arg "math-number-toggle"
29315 The formula number is displayed in LyX behind the formula as number sign
29317 The number sign is replaced in the output by the formula number.
29320 \begin_layout Standard
29321 When numbering is turned on in multiline formulas, all lines will be numbered.
29322 But the numbering can be controlled with the menu
29324 Edit\SpecialChar \menuseparator
29325 Math\SpecialChar \menuseparator
29327 \begin_inset space ~
29331 \begin_inset space ~
29335 \begin_inset space ~
29343 arg "math-number-line-toggle"
29349 \begin_layout Standard
29350 Except of inline formulas, all formulas can be numbered with two different
29352 \begin_inset CommandInset ref
29354 reference "sec:Formula-Styles"
29361 \begin_layout Subsection
29366 \begin_layout Plain Layout
29367 Cross-references ! to formulas
29375 \begin_layout Standard
29376 All labeled formulas can be cross-referenced.
29377 A label is added by the menu
29379 Insert\SpecialChar \menuseparator
29382 or the toolbar button
29383 \begin_inset Graphics
29384 filename ../images/label-insert.png
29390 The cursor must hereby be inside a displayed formula.
29391 A dialog pops up displaying the prefix
29396 The label is inserted there behind the prefix.
29397 The predefined prefix means
29398 \begin_inset Quotes eld
29402 \begin_inset Quotes erd
29405 and makes it easier to find labels in large documents because it marks
29406 it as formula label to divide it from e.g.
29407 \begin_inset space \space{}
29411 To change a label, the menu
29413 Insert\SpecialChar \menuseparator
29419 \begin_layout Standard
29420 The name of the label is displayed in LyX within two parentheses behind
29422 A formula with a label is always numbered.
29425 \begin_layout Standard
29426 Cross-references are inserted via the menu
29428 Insert\SpecialChar \menuseparator
29431 or with the toolbar button
29432 \begin_inset Graphics
29433 filename ../images/dialog-show-new-inset_ref.png
29439 A formula cross-reference appears in the output as formula number.
29440 When in the cross-reference dialog window the format
29444 is chosen, the cross-reference appears in the output as formula number
29446 \begin_inset Newline newline
29449 By right-clicking on a cross-reference in LyX, one jumps to the formula
29450 that is referenced.
29453 \begin_layout Standard
29454 Here are as examples cross-references to formulas of the following subsections:
29455 \begin_inset Note Note
29458 \begin_layout Plain Layout
29459 Note the different cross-reference types.
29467 \begin_layout Standard
29469 \begin_inset CommandInset ref
29476 \begin_inset CommandInset ref
29484 \begin_inset CommandInset ref
29490 ) big Latin letters are used for the numbering in contrary to (
29491 \begin_inset CommandInset ref
29500 \begin_layout Standard
29501 \begin_inset VSpace medskip
29504 When the argument of
29512 \begin_layout Plain Layout
29520 \begin_inset CommandInset ref
29522 reference "sub:User-defined-Numbering"
29533 contains a box like in
29534 \begin_inset CommandInset ref
29536 reference "sub:Paragraph-Boxes"
29540 , the formula cannot be referenced.
29543 \begin_layout Subsection
29548 \begin_layout Plain Layout
29549 Formula numbering ! subnumbering
29557 \begin_layout Standard
29558 With the help of the commands
29562 begin{subequations}
29570 formulas can be subnumbered.
29571 Both commands are inserted in TeX-mode.
29574 \begin_layout Standard
29576 \begin_inset Formula \begin{equation}
29577 A=C-B\label{eq:a}\end{equation}
29585 \begin_layout Plain Layout
29589 addtocounter{equation}{-1}
29598 \begin_layout Plain Layout
29602 begin{subequations}
29608 \begin_inset VSpace -5mm
29612 \begin_inset Formula \begin{equation}
29613 B=C-A\label{eq:b}\end{equation}
29618 \begin_inset Formula \begin{equation}
29619 C=A+B\label{eq:c}\end{equation}
29626 \begin_layout Standard
29630 \begin_layout Plain Layout
29642 \begin_layout Standard
29643 To create the example, the following is done:
29646 \begin_layout Enumerate
29647 first formula is inserted
29650 \begin_layout Enumerate
29655 addtocounter{equation}{-1}
29657 begin{subequations}
29661 \begin_layout Plain Layout
29670 \begin_inset Newline newline
29675 is inserted after the first formula
29678 \begin_layout Enumerate
29679 second formula is inserted
29682 \begin_layout Enumerate
29683 third formula is inserted
29686 \begin_layout Enumerate
29693 is inserted after the third formula
29696 \begin_layout Standard
29697 Every formula between the commands
29709 is subnumbered as a, b,
29710 \begin_inset Newline linebreak
29713 c, \SpecialChar \ldots{}
29714 For multiline formulas every line will be subnumbered.
29715 All subnumbered formulas are treated as
29720 But as every numbered formula increases the counter
29724 by one, the command
29730 is needed to decrease it.
29731 Otherwise the formulas
29732 \begin_inset CommandInset ref
29739 \begin_inset CommandInset ref
29746 \begin_inset CommandInset ref
29752 would be numbered as
29753 \begin_inset CommandInset ref
29760 \begin_inset CommandInset ref
29767 \begin_inset CommandInset ref
29776 \begin_layout Standard
29777 By inserting the commands in TeX-mode, a space is created between the first
29780 \begin_inset space \thinspace{}
29783 mm vertical space is inserted after the command
29787 begin{subequations}
29790 When the formula style
29796 \begin_layout Plain Layout
29798 \begin_inset CommandInset ref
29800 reference "sec:Formula-Styles"
29812 \begin_inset space \thinspace{}
29815 mm space is inserted instead.
29818 \begin_layout Standard
29819 Here is an example for a multiline formula where the numbering was turned
29820 off for the second line:
29824 \begin_layout Plain Layout
29828 begin{subequations}
29834 \begin_inset Formula \begin{eqnarray}
29835 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29836 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29837 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29845 \begin_layout Plain Layout
29857 \begin_layout Subsection
29858 User-defined Numbering
29859 \begin_inset CommandInset label
29861 name "sub:User-defined-Numbering"
29869 \begin_layout Plain Layout
29870 Formula numbering ! user-defined
29878 \begin_layout Standard
29882 \begin_layout Plain Layout
29883 Formula numbering ! self-defined delimiters
29888 With the standard numbering parentheses are set around the formula number.
29889 To replace the parentheses for example by vertical bars, the following
29890 line is added to the LaTeX-preamble:
29893 \begin_layout Standard
29905 \begin_inset Note Note
29908 \begin_layout Plain Layout
29909 This macro is already declared in the LaTeX-preamble for testing.
29910 To activate it, remove the percent sign at the beginning.
29918 \begin_layout Standard
29919 To use other characters, the vertical bars besides the
29923 are replaced by one ore more characters.
29924 To get only the formula number the vertical bars are omitted.
29927 \begin_layout Standard
29928 \begin_inset VSpace bigskip
29931 When there should be an expression of your choice instead of the consecutive
29932 formula number in parentheses behind the formula, the command
29942 \begin_layout Plain Layout
29951 \begin_inset Formula \begin{equation}
29952 A+B=C\tag{something}\label{eq:tag}\end{equation}
29956 In this example the command
29964 \begin_layout Plain Layout
29975 was inserted to the formula.
29978 \begin_layout Standard
29987 \begin_layout Plain Layout
29998 is inserted instead, the star prevents the parentheses around the expression:
29999 \begin_inset Formula \[
30000 A+B=C\tag*{something}\]
30007 \begin_layout Standard
30008 \begin_inset VSpace bigskip
30011 To restart the formula numbering with new document parts or sections, the
30012 following command is used:
30015 \begin_layout Standard
30020 @addtoreset{equation}{part}
30026 \begin_layout Plain Layout
30031 \begin_layout Plain Layout
30042 \begin_layout Plain Layout
30055 \begin_layout Plain Layout
30066 \begin_layout Plain Layout
30079 \begin_inset Newline newline
30083 \begin_inset Newline newline
30090 @addtoreset{equation}{section}
30093 \begin_layout Standard
30094 To be able to use these commands in TeX-mode, the
30095 \begin_inset Quotes eld
30099 \begin_inset Quotes erd
30102 character has to be made
30103 \begin_inset Quotes eld
30107 \begin_inset Quotes erd
30110 for LaTeX using the command
30124 So the command sequence in TeX-mode is:
30127 \begin_layout Standard
30133 \begin_inset Newline newline
30138 @addtoreset{equation}{section}
30139 \begin_inset Newline newline
30147 \begin_layout Standard
30148 In the LaTeX-preamble
30160 can be omitted as they are automatically internally inserted by LyX.
30163 \begin_layout Standard
30178 \begin_layout Plain Layout
30183 is part of the LaTeX-package
30191 \begin_layout Plain Layout
30192 Packages ! carlisle
30197 that is part of every LaTeX standard installation.
30206 \begin_layout Plain Layout
30207 Packages ! remreset
30212 has to be loaded in the LaTeX-preamble with the line
30215 \begin_layout Standard
30220 usepackage{remreset}
30223 \begin_layout Standard
30234 \begin_layout Plain Layout
30239 \begin_layout Plain Layout
30250 \begin_layout Plain Layout
30263 \begin_layout Plain Layout
30274 \begin_layout Plain Layout
30286 can be used with the same scheme as
30295 \begin_layout Standard
30296 \begin_inset VSpace bigskip
30299 Sometimes formulas should be numbered in the following form:
30302 \begin_layout Standard
30305 (section number.formula number)
30308 \begin_layout Standard
30309 The formula number should start with every section with
30310 \begin_inset Quotes eld
30314 \begin_inset Quotes erd
30320 \begin_layout Standard
30321 For this case there is the command
30331 \begin_layout Plain Layout
30339 , which is used with the following scheme:
30342 \begin_layout Standard
30347 numberwithin{counter}{sectioning}
30350 \begin_layout Standard
30351 Counter denotes what kind of numbering is affected, sectioning denotes what
30352 number is before the dot.
30355 \begin_layout Standard
30356 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30359 \begin_layout Standard
30364 numberwithin{equation}{section}
30367 \begin_layout Standard
30368 This is the result:
30372 \begin_layout Plain Layout
30376 numberwithin{equation}{section}
30382 \begin_inset Formula \begin{equation}
30383 A+B=C\end{equation}
30390 \begin_layout Standard
30392 \begin_inset space \space{}
30395 tables so that the number of the part is the sectioning,
30396 \begin_inset Newline newline
30403 numberwithin{table}{part}
30408 \begin_layout Standard
30409 To go back to the standard numbering or to prevent this kind of numbering
30410 when it is defined by the document class, the following command is inserted
30411 as TeX-Code or to the LaTeX-preamble:
30414 \begin_layout Standard
30427 \begin_layout Plain Layout
30441 \begin_layout Plain Layout
30457 \begin_inset Newline newline
30465 \begin_inset Newline newline
30477 \begin_layout Standard
30484 uses internally the command
30490 , described above, that also needs to be reverted.
30494 \begin_layout Plain Layout
30501 \begin_layout Plain Layout
30505 @removefromreset{equation}{section}
30508 \begin_layout Plain Layout
30520 \begin_layout Subsection
30521 Numbering with Roman Numbers and Letters
30525 \begin_layout Plain Layout
30526 Formula numbering ! with letters
30535 \begin_layout Plain Layout
30536 Formula numbering ! with Roman numbers
30544 \begin_layout Standard
30545 Formulas can also be numbered with Roman numbers and Latin letters.
30546 To number for example with small Roman numbers, the command
30549 \begin_layout Standard
30561 \begin_layout Standard
30562 is inserted before the formula in TeX-mode.
30573 \begin_layout Plain Layout
30581 redefines the predefined command
30597 \begin_layout Plain Layout
30604 has the same scheme like the command
30610 that is described in
30611 \begin_inset CommandInset ref
30613 reference "sec:User-defined-Commands"
30627 is the formula counter.
30634 is used as prefix for a counter, the value of the counter is output as
30636 When a formula is numbered, LaTeX sets internally the command
30642 behind the formula.
30651 \begin_layout Plain Layout
30661 outputs the counter as small Roman number.
30664 \begin_layout Standard
30665 All formulas behind the command
30675 are now numbered Roman.
30676 To switch to numbering with big Roman numbers, the command is inserted
30693 \begin_layout Plain Layout
30705 \begin_inset Quotes eld
30709 \begin_inset Quotes erd
30712 with small Latin letters there is the command
30722 \begin_layout Plain Layout
30730 , for big ones there is the command
30740 \begin_layout Plain Layout
30753 \begin_layout Standard
30754 \begin_inset Note Greyedout
30757 \begin_layout Plain Layout
30762 Only maximal 26 formulas can be numbered with Latin letters in one document.
30770 \begin_layout Standard
30774 \begin_layout Plain Layout
30790 \begin_layout Standard
30791 \begin_inset Formula \begin{equation}
30792 A=\textrm{small roman}\label{eq:rom}\end{equation}
30800 \begin_layout Plain Layout
30814 \begin_inset Formula \begin{equation}
30815 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30823 \begin_layout Plain Layout
30837 \begin_inset Formula \begin{equation}
30838 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30846 \begin_layout Plain Layout
30860 \begin_inset Formula \begin{equation}
30861 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30868 \begin_layout Standard
30869 To switch back to the default numbering, insert the command:
30872 \begin_layout Standard
30885 \begin_layout Plain Layout
30896 \begin_layout Standard
30900 \begin_layout Plain Layout
30914 \begin_inset Formula \begin{equation}
30915 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30922 \begin_layout Standard
30923 \begin_inset VSpace medskip
30926 As you see, formulas are numbered serially independent from the numbering
30928 When then numbering should start with
30929 \begin_inset Quotes eld
30933 \begin_inset Quotes erd
30936 when the style is changed, new equation counters have to be defined.
30937 A description about this can be found in the file
30938 \begin_inset CommandInset href
30940 target "Formula-numbering.lyx"
30947 \begin_layout Section
30948 User-defined Commands
30949 \begin_inset CommandInset label
30951 name "sec:User-defined-Commands"
30959 \begin_layout Plain Layout
30960 User-defined commands
30968 \begin_layout Standard
30969 Many LaTeX-commands are too long to be used frequently.
30970 But it is possible to define with the command
30980 \begin_layout Plain Layout
30988 new shorter commands.
30991 \begin_layout Standard
30992 The command scheme of
31001 \begin_layout Standard
31006 newcommand{new command name}[number of arguments][optional
31011 \begin_inset Newline newline
31018 \begin_layout Plain Layout
31033 \begin_layout Plain Layout
31040 {command definition}
31043 \begin_layout Standard
31044 \begin_inset Note Greyedout
31047 \begin_layout Plain Layout
31052 Assure that the name of the new command is not already used in your document
31053 or by LaTeX-packages that you use.
31054 When you for example define the command
31066 , you get an error message because
31072 is already defined as command for
31073 \begin_inset Quotes eld
31077 \begin_inset Formula $\le$
31081 \begin_inset Quotes erd
31092 \begin_layout Standard
31093 \begin_inset Note Greyedout
31096 \begin_layout Plain Layout
31101 The names of user-defined commands may only consist of Latin letters.
31109 \begin_layout Standard
31110 The number of arguments is an integer in the range 0
31111 \begin_inset space \thinspace{}
31115 \begin_inset space \thinspace{}
31118 9 and specifies how many arguments the new command should have.
31119 With the optional value a value for an optional argument can be predefined.
31120 When this is done, the
31128 rgument of the new command is automatically an optional one.
31131 \begin_layout Standard
31132 Here are some examples:
31135 \begin_layout Itemize
31136 To define the command
31148 , the LaTeX-preamble line is:
31152 \begin_layout Plain Layout
31164 \begin_inset Newline newline
31176 \begin_layout Itemize
31177 To define the command
31189 , the argument (that should be underlined) must be taken into account.
31190 For this the preamble line is:
31194 \begin_layout Plain Layout
31206 \begin_inset Newline newline
31221 \begin_layout Plain Layout
31233 \begin_inset Newline newline
31242 acts as argument placeholder, the
31246 behind it denotes that it is the placeholder for the first argument.
31249 \begin_layout Itemize
31257 \begin_inset space \space{}
31270 \begin_layout Plain Layout
31282 \begin_inset Newline newline
31291 framebox#1#2{$#3$}}
31297 \begin_layout Plain Layout
31309 \begin_inset Newline newline
31314 The two Dollar signs creates the extra formula needed for
31321 \begin_inset CommandInset ref
31323 reference "sub:Boxes-with-Frame"
31330 \begin_layout Itemize
31331 To create a new command for
31337 where the color for the box needn't to be specified, the argument for the
31338 color is defined optional:
31342 \begin_layout Plain Layout
31354 \begin_inset Newline newline
31363 fcolorbox{#2}{#1}{$#3$}}
31369 \begin_layout Plain Layout
31379 \begin_inset Newline newline
31382 When the color is not specified when using
31388 , the predefined color
31395 \begin_layout Standard
31396 A test of the new defined commands:
31399 \begin_layout Standard
31401 \begin_inset Tabular
31402 <lyxtabular version="3" rows="6" columns="2">
31404 <column alignment="center" valignment="top" width="0">
31405 <column alignment="center" valignment="top" width="0">
31407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31410 \begin_layout Plain Layout
31416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31419 \begin_layout Plain Layout
31421 \begin_inset Note Note
31424 \begin_layout Plain Layout
31431 is only used as spacer.
31443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31446 \begin_layout Plain Layout
31453 \begin_layout Plain Layout
31467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31470 \begin_layout Plain Layout
31471 \begin_inset Formula $A\gr B$
31481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31484 \begin_layout Plain Layout
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31495 \begin_layout Plain Layout
31496 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31509 \begin_layout Plain Layout
31513 \begin_inset Formula $\to$
31519 \begin_inset Formula $\to$
31530 \begin_layout Plain Layout
31544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31547 \begin_layout Plain Layout
31548 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31561 \begin_layout Plain Layout
31565 \begin_inset Formula $\to$
31576 \begin_layout Plain Layout
31590 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31593 \begin_layout Plain Layout
31594 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31607 \begin_layout Plain Layout
31613 \begin_inset Formula $\to$
31624 \begin_layout Plain Layout
31638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31641 \begin_layout Plain Layout
31642 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31658 \begin_layout Section
31662 \begin_layout Standard
31663 LyX supports two types of commutative diagrams:
31671 that are explained in the following.
31674 \begin_layout Subsection
31679 \begin_layout Plain Layout
31688 \begin_layout Standard
31689 Diagrams of this type visualize relations by vertical and horizontal lines
31691 \begin_inset Formula \[
31692 \begin{CD}A@>>>B@>>>C\\
31694 F@<<<E@<<<D\end{CD}\]
31701 \begin_layout Standard
31702 To get them, the command
31710 \begin_layout Plain Layout
31720 is inserted to a formula.
31721 A blue box appears with two dashed lines where further commands can be
31726 arg "newline-insert newline"
31729 a new line is created.
31730 Horizontal relations are inserted in odd, vertical in even formula lines.
31733 \begin_layout Standard
31734 To create the relations there are the following commands:
31737 \begin_layout Itemize
31742 creates a left arrow,
31753 \begin_layout Itemize
31758 creates an up arrow,
31766 a vertical equal sign
31769 \begin_layout Itemize
31775 is a placeholder for non-existent relations
31778 \begin_layout Standard
31779 All arrows can be labeled as follows:
31782 \begin_layout Itemize
31783 Is text inserted between the first and second < or >, resp., it is placed
31785 When it is inserted between the second and third one, it appears under
31789 \begin_layout Itemize
31790 When text for vertical arrows is inserted between the first and second A
31791 or V, resp., it is placed left beside the arrow.
31792 When it is inserted between the second and third one, it appears right
31794 If the text contains an A or V, these letters must be set into a TeX-brace.
31797 \begin_layout Standard
31798 As example a diagram with all possible relations:
31801 \begin_layout Standard
31802 \begin_inset Formula \[
31803 \begin{CD}A@>j>>B@>>k>C@=F\\
31805 D@<<j<E@>k>>F@=C\end{CD}\]
31812 \begin_layout Standard
31813 The command for this is:
31814 \begin_inset Newline newline
31825 \begin_layout Plain Layout
31834 A@>j>>B@>>k>C@=F Ctrl+Return
31835 \begin_inset Newline newline
31842 \begin_layout Plain Layout
31857 \begin_layout Plain Layout
31870 \begin_layout Plain Layout
31882 \begin_inset Formula $\to$
31888 \begin_inset Newline newline
31895 \begin_layout Plain Layout
31910 \begin_layout Plain Layout
31923 \begin_layout Plain Layout
31933 \begin_layout Subsection
31938 \begin_layout Plain Layout
31939 Diagrams ! xymatrix
31947 \begin_layout Standard
31948 To be able to use xymatrices, the LaTeX-package
31953 A xymatrix is created by inserting the command
31960 Then you are able to add new matrix columns and rows like for normal matrices,
31962 \begin_inset CommandInset ref
31964 reference "sec:Matrices"
31971 \begin_layout Standard
31972 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31974 All possibilities to create commutative diagrams and decorations are explained
31975 in detail in this manual:
31976 \begin_inset CommandInset href
31978 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31985 \begin_layout Standard
31986 \begin_inset Newpage newpage
31992 \begin_layout Section
31997 \begin_layout Plain Layout
32010 \begin_layout Plain Layout
32011 Other useful math tips can be found in
32012 \begin_inset CommandInset citation
32027 \begin_layout Plain Layout
32035 \begin_inset Note Note
32038 \begin_layout Plain Layout
32041 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32044 \begin_layout Plain Layout
32047 texorpdfstring is in section
32048 \begin_inset CommandInset ref
32050 reference "sub:Formulas-in-Section"
32063 \begin_layout Plain Layout
32073 \begin_layout Plain Layout
32078 \begin_layout Plain Layout
32085 Chemical characters
32089 \begin_layout Plain Layout
32104 \begin_layout Subsection
32105 Chemical Symbols and Equations
32106 \begin_inset CommandInset label
32108 name "sub:Chemical-Symbols-and"
32116 \begin_layout Plain Layout
32117 Chemical characters ! Symbols
32126 \begin_layout Plain Layout
32136 \begin_layout Plain Layout
32145 \begin_layout Standard
32146 An example text from chemistry:
32149 \begin_layout Quote
32151 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32154 -ion reacts with two
32155 \begin_inset Formula $\mathrm{Na^{+}}$
32158 -ions to sodium sulfate
32159 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32163 The chemical equation for this is:
32164 \begin_inset Formula \[
32165 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32172 \begin_layout Standard
32173 This chemical equation can directly be created as formula.
32174 To avoid that the symbols appear italic, everything is highlighted and
32175 changed by the shortcut
32181 to the upright font style.
32185 \begin_layout Plain Layout
32191 \begin_inset CommandInset ref
32193 reference "sub:Font-Styles"
32205 \begin_layout Subsection
32210 \begin_layout Plain Layout
32219 \begin_layout Standard
32220 Negative numbers often look ugly in formulas because the minus sign before
32221 the number is set with the same length as the minus operator sign.
32222 When writing the negative number in normal text, the minus sign appears
32226 \begin_layout Standard
32227 Thus, the problem disappears when converting the minus sign to mathematical
32231 \begin_layout Standard
32232 An example to visualize the problem:
32235 \begin_layout Standard
32237 \begin_inset Tabular
32238 <lyxtabular version="3" rows="3" columns="2">
32240 <column alignment="right" valignment="top" width="0">
32241 <column alignment="left" valignment="top" width="0">
32243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32246 \begin_layout Plain Layout
32252 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32255 \begin_layout Plain Layout
32263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32266 \begin_layout Plain Layout
32272 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32275 \begin_layout Plain Layout
32276 \begin_inset Formula $x=-2$
32286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32289 \begin_layout Plain Layout
32295 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32298 \begin_layout Plain Layout
32299 \begin_inset Formula $x=\textrm{-}2$
32315 \begin_layout Subsection
32316 Comma as decimal Separator
32320 \begin_layout Plain Layout
32329 \begin_layout Standard
32330 In LaTeX a comma inside a formula is used, according to the English convention,
32331 as number group separator.
32332 So there will be space added behind all commas in formulas.
32335 \begin_layout Standard
32336 To avoid this, the comma is highlighted and changed to mathematical text
32346 \begin_layout Standard
32347 To use all formula commas in the document as decimal separator, the file
32356 \begin_layout Plain Layout
32361 is part of the LaTeX-package
32369 \begin_layout Plain Layout
32374 \begin_layout Plain Layout
32397 \begin_layout Plain Layout
32403 is loaded with the LaTeX-preamble line
32406 \begin_layout Standard
32414 \begin_layout Subsection
32416 \begin_inset CommandInset label
32418 name "sub:Physical-Vectors"
32426 \begin_layout Plain Layout
32435 \begin_layout Standard
32436 Predefined vectors are offered by the LaTeX-package
32444 \begin_layout Plain Layout
32449 should be part of every LaTeX standard installation.
32458 \begin_layout Plain Layout
32464 that is loaded with the LaTeX-preamble line
32467 \begin_layout Standard
32475 \begin_layout Standard
32479 \begin_layout Plain Layout
32489 \begin_inset Note Note
32492 \begin_layout Plain Layout
32493 The following table will only be displayed when the LaTeX-package
32502 The following commands are defined:
32505 \begin_layout Standard
32507 \begin_inset Tabular
32508 <lyxtabular version="3" rows="4" columns="2">
32510 <column alignment="center" valignment="top" width="0">
32511 <column alignment="center" valignment="top" width="0">
32513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32516 \begin_layout Plain Layout
32522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32525 \begin_layout Plain Layout
32533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32536 \begin_layout Plain Layout
32546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32549 \begin_layout Plain Layout
32550 \begin_inset Formula $\Bra{\psi}$
32560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32563 \begin_layout Plain Layout
32573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32576 \begin_layout Plain Layout
32577 \begin_inset Formula $\Ket{\psi}$
32587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32590 \begin_layout Plain Layout
32602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32605 \begin_layout Plain Layout
32606 \begin_inset Formula $\Braket{\psi|\phi}$
32622 \begin_layout Standard
32629 assures that all vertical bars are set in the size of the surrounding brackets:
32630 \begin_inset Formula \[
32631 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32639 \begin_layout Plain Layout
32649 \begin_inset Note Note
32652 \begin_layout Plain Layout
32653 The following will be displayed when the LaTeX-package
32665 \begin_layout Standard
32666 You need to install the LaTeX-package
32670 to see the rest of this subsection in the output.
32673 \begin_layout Standard
32677 \begin_layout Plain Layout
32689 \begin_layout Standard
32696 can also be achieved using the command
32702 , that is described in
32703 \begin_inset CommandInset ref
32705 reference "sub:Automatic-Bracket-Size"
32712 \begin_layout Subsection
32713 Self-defined Fractions
32714 \begin_inset CommandInset label
32716 name "sub:Self-defined-Fractions"
32724 \begin_layout Plain Layout
32725 Fractions ! self-defined
32733 \begin_layout Standard
32734 To define custom commands for fractions, the command
32744 \begin_layout Plain Layout
32752 is used in the following scheme:
32755 \begin_layout Standard
32768 bracket}{fraction bar thickness}{style}
32769 \begin_inset Newline newline
32776 \begin_layout Plain Layout
32791 \begin_layout Plain Layout
32798 {numerator}{denominator}
32801 \begin_layout Standard
32802 The style is a number in the range of 0
32803 \begin_inset space \thinspace{}
32807 \begin_inset space \thinspace{}
32813 \begin_layout Standard
32815 \begin_inset Tabular
32816 <lyxtabular version="3" rows="5" columns="2">
32818 <column alignment="center" valignment="top" width="0">
32819 <column alignment="center" valignment="top" width="0">
32821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32824 \begin_layout Plain Layout
32830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32833 \begin_layout Plain Layout
32841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32844 \begin_layout Plain Layout
32850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32853 \begin_layout Plain Layout
32854 display style formula
32861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32864 \begin_layout Plain Layout
32870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32873 \begin_layout Plain Layout
32881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32884 \begin_layout Plain Layout
32890 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32893 \begin_layout Plain Layout
32901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32904 \begin_layout Plain Layout
32910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32913 \begin_layout Plain Layout
32927 \begin_layout Standard
32928 When no style is given, the size is adjusted to the surrounding environment
32929 like for the command
32938 \begin_layout Standard
32939 When no fraction bar thickness is given, the predefined value of 0.4
32940 \begin_inset space \thinspace{}
32946 \begin_layout Standard
32947 \begin_inset VSpace medskip
32950 For example, the commands
32963 \begin_inset CommandInset ref
32965 reference "sub:Fractions"
32969 are defined with the commands
32972 \begin_layout Standard
32981 genfrac{}{}{}{0}{#1}{#2}}
32984 \begin_layout Standard
32988 \begin_layout Standard
32997 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33000 \begin_layout Standard
33001 \begin_inset VSpace medskip
33004 To define a fraction where the fraction bar thickness can be given as optional
33005 argument, the following line is inserted to the LaTeX-preamble:
33008 \begin_layout Standard
33017 genfrac{}{}{#1}{}{#2}{#3}}
33020 \begin_layout Standard
33022 \begin_inset Formula \begin{align*}
33023 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33024 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33028 As one can see, the distance of the numerator and the denominator to the
33029 fraction bar is round about three times the bar thickness.
33032 \begin_layout Subsection
33037 \begin_layout Plain Layout
33046 \begin_layout Standard
33047 To cancel formulas or formula parts, the LaTeX-package
33055 \begin_layout Plain Layout
33060 is part of every LaTeX standard installation.
33069 \begin_layout Plain Layout
33075 has to be loaded with the LaTeX-preamble line
33078 \begin_layout Standard
33083 usepackage[samesize]{cancel}
33086 \begin_layout Standard
33087 There are four ways to cancel formulas:
33090 \begin_layout Standard
33092 \begin_inset Tabular
33093 <lyxtabular version="3" rows="5" columns="2">
33095 <column alignment="center" valignment="top" width="0">
33096 <column alignment="center" valignment="top" width="0">
33098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33101 \begin_layout Plain Layout
33107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33110 \begin_layout Plain Layout
33112 \begin_inset Note Note
33115 \begin_layout Plain Layout
33128 are used here as spacer.
33140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33143 \begin_layout Plain Layout
33152 \begin_layout Plain Layout
33166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33169 \begin_layout Plain Layout
33170 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33183 \begin_layout Plain Layout
33192 \begin_layout Plain Layout
33206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33209 \begin_layout Plain Layout
33210 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33223 \begin_layout Plain Layout
33232 \begin_layout Plain Layout
33246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33249 \begin_layout Plain Layout
33250 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33263 \begin_layout Plain Layout
33267 \begin_inset Formula $\to$
33278 \begin_layout Plain Layout
33292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33295 \begin_layout Plain Layout
33296 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33312 \begin_layout Standard
33319 is especially suitable to visualize the reduction of fractions within formulas:
33320 \begin_inset Formula \[
33321 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33328 \begin_layout Subsection
33329 Formulas in Section Headings
33330 \begin_inset CommandInset label
33332 name "sub:Formulas-in-Section"
33340 \begin_layout Plain Layout
33341 Formula ! in section headings
33349 \begin_layout Standard
33350 When formulas are used in section headings, the following has to be taken
33354 \begin_layout Standard
33355 \begin_inset Note Greyedout
33358 \begin_layout Plain Layout
33367 \begin_layout Plain Layout
33368 Packages ! hyperref
33373 support is enabled in the document settings dialog under
33376 \begin_inset space ~
33381 , PDF-bookmarks are created for every section heading in the table of contents.
33382 If a section heading contains formulas, they are incorrectly displayed
33383 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33392 \begin_layout Standard
33393 Both problems can be solved by inserting at the end of the section heading
33394 a short title with the menu
33396 Insert\SpecialChar \menuseparator
33398 \begin_inset space ~
33404 Short titles are used as alternative for multiline section headings to
33405 keep the table of contents clearly arranged.
33406 Only the short title appears in the table of contents and therefore also
33407 in the PDF-bookmark.
33410 \begin_layout Standard
33411 When formulas should be used in the table of contents but
33415 is used, one can use the following command in TeX-mode:
33418 \begin_layout Standard
33423 texorpdfstring{part}{alternative}
33427 \begin_layout Plain Layout
33438 \begin_layout Standard
33439 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33440 This can be characters, formulas, footnotes, but also cross-references.
33441 The alternative is used instead of the part for the bookmark.
33444 \begin_layout Standard
33445 Here are two example headings:
33446 \begin_inset VSpace -3mm
33453 \begin_layout Plain Layout
33465 \begin_layout Subsubsection
33466 Heading without formula in table of contents
33467 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33471 \begin_inset OptArg
33474 \begin_layout Plain Layout
33475 Heading without formula in table of contents
33483 \begin_layout Subsubsection
33484 Heading with formula in table of contents
33488 \begin_layout Plain Layout
33498 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33505 \begin_layout Plain Layout
33515 \begin_layout Standard
33519 \begin_layout Plain Layout
33528 In the first heading a short title was used, in the second one
33537 \begin_layout Standard
33538 To get the same formatting as for the other headings, the complete heading
33547 \begin_layout Plain Layout
33549 \begin_inset CommandInset ref
33551 reference "sub:Bold-Formulas"
33563 \begin_layout Subsection
33564 Formulas in multi-column Text
33568 \begin_layout Plain Layout
33569 Formula ! in multi-column text
33577 \begin_layout Standard
33578 Formulas in multi-column text are often too wide to fit into a column and
33579 thus need to be set over the whole page width.
33580 This is done by using the LaTeX-package
33588 \begin_layout Plain Layout
33593 is part of every LaTeX standard installation.
33602 \begin_layout Plain Layout
33603 Packages ! multicol
33608 , that is loaded with the LaTeX-preamble line
33611 \begin_layout Standard
33616 usepackage{multicol}
33619 \begin_layout Standard
33620 \begin_inset Note Greyedout
33623 \begin_layout Plain Layout
33624 Note herby that the setting
33627 \begin_inset space ~
33634 Document\SpecialChar \menuseparator
33640 \begin_inset space ~
33660 \begin_layout Standard
33661 Before the multi-column text the command
33664 \begin_layout Standard
33669 begin{multicols}{column number}
33672 \begin_layout Standard
33673 is written in TeX-mode.
33674 The column number is a number in the range of 2
33675 \begin_inset space \thinspace{}
33679 \begin_inset space \thinspace{}
33683 Before the formula the multi-column text is ended by inserting the command
33686 \begin_layout Standard
33694 \begin_layout Standard
33698 \begin_layout Standard
33699 Due to the command some space is automatically added before the formula.
33701 \begin_inset space \thinspace{}
33704 mm vertical space is inserted before the formula.
33705 When the formula style
33711 \begin_layout Plain Layout
33713 \begin_inset CommandInset ref
33715 reference "sec:Formula-Styles"
33727 \begin_inset space \thinspace{}
33730 mm space is inserted instead.
33733 \begin_layout Standard
33734 As example a multi-column text with a displayed formula:
33737 \begin_layout Standard
33741 \begin_layout Plain Layout
33745 begin{multicols}{2}
33750 Das Spektrum wird fouriertransformiert.
33751 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33752 , Lösungsmittel) zu trennen.
33753 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33754 nun das Aussehen des Ausgangssignals.
33755 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33756 über alle Phasen integrieren muss.
33758 \begin_inset Formula $S$
33761 unser normiertes Ausgangssignal and
33762 \begin_inset Formula $P$
33765 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33769 \begin_layout Plain Layout
33779 \begin_inset VSpace -6mm
33783 \begin_inset Formula \begin{equation}
33784 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33792 \begin_layout Plain Layout
33796 begin{multicols}{2}
33802 \begin_inset Formula $S_{0}$
33805 das Signal ohne Gradient ist and the Normierungsbedingung
33806 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33810 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33812 \begin_inset Formula $\nicefrac{\pi}{2}$
33816 \begin_inset space \thinspace{}
33819 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33820 das Signal zusätzlich abschwächt.
33821 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33823 \begin_inset Formula $T_{2}$
33829 \begin_layout Standard
33833 \begin_layout Plain Layout
33845 \begin_layout Subsection
33846 Formulas with Description of Variables
33850 \begin_layout Plain Layout
33851 Formula ! with description of variables
33859 \begin_layout Standard
33860 To describe variables within a formula, like in formula
33861 \begin_inset CommandInset ref
33863 reference "eq:within"
33872 \begin_inset Formula $n$
33876 \begin_inset space ~
33879 matrix is used with left aligned columns for the
33880 \begin_inset Formula $n$
33887 \begin_layout Plain Layout
33889 \begin_inset CommandInset ref
33891 reference "sec:Matrices"
33900 To set the description in a smaller size, before the matrix e.g.
33901 \begin_inset space \space{}
33914 \begin_layout Plain Layout
33916 \begin_inset CommandInset ref
33918 reference "sub:Font-Sizes"
33930 \begin_layout Standard
33931 When the formula style
33937 \begin_layout Plain Layout
33939 \begin_inset CommandInset ref
33941 reference "sec:Formula-Styles"
33962 \begin_layout Plain Layout
33969 only works in formulas with the style
33974 \begin_inset CommandInset ref
33976 reference "sub:Variable-Space"
33985 is inserted before and after the matrix to have the same separation of
33986 the matrix from the equation and the side margin.
33989 \begin_layout Standard
33990 When the formula style
33994 is used, the method described in
33995 \begin_inset CommandInset ref
33997 reference "sub:Flalign-Environment"
34001 is used to indent formulas.
34003 \begin_inset CommandInset ref
34005 reference "eq:within"
34009 consists of five columns whereas in the first two columns contain the equation,
34010 the third the matrix, and the last one an empty TeX-brace.
34011 \begin_inset Formula \begin{flalign}
34012 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34013 \rho & \textrm{density}\\
34014 V & \textrm{volume}\\
34015 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34022 \begin_layout Subsection
34023 Upright small Greek Letters
34024 \begin_inset CommandInset label
34026 name "sub:Upright-small-Greek"
34034 \begin_layout Plain Layout
34035 Greek letters ! upright
34043 \begin_layout Standard
34044 Most of the math fonts only provide italic small Greek letters.
34045 But for symbols of elementary particles like pions and neutrinos, upright
34046 Greek letters are needed.
34055 \begin_layout Plain Layout
34060 is part of the LaTeX-package
34068 \begin_layout Plain Layout
34073 \begin_layout Plain Layout
34096 \begin_layout Plain Layout
34102 that is loaded with the LaTeX-preamble line
34105 \begin_layout Standard
34110 usepackage{upgreek}
34113 \begin_layout Standard
34119 \begin_layout Plain Layout
34129 \begin_inset Note Note
34132 \begin_layout Plain Layout
34133 The following table will only be displayed when the LaTeX-package
34142 They are created when the command for a small Greek letters is started
34148 For example the command
34155 \begin_inset Formula $\uptau$
34161 \begin_layout Standard
34162 With these commands reactions of elementary particles can be typeset:
34163 \begin_inset Formula \[
34164 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34171 \begin_layout Standard
34172 The upright letters are more bold and wider than the italic ones.
34173 They should therefore not be used for units like
34174 \begin_inset Quotes eld
34178 \begin_inset Quotes erd
34184 \begin_layout Standard
34188 \begin_layout Plain Layout
34198 \begin_inset Note Note
34201 \begin_layout Plain Layout
34202 The following will be displayed when the LaTeX-package
34214 \begin_layout Standard
34215 You need to install the LaTeX-package
34219 to see the rest of this subsection in the output.
34222 \begin_layout Standard
34226 \begin_layout Plain Layout
34238 \begin_layout Subsection
34239 Text Characters in Formulas
34240 \begin_inset CommandInset label
34242 name "sub:Text-Characters-in"
34250 \begin_layout Plain Layout
34259 \begin_layout Standard
34260 In some cases you might want to insert text characters directly into formulas.
34261 When for example the centered dot · is often used in formulas like
34262 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34265 , one would have to insert the command
34275 \begin_layout Plain Layout
34277 \begin_inset CommandInset ref
34279 reference "sub:Binary-Operators"
34288 all the time, because this character is defined in all encodings as text
34290 But the encoding can be changed by this LaTeX-preamble line:
34293 \begin_layout Standard
34298 Declare Inputtext{183}{
34308 f\SpecialChar \textcompwordmark{}
34312 \begin_layout Standard
34313 The character encoding (menu
34315 Document\SpecialChar \menuseparator
34316 Settings\SpecialChar \menuseparator
34319 ) specifies what character appears when a keyboard key is pressed.
34320 When the key for the character '·' is pressed, internally the command
34327 But this command is not available in a formula so that you would get LaTeX-erro
34329 With the changed encoding the right command is chosen automatically, depending
34330 on if the character was inserted into a formula or not.
34333 \begin_layout Standard
34334 The encoding of several characters is saved in definition files.
34335 Fore example the encoding
34339 is defined in the file
34343 that is in the installation folder of LaTeX.
34344 Encodings should only be changed via the LaTeX-preamble and not in the
34346 Otherwise own documents could not be edited by other LyX users working
34347 on other computers.
34350 \begin_layout Standard
34351 \begin_inset VSpace medskip
34354 Besides the centered dot, in this document the degree sign ° is defined
34355 with the following LaTeX-preamble line so that it can directly be inserted
34359 \begin_layout Standard
34364 DeclareInputtext{176}{
34374 f\SpecialChar \textcompwordmark{}
34378 \begin_layout Standard
34379 \begin_inset Newpage newpage
34385 \begin_layout Section
34391 \begin_layout Plain Layout
34400 \begin_layout Standard
34401 This section is a summary of the most important typographic rules, listed
34406 \begin_layout Plain Layout
34407 This collection was partly taken from the German semi-official dictionary
34409 \begin_inset Quotes eld
34413 \begin_inset Quotes erd
34417 \begin_inset CommandInset citation
34423 that lists some of the ISO rules.
34431 \begin_layout Itemize
34440 \begin_layout Plain Layout
34441 done with font styles, see
34442 \begin_inset CommandInset ref
34444 reference "sub:Font-Styles"
34454 \begin_inset space \thinspace{}
34458 \begin_inset Newline newline
34461 Between the value and the unit is the smallest space, see
34462 \begin_inset CommandInset ref
34464 reference "sub:Predefined-Space"
34469 \begin_inset Newline newline
34472 This convention is automatically fulfilled when the command
34479 When it is entered to a formula, two boxes appear.
34480 In the first one the value is inserted, in the second one the unit, and
34482 \begin_inset Formula $\unit[30]{km/h}$
34486 \begin_inset space \thinspace{}
34496 is not a real LaTeX command but the command
34502 , therefore you cannot use it in TeX code.
34505 \begin_layout Itemize
34506 Percent and perthousand signs are set like physical units:
34507 \begin_inset Newline newline
34511 \begin_inset space \thinspace{}
34517 \begin_layout Itemize
34518 The degree sign follows directly on the value: 15°, but not when it is used
34520 \begin_inset space \thinspace{}
34526 \begin_layout Itemize
34527 In numbers with more than four digits the smallest space is inserted before
34528 every third digit to group them:
34538 \begin_inset space \thinspace{}
34542 \begin_inset space \thinspace{}
34548 \begin_layout Itemize
34549 For dimensions like 120×90×40
34550 \begin_inset space \thinspace{}
34553 cm the multiplication sign
34554 \begin_inset Quotes eld
34558 \begin_inset Quotes erd
34562 It is available via the menu
34564 Insert\SpecialChar \menuseparator
34565 Special Character\SpecialChar \menuseparator
34569 With some keyboard definitions it can also be inserted directly.
34572 \begin_layout Itemize
34573 Functions with names consisting of several letters are set upright to avoid
34575 \begin_inset CommandInset ref
34577 reference "sub:Predefined-Functions"
34584 \begin_layout Itemize
34585 Indices consisting of several letters, are set upright:
34586 \begin_inset Formula $E_{\mathrm{kin}}$
34590 \begin_inset Newline newline
34593 Components of matrices are set italic:
34594 \begin_inset Formula $\hat{H}_{kl}$
34600 \begin_layout Itemize
34601 The differentiation/integration operator 'd', the Euler's number 'e', and
34602 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34606 \begin_layout Standard
34607 \begin_inset Newpage newpage
34613 \begin_layout Section
34618 \begin_layout Plain Layout
34627 \begin_layout Standard
34628 Some characters and symbols can be created with several commands.
34629 Here is a list of the synonym commands:
34632 \begin_layout Standard
34633 \begin_inset VSpace bigskip
34637 \begin_inset space \hfill{}
34641 \begin_inset Tabular
34642 <lyxtabular version="3" rows="12" columns="2">
34644 <column alignment="center" valignment="top" width="0pt">
34645 <column alignment="center" valignment="top" width="0pt">
34647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34650 \begin_layout Plain Layout
34656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34659 \begin_layout Plain Layout
34661 \begin_inset Note Note
34664 \begin_layout Plain Layout
34671 is only used as spacer.
34683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34686 \begin_layout Plain Layout
34694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34697 \begin_layout Plain Layout
34701 \begin_layout Plain Layout
34714 \begin_layout Plain Layout
34728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34731 \begin_layout Plain Layout
34739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34742 \begin_layout Plain Layout
34752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34755 \begin_layout Plain Layout
34763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34766 \begin_layout Plain Layout
34776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34779 \begin_layout Plain Layout
34787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34790 \begin_layout Plain Layout
34798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34801 \begin_layout Plain Layout
34809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34812 \begin_layout Plain Layout
34820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34823 \begin_layout Plain Layout
34831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34834 \begin_layout Plain Layout
34844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34847 \begin_layout Plain Layout
34855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34858 \begin_layout Plain Layout
34868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34871 \begin_layout Plain Layout
34879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34882 \begin_layout Plain Layout
34892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34895 \begin_layout Plain Layout
34903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34906 \begin_layout Plain Layout
34916 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34919 \begin_layout Plain Layout
34927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34930 \begin_layout Plain Layout
34938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34941 \begin_layout Plain Layout
34949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34952 \begin_layout Plain Layout
34964 \begin_inset space \hfill{}
34968 \begin_inset Tabular
34969 <lyxtabular version="3" rows="12" columns="2">
34971 <column alignment="center" valignment="top" width="0pt">
34972 <column alignment="center" valignment="top" width="0pt">
34974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34977 \begin_layout Plain Layout
34983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34986 \begin_layout Plain Layout
34994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34997 \begin_layout Plain Layout
35005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35008 \begin_layout Plain Layout
35020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35023 \begin_layout Plain Layout
35031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35034 \begin_layout Plain Layout
35044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35047 \begin_layout Plain Layout
35055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35058 \begin_layout Plain Layout
35068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35071 \begin_layout Plain Layout
35079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35082 \begin_layout Plain Layout
35090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35093 \begin_layout Plain Layout
35101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35104 \begin_layout Plain Layout
35112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35115 \begin_layout Plain Layout
35123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35126 \begin_layout Plain Layout
35136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35139 \begin_layout Plain Layout
35147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35150 \begin_layout Plain Layout
35160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35163 \begin_layout Plain Layout
35171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35174 \begin_layout Plain Layout
35184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35187 \begin_layout Plain Layout
35195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35198 \begin_layout Plain Layout
35208 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35211 \begin_layout Plain Layout
35219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35222 \begin_layout Plain Layout
35232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35235 \begin_layout Plain Layout
35243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35246 \begin_layout Plain Layout
35260 \begin_inset space \hfill{}
35266 \begin_layout Standard
35267 \begin_inset Newpage newpage
35273 \begin_layout Bibliography
35274 \begin_inset CommandInset bibitem
35275 LatexCommand bibitem
35287 The LaTeX Companion
35290 Addison Wesley, 2004
35293 \begin_layout Bibliography
35294 \begin_inset CommandInset bibitem
35295 LatexCommand bibitem
35301 \begin_inset CommandInset href
35304 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35308 of LaTeX's math abilities
35311 \begin_layout Bibliography
35312 \begin_inset CommandInset bibitem
35313 LatexCommand bibitem
35318 LaTeX tips and tricks-
35319 \begin_inset CommandInset href
35322 target "http://tug.org/TeXnik/"
35329 \begin_layout Bibliography
35330 \begin_inset CommandInset bibitem
35331 LatexCommand bibitem
35337 \begin_inset CommandInset href
35340 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35348 \begin_layout Plain Layout
35360 \begin_layout Bibliography
35361 \begin_inset CommandInset bibitem
35362 LatexCommand bibitem
35368 \begin_inset CommandInset href
35371 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35375 of all symbols available with LaTeX-packages
35378 \begin_layout Bibliography
35379 \begin_inset CommandInset bibitem
35380 LatexCommand bibitem
35386 \begin_inset CommandInset href
35388 name "Documentation"
35389 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35393 of the LaTeX-package
35401 \begin_layout Plain Layout
35402 Packages ! hyperref
35410 \begin_layout Bibliography
35411 \begin_inset CommandInset bibitem
35412 LatexCommand bibitem
35418 \begin_inset CommandInset href
35421 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35432 \begin_inset CommandInset ref
35434 reference "sub:Operator-Limits"
35442 \begin_layout Plain Layout
35453 \begin_layout Bibliography
35454 \begin_inset CommandInset bibitem
35455 LatexCommand bibitem
35466 Auflage, Duden 2001
35469 \begin_layout Subsubsection*
35470 \begin_inset CommandInset index_print
35471 LatexCommand printindex