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
3437 \begin_inset space \thinspace{}
3441 \begin_inset space ~
3448 \begin_layout Plain Layout
3449 More about chemical symbols is written in
3450 \begin_inset CommandInset ref
3452 reference "sub:Chemical-Symbols-and"
3461 the following problem occurs:
3464 \begin_layout Standard
3466 \begin_inset Tabular
3467 <lyxtabular version="3" rows="2" columns="2">
3469 <column alignment="center" valignment="top" width="0pt">
3470 <column alignment="center" valignment="top" width="0pt">
3472 <cell alignment="center" valignment="top" usebox="none">
3475 \begin_layout Plain Layout
3476 Indices created with sub- and superscripts:
3481 <cell alignment="center" valignment="top" usebox="none">
3484 \begin_layout Plain Layout
3485 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3495 <cell alignment="center" valignment="top" usebox="none">
3498 \begin_layout Plain Layout
3504 <cell alignment="center" valignment="top" usebox="none">
3507 \begin_layout Plain Layout
3508 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3522 \begin_inset Note Note
3525 \begin_layout Plain Layout
3532 is only used as spacer.
3540 \begin_layout Standard
3541 The shorter index is by default placed below or above the first character
3542 of the longer index.
3543 To avoid this there is the command
3553 \begin_layout Plain Layout
3561 or the math toolbar button
3562 \begin_inset space \thinspace{}
3569 \begin_layout Plain Layout
3570 can be found in the submenu of the toolbar button
3571 \begin_inset Graphics
3572 filename ../images/math/space.png
3583 \begin_inset Graphics
3584 filename ../images/math/phantom.png
3589 that creates one or more phantom characters.
3596 a small blue box appears that is superposed with two red arrows.
3597 The arrows indicate that the complete width and height of the box content
3598 will be created as placeholder.
3599 Phantom characters are accordingly placeholders with the size of the characters.
3602 \begin_layout Standard
3604 \begin_inset Tabular
3605 <lyxtabular version="3" rows="4" columns="2">
3607 <column alignment="center" valignment="top" width="0">
3608 <column alignment="center" valignment="top" width="0">
3610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3613 \begin_layout Plain Layout
3619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3622 \begin_layout Plain Layout
3624 \begin_inset Note Note
3627 \begin_layout Plain Layout
3634 is only used as spacer.
3646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3649 \begin_layout Plain Layout
3654 \begin_layout Plain Layout
3669 \begin_layout Plain Layout
3679 \begin_inset Formula $\to$
3686 \begin_layout Plain Layout
3700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3703 \begin_layout Plain Layout
3704 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3717 \begin_layout Plain Layout
3722 \begin_layout Plain Layout
3737 \begin_layout Plain Layout
3747 \begin_inset Formula $\to$
3754 \begin_layout Plain Layout
3768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3771 \begin_layout Plain Layout
3772 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3785 \begin_layout Plain Layout
3792 \begin_layout Plain Layout
3807 \begin_layout Plain Layout
3817 \begin_inset Formula $\to$
3824 \begin_layout Plain Layout
3838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3841 \begin_layout Plain Layout
3842 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3858 \begin_layout Standard
3859 Furthermore there are the commands
3869 \begin_layout Plain Layout
3878 \begin_inset space ~
3882 \begin_inset Graphics
3883 filename ../images/math/vphantom.png
3898 \begin_layout Plain Layout
3907 \begin_inset space ~
3911 \begin_inset Graphics
3912 filename ../images/math/hphantom.png
3924 creates only space for the maximal height of the characters in the box
3925 but not for its width.
3932 creates only space for the width of the box content.
3933 Therefore the boxes of both commands have only one red arrow.
3936 \begin_layout Standard
3947 \begin_layout Plain Layout
3962 space for the height of the integral sign,
3966 \begin_layout Plain Layout
3973 creates an integral sign, see
3974 \begin_inset CommandInset ref
3976 reference "sub:Big-Operators"
3985 because this is the larger character.
3986 An example application is in
3987 \begin_inset CommandInset ref
3989 reference "sub:Multiline-Brackets"
3996 \begin_layout Subsection
4001 \begin_layout Plain Layout
4011 \begin_layout Plain Layout
4012 Formula ! underlined
4020 \begin_layout Standard
4022 \begin_inset Tabular
4023 <lyxtabular version="3" rows="4" columns="2">
4025 <column alignment="center" valignment="top" width="0pt">
4026 <column alignment="center" valignment="top" width="0pt">
4028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4031 \begin_layout Plain Layout
4037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4040 \begin_layout Plain Layout
4042 \begin_inset Note Note
4045 \begin_layout Plain Layout
4052 is only used as spacer.
4064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4067 \begin_layout Plain Layout
4074 \begin_layout Plain Layout
4087 \begin_layout Plain Layout
4100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4103 \begin_layout Plain Layout
4104 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4114 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4117 \begin_layout Plain Layout
4124 \begin_layout Plain Layout
4137 \begin_layout Plain Layout
4150 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4153 \begin_layout Plain Layout
4154 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4167 \begin_layout Plain Layout
4174 \begin_layout Plain Layout
4189 \begin_layout Plain Layout
4203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4206 \begin_layout Plain Layout
4207 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4223 \begin_layout Standard
4224 In the last example it doesn't matter if first
4239 \begin_layout Standard
4240 To double underline e.
4241 \begin_inset space \thinspace{}
4254 \begin_layout Standard
4255 It is possible to place up to 6 lines above or below characters.
4258 \begin_layout Standard
4259 \begin_inset VSpace bigskip
4262 Custom lines can be created using the command
4272 \begin_layout Plain Layout
4280 which has the following scheme:
4283 \begin_layout Standard
4288 rule[vertical offset]{length}{thickness}
4291 \begin_layout Standard
4292 The optional vertical offset shifts the line upwards (or downwards, when
4293 the value is negative).
4295 \begin_inset CommandInset ref
4297 reference "tab:Available-units"
4301 can be used for the values.
4302 Here are two example lines created with the commands
4303 \begin_inset Newline newline
4310 rule[-2ex]{3cm}{2pt}
4321 \begin_layout Standard
4323 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4329 \begin_layout Standard
4336 can also be used for text when it is inserted in TeX-mode.
4339 \begin_layout Subsection
4341 \begin_inset CommandInset label
4351 \begin_layout Plain Layout
4360 \begin_layout Standard
4361 There are different types of ellipses available.
4365 \begin_layout Plain Layout
4366 In the math toolbar in the submenu of the button
4367 \begin_inset Graphics
4368 filename ../images/math/ldots.png
4378 For listings dots at the baseline are used (
4388 \begin_layout Plain Layout
4396 ), while for operations dots are needed that are on the same height as the
4407 \begin_layout Plain Layout
4416 When using the command
4426 \begin_layout Plain Layout
4434 , LaTeX decides on the basis of the next character what type is used.
4437 \begin_layout Standard
4439 \begin_inset Tabular
4440 <lyxtabular version="3" rows="8" columns="2">
4442 <column alignment="center" valignment="top" width="0pt">
4443 <column alignment="center" valignment="top" width="0pt">
4445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4448 \begin_layout Plain Layout
4454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4457 \begin_layout Plain Layout
4465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4468 \begin_layout Plain Layout
4473 \begin_layout Plain Layout
4488 \begin_layout Plain Layout
4502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4505 \begin_layout Plain Layout
4506 \begin_inset Formula $A_{1},\dots,A_{n}$
4516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4519 \begin_layout Plain Layout
4524 \begin_layout Plain Layout
4539 \begin_layout Plain Layout
4553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4556 \begin_layout Plain Layout
4557 \begin_inset Formula $A_{1}+\dots+A_{n}$
4567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4570 \begin_layout Plain Layout
4575 \begin_layout Plain Layout
4590 \begin_layout Plain Layout
4604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4607 \begin_layout Plain Layout
4608 \begin_inset Formula $A_{1},\ldots,A_{n}$
4618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4621 \begin_layout Plain Layout
4626 \begin_layout Plain Layout
4641 \begin_layout Plain Layout
4655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4658 \begin_layout Plain Layout
4659 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4672 \begin_layout Plain Layout
4680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4683 \begin_layout Plain Layout
4684 \begin_inset Formula $\vdots$
4694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4697 \begin_layout Plain Layout
4705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4708 \begin_layout Plain Layout
4709 \begin_inset Formula $\ddots$
4719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4722 \begin_layout Plain Layout
4724 \begin_inset space \thinspace{}
4727 matrix with the different dots
4732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4735 \begin_layout Plain Layout
4736 \begin_inset Formula $\begin{array}{ccc}
4737 A_{11} & \cdots & A_{1m}\\
4738 \vdots & \ddots & \vdots\\
4739 A_{n1} & \cdots & A_{nm}\end{array}$
4755 \begin_layout Standard
4756 The ellipses available in menu
4758 Insert\SpecialChar \menuseparator
4760 \begin_inset space ~
4774 \begin_layout Standard
4775 \begin_inset VSpace medskip
4778 Specially for matrices there are ellipses that span over several columns.
4779 They are created with the command
4789 \begin_layout Plain Layout
4797 , that has the following scheme:
4800 \begin_layout Standard
4805 hdotsfor[distance]{number of columns}
4808 \begin_layout Standard
4809 The number of columns specifies how many columns should be spanned.
4810 Distance is a factor for the distance between the dots.
4813 \begin_layout Standard
4814 In the following matrix the command
4820 was inserted in the first box of the second line, to get an ellipsis with
4821 a dot distance twice as long as with the command
4828 \begin_inset Formula \[
4829 \left(\begin{array}{cccc}
4832 q & w & e & r\end{array}\right)\]
4836 Note that the matrix fields that should be spanned must be empty, otherwise
4837 you get LaTeX-errors.
4840 \begin_layout Standard
4841 \begin_inset VSpace bigskip
4844 Furthermore you can fill with the command
4854 \begin_layout Plain Layout
4862 the rest of a line with dots.
4863 The effect of these commands is the same like with
4870 \begin_inset CommandInset ref
4872 reference "sub:Variable-Space"
4879 \begin_layout Standard
4880 For example the command
4888 \begin_layout Plain Layout
4902 \begin_layout Standard
4903 \begin_inset Formula $A\dotfill B$
4909 \begin_layout Standard
4916 there is for a line the command
4926 \begin_layout Plain Layout
4937 \begin_layout Standard
4938 \begin_inset Formula $A\hrulefill B$
4944 \begin_layout Standard
4945 To use the commands for text, they have to be inserted in TeX-mode.
4948 \begin_layout Section
4950 \begin_inset CommandInset label
4960 \begin_layout Plain Layout
4969 \begin_layout Standard
4970 Matrices can be inserted via the math toolbar button
4971 \begin_inset Graphics
4972 filename ../images/dialog-show_mathmatrix.png
4979 Insert\SpecialChar \menuseparator
4980 Math\SpecialChar \menuseparator
4984 You will be asked for the number of matrix columns and rows, and the alignment.
4985 The vertical alignment is hereby only of importance for matrices in inline
4989 \begin_layout Standard
4990 The first matrix is top
4991 \begin_inset Formula $\begin{array}[t]{cccc}
4994 C & F & I & L\end{array}$
4998 \begin_inset Formula $\begin{array}{cccc}
5001 C & F & I & L\end{array}$
5004 , and the third bottom
5005 \begin_inset Formula $\begin{array}[b]{cccc}
5008 C & F & I & L\end{array}$
5014 \begin_layout Standard
5015 The horizontal alignment specifies how the column entries should be aligned.
5016 It is set by entering a letter for every column.
5021 denotes left aligned,
5030 To create for example a 4
5035 \begin_inset space ~
5038 matrix where the first column is left aligned, the second and third are
5039 centered, and the last one is right aligned, one enters for the horizontal
5045 Normally are in a matrix all columns centered, therefore the default is
5046 for every column is a
5053 \begin_layout Standard
5054 Horizontal alignment:
5057 \begin_layout Standard
5063 \begin_inset Formula $\begin{array}{lll}
5066 C & F & 10000\end{array}$
5074 \begin_inset Formula $\begin{array}{ccc}
5077 C & F & 10000\end{array}$
5085 \begin_inset Formula $\begin{array}{rrr}
5088 C & F & 10000\end{array}$
5094 \begin_layout Standard
5095 To add or delete rows and columns subsequently, the math toolbar buttons
5097 \begin_inset Graphics
5098 filename ../images/tabular-feature_append-row.png
5104 \begin_inset Graphics
5105 filename ../images/tabular-feature_delete-row.png
5111 \begin_inset space \thinspace{}
5116 Edit\SpecialChar \menuseparator
5120 New rows can also be created with
5123 arg "newline-insert newline"
5129 \begin_layout Standard
5130 \begin_inset VSpace bigskip
5133 Parentheses around a matrix can can either be created with the commands
5144 \begin_layout Plain Layout
5162 \begin_layout Plain Layout
5173 \begin_inset space ~
5179 \begin_inset CommandInset ref
5181 reference "sub:Automatic-Bracket-Size"
5185 , or by using the following commands:
5186 \begin_inset VSpace medskip
5192 \begin_layout Standard
5193 \begin_inset space \hfill{}
5197 \begin_inset Tabular
5198 <lyxtabular version="3" rows="4" columns="2">
5200 <column alignment="center" valignment="top" width="0">
5201 <column alignment="center" valignment="top" width="0">
5203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5206 \begin_layout Plain Layout
5212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5215 \begin_layout Plain Layout
5217 \begin_inset Note Note
5220 \begin_layout Plain Layout
5227 is only used as spacer.
5239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5242 \begin_layout Plain Layout
5249 \begin_layout Plain Layout
5263 \begin_inset space \thinspace{}
5271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5274 \begin_layout Plain Layout
5275 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5276 0 & \textrm{-}\mathrm{i}\\
5277 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5290 \begin_layout Plain Layout
5297 \begin_layout Plain Layout
5311 \begin_inset space \thinspace{}
5319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5322 \begin_layout Plain Layout
5323 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5324 0 & \textrm{-}\mathrm{i}\\
5325 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5338 \begin_layout Plain Layout
5345 \begin_layout Plain Layout
5359 \begin_inset space \thinspace{}
5367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5370 \begin_layout Plain Layout
5371 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5372 0 & \textrm{-}\mathrm{i}\\
5373 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5387 \begin_inset space \hfill{}
5391 \begin_inset Tabular
5392 <lyxtabular version="3" rows="4" columns="2">
5394 <column alignment="center" valignment="top" width="0">
5395 <column alignment="center" valignment="top" width="0">
5397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5400 \begin_layout Plain Layout
5406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5409 \begin_layout Plain Layout
5417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5420 \begin_layout Plain Layout
5427 \begin_layout Plain Layout
5441 \begin_inset space \thinspace{}
5449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5452 \begin_layout Plain Layout
5453 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5454 0 & \textrm{-}\mathrm{i}\\
5455 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5468 \begin_layout Plain Layout
5475 \begin_layout Plain Layout
5489 \begin_inset space \thinspace{}
5497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5500 \begin_layout Plain Layout
5501 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5502 0 & \textrm{-}\mathrm{i}\\
5503 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5516 \begin_layout Plain Layout
5523 \begin_layout Plain Layout
5537 \begin_inset space \thinspace{}
5545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5548 \begin_layout Plain Layout
5549 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5550 0 & \textrm{-}\mathrm{i}\\
5551 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5565 \begin_inset space \hfill{}
5571 \begin_layout Standard
5572 \begin_inset VSpace medskip
5576 \begin_inset space \thinspace{}
5580 \begin_inset space ~
5589 is inserted, a blue box appears between two vertical lines where the matrix
5593 \begin_layout Standard
5594 \begin_inset VSpace bigskip
5597 As all multiline formulas are matrices, the length
5607 \begin_layout Plain Layout
5615 that is described in
5616 \begin_inset CommandInset ref
5618 reference "sub:Column-Separation"
5622 can also be used to change the column separation of matrices.
5625 \begin_layout Standard
5626 To change the row separation, the command
5636 \begin_layout Plain Layout
5645 It is used as follows:
5648 \begin_layout Standard
5655 arraystretch}{stretch factor}
5659 \begin_layout Plain Layout
5670 \begin_layout Standard
5677 assigns the stretch factor to the predefined command
5685 \begin_inset space \thinspace{}
5689 \begin_inset space ~
5692 the row separation, use the factor 2.
5693 This is then used for all following matrices.
5694 To go back to the original separation, assign the factor 1 to
5703 \begin_layout Standard
5704 To set matrices into a text line, the command
5714 \begin_layout Plain Layout
5723 When it is inserted a blue box with two dashed lines appears.
5724 In this box the matrix is inserted.
5727 \begin_layout Standard
5729 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5730 C & D\end{smallmatrix}\right)$
5736 \begin_layout Section
5737 Brackets and Delimiters
5741 \begin_layout Plain Layout
5751 \begin_layout Plain Layout
5760 \begin_layout Subsection
5761 Vertical Brackets and Delimiters
5765 \begin_layout Plain Layout
5774 \begin_layout Standard
5775 \begin_inset space \hfill{}
5779 \begin_inset Tabular
5780 <lyxtabular version="3" rows="9" columns="2">
5782 <column alignment="center" valignment="top" width="0pt">
5783 <column alignment="center" valignment="top" width="0pt">
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5788 \begin_layout Plain Layout
5794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5797 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5808 \begin_layout Plain Layout
5814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5817 \begin_layout Plain Layout
5818 \begin_inset Formula $($
5828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5831 \begin_layout Plain Layout
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5840 \begin_layout Plain Layout
5841 \begin_inset Formula $\{$
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5854 \begin_layout Plain Layout
5860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5863 \begin_layout Plain Layout
5864 \begin_inset Formula $[$
5874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5877 \begin_layout Plain Layout
5885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5888 \begin_layout Plain Layout
5889 \begin_inset Formula $\langle$
5899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5902 \begin_layout Plain Layout
5910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5913 \begin_layout Plain Layout
5914 \begin_inset Formula $\lceil$
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5938 \begin_layout Plain Layout
5939 \begin_inset Formula $\lfloor$
5949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5952 \begin_layout Plain Layout
5958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5961 \begin_layout Plain Layout
5962 \begin_inset Formula $/$
5972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5975 \begin_layout Plain Layout
5981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5984 \begin_layout Plain Layout
5985 \begin_inset Formula $|$
5999 \begin_inset space \hfill{}
6003 \begin_inset Tabular
6004 <lyxtabular version="3" rows="9" columns="2">
6006 <column alignment="center" valignment="top" width="0pt">
6007 <column alignment="center" valignment="top" width="0pt">
6009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6012 \begin_layout Plain Layout
6018 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6021 \begin_layout Plain Layout
6029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6032 \begin_layout Plain Layout
6038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6041 \begin_layout Plain Layout
6042 \begin_inset Formula $)$
6052 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6055 \begin_layout Plain Layout
6061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6064 \begin_layout Plain Layout
6065 \begin_inset Formula $\}$
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6078 \begin_layout Plain Layout
6084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6087 \begin_layout Plain Layout
6088 \begin_inset Formula $]$
6098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6101 \begin_layout Plain Layout
6109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6112 \begin_layout Plain Layout
6113 \begin_inset Formula $\rangle$
6123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6126 \begin_layout Plain Layout
6134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6137 \begin_layout Plain Layout
6138 \begin_inset Formula $\rceil$
6148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6151 \begin_layout Plain Layout
6159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6162 \begin_layout Plain Layout
6163 \begin_inset Formula $\rfloor$
6173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6176 \begin_layout Plain Layout
6186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6189 \begin_layout Plain Layout
6190 \begin_inset Formula $\backslash$
6200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6203 \begin_layout Plain Layout
6211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6214 \begin_layout Plain Layout
6215 \begin_inset Formula $\|$
6229 \begin_inset space \hfill{}
6235 \begin_layout Standard
6238 \begin_inset Note Greyedout
6241 \begin_layout Plain Layout
6246 In TeX-mode the command
6256 \begin_layout Plain Layout
6264 must be used for the backslash, because the command
6272 produces there a line break.
6280 \begin_layout Standard
6281 For all characters listed above the size can be adjusted with the commands
6282 described in the following two subsections.
6283 When using these commands, the characters < and > can directly be used
6284 instead of the commands
6299 \begin_layout Subsubsection
6301 \begin_inset CommandInset label
6303 name "sub:Manual-Bracket-Size"
6311 \begin_layout Plain Layout
6312 Bracket size ! manual
6320 \begin_layout Standard
6321 The bracket size can be specified manually by the LaTeX-commands
6331 \begin_layout Plain Layout
6364 denotes the smallest and
6370 the largest bracket size.
6373 \begin_layout Standard
6374 These commands are used to emphasize levels of brackets:
6377 \begin_layout Standard
6379 \begin_inset Tabular
6380 <lyxtabular version="3" rows="2" columns="2">
6382 <column alignment="center" valignment="top" width="0pt">
6383 <column alignment="center" valignment="top" width="0pt">
6385 <cell alignment="center" valignment="top" usebox="none">
6388 \begin_layout Plain Layout
6389 all brackets in the same size:
6394 <cell alignment="center" valignment="top" usebox="none">
6397 \begin_layout Plain Layout
6398 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6408 <cell alignment="center" valignment="top" usebox="none">
6411 \begin_layout Plain Layout
6417 <cell alignment="center" valignment="top" usebox="none">
6420 \begin_layout Plain Layout
6421 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6435 \begin_inset Note Note
6438 \begin_layout Plain Layout
6445 is only used as spacer.
6453 \begin_layout Standard
6454 For the second formula the command
6464 \begin_layout Plain Layout
6478 \begin_layout Standard
6479 Here is an overview about all bracket sizes:
6482 \begin_layout Standard
6502 \begin_layout Plain Layout
6519 \begin_layout Plain Layout
6532 \begin_layout Plain Layout
6548 \begin_layout Standard
6550 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6556 \begin_layout Standard
6563 -commands there is the variant
6573 \begin_layout Plain Layout
6581 that adds a bit more space between the bracket and its content, and the
6598 \begin_layout Plain Layout
6608 , that don't add additional space.
6613 at the end of the command
6619 is for a left bracket; for a right bracket this will be replaced by an
6625 A left or right bracket can each be an opening or closing bracket.
6628 \begin_layout Standard
6629 In the following table is a comparison of the variants:
6632 \begin_layout Standard
6634 \begin_inset Tabular
6635 <lyxtabular version="3" rows="5" columns="2">
6637 <column alignment="center" valignment="middle" width="0">
6638 <column alignment="center" valignment="middle" width="0">
6640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6643 \begin_layout Plain Layout
6649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6652 \begin_layout Plain Layout
6654 \begin_inset Note Note
6657 \begin_layout Plain Layout
6664 is only used as spacer.
6676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6679 \begin_layout Plain Layout
6694 \begin_layout Plain Layout
6712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6715 \begin_layout Plain Layout
6716 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6729 \begin_layout Plain Layout
6744 \begin_layout Plain Layout
6762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6765 \begin_layout Plain Layout
6766 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6779 \begin_layout Plain Layout
6794 \begin_layout Plain Layout
6812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6815 \begin_layout Plain Layout
6816 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6829 \begin_layout Plain Layout
6841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6844 \begin_layout Plain Layout
6845 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6861 \begin_layout Subsubsection
6862 Automatic Bracket Size
6863 \begin_inset CommandInset label
6865 name "sub:Automatic-Bracket-Size"
6873 \begin_layout Plain Layout
6874 Bracket size ! automatic
6882 \begin_layout Standard
6883 Brackets with variable size can be inserted with the commands
6893 \begin_layout Plain Layout
6911 \begin_layout Plain Layout
6919 or via the math toolbar button
6920 \begin_inset Graphics
6921 filename ../images/dialog-show_mathdelimiter.png
6939 the wanted bracket must be inserted.
6940 The bracket size will then automatically be calculated for the output.
6943 \begin_layout Standard
6945 normal bracket: The command
6955 \begin_layout Plain Layout
6965 \begin_inset Formula $\downarrow$
6972 \begin_layout Plain Layout
6984 \begin_inset Formula \[
6992 \begin_layout Standard
6994 multiline bracket: The command
7006 \begin_layout Plain Layout
7016 \begin_inset Formula $\downarrow$
7023 \begin_layout Plain Layout
7037 \begin_inset Formula \[
7038 \ln\left(\frac{A}{C}\right)\]
7045 \begin_layout Standard
7061 \begin_inset space ~
7067 This has the advantage that you can see in LyX immediately the real bracket
7068 size and that the matching right bracket will be created too.
7069 \begin_inset Newline newline
7072 The command for the last example would then be:
7086 \begin_layout Plain Layout
7096 \begin_inset Formula $\downarrow$
7102 \begin_layout Standard
7103 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7104 For example the command
7114 \begin_layout Plain Layout
7124 \begin_inset Formula $\downarrow$
7131 \begin_layout Plain Layout
7147 \begin_inset Formula \[
7148 \left.\frac{A}{B}\right\} \]
7166 will be converted by LyX to brackets in the right size when the document
7167 is reloaded and an omitted bracket will appear as dashed line.
7170 \begin_layout Standard
7171 \begin_inset VSpace bigskip
7174 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7185 \begin_layout Plain Layout
7193 is additionally available for all brackets and limits.
7194 With this command the height of the following character is adapted to the
7195 one of the surrounding brackets, what is e.
7196 \begin_inset space \thinspace{}
7200 \begin_inset space ~
7203 needed for physical vectors:
7204 \begin_inset Formula \[
7205 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7209 For physical vectors there is a special LaTeX-package, described in
7210 \begin_inset CommandInset ref
7212 reference "sub:Physical-Vectors"
7219 \begin_layout Subsection
7224 \begin_layout Plain Layout
7225 Brackets ! horizontal
7233 \begin_layout Standard
7235 \begin_inset Tabular
7236 <lyxtabular version="3" rows="4" columns="2">
7238 <column alignment="center" valignment="top" width="0pt">
7239 <column alignment="center" valignment="top" width="0pt">
7241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7244 \begin_layout Plain Layout
7246 \begin_inset Note Note
7249 \begin_layout Plain Layout
7256 is only used as spacer.
7266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7269 \begin_layout Plain Layout
7277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7280 \begin_layout Plain Layout
7284 \begin_layout Plain Layout
7299 \begin_layout Plain Layout
7312 \begin_layout Plain Layout
7325 \begin_layout Plain Layout
7338 \begin_layout Plain Layout
7349 \begin_layout Plain Layout
7362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7365 \begin_layout Plain Layout
7366 \begin_inset Formula $\overbrace{A+B}^{3}$
7376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7379 \begin_layout Plain Layout
7383 \begin_layout Plain Layout
7398 \begin_layout Plain Layout
7411 \begin_layout Plain Layout
7424 \begin_layout Plain Layout
7435 \begin_layout Plain Layout
7448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7451 \begin_layout Plain Layout
7452 \begin_inset Formula $\underbrace{A+B}_{5}$
7462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7465 \begin_layout Plain Layout
7472 \begin_layout Plain Layout
7487 \begin_layout Plain Layout
7500 \begin_layout Plain Layout
7513 \begin_layout Plain Layout
7526 \begin_layout Plain Layout
7539 \begin_layout Plain Layout
7552 \begin_layout Plain Layout
7566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7569 \begin_layout Plain Layout
7570 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7586 \begin_layout Standard
7587 In the last example it doesn't matter if
7599 is inserted at first.
7602 \begin_layout Standard
7603 \begin_inset VSpace bigskip
7606 When brackets are needed that overlap each other, multiline formulas, as
7608 \begin_inset CommandInset ref
7610 reference "sec:Multiline-Formulas"
7615 \begin_inset Formula \begin{eqnarray*}
7616 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7617 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7621 In the first row the formula is inserted together with the first brace.
7622 It is hereby important that the space command
7626 \begin_layout Plain Layout
7627 Space commands are explained in
7628 \begin_inset CommandInset ref
7630 reference "sub:Predefined-Space"
7645 is inserted before the first
7646 \begin_inset Formula $d$
7649 , because the brace that ends behind the
7650 \begin_inset Formula $q$
7653 prevents that the following
7654 \begin_inset Quotes eld
7658 \begin_inset Quotes erd
7661 is surrounded by space.
7665 \begin_layout Plain Layout
7666 because a bracket is not handled as character, see
7667 \begin_inset CommandInset ref
7669 reference "sub:Binary-Operators"
7678 In the second row the second brace is inserted.
7679 As it should begin before the
7680 \begin_inset Formula $b$
7695 \begin_layout Plain Layout
7703 \begin_inset CommandInset ref
7705 reference "sub:Placeholders"
7714 This space is needed because the
7715 \begin_inset Quotes eld
7719 \begin_inset Quotes erd
7722 is also surrounded by space in the formula.
7723 The brace is placed under the command
7732 \begin_layout Standard
7733 It gets more complicated when brackets overlap each other, like in the following
7738 \begin_layout Plain Layout
7750 \begin_inset Formula \begin{eqnarray*}
7751 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7752 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7760 \begin_layout Plain Layout
7771 The first formula row is the same as the second row of the previous example,
7772 with the difference that the brace is above.
7773 The second row contains the formula together with the second brace.
7774 To avoid that there is space between the upper brace in the first row and
7775 the formula, the row spacing need to be reduced.
7776 This is not easily possible due to a bug in LyX
7780 \begin_layout Plain Layout
7781 \begin_inset CommandInset href
7783 name "LyX-bug #1505"
7784 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7794 As solution for the problem, the global formula row separation
7804 \begin_layout Plain Layout
7812 must be changed to -6
7813 \begin_inset space \thinspace{}
7816 pt before the formula with the command
7831 is set back after the formula to the standard value of 3
7832 \begin_inset space \thinspace{}
7835 pt using the same command.
7836 More about the row separation in formulas is explained in
7837 \begin_inset CommandInset ref
7839 reference "sub:Line-Separation"
7846 \begin_layout Section
7851 \begin_layout Plain Layout
7860 \begin_layout Standard
7861 Arrows can be inserted via the math toolbar button
7862 \begin_inset Graphics
7863 filename ../images/math/leftarrow.png
7868 or the commands listed in the following subsections.
7871 \begin_layout Standard
7872 \begin_inset Newpage newpage
7878 \begin_layout Subsection
7883 \begin_layout Plain Layout
7892 \begin_layout Standard
7893 \begin_inset space \hfill{}
7897 \begin_inset Tabular
7898 <lyxtabular version="3" rows="8" columns="2">
7900 <column alignment="center" valignment="top" width="0pt">
7901 <column alignment="center" valignment="top" width="0pt">
7903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7906 \begin_layout Plain Layout
7912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7915 \begin_layout Plain Layout
7923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7926 \begin_layout Plain Layout
7934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7937 \begin_layout Plain Layout
7938 \begin_inset Formula $\gets$
7948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7951 \begin_layout Plain Layout
7959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7962 \begin_layout Plain Layout
7963 \begin_inset Formula $\Leftarrow$
7973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7976 \begin_layout Plain Layout
7984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7987 \begin_layout Plain Layout
7988 \begin_inset Formula $\longleftarrow$
7998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8001 \begin_layout Plain Layout
8009 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8012 \begin_layout Plain Layout
8013 \begin_inset Formula $\Longleftarrow$
8023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8026 \begin_layout Plain Layout
8034 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8037 \begin_layout Plain Layout
8038 \begin_inset Formula $\leftharpoonup$
8048 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8051 \begin_layout Plain Layout
8059 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8062 \begin_layout Plain Layout
8063 \begin_inset Formula $\leftharpoondown$
8073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8076 \begin_layout Plain Layout
8084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8087 \begin_layout Plain Layout
8088 \begin_inset Formula $\hookleftarrow$
8102 \begin_inset space \hfill{}
8106 \begin_inset Tabular
8107 <lyxtabular version="3" rows="8" columns="2">
8109 <column alignment="center" valignment="top" width="0pt">
8110 <column alignment="center" valignment="top" width="0pt">
8112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8115 \begin_layout Plain Layout
8121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8124 \begin_layout Plain Layout
8132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8135 \begin_layout Plain Layout
8143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8146 \begin_layout Plain Layout
8147 \begin_inset Formula $\to$
8157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8160 \begin_layout Plain Layout
8168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8171 \begin_layout Plain Layout
8172 \begin_inset Formula $\Rightarrow$
8182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8185 \begin_layout Plain Layout
8193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8196 \begin_layout Plain Layout
8197 \begin_inset Formula $\longrightarrow$
8207 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8221 \begin_layout Plain Layout
8222 \begin_inset Formula $\Longrightarrow$
8232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8235 \begin_layout Plain Layout
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8246 \begin_layout Plain Layout
8247 \begin_inset Formula $\rightharpoonup$
8257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8260 \begin_layout Plain Layout
8268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8271 \begin_layout Plain Layout
8272 \begin_inset Formula $\rightharpoondown$
8282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8285 \begin_layout Plain Layout
8293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8296 \begin_layout Plain Layout
8297 \begin_inset Formula $\hookrightarrow$
8311 \begin_inset space \hfill{}
8317 \begin_layout Standard
8318 \begin_inset space \hfill{}
8322 \begin_inset Tabular
8323 <lyxtabular version="3" rows="6" columns="2">
8325 <column alignment="center" valignment="top" width="0pt">
8326 <column alignment="center" valignment="top" width="0pt">
8328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8331 \begin_layout Plain Layout
8337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8340 \begin_layout Plain Layout
8348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8351 \begin_layout Plain Layout
8359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8362 \begin_layout Plain Layout
8363 \begin_inset Formula $\leftrightarrow$
8373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8376 \begin_layout Plain Layout
8384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8387 \begin_layout Plain Layout
8388 \begin_inset Formula $\Leftrightarrow$
8398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8401 \begin_layout Plain Layout
8409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8412 \begin_layout Plain Layout
8413 \begin_inset Formula $\longleftrightarrow$
8423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8426 \begin_layout Plain Layout
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8437 \begin_layout Plain Layout
8438 \begin_inset Formula $\Longleftrightarrow$
8448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8451 \begin_layout Plain Layout
8459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8462 \begin_layout Plain Layout
8463 \begin_inset Formula $\rightleftharpoons$
8477 \begin_inset space \hspace{}
8482 \begin_inset space \hfill{}
8486 \begin_inset Tabular
8487 <lyxtabular version="3" rows="5" columns="2">
8489 <column alignment="center" valignment="top" width="0pt">
8490 <column alignment="center" valignment="top" width="0pt">
8492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8495 \begin_layout Plain Layout
8501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8504 \begin_layout Plain Layout
8512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8515 \begin_layout Plain Layout
8523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8526 \begin_layout Plain Layout
8527 \begin_inset Formula $\mapsto$
8537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8540 \begin_layout Plain Layout
8548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8551 \begin_layout Plain Layout
8552 \begin_inset Formula $\longmapsto$
8562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8565 \begin_layout Plain Layout
8573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8576 \begin_layout Plain Layout
8577 \begin_inset Formula $\leadsto$
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8601 \begin_layout Plain Layout
8602 \begin_inset Formula $\dasharrow$
8616 \begin_inset space \hfill{}
8622 \begin_layout Standard
8623 \begin_inset VSpace medskip
8626 Arrows used as accent like e.
8627 \begin_inset space \thinspace{}
8631 \begin_inset space ~
8634 vector arrows are listed in
8635 \begin_inset CommandInset ref
8637 reference "sec:Accents"
8644 \begin_layout Standard
8645 \begin_inset VSpace bigskip
8648 Furthermore there are the labeled arrows
8652 \begin_layout Plain Layout
8668 \begin_layout Plain Layout
8686 \begin_layout Plain Layout
8693 \begin_layout Plain Layout
8708 When inserting one of these commands in a formula, an arrow with two blue
8709 boxes appear where the label can be inserted.
8710 The length of the arrow adapts to the label width.
8713 \begin_layout Standard
8715 \begin_inset Tabular
8716 <lyxtabular version="3" rows="3" columns="2">
8718 <column alignment="center" valignment="top" width="0pt">
8719 <column alignment="center" valignment="top" width="0pt">
8721 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8724 \begin_layout Plain Layout
8730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8733 \begin_layout Plain Layout
8735 \begin_inset Note Note
8738 \begin_layout Plain Layout
8745 is only used as spacer.
8757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8760 \begin_layout Plain Layout
8767 \begin_layout Plain Layout
8777 \begin_inset Formula $\downarrow$
8781 \begin_inset Formula $\to$
8789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8792 \begin_layout Plain Layout
8793 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8806 \begin_layout Plain Layout
8813 \begin_layout Plain Layout
8823 \begin_inset Formula $\downarrow$
8827 \begin_inset Formula $\to$
8835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8855 \begin_layout Subsection
8856 Vertical and diagonal Arrows
8860 \begin_layout Plain Layout
8870 \begin_layout Plain Layout
8879 \begin_layout Standard
8880 \begin_inset space \hfill{}
8884 \begin_inset Tabular
8885 <lyxtabular version="3" rows="7" columns="2">
8887 <column alignment="center" valignment="top" width="0pt">
8888 <column alignment="center" valignment="top" width="0pt">
8890 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8893 \begin_layout Plain Layout
8899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8902 \begin_layout Plain Layout
8910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8913 \begin_layout Plain Layout
8921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8924 \begin_layout Plain Layout
8925 \begin_inset Formula $\uparrow$
8935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8938 \begin_layout Plain Layout
8946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8949 \begin_layout Plain Layout
8950 \begin_inset Formula $\Uparrow$
8960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8963 \begin_layout Plain Layout
8971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8974 \begin_layout Plain Layout
8975 \begin_inset Formula $\updownarrow$
8985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8988 \begin_layout Plain Layout
8996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8999 \begin_layout Plain Layout
9000 \begin_inset Formula $\Updownarrow$
9010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9013 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9025 \begin_inset Formula $\Downarrow$
9035 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9038 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\downarrow$
9064 \begin_inset space \hfill{}
9068 \begin_inset Tabular
9069 <lyxtabular version="3" rows="5" columns="2">
9071 <column alignment="center" valignment="top" width="0pt">
9072 <column alignment="center" valignment="top" width="0pt">
9074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9077 \begin_layout Plain Layout
9083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9086 \begin_layout Plain Layout
9094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9097 \begin_layout Plain Layout
9105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9108 \begin_layout Plain Layout
9109 \begin_inset Formula $\nearrow$
9119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9122 \begin_layout Plain Layout
9130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9133 \begin_layout Plain Layout
9134 \begin_inset Formula $\searrow$
9144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9147 \begin_layout Plain Layout
9155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9158 \begin_layout Plain Layout
9159 \begin_inset Formula $\swarrow$
9169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9172 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9183 \begin_layout Plain Layout
9184 \begin_inset Formula $\nwarrow$
9198 \begin_inset space \hfill{}
9204 \begin_layout Standard
9205 \begin_inset VSpace medskip
9208 Vertical arrows can be used also as delimiter together with the commands
9210 \begin_inset CommandInset ref
9212 reference "sub:Manual-Bracket-Size"
9217 \begin_inset CommandInset ref
9219 reference "sub:Automatic-Bracket-Size"
9226 \begin_layout Standard
9227 \begin_inset Newpage newpage
9233 \begin_layout Section
9235 \begin_inset CommandInset label
9245 \begin_layout Plain Layout
9254 \begin_layout Standard
9255 Accents can be inserted via the math toolbar button
9256 \begin_inset Graphics
9257 filename ../images/math/hat.png
9262 or the commands listed in the following subsections.
9265 \begin_layout Subsection
9266 Accents for one Character
9270 \begin_layout Plain Layout
9283 \begin_layout Plain Layout
9285 \begin_inset CommandInset ref
9287 reference "sub:Accents-in-Text"
9300 \begin_layout Plain Layout
9308 \begin_inset Note Note
9311 \begin_layout Plain Layout
9314 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9317 \begin_layout Plain Layout
9320 texorpdfstring is in section
9321 \begin_inset CommandInset ref
9323 reference "sub:Formulas-in-Section"
9333 \begin_inset CommandInset label
9335 name "sub:Accents-for-one"
9343 \begin_layout Plain Layout
9344 Accents ! for one character
9352 \begin_layout Standard
9353 \begin_inset space \hfill{}
9357 \begin_inset Tabular
9358 <lyxtabular version="3" rows="8" columns="2">
9360 <column alignment="center" valignment="top" width="0pt">
9361 <column alignment="center" valignment="top" width="0pt">
9363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9366 \begin_layout Plain Layout
9372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9375 \begin_layout Plain Layout
9377 \begin_inset Note Note
9380 \begin_layout Plain Layout
9387 is only used as spacer.
9399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9402 \begin_layout Plain Layout
9409 \begin_layout Plain Layout
9423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9426 \begin_layout Plain Layout
9427 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9437 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9440 \begin_layout Plain Layout
9447 \begin_layout Plain Layout
9461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9464 \begin_layout Plain Layout
9465 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9478 \begin_layout Plain Layout
9485 \begin_layout Plain Layout
9499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9502 \begin_layout Plain Layout
9503 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9516 \begin_layout Plain Layout
9524 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9527 \begin_layout Plain Layout
9528 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9541 \begin_layout Plain Layout
9548 \begin_layout Plain Layout
9561 \begin_layout Plain Layout
9572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9575 \begin_layout Plain Layout
9576 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9589 \begin_layout Plain Layout
9596 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Plain Layout
9614 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9634 \begin_layout Plain Layout
9648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9651 \begin_layout Plain Layout
9652 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9666 \begin_inset space \hfill{}
9670 \begin_inset Tabular
9671 <lyxtabular version="3" rows="7" columns="2">
9673 <column alignment="center" valignment="top" width="0pt">
9674 <column alignment="center" valignment="top" width="0pt">
9676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9679 \begin_layout Plain Layout
9685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9688 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9699 \begin_layout Plain Layout
9706 \begin_layout Plain Layout
9720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9723 \begin_layout Plain Layout
9724 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9737 \begin_layout Plain Layout
9744 \begin_layout Plain Layout
9758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9761 \begin_layout Plain Layout
9762 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9775 \begin_layout Plain Layout
9782 \begin_layout Plain Layout
9796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9799 \begin_layout Plain Layout
9800 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9810 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9813 \begin_layout Plain Layout
9820 \begin_layout Plain Layout
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9837 \begin_layout Plain Layout
9838 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9851 \begin_layout Plain Layout
9858 \begin_layout Plain Layout
9872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9875 \begin_layout Plain Layout
9876 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9886 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9889 \begin_layout Plain Layout
9896 \begin_layout Plain Layout
9910 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9913 \begin_layout Plain Layout
9914 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9928 \begin_inset space \hfill{}
9934 \begin_layout Standard
9935 \begin_inset VSpace bigskip
9941 \begin_layout Standard
9942 You can directly insert accents like é to formulas.
9943 LyX will transform them to the corresponding accent command.
9948 \begin_layout Plain Layout
9954 it is better to insert a quotation mark before the vowel.
9955 These two characters are then treated by LaTeX as
9959 character when the formula part with the umlaut is marked as German.
9967 \begin_inset Quotes eld
9971 \begin_inset Quotes erd
9974 umlauts are created as demonstrated in the following example:
9977 \begin_layout Standard
9978 \begin_inset VSpace -2mm
9984 \begin_layout Standard
9986 \begin_inset Tabular
9987 <lyxtabular version="3" rows="3" columns="2">
9989 <column alignment="center" valignment="top" width="0">
9990 <column alignment="center" valignment="top" width="0">
9992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9995 \begin_layout Plain Layout
10001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10004 \begin_layout Plain Layout
10006 \begin_inset Note Note
10009 \begin_layout Plain Layout
10017 \begin_inset space \thinspace{}
10020 pt space are only used as spacer.
10032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10035 \begin_layout Plain Layout
10038 \begin_inset Quotes grd
10046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10049 \begin_layout Plain Layout
10050 \begin_inset space \hspace{}
10057 \begin_inset Formula $"i$
10067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10070 \begin_layout Plain Layout
10077 \begin_layout Plain Layout
10091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10094 \begin_layout Plain Layout
10095 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10111 \begin_layout Standard
10112 Another advantage to
10118 is that umlauts can directly be converted to mathematical text because
10119 the accent commands above are
10125 in mathematical text
10128 To convert an accented character to mathematical text, only the character
10129 under the accent may be converted.
10130 This applies also for all other conversions, e.
10131 \begin_inset space \thinspace{}
10135 \begin_inset space ~
10141 \begin_layout Standard
10142 In mathematical text, umlauts and other accented characters can directly
10146 \begin_layout Subsection
10147 Accents for Operators
10151 \begin_layout Plain Layout
10152 Accents ! for operators
10160 \begin_layout Standard
10171 \begin_layout Plain Layout
10189 \begin_layout Plain Layout
10197 characters can be placed above or below an operator, respectively, to accent
10209 \begin_layout Plain Layout
10217 characters can be set before and behind an operator.
10218 The command scheme is:
10221 \begin_layout Standard
10237 \begin_layout Standard
10244 must always be before the operator that should be accented.
10245 You can accent with several characters and even with other operators and
10253 for example only characters behind an operator, write nothing between the
10254 first braces but don't omit the braces.
10257 \begin_layout Standard
10258 For example the command
10263 \begin_inset Formula $\to$
10273 \begin_inset Formula $\to$
10282 \begin_layout Plain Layout
10298 \begin_inset Formula \[
10299 \sideset{}{'}\sum_{k=1}^{n}\]
10306 \begin_layout Standard
10315 \begin_layout Plain Layout
10330 \begin_layout Plain Layout
10342 \begin_inset Formula $\uparrow$
10350 \begin_inset Formula \[
10351 \overset{a}{\maltese}\]
10355 As seen in the last example, with
10367 also symbols and characters can be accented; with
10373 this is not possible.
10376 \begin_layout Subsection
10377 Accents for several Characters
10381 \begin_layout Plain Layout
10382 Accents ! for several characters
10390 \begin_layout Standard
10391 \begin_inset space \hfill{}
10395 \begin_inset Tabular
10396 <lyxtabular version="3" rows="5" columns="2">
10398 <column alignment="center" valignment="top" width="0pt">
10399 <column alignment="center" valignment="top" width="0pt">
10401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10404 \begin_layout Plain Layout
10410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10413 \begin_layout Plain Layout
10415 \begin_inset Note Note
10418 \begin_layout Plain Layout
10425 is only used as spacer.
10437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10440 \begin_layout Plain Layout
10447 \begin_layout Plain Layout
10461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10464 \begin_layout Plain Layout
10465 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10478 \begin_layout Plain Layout
10485 \begin_layout Plain Layout
10499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10502 \begin_layout Plain Layout
10503 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10516 \begin_layout Plain Layout
10523 \begin_layout Plain Layout
10537 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10540 \begin_layout Plain Layout
10541 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10551 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10554 \begin_layout Plain Layout
10557 underleftrightarrow
10561 \begin_layout Plain Layout
10575 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10578 \begin_layout Plain Layout
10579 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10593 \begin_inset space \hfill{}
10597 \begin_inset Tabular
10598 <lyxtabular version="3" rows="5" columns="2">
10600 <column alignment="center" valignment="top" width="0pt">
10601 <column alignment="center" valignment="top" width="0pt">
10603 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10606 \begin_layout Plain Layout
10612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10615 \begin_layout Plain Layout
10623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10626 \begin_layout Plain Layout
10633 \begin_layout Plain Layout
10647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10650 \begin_layout Plain Layout
10651 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10664 \begin_layout Plain Layout
10671 \begin_layout Plain Layout
10685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10688 \begin_layout Plain Layout
10689 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10702 \begin_layout Plain Layout
10709 \begin_layout Plain Layout
10723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10726 \begin_layout Plain Layout
10727 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10740 \begin_layout Plain Layout
10747 \begin_layout Plain Layout
10761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10764 \begin_layout Plain Layout
10765 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10779 \begin_inset space \hfill{}
10785 \begin_layout Standard
10786 \begin_inset VSpace medskip
10789 With these commands as many characters as you like can be accented.
10802 will only be set in the output with a length of three characters, as shown
10803 in the following example:
10804 \begin_inset Formula \[
10805 \widetilde{A+B=C-D}\]
10812 \begin_layout Standard
10823 \begin_layout Plain Layout
10841 \begin_layout Plain Layout
10849 described in the previous subsection it is also possible to accent several
10859 \begin_layout Plain Layout
10869 \begin_inset Formula $\downarrow$
10875 \begin_inset Formula \[
10876 \underset{***}{A=B}\]
10883 \begin_layout Section
10885 \begin_inset CommandInset label
10895 \begin_layout Plain Layout
10904 \begin_layout Subsection
10906 \begin_inset CommandInset label
10908 name "sub:Predefined-Space"
10916 \begin_layout Plain Layout
10917 Space ! horizontal ! predefined
10925 \begin_layout Standard
10926 Sometimes it is necessary to insert horizontal space to a formula.
10927 This is done by inserting a protected space (shortcut
10933 \begin_inset Quotes eld
10943 \begin_layout Plain Layout
10956 \begin_inset Quotes erd
10959 appears and by pressing
10963 several times one can select one of eight different space sizes.
10964 The spaces can also be inserted using the math toolbar button
10965 \begin_inset Graphics
10966 filename ../images/math/space.png
10971 or special commands.
10972 Independent from the inserted command, one can select the size again by
10980 \begin_layout Standard
10983 \begin_inset VSpace -5mm
10987 \begin_inset Tabular
10988 <lyxtabular version="3" rows="3" columns="7">
10990 <column alignment="center" valignment="middle" width="6.8cm">
10991 <column alignment="center" valignment="top" width="0">
10992 <column alignment="center" valignment="top" width="0">
10993 <column alignment="center" valignment="top" width="0">
10994 <column alignment="center" valignment="top" width="0">
10995 <column alignment="center" valignment="top" width="0">
10996 <column alignment="center" valignment="top" width="0">
10998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11021 \begin_layout Plain Layout
11029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11032 \begin_layout Plain Layout
11040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11043 \begin_layout Plain Layout
11051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11054 \begin_layout Plain Layout
11062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11065 \begin_layout Plain Layout
11075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11078 \begin_layout Plain Layout
11083 keystrokes after inserting the protected space
11088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11091 \begin_layout Plain Layout
11097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11100 \begin_layout Plain Layout
11106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11109 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11118 \begin_layout Plain Layout
11124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11127 \begin_layout Plain Layout
11133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11136 \begin_layout Plain Layout
11144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11147 \begin_layout Plain Layout
11153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11156 \begin_layout Plain Layout
11157 \begin_inset Formula $A\, B$
11165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11169 \begin_inset Formula $A\: B$
11177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11181 \begin_inset Formula $A\; B$
11189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\quad B$
11201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11205 \begin_inset Formula $A\qquad B$
11213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11216 \begin_layout Plain Layout
11217 \begin_inset Formula $A\! B$
11233 \begin_layout Standard
11234 The last size seem to produce no space.
11235 It is displayed red in LyX contrary to the other sizes, because it is a
11237 There are two more negative spaces:
11240 \begin_layout Standard
11242 \begin_inset Tabular
11243 <lyxtabular version="3" rows="3" columns="3">
11245 <column alignment="center" valignment="middle" width="6.8cm">
11246 <column alignment="center" valignment="top" width="0pt">
11247 <column alignment="center" valignment="top" width="0pt">
11249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11252 \begin_layout Plain Layout
11258 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11261 \begin_layout Plain Layout
11269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11272 \begin_layout Plain Layout
11282 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11285 \begin_layout Plain Layout
11290 keystrokes after inserting the protected space
11295 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11307 \begin_layout Plain Layout
11315 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11318 \begin_layout Plain Layout
11324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11327 \begin_layout Plain Layout
11328 \begin_inset Formula $A\negmedspace B$
11336 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11339 \begin_layout Plain Layout
11340 \begin_inset Formula $A\negthickspace B$
11356 \begin_layout Standard
11357 Negative spaces can lead to characters overlapping each other.
11358 Thus they can be used to enforce ligatures, what is e.
11359 \begin_inset space \thinspace{}
11363 \begin_inset space ~
11366 useful for summation operators:
11369 \begin_layout Standard
11371 \begin_inset Tabular
11372 <lyxtabular version="3" rows="3" columns="2">
11374 <column alignment="center" valignment="top" width="0">
11375 <column alignment="center" valignment="top" width="0">
11377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11380 \begin_layout Plain Layout
11386 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11389 \begin_layout Plain Layout
11391 \begin_inset Note Note
11394 \begin_layout Plain Layout
11401 is only used as spacer.
11413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11416 \begin_layout Plain Layout
11425 \begin_layout Plain Layout
11439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11442 \begin_layout Plain Layout
11443 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11456 \begin_layout Plain Layout
11467 \begin_layout Plain Layout
11481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11484 \begin_layout Plain Layout
11485 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11501 \begin_layout Standard
11502 Relations like for example equal signs, are always surrounded by space.
11503 To suppress this, the equal sign is placed into a TeX-brace.
11504 The following example demonstrates this:
11507 \begin_layout Standard
11509 \begin_inset Tabular
11510 <lyxtabular version="3" rows="2" columns="2">
11512 <column alignment="center" valignment="top" width="0pt">
11513 <column alignment="center" valignment="top" width="0pt">
11515 <cell alignment="center" valignment="top" usebox="none">
11518 \begin_layout Plain Layout
11524 <cell alignment="center" valignment="top" usebox="none">
11527 \begin_layout Plain Layout
11528 \begin_inset Formula $A=B$
11538 <cell alignment="center" valignment="top" usebox="none">
11541 \begin_layout Plain Layout
11542 \begin_inset Note Note
11545 \begin_layout Plain Layout
11552 is only used as spacer.
11558 \begin_inset Formula $\raisebox{5mm}{}$
11561 equation without space
11566 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11569 \begin_layout Plain Layout
11570 \begin_inset Formula $A{=}B$
11586 \begin_layout Standard
11588 The command for the last formula is:
11593 \begin_inset Formula $\to$
11599 \begin_layout Standard
11600 \begin_inset VSpace bigskip
11603 Spaces are needed for physical units, because the space between the value
11604 and the unit is the smallest one and not a normal space.
11605 For units in text, the smallest space is inserted via the menu
11607 Insert\SpecialChar \menuseparator
11608 Formatting\SpecialChar \menuseparator
11610 \begin_inset space ~
11618 arg "space-insert thin"
11624 \begin_layout Standard
11625 An example to visualize the difference:
11628 \begin_layout Standard
11629 \begin_inset Tabular
11630 <lyxtabular version="3" rows="2" columns="2">
11632 <column alignment="left" valignment="top" width="0">
11633 <column alignment="left" valignment="top" width="0">
11635 <cell alignment="center" valignment="top" usebox="none">
11638 \begin_layout Plain Layout
11640 \begin_inset Formula $\cdot$
11648 <cell alignment="center" valignment="top" usebox="none">
11651 \begin_layout Plain Layout
11652 space between value and unit
11659 <cell alignment="center" valignment="top" usebox="none">
11662 \begin_layout Plain Layout
11664 \begin_inset space \thinspace{}
11668 \begin_inset Formula $\cdot$
11676 <cell alignment="center" valignment="top" usebox="none">
11679 \begin_layout Plain Layout
11680 smallest space between value and unit
11693 \begin_layout Subsection
11698 \begin_layout Plain Layout
11711 \begin_layout Plain Layout
11712 for vertical space in formulas see
11713 \begin_inset CommandInset ref
11715 reference "sub:Line-Separation"
11728 \begin_layout Plain Layout
11736 \begin_inset Note Note
11739 \begin_layout Plain Layout
11742 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11745 \begin_layout Plain Layout
11748 texorpdfstring is in section
11749 \begin_inset CommandInset ref
11751 reference "sub:Formulas-in-Section"
11761 \begin_inset CommandInset label
11763 name "sub:Variable-Space"
11771 \begin_layout Plain Layout
11772 Space ! horizontal ! variable
11780 \begin_layout Standard
11781 Space with a defined length can be inserted in LyX with the command
11782 \begin_inset Newline newline
11795 \begin_layout Plain Layout
11804 For the length all units listed in
11805 \begin_inset CommandInset ref
11807 reference "tab:Available-units"
11811 are allowed, except of the unit
11812 \begin_inset Quotes eld
11816 \begin_inset Quotes erd
11820 The length may also be negative.
11821 To insert so many space that the formula uses all available space, the
11832 \begin_layout Plain Layout
11843 \begin_layout Standard
11844 \begin_inset VSpace -1mm
11850 \begin_layout Standard
11852 \begin_inset Tabular
11853 <lyxtabular version="3" rows="4" columns="2">
11855 <column alignment="center" valignment="top" width="0">
11856 <column alignment="center" valignment="top" width="0">
11858 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11861 \begin_layout Plain Layout
11867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11870 \begin_layout Plain Layout
11878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11881 \begin_layout Plain Layout
11885 \begin_inset Formula $\to$
11895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11898 \begin_layout Plain Layout
11899 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11912 \begin_layout Plain Layout
11916 \begin_inset Formula $\to$
11926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11929 \begin_layout Plain Layout
11930 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11943 \begin_layout Plain Layout
11950 \begin_layout Plain Layout
11964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11967 \begin_layout Plain Layout
11968 \begin_inset Formula $A=A\hfill B=B$
11984 \begin_layout Standard
11985 In the last example the available space is given by the longest column entry
11987 In an inline formula the space depends on the length of the line in which
11995 Thus, when the line uses the full width, no space will be created.
12002 only has an effect on displayed formulas when the formula style
12007 (Formula styles are explained in
12008 \begin_inset CommandInset ref
12010 reference "sec:Formula-Styles"
12017 \begin_layout Standard
12024 , there are the commands
12036 that fill the space with a pattern, see
12037 \begin_inset CommandInset ref
12039 reference "sub:Ellipses"
12046 \begin_layout Standard
12047 For text, variable space can be inserted via the menu
12049 Insert\SpecialChar \menuseparator
12050 Formatting\SpecialChar \menuseparator
12052 \begin_inset space ~
12057 , what is not possible in formulas:
12060 \begin_layout Standard
12061 This is a line with
12062 \begin_inset space \hspace{}
12067 \begin_inset space \thinspace{}
12073 \begin_layout Standard
12074 This is a line with
12075 \begin_inset space \hfill{}
12081 \begin_layout Subsection
12082 Space besides inline Formulas
12086 \begin_layout Plain Layout
12087 Space ! besides inline formulas
12095 \begin_layout Standard
12096 The space that surrounds inline formulas can be adjusted with the length
12105 \begin_layout Plain Layout
12116 The value of a length is set with the command
12124 \begin_layout Plain Layout
12134 that has the following scheme:
12137 \begin_layout Standard
12142 setlength{length name}{value}
12145 \begin_layout Standard
12153 \begin_inset space \thinspace{}
12159 \begin_layout Standard
12169 \begin_layout Standard
12170 is inserted in TeX-mode.
12172 \begin_inset space \thinspace{}
12175 mm space will now be set around all inline formulas:
12179 \begin_layout Plain Layout
12193 \begin_layout Standard
12194 This is a line with an inline formula
12195 \begin_inset Formula $A=B$
12199 \begin_inset space \thinspace{}
12202 mm surrounding space.
12206 \begin_layout Plain Layout
12220 \begin_layout Standard
12221 To return to the predefined value,
12227 is set to the value 0
12228 \begin_inset space \thinspace{}
12234 \begin_layout Section
12239 \begin_layout Plain Layout
12249 \begin_layout Plain Layout
12254 \begin_layout Plain Layout
12265 \begin_layout Plain Layout
12280 \begin_layout Standard
12281 Boxes for text are described in chapter
12288 \begin_inset space ~
12296 \begin_layout Subsection
12298 \begin_inset CommandInset label
12300 name "sub:Boxes-with-Frame"
12308 \begin_layout Plain Layout
12317 \begin_layout Standard
12318 It is possible to frame formulas or parts of it with the commands
12328 \begin_layout Plain Layout
12346 \begin_layout Plain Layout
12357 \begin_layout Standard
12358 When one of these commands is inserted to a formula, a blue box appears
12359 within a frame to enter formula parts.
12366 an additional formula has to be created by
12374 \begin_layout Plain Layout
12375 Due to a bug in LyX it is not possible to create a new formula with
12380 \begin_inset CommandInset href
12382 name "LyX-bug #1435"
12383 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12392 , because the box content will otherwise be treated as mathematical text.
12399 is used, a new formula is automatically created inside the frame.
12402 \begin_layout Standard
12409 is not suitable to frame displayed formulas, because the formula will always
12410 be set in the size of the text.
12417 is in contrary not suitable to frame inline formulas, because the formula
12418 will always be set in the size of a displayed formula.
12421 \begin_layout Standard
12428 there is the command
12438 \begin_layout Plain Layout
12446 where additionally the frame width and the alignment can be specified.
12453 is used in the following scheme:
12456 \begin_layout Standard
12461 framebox[frame width][position]{box content}
12464 \begin_layout Standard
12465 The position can either be
12482 right aligns the formula in the box.
12483 When no position is given, the formula will be centered.
12484 \begin_inset Newline newline
12487 Is no width given, also no position can be given.
12488 In this case the frame width is adjusted to the box content like for
12497 \begin_layout Standard
12504 is inserted, a box appears containing three blue boxes.
12505 The first two boxes are surrounded by brackets and denote the two optional
12507 The third box is for formula parts like for
12516 \begin_layout Standard
12518 \begin_inset Note Note
12521 \begin_layout Plain Layout
12522 The table has been set into a minipage to make the footnote appearing.
12523 Otherwise the footnote text would not be displayed.
12529 \begin_inset Box Frameless
12538 height_special "totalheight"
12541 \begin_layout Plain Layout
12543 \begin_inset Tabular
12544 <lyxtabular version="3" rows="5" columns="2">
12546 <column alignment="center" valignment="top" width="0">
12547 <column alignment="center" valignment="top" width="0">
12549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12552 \begin_layout Plain Layout
12557 \begin_layout Plain Layout
12558 Due to a bug in LyX it is not possible to create a new formula with
12563 \begin_inset CommandInset href
12565 name "LyX-bug #1435"
12566 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12583 \begin_layout Plain Layout
12585 \begin_inset Note Note
12588 \begin_layout Plain Layout
12595 is only used as spacer.
12607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12610 \begin_layout Plain Layout
12617 \begin_layout Plain Layout
12636 \begin_layout Plain Layout
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12653 \begin_layout Plain Layout
12654 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12667 \begin_layout Plain Layout
12674 \begin_layout Plain Layout
12689 \begin_layout Plain Layout
12703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12706 \begin_layout Plain Layout
12707 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12720 \begin_layout Plain Layout
12727 \begin_layout Plain Layout
12741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12744 \begin_layout Plain Layout
12745 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12758 \begin_layout Plain Layout
12765 \begin_layout Plain Layout
12775 \begin_inset Formula $\to$
12779 \begin_inset Formula $\to$
12792 \begin_layout Plain Layout
12802 \begin_inset Formula $\downarrow$
12810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12813 \begin_layout Plain Layout
12814 \begin_inset Formula $\raisebox{6mm}{}$
12818 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12822 \begin_inset Formula $\raisebox{-4mm}{}$
12843 \begin_layout Standard
12844 The frame thickness can also be adjusted.
12845 To do this the following commands have to be inserted in TeX-mode before
12849 \begin_layout Standard
12859 \begin_inset Quotes eld
12863 \begin_inset Quotes erd
12877 \begin_inset Quotes eld
12881 \begin_inset Quotes erd
12887 \begin_layout Standard
12888 \begin_inset Quotes eld
12892 \begin_inset Quotes erd
12895 specifies the minimal distance between the frame and the first character
12897 An example for this is the following framed formula:
12901 \begin_layout Plain Layout
12913 \begin_inset Formula \[
12918 Before this formula the commands
12921 \begin_layout Standard
12943 \begin_layout Standard
12944 were inserted in TeX-mode.
12945 The given values are used for all following boxes.
12948 \begin_layout Standard
12949 To return to the standard frame size, the command
12952 \begin_layout Standard
12977 \begin_layout Plain Layout
12991 \begin_layout Standard
12992 is inserted in TeX-mode before the next formula.
12995 \begin_layout Subsection
12996 Boxes without Frame
12997 \begin_inset CommandInset label
12999 name "sub:Boxes-without-Frame"
13007 \begin_layout Plain Layout
13008 Boxes ! without frame
13016 \begin_layout Standard
13017 For boxes without a frame there are the following box commands:
13027 \begin_layout Plain Layout
13045 \begin_layout Plain Layout
13063 \begin_layout Plain Layout
13074 \begin_layout Standard
13081 a box can be super- or subscripted.
13082 But in contrary to normal super- and subscripting, the characters in the
13083 box keep their font size.
13090 is used in the following scheme:
13093 \begin_layout Standard
13098 raisebox{height}{box content}
13101 \begin_layout Standard
13102 When the box should contain a formula, an extra formula is needed like for
13112 \begin_layout Standard
13114 \begin_inset Tabular
13115 <lyxtabular version="3" rows="4" columns="2">
13117 <column alignment="center" valignment="top" width="0">
13118 <column alignment="center" valignment="top" width="0">
13120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13123 \begin_layout Plain Layout
13129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13132 \begin_layout Plain Layout
13140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13143 \begin_layout Plain Layout
13147 \begin_inset Formula $\to$
13153 \begin_inset Formula $\to$
13161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13164 \begin_layout Plain Layout
13165 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13178 \begin_layout Plain Layout
13182 \begin_inset Formula $\to$
13188 \begin_inset Formula $\to$
13196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13199 \begin_layout Plain Layout
13200 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13213 \begin_layout Plain Layout
13217 \begin_inset Formula $\to$
13232 \begin_layout Plain Layout
13246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13249 \begin_layout Plain Layout
13253 \begin_layout Plain Layout
13277 \begin_layout Standard
13278 The last formula can currently only be created using TeX-mode because LyX
13279 inserts a box instead of the needed extra formula.
13283 \begin_layout Plain Layout
13285 \begin_inset CommandInset href
13287 name "LyX-bug #1435"
13288 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13300 \begin_layout Standard
13325 , with the difference that there is no frame.
13328 \begin_layout Subsection
13330 \begin_inset CommandInset label
13332 name "sub:Colored-Boxes"
13340 \begin_layout Plain Layout
13349 \begin_layout Standard
13350 To be able to use all commands explained in this section, the LaTeX-package
13359 \begin_layout Plain Layout
13364 is part of every LaTeX standard installation.
13373 \begin_layout Plain Layout
13379 has to be loaded in the LaTeX-preamble with the line
13383 \begin_layout Plain Layout
13384 When text is colored somewhere in the document with a predefined color,
13385 LyX loads the LaTeX-package
13390 Thus it is possible that the package is loaded twice, but this doesn't
13397 \begin_inset Note Note
13400 \begin_layout Plain Layout
13401 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13410 \begin_layout Standard
13418 \begin_layout Standard
13419 \begin_inset VSpace medskip
13422 To color boxes, the command
13432 \begin_layout Plain Layout
13440 is used in the following scheme:
13443 \begin_layout Standard
13448 colorbox{color}{box content}
13451 \begin_layout Standard
13452 The box content can also be a box and a
13458 can also be part of another box (see the 2nd and 3rd example).
13459 When the box should contain a formula, an extra formula has to be created,
13470 \begin_layout Plain Layout
13471 This also applies for the command
13479 \begin_inset CommandInset href
13481 name "LyX-bug #1435"
13482 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13494 \begin_layout Standard
13495 One of the following predefined colors can be chosen:
13498 \begin_layout Standard
13532 \begin_layout Standard
13534 \begin_inset Tabular
13535 <lyxtabular version="3" rows="4" columns="2">
13537 <column alignment="center" valignment="top" width="0">
13538 <column alignment="center" valignment="top" width="0">
13540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13543 \begin_layout Plain Layout
13549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13552 \begin_layout Plain Layout
13554 \begin_inset Note Note
13557 \begin_layout Plain Layout
13564 is only used as spacer.
13576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13579 \begin_layout Plain Layout
13583 \begin_inset Formula $\to$
13593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13596 \begin_layout Plain Layout
13597 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13610 \begin_layout Plain Layout
13614 \begin_inset Formula $\to$
13625 \begin_layout Plain Layout
13639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13642 \begin_layout Plain Layout
13643 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13656 \begin_layout Plain Layout
13663 \begin_layout Plain Layout
13675 \begin_inset Formula $\to$
13685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13688 \begin_layout Plain Layout
13689 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13705 \begin_layout Standard
13712 only colors the box but not the characters in the box.
13713 To color all characters, the whole formula is highlighted and the wanted
13714 color is chosen in the
13717 \begin_inset space ~
13723 The dialog can be called with the toolbar button
13724 \begin_inset Graphics
13725 filename ../images/dialog-show_character.png
13732 Edit\SpecialChar \menuseparator
13734 \begin_inset space ~
13737 Style\SpecialChar \menuseparator
13741 The formula number has then the same color as the formula.
13742 When the formula number should get another color than the formula characters,
13743 the color must be changed within the formula.
13746 \begin_layout Standard
13750 \begin_layout Standard
13753 \begin_inset Formula \begin{equation}
13754 \int A=B\label{eq:red}\end{equation}
13761 \begin_inset Formula \begin{equation}
13762 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13769 \begin_layout Standard
13771 \begin_inset CommandInset ref
13777 is completely colored red.
13778 \begin_inset Newline newline
13782 \begin_inset CommandInset ref
13784 reference "eq:redgreen"
13788 was first completely colored green to set the color for the formula number.
13789 Subsequently the formula characters were colored red.
13792 \begin_layout Standard
13793 \begin_inset VSpace bigskip
13796 To color the frame different than the rest of the box, the command
13806 \begin_layout Plain Layout
13814 is used in the following scheme:
13817 \begin_layout Standard
13822 fcolorbox{frame color}{color}{box content}
13825 \begin_layout Standard
13832 is an extension of the command
13839 The frame width is set, like for
13862 \begin_layout Plain Layout
13874 \begin_inset Formula \[
13875 \fcolorbox{cyan}{magenta}{A=B}\]
13883 \begin_layout Plain Layout
13897 \begin_layout Standard
13898 This formula was created with the command
13899 \begin_inset Newline newline
13907 \begin_inset Formula $\to$
13913 \begin_inset Formula $\to$
13923 \begin_layout Standard
13924 \begin_inset VSpace bigskip
13927 To use other colors than the predefined ones, they have to be defined first.
13930 \begin_layout Standard
13931 One can for example define the color
13932 \begin_inset Quotes eld
13940 \begin_inset Quotes erd
13943 with the LaTeX-preamble line:
13946 \begin_layout Standard
13951 definecolor{darkgreen}{cmyk}{0.5,
13969 \begin_layout Plain Layout
13980 \begin_layout Standard
13985 is the color space that denotes the colors
14002 The four comma separated numbers are the portion factor for the corresponding
14003 colors of the color space.
14004 The factors can be in the range of 0
14005 \begin_inset space \thinspace{}
14009 \begin_inset space \thinspace{}
14017 also the color space
14021 can be used for definitions.
14038 , so that there are in this case three portion factors for the corresponding
14040 Furthermore there is the color space
14044 with one portion factor for the gray value.
14047 \begin_layout Standard
14048 As example a framed box with the new defined color
14052 where the characters have been colored
14057 \begin_inset Formula \begin{equation}
14058 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14065 \begin_layout Standard
14066 Self-defined colors can also be used for text with the help of the command
14077 \begin_layout Plain Layout
14086 \begin_layout Standard
14090 \begin_layout Plain Layout
14094 textcolor{darkgreen}{
14100 \begin_inset Quotes eld
14104 \begin_inset Quotes erd
14111 \begin_layout Plain Layout
14121 \begin_layout Standard
14132 \begin_layout Plain Layout
14140 is used in the scheme
14144 textcolor{color}{characters to color}
14149 \begin_layout Subsection
14151 \begin_inset CommandInset label
14153 name "sub:Paragraph-Boxes"
14161 \begin_layout Plain Layout
14162 Boxes ! as paragraph
14170 \begin_layout Standard
14171 A box that can contain several lines and paragraphs, a so called paragraph
14172 box (parbox), can be created with the menu
14174 Insert\SpecialChar \menuseparator
14177 or the toolbar button
14178 \begin_inset Graphics
14179 filename ../images/box-insert.png
14187 \begin_layout Standard
14188 The following example shows a framed parbox in a line:
14191 \begin_layout Standard
14192 \begin_inset VSpace medskip
14196 \begin_inset Box Boxed
14205 height_special "totalheight"
14208 \begin_layout Plain Layout
14209 This is a paragraph box.
14211 \begin_inset space \thinspace{}
14214 cm long and can also contain formulas:
14215 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14226 \begin_layout Standard
14227 \begin_inset VSpace medskip
14233 \begin_layout Standard
14234 Such a box is created by right-clicking on the gray box inset.
14235 A dialog pops up showing the box properties.
14249 \begin_inset space \thinspace{}
14254 Vertical Box Alignment
14259 \begin_layout Standard
14260 \begin_inset VSpace medskip
14263 In LaTeX a parbox is created with the command
14273 \begin_layout Plain Layout
14281 that has the following scheme:
14284 \begin_layout Standard
14289 parbox[position]{width}{box content}
14292 \begin_layout Standard
14306 for bottom means that the box is aligned within the surrounding text with
14312 for top this is done with the first line.
14313 When no position is given, the box will be vertically centered, see section
14321 \begin_inset space ~
14326 manual for examples.
14329 \begin_layout Standard
14330 \begin_inset VSpace bigskip
14333 To frame formulas completely, including the formula number, the formula
14334 must be set into a parbox.
14335 To do this, the command
14349 is inserted in TeX-mode before the formula.
14358 \begin_layout Plain Layout
14368 is hereby the line width set for the document.
14369 Because the frame is outside the parbox, 2
14370 \begin_inset space \thinspace{}
14373 times the frame separation and the frame thickness must be subtracted from
14375 As this is not automatically done by LyX due to a bug
14379 \begin_layout Plain Layout
14380 \begin_inset CommandInset href
14382 name "LyX-bug #4483"
14383 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14392 , TeX-mode has to be used.
14393 To be able to multiply and subtract in arguments, the LaTeX-package
14401 \begin_layout Plain Layout
14406 is part of every LaTeX standard installation.
14415 \begin_layout Plain Layout
14421 must be loaded in the LaTeX-preamble with the line
14424 \begin_layout Standard
14432 \begin_layout Standard
14433 Behind the formula both boxes are closed by entering
14438 Here is an example:
14442 \begin_layout Plain Layout
14456 \begin_layout Standard
14460 \begin_layout Plain Layout
14478 \begin_inset Formula \begin{equation}
14479 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14487 \begin_layout Plain Layout
14498 \begin_layout Plain Layout
14512 \begin_layout Standard
14513 \begin_inset VSpace medskip
14516 As a parbox is used as argument of
14522 , there is in this case no difference between
14537 \begin_layout Standard
14538 \begin_inset VSpace bigskip
14541 Paragraph boxes are very useful to comment formulas directly.
14548 is used in combination with the command
14562 \begin_inset CommandInset ref
14564 reference "sub:User-defined-Numbering"
14571 \begin_layout Standard
14572 An example of a formula commented with
14581 \begin_layout Standard
14585 \begin_layout Plain Layout
14598 This is a description.
14599 It is distinctly separated from the formula and multiline.
14603 \begin_layout Plain Layout
14615 \begin_layout Standard
14616 Such a formula must be inserted completely in TeX-mode because LyX does
14617 not yet support the command
14624 The formula is created with the following command sequence:
14627 \begin_layout Standard
14640 is inserted in TeX-mode.
14644 \begin_layout Plain Layout
14645 When the formula style
14657 can also be replaced by
14664 (formula styles see
14665 \begin_inset CommandInset ref
14667 reference "sec:Formula-Styles"
14676 Then the description follows as normal text, and finally
14682 is inserted in TeX-mode.
14695 hereby create a displayed formula.
14698 \begin_layout Standard
14705 can be seen in this example that was
14706 \begin_inset Quotes eld
14710 \begin_inset Quotes erd
14713 using the mathematical textmode:
14714 \begin_inset Formula \[
14715 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14722 \begin_layout Section
14727 \begin_layout Plain Layout
14736 \begin_layout Subsection
14738 \begin_inset CommandInset label
14740 name "sub:Big-Operators"
14748 \begin_layout Plain Layout
14758 \begin_layout Plain Layout
14768 \begin_layout Plain Layout
14777 \begin_layout Standard
14778 To be able to use all integral operators listed here, the option
14780 Use esint package automatically
14782 must be set in the document settings under
14785 \begin_inset space ~
14793 \begin_layout Standard
14794 \begin_inset space \hfill{}
14798 \begin_inset Tabular
14799 <lyxtabular version="3" rows="11" columns="2">
14801 <column alignment="center" valignment="top" width="0pt">
14802 <column alignment="center" valignment="top" width="0pt">
14804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14807 \begin_layout Plain Layout
14813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14816 \begin_layout Plain Layout
14824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14827 \begin_layout Plain Layout
14834 \begin_layout Plain Layout
14847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14850 \begin_layout Plain Layout
14851 \begin_inset Formula $\sum$
14861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14864 \begin_layout Plain Layout
14871 \begin_layout Plain Layout
14884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14887 \begin_layout Plain Layout
14888 \begin_inset Formula $\int$
14898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14901 \begin_layout Plain Layout
14909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14912 \begin_layout Plain Layout
14913 \begin_inset Formula $\intop$
14923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14926 \begin_layout Plain Layout
14934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14937 \begin_layout Plain Layout
14938 \begin_inset Formula $\oint$
14948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14951 \begin_layout Plain Layout
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14962 \begin_layout Plain Layout
14963 \begin_inset Formula $\ointop$
14973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14976 \begin_layout Plain Layout
14984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14987 \begin_layout Plain Layout
14988 \begin_inset Formula $\ointctrclockwise$
14998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15001 \begin_layout Plain Layout
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15012 \begin_layout Plain Layout
15013 \begin_inset Formula $\ointclockwise$
15023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15026 \begin_layout Plain Layout
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15037 \begin_layout Plain Layout
15038 \begin_inset Formula $\sqint$
15048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15051 \begin_layout Plain Layout
15059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15062 \begin_layout Plain Layout
15063 \begin_inset Formula $\bigcap$
15073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15076 \begin_layout Plain Layout
15084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15087 \begin_layout Plain Layout
15088 \begin_inset Formula $\bigcup$
15102 \begin_inset space \hfill{}
15106 \begin_inset Tabular
15107 <lyxtabular version="3" rows="10" columns="2">
15109 <column alignment="center" valignment="top" width="0pt">
15110 <column alignment="center" valignment="top" width="0pt">
15112 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15115 \begin_layout Plain Layout
15121 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15124 \begin_layout Plain Layout
15132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15135 \begin_layout Plain Layout
15142 \begin_layout Plain Layout
15155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15158 \begin_layout Plain Layout
15159 \begin_inset Formula $\prod$
15169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15172 \begin_layout Plain Layout
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15183 \begin_layout Plain Layout
15184 \begin_inset Formula $\coprod$
15194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15197 \begin_layout Plain Layout
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15208 \begin_layout Plain Layout
15209 \begin_inset Formula $\bigodot$
15219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15222 \begin_layout Plain Layout
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15233 \begin_layout Plain Layout
15234 \begin_inset Formula $\bigotimes$
15244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15247 \begin_layout Plain Layout
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15258 \begin_layout Plain Layout
15259 \begin_inset Formula $\bigoplus$
15269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15272 \begin_layout Plain Layout
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15283 \begin_layout Plain Layout
15284 \begin_inset Formula $\bigwedge$
15294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15297 \begin_layout Plain Layout
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15308 \begin_layout Plain Layout
15309 \begin_inset Formula $\bigvee$
15319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15322 \begin_layout Plain Layout
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15333 \begin_layout Plain Layout
15334 \begin_inset Formula $\bigsqcup$
15344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15347 \begin_layout Plain Layout
15355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15358 \begin_layout Plain Layout
15359 \begin_inset Formula $\biguplus$
15373 \begin_inset space \hfill{}
15379 \begin_layout Standard
15380 All big operators can also be inserted via the math toolbar button
15381 \begin_inset Graphics
15382 filename ../images/math/intop.png
15390 \begin_layout Standard
15391 The operators are called big because they are bigger than the sometimes
15392 equal looking binary operators.
15393 All big operators can have limits as described in the next subsection.
15396 \begin_layout Standard
15422 \begin_inset space ~
15425 in the style the operator limits are displayed, see
15426 \begin_inset CommandInset ref
15428 reference "sub:Operator-Limits"
15436 \begin_layout Subsubsection*
15437 Advices for Integrals
15440 \begin_layout Standard
15445 in an integral is an operator, that therefore has to be set upright.
15446 This is done by highlighting the
15450 and using the keyboard shortcut
15460 \begin_layout Plain Layout
15466 \begin_inset CommandInset ref
15468 reference "sub:Font-Styles"
15478 Finally the smallest space is inserted before the
15482 , as this is usual for operators.
15486 \begin_layout Standard
15488 \begin_inset Formula $\int A(x)dx$
15492 \begin_inset Newline newline
15499 \begin_layout Plain Layout
15509 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15515 \begin_layout Standard
15516 For multiple integrals there are the following commands:
15517 \begin_inset VSpace medskip
15523 \begin_layout Standard
15524 \begin_inset space \hfill{}
15528 \begin_inset Tabular
15529 <lyxtabular version="3" rows="4" columns="2">
15531 <column alignment="center" valignment="top" width="0">
15532 <column alignment="center" valignment="top" width="0">
15534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15537 \begin_layout Plain Layout
15543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15546 \begin_layout Plain Layout
15548 \begin_inset Note Note
15551 \begin_layout Plain Layout
15558 is only used as spacer.
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15573 \begin_layout Plain Layout
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15584 \begin_layout Plain Layout
15585 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15598 \begin_layout Plain Layout
15606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15609 \begin_layout Plain Layout
15610 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15620 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15623 \begin_layout Plain Layout
15631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15634 \begin_layout Plain Layout
15635 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15649 \begin_inset space \hfill{}
15653 \begin_inset Tabular
15654 <lyxtabular version="3" rows="4" columns="2">
15656 <column alignment="center" valignment="top" width="0">
15657 <column alignment="center" valignment="top" width="0">
15659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15662 \begin_layout Plain Layout
15668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15671 \begin_layout Plain Layout
15679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15682 \begin_layout Plain Layout
15690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15693 \begin_layout Plain Layout
15694 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15707 \begin_layout Plain Layout
15715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15718 \begin_layout Plain Layout
15719 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15732 \begin_layout Plain Layout
15740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15743 \begin_layout Plain Layout
15744 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15758 \begin_inset space \hfill{}
15764 \begin_layout Subsection
15766 \begin_inset CommandInset label
15768 name "sub:Operator-Limits"
15776 \begin_layout Plain Layout
15785 \begin_layout Standard
15786 Limits are created by super- and subscripts:
15789 \begin_layout Standard
15791 \begin_inset Tabular
15792 <lyxtabular version="3" rows="2" columns="2">
15794 <column alignment="center" valignment="top" width="0pt">
15795 <column alignment="center" valignment="top" width="0pt">
15797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15800 \begin_layout Plain Layout
15806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15809 \begin_layout Plain Layout
15811 \begin_inset Note Note
15814 \begin_layout Plain Layout
15821 is only used as spacer.
15833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15836 \begin_layout Plain Layout
15845 \begin_layout Plain Layout
15855 \begin_inset Formula $\to$
15859 \begin_inset Formula $\to$
15867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15870 \begin_layout Plain Layout
15871 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15887 \begin_layout Standard
15888 Limits of inline formulas are set right beside the operator.
15889 Limits in displayed formulas are set above or below the operator, except
15890 of integral limits.
15893 \begin_layout Standard
15894 To force that the limits are set beside the operator, the cursor is set
15895 directly behind the operator and the limits type is changed with the menu
15898 Edit\SpecialChar \menuseparator
15899 Math\SpecialChar \menuseparator
15918 \begin_layout Standard
15919 The default limits type is this:
15920 \begin_inset Formula \[
15921 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15925 This is how it looks when the limits type was changed to
15932 \begin_inset Formula \[
15933 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15937 For integrals, except of
15949 , the limits are by default set beside the operator.
15950 But for multiple integrals the limits are often set below the operator.
15951 In the following example the limits type was therefore set to
15955 and so set below the integrals:
15956 \begin_inset Formula \begin{equation}
15957 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15964 \begin_layout Standard
15965 \begin_inset VSpace medskip
15968 To specify conditions for limits, the commands
15978 \begin_layout Plain Layout
15996 \begin_layout Plain Layout
16005 To create for example this expression
16006 \begin_inset Formula \begin{equation}
16007 \sum_{\begin{subarray}{c}
16009 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16016 \begin_layout Standard
16017 the following has to be done:
16018 \begin_inset Newline newline
16033 \begin_layout Plain Layout
16045 One is now in a blue box under the summation operator and insert there
16054 \begin_layout Plain Layout
16066 The blue box is now within a purple box and now several lines can be written
16068 A new line is created by inserting a line break (
16071 arg "newline-insert newline"
16076 \begin_inset Newline newline
16081 0<k<1000 Ctrl+Return
16082 \begin_inset Newline newline
16087 is typed in, a new box appears below for the new line.
16090 \begin_layout Standard
16091 The alignment of the lines can be changed to left aligned with the
16101 Edit\SpecialChar \menuseparator
16105 To get right alignment,
16113 \begin_layout Plain Layout
16124 is inserted at the beginning of the line.
16127 \begin_layout Standard
16140 with the difference that the lines are always centered.
16143 \begin_layout Standard
16144 \begin_inset VSpace bigskip
16148 \begin_inset CommandInset ref
16150 reference "eq:substack"
16154 there can be too much space beside an operator, because the characters
16155 following the operator are set beside the limits.
16158 \begin_layout Standard
16159 To avoid this, the following macro can be used in the LaTeX-preamble:
16162 \begin_layout Standard
16176 \begin_inset Newline newline
16188 \begin_inset Newline newline
16195 mathclapinternal #1#2{
16199 mathsurround =0pt #1{#2}$}}
16202 \begin_layout Standard
16203 This defines the command
16213 \begin_layout Plain Layout
16221 that sets the width of the limit to 0
16222 \begin_inset space \thinspace{}
16226 The command scheme is
16229 \begin_layout Standard
16237 \begin_layout Standard
16238 where the limit can consist of several conditions.
16241 \begin_layout Standard
16243 \begin_inset CommandInset ref
16245 reference "eq:substack"
16249 , one uses the command
16252 \begin_layout Standard
16265 \begin_layout Plain Layout
16274 0<k<1000 Ctrl+Return
16277 \begin_layout Standard
16278 to create the lower limit.
16279 The summand is now directly behind the summation operator:
16280 \begin_inset Formula \[
16281 \sum_{\mathclap{\substack{0<k<1000\\
16282 \\k\,\in\,\mathbb{N}}
16290 \begin_layout Standard
16291 \begin_inset VSpace bigskip
16294 How to use one limit for several operators is described in
16295 \begin_inset CommandInset ref
16297 reference "sub:Self-defined-Operators"
16304 \begin_layout Standard
16305 \begin_inset Newpage newpage
16311 \begin_layout Subsection
16313 \begin_inset CommandInset label
16315 name "sub:Binary-Operators"
16323 \begin_layout Plain Layout
16332 \begin_layout Standard
16333 Binary operators are surrounded by space when there is a character before
16335 \begin_inset VSpace medskip
16341 \begin_layout Standard
16342 \begin_inset space \hfill{}
16346 \begin_inset Tabular
16347 <lyxtabular version="3" rows="13" columns="2">
16349 <column alignment="center" valignment="top" width="0pt">
16350 <column alignment="center" valignment="top" width="0pt">
16352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16355 \begin_layout Plain Layout
16357 \begin_inset Note Note
16360 \begin_layout Plain Layout
16367 is only used as spacer.
16377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16380 \begin_layout Plain Layout
16388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16391 \begin_layout Plain Layout
16397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16400 \begin_layout Plain Layout
16401 \begin_inset Formula $+$
16411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16414 \begin_layout Plain Layout
16420 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16423 \begin_layout Plain Layout
16424 \begin_inset Formula $-$
16434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16437 \begin_layout Plain Layout
16445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16448 \begin_layout Plain Layout
16449 \begin_inset Formula $\pm$
16459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16462 \begin_layout Plain Layout
16470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16473 \begin_layout Plain Layout
16474 \begin_inset Formula $\mp$
16484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16487 \begin_layout Plain Layout
16495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16498 \begin_layout Plain Layout
16499 \begin_inset Formula $\cdot$
16509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16512 \begin_layout Plain Layout
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16523 \begin_layout Plain Layout
16524 \begin_inset Formula $\times$
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16537 \begin_layout Plain Layout
16545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16548 \begin_layout Plain Layout
16549 \begin_inset Formula $\div$
16559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16562 \begin_layout Plain Layout
16566 \begin_layout Plain Layout
16579 \begin_layout Plain Layout
16591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16594 \begin_layout Plain Layout
16595 \begin_inset Formula $*$
16605 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16608 \begin_layout Plain Layout
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16619 \begin_layout Plain Layout
16620 \begin_inset Formula $\star$
16630 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16633 \begin_layout Plain Layout
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16644 \begin_layout Plain Layout
16645 \begin_inset Formula $\circ$
16655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16658 \begin_layout Plain Layout
16666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16669 \begin_layout Plain Layout
16670 \begin_inset Formula $\diamond$
16680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16683 \begin_layout Plain Layout
16691 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16694 \begin_layout Plain Layout
16695 \begin_inset Formula $\bullet$
16709 \begin_inset space \hfill{}
16713 \begin_inset Tabular
16714 <lyxtabular version="3" rows="13" columns="2">
16716 <column alignment="center" valignment="top" width="0pt">
16717 <column alignment="center" valignment="top" width="0pt">
16719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16722 \begin_layout Plain Layout
16728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16731 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16742 \begin_layout Plain Layout
16750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16753 \begin_layout Plain Layout
16754 \begin_inset Formula $\nabla$
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16767 \begin_layout Plain Layout
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16778 \begin_layout Plain Layout
16779 \begin_inset Formula $\bigtriangledown$
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16792 \begin_layout Plain Layout
16800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16803 \begin_layout Plain Layout
16804 \begin_inset Formula $\bigtriangleup$
16814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16817 \begin_layout Plain Layout
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16828 \begin_layout Plain Layout
16829 \begin_inset Formula $\Box$
16839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16842 \begin_layout Plain Layout
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16853 \begin_layout Plain Layout
16854 \begin_inset Formula $\cap$
16864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16867 \begin_layout Plain Layout
16875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16878 \begin_layout Plain Layout
16879 \begin_inset Formula $\cup$
16889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16892 \begin_layout Plain Layout
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16903 \begin_layout Plain Layout
16904 \begin_inset Formula $\dagger$
16914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16917 \begin_layout Plain Layout
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16928 \begin_layout Plain Layout
16929 \begin_inset Formula $\ddagger$
16939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16942 \begin_layout Plain Layout
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16953 \begin_layout Plain Layout
16954 \begin_inset Formula $\wr$
16964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16967 \begin_layout Plain Layout
16975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16978 \begin_layout Plain Layout
16979 \begin_inset Formula $\bigcirc$
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16992 \begin_layout Plain Layout
17000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17003 \begin_layout Plain Layout
17004 \begin_inset Formula $\wedge$
17014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17017 \begin_layout Plain Layout
17025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17028 \begin_layout Plain Layout
17029 \begin_inset Formula $\vee$
17043 \begin_inset space \hfill{}
17047 \begin_inset Tabular
17048 <lyxtabular version="3" rows="13" columns="2">
17050 <column alignment="center" valignment="top" width="0pt">
17051 <column alignment="center" valignment="top" width="0pt">
17053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17065 \begin_layout Plain Layout
17073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17076 \begin_layout Plain Layout
17084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17087 \begin_layout Plain Layout
17088 \begin_inset Formula $\oplus$
17098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17101 \begin_layout Plain Layout
17109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17112 \begin_layout Plain Layout
17113 \begin_inset Formula $\ominus$
17123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17126 \begin_layout Plain Layout
17134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17137 \begin_layout Plain Layout
17138 \begin_inset Formula $\otimes$
17148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17151 \begin_layout Plain Layout
17159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17162 \begin_layout Plain Layout
17163 \begin_inset Formula $\oslash$
17173 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17176 \begin_layout Plain Layout
17184 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17187 \begin_layout Plain Layout
17188 \begin_inset Formula $\odot$
17198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17201 \begin_layout Plain Layout
17209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17212 \begin_layout Plain Layout
17213 \begin_inset Formula $\amalg$
17223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17226 \begin_layout Plain Layout
17234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17237 \begin_layout Plain Layout
17238 \begin_inset Formula $\uplus$
17248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17251 \begin_layout Plain Layout
17259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17262 \begin_layout Plain Layout
17263 \begin_inset Formula $\setminus$
17273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17276 \begin_layout Plain Layout
17284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17287 \begin_layout Plain Layout
17288 \begin_inset Formula $\sqcap$
17298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17301 \begin_layout Plain Layout
17309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17312 \begin_layout Plain Layout
17313 \begin_inset Formula $\sqcup$
17323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17326 \begin_layout Plain Layout
17334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17337 \begin_layout Plain Layout
17338 \begin_inset Formula $\triangleleft$
17348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17351 \begin_layout Plain Layout
17359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17362 \begin_layout Plain Layout
17363 \begin_inset Formula $\triangleright$
17377 \begin_inset space \hfill{}
17383 \begin_layout Standard
17384 All binary operators can also be inserted via the math toolbar button
17385 \begin_inset Graphics
17386 filename ../images/math/pm.png
17394 \begin_layout Standard
17395 To typeset the Laplace operator also
17412 \begin_inset Formula $\nabla^{2}$
17415 ) can be used instead of
17424 \begin_layout Standard
17431 Insert\SpecialChar \menuseparator
17443 \begin_layout Subsection
17444 Self-defined Operators
17445 \begin_inset CommandInset label
17447 name "sub:Self-defined-Operators"
17455 \begin_layout Plain Layout
17456 Operators ! self-defined
17464 \begin_layout Standard
17465 With the help of the command
17469 DeclareMathOperator
17475 \begin_layout Plain Layout
17480 DeclareMathOperator
17485 custom operators can be defined in the LaTeX-preamble.
17486 Its command scheme is:
17489 \begin_layout Standard
17494 DeclareMathOperator{new command}{display}
17497 \begin_layout Standard
17498 Display can be characters or symbols that define how the operator looks
17500 To define a big operator a * is set behind the command.
17501 All self-defined big operators can have limits as described in
17502 \begin_inset CommandInset ref
17504 reference "sub:Operator-Limits"
17511 \begin_layout Standard
17512 For example the LaTeX-preamble line
17515 \begin_layout Standard
17520 DeclareMathOperator*{
17527 \begin_layout Standard
17528 defines the command
17534 , that inserts a big operator consisting of the lozenge symbol from
17535 \begin_inset CommandInset ref
17537 reference "sub:Miscellaneous-Symbols"
17542 \begin_inset Formula \[
17543 \Lozenge_{n=1}^{\infty}\]
17547 The command for this formula is:
17558 \begin_inset Formula $\to$
17564 \begin_layout Standard
17565 \begin_inset VSpace bigskip
17568 When self-defined operators are not used several times in the document,
17569 they can also be defined with the commands
17579 \begin_layout Plain Layout
17597 \begin_layout Plain Layout
17605 , which have the following scheme:
17608 \begin_layout Standard
17622 \begin_layout Standard
17629 defines big operators,
17638 \begin_layout Standard
17646 \begin_inset space \thinspace{}
17650 \begin_inset space ~
17653 be used to use one limit for several operators:
17656 \begin_layout Standard
17657 \begin_inset Formula \[
17658 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17665 \begin_layout Standard
17666 The command for the formula above is:
17667 \begin_inset Newline newline
17686 \begin_layout Plain Layout
17698 \begin_inset Formula $\to$
17707 \begin_layout Plain Layout
17721 \begin_layout Section
17726 \begin_layout Plain Layout
17735 \begin_layout Subsection
17737 \begin_inset CommandInset label
17739 name "sub:Font-Styles"
17747 \begin_layout Plain Layout
17756 \begin_layout Standard
17757 Latin letters in formulas can be set in one of the following font styles:
17758 \begin_inset VSpace -2mm
17764 \begin_layout Standard
17766 \begin_inset Tabular
17767 <lyxtabular version="3" rows="6" columns="3">
17769 <column alignment="center" valignment="top" width="0">
17770 <column alignment="center" valignment="top" width="0">
17771 <column alignment="center" valignment="top" width="0">
17773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17776 \begin_layout Plain Layout
17782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17785 \begin_layout Plain Layout
17791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17794 \begin_layout Plain Layout
17802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17805 \begin_layout Plain Layout
17814 \begin_layout Plain Layout
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17833 \begin_layout Plain Layout
17834 \begin_inset Formula $\mathbb{ABC}$
17842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17845 \begin_layout Plain Layout
17858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17861 \begin_layout Plain Layout
17870 \begin_layout Plain Layout
17886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17889 \begin_layout Plain Layout
17890 \begin_inset Formula $\mathbf{AbC}$
17898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17901 \begin_layout Plain Layout
17914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17917 \begin_layout Plain Layout
17926 \begin_layout Plain Layout
17942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17945 \begin_layout Plain Layout
17946 \begin_inset Formula $\boldsymbol{AbC}$
17954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17957 \begin_layout Plain Layout
17960 arg "font-boldsymbol"
17970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17973 \begin_layout Plain Layout
17982 \begin_layout Plain Layout
17998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18001 \begin_layout Plain Layout
18002 \begin_inset Formula $\mathcal{ABC}$
18010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18013 \begin_layout Plain Layout
18026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18029 \begin_layout Plain Layout
18038 \begin_layout Plain Layout
18054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18057 \begin_layout Plain Layout
18058 \begin_inset Formula $\mathfrak{AbC}$
18066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18069 \begin_layout Plain Layout
18083 \begin_layout Standard
18085 \begin_inset Tabular
18086 <lyxtabular version="3" rows="5" columns="3">
18088 <column alignment="center" valignment="top" width="0">
18089 <column alignment="center" valignment="top" width="0">
18090 <column alignment="center" valignment="top" width="0">
18092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18095 \begin_layout Plain Layout
18101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18104 \begin_layout Plain Layout
18110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18113 \begin_layout Plain Layout
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18124 \begin_layout Plain Layout
18133 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18152 \begin_layout Plain Layout
18153 \begin_inset Formula $\mathit{AbC}$
18161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18164 \begin_layout Plain Layout
18172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18175 \begin_layout Plain Layout
18184 \begin_layout Plain Layout
18200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18203 \begin_layout Plain Layout
18204 \begin_inset Formula $\mathrm{AbC}$
18212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18215 \begin_layout Plain Layout
18228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18231 \begin_layout Plain Layout
18240 \begin_layout Plain Layout
18256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18259 \begin_layout Plain Layout
18260 \begin_inset Formula $\mathsf{AbC}$
18268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18271 \begin_layout Plain Layout
18284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18287 \begin_layout Plain Layout
18296 \begin_layout Plain Layout
18312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18315 \begin_layout Plain Layout
18316 \begin_inset Formula $\mathtt{AbC}$
18324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18327 \begin_layout Plain Layout
18330 arg "font-typewriter"
18346 \begin_layout Standard
18347 \begin_inset Note Greyedout
18350 \begin_layout Plain Layout
18367 can only be used for big letters.
18375 \begin_layout Standard
18376 Predefined is the style
18385 \begin_layout Standard
18386 The style commands work also for letters in mathematical constructs:
18387 \begin_inset Formula \[
18388 \mathfrak{A=\frac{b}{C}}\]
18395 \begin_layout Standard
18396 Characters in mathematical text don't appear in a math font style but in
18397 the text font style
18404 That their style can't be set correctly via the text style dialog is a
18409 \begin_layout Plain Layout
18410 \begin_inset CommandInset href
18412 name "LyX-bug #4091"
18413 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18425 \begin_layout Standard
18426 Instead of the style commands the dialog
18428 Edit\SpecialChar \menuseparator
18429 Math\SpecialChar \menuseparator
18432 or the toolbar button
18433 \begin_inset Graphics
18434 filename ../images/math/font.png
18442 \begin_layout Subsection
18444 \begin_inset CommandInset label
18446 name "sub:Bold-Formulas"
18454 \begin_layout Plain Layout
18463 \begin_layout Standard
18464 To make a complete formula bold, the command
18470 from the previous subsection cannot be used, because it doesn't work for
18471 small Greek letters.
18472 Furthermore it prints Latin letters always upright, like in the following
18476 \begin_layout Standard
18477 \begin_inset Formula \[
18478 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18485 \begin_layout Standard
18486 To display the formula correctly, the command
18493 \begin_inset Formula \[
18494 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18498 It is also possible to set the formula in a
18500 boldmath environment
18503 This environment is created by inserting the command
18511 \begin_layout Plain Layout
18522 To end the environment, the command
18530 \begin_layout Plain Layout
18540 is inserted in TeX-mode.
18544 \begin_layout Plain Layout
18554 \begin_inset Formula \[
18555 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18563 \begin_layout Plain Layout
18575 \begin_layout Subsection
18580 \begin_layout Plain Layout
18589 \begin_layout Standard
18590 Formulas can be colored like normal text: Highlight a formula or a formula
18596 Here is a formula in magenta:
18597 \begin_inset Formula \[
18598 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18605 \begin_layout Standard
18606 You can also define your own colors as described in
18607 \begin_inset CommandInset ref
18609 reference "sub:Colored-Boxes"
18614 They can be used with the TeX code command
18624 \begin_layout Plain Layout
18635 \begin_layout Standard
18640 textcolor{color}{characters or formula}
18643 \begin_layout Standard
18644 The following example was colored completely dark green and partly red:
18647 \begin_layout Standard
18651 \begin_layout Plain Layout
18655 textcolor{darkgreen}{
18661 \begin_inset Formula \[
18662 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18670 \begin_layout Plain Layout
18680 \begin_layout Standard
18681 Due to a bug in LyX only complete formulas can be colored with self-defined
18686 \begin_layout Plain Layout
18687 \begin_inset CommandInset href
18689 name "LyX-bug #5269"
18690 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18702 \begin_layout Subsection
18704 \begin_inset CommandInset label
18706 name "sub:Font-Sizes"
18714 \begin_layout Plain Layout
18723 \begin_layout Standard
18724 For characters in formulas there are, analog to characters in text, the
18725 following size commands:
18728 \begin_layout Standard
18772 \begin_inset Newline newline
18794 \begin_layout Standard
18795 The size produced by the commands depends on the document font size, that
18796 corresponds with the command
18803 The other commands produce smaller or larger sizes than
18810 The font size can however not exceed a certain value.
18811 Is for example the document font size 12
18812 \begin_inset space \thinspace{}
18821 switches to the same size as
18831 \begin_layout Standard
18832 A size command is inserted in TeX-mode before the formula and sets the size
18833 for all following formula and text characters.
18834 To switch back to the initial size, the command
18840 is inserted behind the formula in TeX-mode.
18843 \begin_layout Standard
18844 Within a formula the size can only be changed for symbols or letters in
18846 To do this, the size command is inserted in mathematical text.
18847 All following characters until the end of the mathematical text or until
18848 another size command will have the selected size.
18850 \begin_inset VSpace -2mm
18856 \begin_layout Standard
18860 \begin_layout Plain Layout
18870 \begin_inset Formula \[
18871 A=\frac{B}{c}\cdot\maltese\]
18876 \begin_inset Formula \[
18877 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18885 \begin_layout Plain Layout
18897 \begin_layout Standard
18898 \begin_inset VSpace medskip
18901 Before both formulas the command
18908 The command for the second formula is:
18909 \begin_inset Newline newline
18920 \begin_layout Plain Layout
18935 \begin_layout Plain Layout
18950 \begin_layout Plain Layout
18965 \begin_layout Plain Layout
18975 \begin_inset Formula $\to$
18979 \begin_inset Formula $\to$
18983 \begin_inset Newline newline
18987 \begin_inset space \hspace*{}
19001 \begin_layout Plain Layout
19016 \begin_layout Plain Layout
19031 \begin_layout Plain Layout
19043 \begin_layout Standard
19044 If a symbol cannot be displayed in different sizes, it will always be displayed
19045 in the default size.
19048 \begin_layout Section
19053 \begin_layout Plain Layout
19062 \begin_layout Standard
19063 All Greek letters can also be inserted via the toolbar button
19064 \begin_inset Graphics
19065 filename ../images/math/alpha.png
19073 \begin_layout Subsection
19078 \begin_layout Plain Layout
19079 Greek letters ! small
19087 \begin_layout Standard
19088 \begin_inset space \hfill{}
19092 \begin_inset Tabular
19093 <lyxtabular version="3" rows="11" columns="2">
19095 <column alignment="center" valignment="top" width="0pt">
19096 <column alignment="center" valignment="top" width="0pt">
19098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19101 \begin_layout Plain Layout
19107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19110 \begin_layout Plain Layout
19118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19121 \begin_layout Plain Layout
19129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19132 \begin_layout Plain Layout
19133 \begin_inset Formula $\alpha$
19143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19146 \begin_layout Plain Layout
19154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19157 \begin_layout Plain Layout
19158 \begin_inset Formula $\beta$
19168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19171 \begin_layout Plain Layout
19179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19182 \begin_layout Plain Layout
19183 \begin_inset Formula $\gamma$
19193 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19196 \begin_layout Plain Layout
19204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19207 \begin_layout Plain Layout
19208 \begin_inset Formula $\delta$
19218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19221 \begin_layout Plain Layout
19229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19232 \begin_layout Plain Layout
19233 \begin_inset Formula $\epsilon$
19243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19246 \begin_layout Plain Layout
19254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19257 \begin_layout Plain Layout
19258 \begin_inset Formula $\varepsilon$
19268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19271 \begin_layout Plain Layout
19279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19282 \begin_layout Plain Layout
19283 \begin_inset Formula $\zeta$
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19296 \begin_layout Plain Layout
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19307 \begin_layout Plain Layout
19308 \begin_inset Formula $\eta$
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19321 \begin_layout Plain Layout
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19332 \begin_layout Plain Layout
19333 \begin_inset Formula $\theta$
19343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19346 \begin_layout Plain Layout
19354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19357 \begin_layout Plain Layout
19358 \begin_inset Formula $\vartheta$
19372 \begin_inset space \hfill{}
19376 \begin_inset Tabular
19377 <lyxtabular version="3" rows="12" columns="2">
19379 <column alignment="center" valignment="top" width="0pt">
19380 <column alignment="center" valignment="top" width="0pt">
19382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19385 \begin_layout Plain Layout
19391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19394 \begin_layout Plain Layout
19402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19405 \begin_layout Plain Layout
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19416 \begin_layout Plain Layout
19417 \begin_inset Formula $\iota$
19427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19430 \begin_layout Plain Layout
19438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19441 \begin_layout Plain Layout
19442 \begin_inset Formula $\kappa$
19452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19455 \begin_layout Plain Layout
19463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19466 \begin_layout Plain Layout
19467 \begin_inset Formula $\varkappa$
19477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19480 \begin_layout Plain Layout
19488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19491 \begin_layout Plain Layout
19492 \begin_inset Formula $\lambda$
19502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19505 \begin_layout Plain Layout
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19516 \begin_layout Plain Layout
19517 \begin_inset Formula $\mu$
19527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19530 \begin_layout Plain Layout
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19541 \begin_layout Plain Layout
19542 \begin_inset Formula $\nu$
19552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19555 \begin_layout Plain Layout
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19566 \begin_layout Plain Layout
19567 \begin_inset Formula $\xi$
19577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19580 \begin_layout Plain Layout
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19589 \begin_layout Plain Layout
19590 \begin_inset Formula $o$
19600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19603 \begin_layout Plain Layout
19611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19614 \begin_layout Plain Layout
19615 \begin_inset Formula $\pi$
19625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19628 \begin_layout Plain Layout
19636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Plain Layout
19640 \begin_inset Formula $\varpi$
19650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19664 \begin_layout Plain Layout
19665 \begin_inset Formula $\rho$
19679 \begin_inset space \hfill{}
19683 \begin_inset Tabular
19684 <lyxtabular version="3" rows="11" columns="2">
19686 <column alignment="center" valignment="top" width="0pt">
19687 <column alignment="center" valignment="top" width="0pt">
19689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19692 \begin_layout Plain Layout
19698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19701 \begin_layout Plain Layout
19709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19712 \begin_layout Plain Layout
19720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19723 \begin_layout Plain Layout
19724 \begin_inset Formula $\varrho$
19734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19737 \begin_layout Plain Layout
19745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19748 \begin_layout Plain Layout
19749 \begin_inset Formula $\sigma$
19759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19762 \begin_layout Plain Layout
19770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19773 \begin_layout Plain Layout
19774 \begin_inset Formula $\varsigma$
19784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19787 \begin_layout Plain Layout
19795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19798 \begin_layout Plain Layout
19799 \begin_inset Formula $\tau$
19809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19812 \begin_layout Plain Layout
19820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19823 \begin_layout Plain Layout
19824 \begin_inset Formula $\upsilon$
19834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19837 \begin_layout Plain Layout
19845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19848 \begin_layout Plain Layout
19849 \begin_inset Formula $\phi$
19859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19862 \begin_layout Plain Layout
19870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19873 \begin_layout Plain Layout
19874 \begin_inset Formula $\varphi$
19884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19887 \begin_layout Plain Layout
19895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19898 \begin_layout Plain Layout
19899 \begin_inset Formula $\chi$
19909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19912 \begin_layout Plain Layout
19920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19923 \begin_layout Plain Layout
19924 \begin_inset Formula $\psi$
19934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19937 \begin_layout Plain Layout
19945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19948 \begin_layout Plain Layout
19949 \begin_inset Formula $\omega$
19963 \begin_inset space \hfill{}
19969 \begin_layout Standard
19970 \begin_inset VSpace medskip
19976 \begin_layout Standard
19977 How to create upright Greek letters is explained in
19978 \begin_inset CommandInset ref
19980 reference "sub:Upright-small-Greek"
19987 \begin_layout Subsection
19992 \begin_layout Plain Layout
19993 Greek letters ! big
20001 \begin_layout Standard
20002 \begin_inset space \hfill{}
20006 \begin_inset Tabular
20007 <lyxtabular version="3" rows="7" columns="2">
20009 <column alignment="center" valignment="top" width="0pt">
20010 <column alignment="center" valignment="top" width="0pt">
20012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20015 \begin_layout Plain Layout
20021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20024 \begin_layout Plain Layout
20032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20035 \begin_layout Plain Layout
20043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20046 \begin_layout Plain Layout
20047 \begin_inset Formula $\Gamma$
20057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20060 \begin_layout Plain Layout
20068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20071 \begin_layout Plain Layout
20072 \begin_inset Formula $\Delta$
20082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20085 \begin_layout Plain Layout
20093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20096 \begin_layout Plain Layout
20097 \begin_inset Formula $\Theta$
20107 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20110 \begin_layout Plain Layout
20118 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20121 \begin_layout Plain Layout
20122 \begin_inset Formula $\Lambda$
20132 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20135 \begin_layout Plain Layout
20143 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20146 \begin_layout Plain Layout
20147 \begin_inset Formula $\Xi$
20157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20160 \begin_layout Plain Layout
20168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20171 \begin_layout Plain Layout
20172 \begin_inset Formula $\Pi$
20186 \begin_inset space \hfill{}
20190 \begin_inset Tabular
20191 <lyxtabular version="3" rows="6" columns="2">
20193 <column alignment="center" valignment="top" width="0pt">
20194 <column alignment="center" valignment="top" width="0pt">
20196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20199 \begin_layout Plain Layout
20205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20208 \begin_layout Plain Layout
20216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20219 \begin_layout Plain Layout
20227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20230 \begin_layout Plain Layout
20231 \begin_inset Formula $\Sigma$
20241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20244 \begin_layout Plain Layout
20252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20255 \begin_layout Plain Layout
20256 \begin_inset Formula $\Upsilon$
20266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20269 \begin_layout Plain Layout
20277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20280 \begin_layout Plain Layout
20281 \begin_inset Formula $\Phi$
20291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20294 \begin_layout Plain Layout
20302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20305 \begin_layout Plain Layout
20306 \begin_inset Formula $\Psi$
20316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20319 \begin_layout Plain Layout
20327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20330 \begin_layout Plain Layout
20331 \begin_inset Formula $\Omega$
20345 \begin_inset space \hfill{}
20351 \begin_layout Standard
20352 \begin_inset VSpace medskip
20355 That the big Greek letters appear upright is caused by a design bug when
20357 To get correct italic big letters, begin every command with
20362 For example the command
20369 \begin_inset Formula $\varGamma$
20375 \begin_layout Subsection
20380 \begin_layout Plain Layout
20381 Greek letters ! bold
20389 \begin_layout Standard
20390 Greek letters cannot be set with different font styles like Latin letters.
20391 They can only be made bold with the command
20401 \begin_layout Plain Layout
20412 \begin_layout Standard
20414 \begin_inset Tabular
20415 <lyxtabular version="3" rows="3" columns="2">
20417 <column alignment="center" valignment="top" width="0">
20418 <column alignment="center" valignment="top" width="0">
20420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20423 \begin_layout Plain Layout
20429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20432 \begin_layout Plain Layout
20440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20443 \begin_layout Plain Layout
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20458 \begin_layout Plain Layout
20459 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20472 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20487 \begin_layout Plain Layout
20488 \begin_inset Formula $\theta\boldsymbol{\theta}$
20504 \begin_layout Section
20509 \begin_layout Plain Layout
20522 \begin_layout Plain Layout
20523 A list with all symbols of most of the LaTeX-packages can be found in
20524 \begin_inset CommandInset citation
20539 \begin_layout Plain Layout
20547 \begin_inset Note Note
20550 \begin_layout Plain Layout
20553 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20556 \begin_layout Plain Layout
20559 texorpdfstring is in section
20560 \begin_inset CommandInset ref
20562 reference "sub:Formulas-in-Section"
20575 \begin_layout Plain Layout
20584 \begin_layout Standard
20585 Many of the symbols listed in this section can also be inserted via the
20587 \begin_inset Graphics
20588 filename ../images/math/nabla.png
20594 \begin_inset Graphics
20595 filename ../images/math/digamma.png
20603 \begin_layout Subsection
20604 Mathematical Symbols
20605 \begin_inset CommandInset label
20607 name "sub:Mathematical-Symbols"
20615 \begin_layout Plain Layout
20616 Symbols ! mathematical
20624 \begin_layout Standard
20625 \begin_inset space \hfill{}
20629 \begin_inset Tabular
20630 <lyxtabular version="3" rows="10" columns="2">
20632 <column alignment="center" valignment="top" width="0pt">
20633 <column alignment="center" valignment="top" width="0pt">
20635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20638 \begin_layout Plain Layout
20644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20647 \begin_layout Plain Layout
20655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20658 \begin_layout Plain Layout
20666 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20669 \begin_layout Plain Layout
20670 \begin_inset Formula $\neg$
20680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20683 \begin_layout Plain Layout
20691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20694 \begin_layout Plain Layout
20695 \begin_inset Formula $\Im$
20705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20708 \begin_layout Plain Layout
20716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20719 \begin_layout Plain Layout
20720 \begin_inset Formula $\Re$
20730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20733 \begin_layout Plain Layout
20741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20744 \begin_layout Plain Layout
20745 \begin_inset Formula $\aleph$
20755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20758 \begin_layout Plain Layout
20766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20769 \begin_layout Plain Layout
20770 \begin_inset Formula $\partial$
20780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20783 \begin_layout Plain Layout
20791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20794 \begin_layout Plain Layout
20795 \begin_inset Formula $\infty$
20805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20808 \begin_layout Plain Layout
20816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20819 \begin_layout Plain Layout
20820 \begin_inset Formula $\wp$
20830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20833 \begin_layout Plain Layout
20841 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20844 \begin_layout Plain Layout
20845 \begin_inset Formula $\imath$
20855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20858 \begin_layout Plain Layout
20866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20869 \begin_layout Plain Layout
20870 \begin_inset Formula $\jmath$
20884 \begin_inset space \hfill{}
20888 \begin_inset Tabular
20889 <lyxtabular version="3" rows="10" columns="2">
20891 <column alignment="center" valignment="top" width="0pt">
20892 <column alignment="center" valignment="top" width="0pt">
20894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20897 \begin_layout Plain Layout
20903 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20906 \begin_layout Plain Layout
20908 \begin_inset Note Note
20911 \begin_layout Plain Layout
20918 is only used as spacer.
20930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20933 \begin_layout Plain Layout
20941 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20944 \begin_layout Plain Layout
20945 \begin_inset Formula $\forall$
20955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20958 \begin_layout Plain Layout
20966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20969 \begin_layout Plain Layout
20970 \begin_inset Formula $\exists$
20980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20983 \begin_layout Plain Layout
20991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20994 \begin_layout Plain Layout
20995 \begin_inset Formula $\nexists$
21005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21008 \begin_layout Plain Layout
21016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21019 \begin_layout Plain Layout
21020 \begin_inset Formula $\emptyset$
21030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21033 \begin_layout Plain Layout
21041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21044 \begin_layout Plain Layout
21045 \begin_inset Formula $\varnothing$
21055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21058 \begin_layout Plain Layout
21066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21069 \begin_layout Plain Layout
21070 \begin_inset Formula $\dag$
21080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21083 \begin_layout Plain Layout
21091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21094 \begin_layout Plain Layout
21095 \begin_inset Formula $\ddag$
21105 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21108 \begin_layout Plain Layout
21116 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21119 \begin_layout Plain Layout
21123 \begin_layout Plain Layout
21133 \begin_inset Formula $\complement$
21140 \begin_layout Plain Layout
21154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21157 \begin_layout Plain Layout
21165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21168 \begin_layout Plain Layout
21169 \begin_inset Formula $\Bbbk$
21183 \begin_inset space \hfill{}
21187 \begin_inset Tabular
21188 <lyxtabular version="3" rows="10" columns="2">
21190 <column alignment="center" valignment="top" width="0pt">
21191 <column alignment="center" valignment="top" width="0pt">
21193 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21196 \begin_layout Plain Layout
21202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21205 \begin_layout Plain Layout
21213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21216 \begin_layout Plain Layout
21224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21227 \begin_layout Plain Layout
21228 \begin_inset Formula $\prime$
21238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21241 \begin_layout Plain Layout
21249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21252 \begin_layout Plain Layout
21253 \begin_inset Formula $\backprime$
21263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21266 \begin_layout Plain Layout
21274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21277 \begin_layout Plain Layout
21278 \begin_inset Formula $\mho$
21288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21291 \begin_layout Plain Layout
21299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21302 \begin_layout Plain Layout
21303 \begin_inset Formula $\triangle$
21313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21316 \begin_layout Plain Layout
21324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21327 \begin_layout Plain Layout
21328 \begin_inset Formula $\angle$
21338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\measuredangle$
21363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\sphericalangle$
21388 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\top$
21413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21424 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21427 \begin_layout Plain Layout
21428 \begin_inset Formula $\bot$
21442 \begin_inset space \hfill{}
21448 \begin_layout Subsection
21449 Miscellaneous Symbols
21450 \begin_inset CommandInset label
21452 name "sub:Miscellaneous-Symbols"
21460 \begin_layout Plain Layout
21461 Symbols ! miscellaneous
21469 \begin_layout Standard
21472 \begin_inset Tabular
21473 <lyxtabular version="3" rows="10" columns="2">
21475 <column alignment="center" valignment="top" width="0pt">
21476 <column alignment="center" valignment="top" width="0pt">
21478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21481 \begin_layout Plain Layout
21487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21490 \begin_layout Plain Layout
21498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21501 \begin_layout Plain Layout
21509 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21512 \begin_layout Plain Layout
21513 \begin_inset Formula $\flat$
21523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\natural$
21548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\sharp$
21573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21587 \begin_layout Plain Layout
21588 \begin_inset Formula $\surd$
21598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21612 \begin_layout Plain Layout
21613 \begin_inset Formula $\checkmark$
21623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21638 \begin_inset Formula $\yen$
21648 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21651 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21662 \begin_layout Plain Layout
21663 \begin_inset Formula $\pounds$
21673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21676 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\$$
21696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21705 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21708 \begin_layout Plain Layout
21709 \begin_inset Formula $§$
21723 \begin_inset Tabular
21724 <lyxtabular version="3" rows="10" columns="2">
21726 <column alignment="center" valignment="top" width="0">
21727 <column alignment="center" valignment="top" width="0">
21729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21732 \begin_layout Plain Layout
21738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21741 \begin_layout Plain Layout
21749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21752 \begin_layout Plain Layout
21760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21763 \begin_layout Plain Layout
21764 \begin_inset Formula $\hbar$
21774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21777 \begin_layout Plain Layout
21785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21788 \begin_layout Plain Layout
21789 \begin_inset Formula $\hslash$
21799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21802 \begin_layout Plain Layout
21810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21813 \begin_layout Plain Layout
21814 \begin_inset Formula $\clubsuit$
21824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21827 \begin_layout Plain Layout
21835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21838 \begin_layout Plain Layout
21839 \begin_inset Formula $\spadesuit$
21849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21852 \begin_layout Plain Layout
21860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21863 \begin_layout Plain Layout
21864 \begin_inset Formula $\bigstar$
21874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21877 \begin_layout Plain Layout
21885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21888 \begin_layout Plain Layout
21889 \begin_inset Formula $\blacklozenge$
21899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21902 \begin_layout Plain Layout
21910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21913 \begin_layout Plain Layout
21914 \begin_inset Formula $\blacktriangle$
21924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21927 \begin_layout Plain Layout
21935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21938 \begin_layout Plain Layout
21939 \begin_inset Formula $\blacktriangledown$
21949 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21952 \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
21964 \begin_inset Formula $\bullet$
21978 \begin_inset Tabular
21979 <lyxtabular version="3" rows="10" columns="2">
21981 <column alignment="center" valignment="top" width="0pt">
21982 <column alignment="center" valignment="top" width="0pt">
21984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21987 \begin_layout Plain Layout
21993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21996 \begin_layout Plain Layout
22004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22007 \begin_layout Plain Layout
22015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22018 \begin_layout Plain Layout
22019 \begin_inset Formula $\diamondsuit$
22029 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22032 \begin_layout Plain Layout
22040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22043 \begin_layout Plain Layout
22044 \begin_inset Formula $\Diamond$
22054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22057 \begin_layout Plain Layout
22065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22068 \begin_layout Plain Layout
22069 \begin_inset Formula $\heartsuit$
22079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22082 \begin_layout Plain Layout
22090 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22093 \begin_layout Plain Layout
22094 \begin_inset Formula $\P$
22104 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22107 \begin_layout Plain Layout
22115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22118 \begin_layout Plain Layout
22119 \begin_inset Formula $\copyright$
22129 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22132 \begin_layout Plain Layout
22140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22143 \begin_layout Plain Layout
22144 \begin_inset Formula $\circledR$
22154 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22157 \begin_layout Plain Layout
22165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22168 \begin_layout Plain Layout
22169 \begin_inset Formula $\maltese$
22179 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22182 \begin_layout Plain Layout
22190 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22193 \begin_layout Plain Layout
22194 \begin_inset Formula $\diagup$
22204 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22207 \begin_layout Plain Layout
22215 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22218 \begin_layout Plain Layout
22219 \begin_inset Formula $\diagdown$
22235 \begin_layout Standard
22236 \begin_inset VSpace medskip
22239 More symbols are listed in
22240 \begin_inset CommandInset ref
22242 reference "sub:Miscellaneous-special-Characters"
22249 \begin_layout Standard
22250 Some symbols can be displayed in different sizes, see
22251 \begin_inset CommandInset ref
22253 reference "sub:Font-Sizes"
22260 \begin_layout Subsection
22265 \begin_layout Plain Layout
22266 Symbols ! Euro-symbol
22275 \begin_layout Plain Layout
22282 \begin_layout Plain Layout
22299 \begin_layout Standard
22300 To use the Euro symbol in formulas, the LaTeX-package
22308 \begin_layout Plain Layout
22314 must be installed and loaded with the LaTeX-preamble line
22317 \begin_layout Standard
22322 usepackage[gennarrow]{eurosym}
22325 \begin_layout Standard
22326 The Euro symbol can now be inserted with the command
22336 \begin_layout Plain Layout
22347 \begin_layout Standard
22348 The Euro symbol can directly be inserted with the € key in mathematical
22349 text, without having
22364 can also be inserted in TeX-mode.
22365 The official currency symbol can then be inserted with the command
22375 \begin_layout Plain Layout
22383 , that is only available in TeX-mode.
22386 \begin_layout Standard
22390 \begin_layout Plain Layout
22400 \begin_inset Note Note
22403 \begin_layout Plain Layout
22404 The following table will only be displayed when the LaTeX-package
22416 \begin_layout Standard
22417 An overview about the different Euro symbols:
22420 \begin_layout Standard
22422 \begin_inset Tabular
22423 <lyxtabular version="3" rows="4" columns="3">
22425 <column alignment="center" valignment="top" width="0pt">
22426 <column alignment="center" valignment="top" width="0pt">
22427 <column alignment="center" valignment="top" width="0pt">
22429 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22432 \begin_layout Plain Layout
22438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22441 \begin_layout Plain Layout
22447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22450 \begin_layout Plain Layout
22458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22461 \begin_layout Plain Layout
22467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22470 \begin_layout Plain Layout
22478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22481 \begin_layout Plain Layout
22482 \begin_inset Formula $\euro$
22492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22495 \begin_layout Plain Layout
22501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22504 \begin_layout Plain Layout
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22513 \begin_layout Plain Layout
22514 \begin_inset Formula $\mbox{€}$
22524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22527 \begin_layout Plain Layout
22533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22536 \begin_layout Plain Layout
22544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22547 \begin_layout Plain Layout
22551 \begin_layout Plain Layout
22573 \begin_layout Standard
22577 \begin_layout Plain Layout
22587 \begin_inset Note Note
22590 \begin_layout Plain Layout
22591 The following will be displayed when the LaTeX-package
22603 \begin_layout Standard
22604 You need to install the LaTeX-package
22608 to see the rest of this subsection in the output.
22611 \begin_layout Standard
22615 \begin_layout Plain Layout
22627 \begin_layout Section
22629 \begin_inset CommandInset label
22631 name "sec:Relations"
22639 \begin_layout Plain Layout
22649 \begin_layout Plain Layout
22654 \begin_layout Plain Layout
22665 \begin_layout Plain Layout
22680 \begin_layout Standard
22681 All relations can also be inserted via the toolbar button
22682 \begin_inset Graphics
22683 filename ../images/math/leq.png
22691 \begin_layout Standard
22692 \begin_inset space \hfill{}
22696 \begin_inset Tabular
22697 <lyxtabular version="3" rows="17" columns="2">
22699 <column alignment="center" valignment="top" width="0pt">
22700 <column alignment="center" valignment="top" width="0pt">
22702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22705 \begin_layout Plain Layout
22711 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22714 \begin_layout Plain Layout
22722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22725 \begin_layout Plain Layout
22731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22734 \begin_layout Plain Layout
22735 \begin_inset Formula $<$
22745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22748 \begin_layout Plain Layout
22756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22759 \begin_layout Plain Layout
22760 \begin_inset Formula $\le$
22770 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22773 \begin_layout Plain Layout
22781 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22784 \begin_layout Plain Layout
22785 \begin_inset Formula $\ll$
22795 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22798 \begin_layout Plain Layout
22806 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22809 \begin_layout Plain Layout
22810 \begin_inset Formula $\prec$
22820 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22823 \begin_layout Plain Layout
22831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22834 \begin_layout Plain Layout
22835 \begin_inset Formula $\preceq$
22845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22848 \begin_layout Plain Layout
22856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22859 \begin_layout Plain Layout
22860 \begin_inset Formula $\subset$
22870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22873 \begin_layout Plain Layout
22881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22884 \begin_layout Plain Layout
22885 \begin_inset Formula $\subseteq$
22895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22898 \begin_layout Plain Layout
22906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22909 \begin_layout Plain Layout
22910 \begin_inset Formula $\sqsubseteq$
22920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22923 \begin_layout Plain Layout
22931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22934 \begin_layout Plain Layout
22935 \begin_inset Formula $\in$
22945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22948 \begin_layout Plain Layout
22956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22959 \begin_layout Plain Layout
22960 \begin_inset Formula $\vdash$
22970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22973 \begin_layout Plain Layout
22981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22984 \begin_layout Plain Layout
22985 \begin_inset Formula $\smile$
22995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22998 \begin_layout Plain Layout
23006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23009 \begin_layout Plain Layout
23010 \begin_inset Formula $\lhd$
23020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23023 \begin_layout Plain Layout
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23034 \begin_layout Plain Layout
23035 \begin_inset Formula $\unlhd$
23045 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23048 \begin_layout Plain Layout
23056 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23059 \begin_layout Plain Layout
23060 \begin_inset Formula $\gtrless$
23070 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23073 \begin_layout Plain Layout
23081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23084 \begin_layout Plain Layout
23085 \begin_inset Formula $\mid$
23095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23098 \begin_layout Plain Layout
23106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23109 \begin_layout Plain Layout
23110 \begin_inset Formula $\nmid$
23124 \begin_inset space \hfill{}
23128 \begin_inset Tabular
23129 <lyxtabular version="3" rows="17" columns="2">
23131 <column alignment="center" valignment="top" width="0pt">
23132 <column alignment="center" valignment="top" width="0pt">
23134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23137 \begin_layout Plain Layout
23143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23146 \begin_layout Plain Layout
23154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23157 \begin_layout Plain Layout
23163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23166 \begin_layout Plain Layout
23167 \begin_inset Formula $=$
23177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23180 \begin_layout Plain Layout
23188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23191 \begin_layout Plain Layout
23192 \begin_inset Formula $\not=$
23202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23205 \begin_layout Plain Layout
23213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23216 \begin_layout Plain Layout
23217 \begin_inset Formula $\equiv$
23227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23230 \begin_layout Plain Layout
23238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23241 \begin_layout Plain Layout
23242 \begin_inset Formula $\sim$
23252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23255 \begin_layout Plain Layout
23263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23266 \begin_layout Plain Layout
23267 \begin_inset Formula $\simeq$
23277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23280 \begin_layout Plain Layout
23288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23291 \begin_layout Plain Layout
23292 \begin_inset Formula $\approx$
23302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23305 \begin_layout Plain Layout
23313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23316 \begin_layout Plain Layout
23317 \begin_inset Formula $\cong$
23327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23330 \begin_layout Plain Layout
23338 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23341 \begin_layout Plain Layout
23342 \begin_inset Formula $\bowtie$
23352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23355 \begin_layout Plain Layout
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23366 \begin_layout Plain Layout
23367 \begin_inset Formula $\notin$
23377 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23380 \begin_layout Plain Layout
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23391 \begin_layout Plain Layout
23392 \begin_inset Formula $\perp$
23402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23405 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23417 \begin_inset Formula $\propto$
23427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23430 \begin_layout Plain Layout
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23441 \begin_layout Plain Layout
23442 \begin_inset Formula $\asymp$
23452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23455 \begin_layout Plain Layout
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23466 \begin_layout Plain Layout
23467 \begin_inset Formula $\doteq$
23477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23480 \begin_layout Plain Layout
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23491 \begin_layout Plain Layout
23492 \begin_inset Formula $\circeq$
23502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23505 \begin_layout Plain Layout
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23516 \begin_layout Plain Layout
23517 \begin_inset Formula $\models$
23527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23530 \begin_layout Plain Layout
23538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23541 \begin_layout Plain Layout
23542 \begin_inset Formula $\widehat{=}$
23556 \begin_inset space \hfill{}
23560 \begin_inset Tabular
23561 <lyxtabular version="3" rows="17" columns="2">
23563 <column alignment="center" valignment="top" width="0pt">
23564 <column alignment="center" valignment="top" width="0pt">
23566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23569 \begin_layout Plain Layout
23575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23578 \begin_layout Plain Layout
23586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23589 \begin_layout Plain Layout
23595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23598 \begin_layout Plain Layout
23599 \begin_inset Formula $>$
23609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23612 \begin_layout Plain Layout
23620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23623 \begin_layout Plain Layout
23624 \begin_inset Formula $\ge$
23634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23637 \begin_layout Plain Layout
23645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23648 \begin_layout Plain Layout
23649 \begin_inset Formula $\gg$
23659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23662 \begin_layout Plain Layout
23670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23673 \begin_layout Plain Layout
23674 \begin_inset Formula $\succ$
23684 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23687 \begin_layout Plain Layout
23695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23698 \begin_layout Plain Layout
23699 \begin_inset Formula $\succeq$
23709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23712 \begin_layout Plain Layout
23720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23723 \begin_layout Plain Layout
23724 \begin_inset Formula $\supset$
23734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23737 \begin_layout Plain Layout
23745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23748 \begin_layout Plain Layout
23749 \begin_inset Formula $\supseteq$
23759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23762 \begin_layout Plain Layout
23770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23773 \begin_layout Plain Layout
23774 \begin_inset Formula $\sqsupseteq$
23784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23787 \begin_layout Plain Layout
23795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23798 \begin_layout Plain Layout
23799 \begin_inset Formula $\ni$
23809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23812 \begin_layout Plain Layout
23820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23823 \begin_layout Plain Layout
23824 \begin_inset Formula $\dashv$
23834 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23837 \begin_layout Plain Layout
23845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23848 \begin_layout Plain Layout
23849 \begin_inset Formula $\frown$
23859 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23862 \begin_layout Plain Layout
23870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23873 \begin_layout Plain Layout
23874 \begin_inset Formula $\rhd$
23884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23887 \begin_layout Plain Layout
23895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23898 \begin_layout Plain Layout
23899 \begin_inset Formula $\unrhd$
23909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23912 \begin_layout Plain Layout
23920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23923 \begin_layout Plain Layout
23924 \begin_inset Formula $\lessgtr$
23934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23937 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23948 \begin_layout Plain Layout
23949 \begin_inset Formula $\parallel$
23959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23962 \begin_layout Plain Layout
23970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23973 \begin_layout Plain Layout
23974 \begin_inset Formula $\nparallel$
23988 \begin_inset space \hfill{}
23994 \begin_layout Standard
23995 \begin_inset VSpace medskip
24010 are bigger than the equal looking operators
24025 \begin_layout Standard
24026 Relations are, in contrary to symbols, always surrounded by space.
24029 \begin_layout Standard
24030 Relations with labels can be created with the command
24040 \begin_layout Plain Layout
24051 \begin_layout Standard
24053 \begin_inset Tabular
24054 <lyxtabular version="3" rows="2" columns="2">
24056 <column alignment="center" valignment="top" width="0">
24057 <column alignment="center" valignment="top" width="0">
24059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24062 \begin_layout Plain Layout
24068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24071 \begin_layout Plain Layout
24073 \begin_inset Note Note
24076 \begin_layout Plain Layout
24083 is only used as spacer.
24095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24098 \begin_layout Plain Layout
24105 \begin_layout Plain Layout
24122 \begin_layout Plain Layout
24132 \begin_inset Formula $\downarrow$
24141 \begin_layout Plain Layout
24154 \begin_layout Plain Layout
24168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24171 \begin_layout Plain Layout
24172 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24188 \begin_layout Section
24192 \begin_layout Subsection
24193 Predefined Functions
24194 \begin_inset CommandInset label
24196 name "sub:Predefined-Functions"
24204 \begin_layout Plain Layout
24205 Functions ! predefined
24213 \begin_layout Standard
24214 In general, variables are set
24218 in mathematical expressions, but not function names, because
24219 \begin_inset Formula $sin$
24222 could be misunderstood as
24223 \begin_inset Formula $s\cdot i\cdot n$
24227 Therefore there are predefined functions, that are additionally a bit separated
24229 They are inserted as commands starting with a backslash before their name.
24232 \begin_layout Standard
24234 \begin_inset Tabular
24235 <lyxtabular version="3" rows="2" columns="4">
24237 <column alignment="center" valignment="top" width="0pt">
24238 <column alignment="center" valignment="top" width="0pt">
24239 <column alignment="center" valignment="top" width="0pt">
24240 <column alignment="center" valignment="top" width="0pt">
24242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24245 \begin_layout Plain Layout
24251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24254 \begin_layout Plain Layout
24260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24263 \begin_layout Plain Layout
24269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24272 \begin_layout Plain Layout
24280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24283 \begin_layout Plain Layout
24289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24292 \begin_layout Plain Layout
24293 \begin_inset Formula $Asin(x)+B$
24301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24315 \begin_layout Plain Layout
24316 \begin_inset Formula $A\sin(x)+B$
24332 \begin_layout Standard
24333 The following functions are predefined:
24336 \begin_layout Standard
24337 \begin_inset VSpace -2mm
24343 \begin_layout Standard
24345 \begin_inset Tabular
24346 <lyxtabular version="3" rows="9" columns="4">
24348 <column alignment="center" valignment="top" width="0pt">
24349 <column alignment="center" valignment="top" width="0pt">
24350 <column alignment="center" valignment="top" width="0pt">
24351 <column alignment="center" valignment="top" width="0pt">
24353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24356 \begin_layout Plain Layout
24362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24365 \begin_layout Plain Layout
24371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24383 \begin_layout Plain Layout
24391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24394 \begin_layout Plain Layout
24402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24405 \begin_layout Plain Layout
24413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24416 \begin_layout Plain Layout
24424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24427 \begin_layout Plain Layout
24437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24440 \begin_layout Plain Layout
24448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24451 \begin_layout Plain Layout
24459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24462 \begin_layout Plain Layout
24470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24473 \begin_layout Plain Layout
24483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24494 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24497 \begin_layout Plain Layout
24505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24508 \begin_layout Plain Layout
24516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24519 \begin_layout Plain Layout
24529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24532 \begin_layout Plain Layout
24540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24543 \begin_layout Plain Layout
24551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24554 \begin_layout Plain Layout
24562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24565 \begin_layout Plain Layout
24575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24578 \begin_layout Plain Layout
24586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24589 \begin_layout Plain Layout
24597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24600 \begin_layout Plain Layout
24608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24611 \begin_layout Plain Layout
24621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24624 \begin_layout Plain Layout
24632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24635 \begin_layout Plain Layout
24643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24646 \begin_layout Plain Layout
24654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24657 \begin_layout Plain Layout
24667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24670 \begin_layout Plain Layout
24678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24681 \begin_layout Plain Layout
24689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24692 \begin_layout Plain Layout
24700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24703 \begin_layout Plain Layout
24713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24716 \begin_layout Plain Layout
24724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24727 \begin_layout Plain Layout
24735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24738 \begin_layout Plain Layout
24746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24749 \begin_layout Plain Layout
24765 \begin_layout Standard
24766 They can also be inserted with the math toolbar button
24767 \begin_inset Graphics
24768 filename ../images/math/functions.png
24776 \begin_layout Subsection
24777 Self-defined Functions
24781 \begin_layout Plain Layout
24782 Functions ! self-defined
24790 \begin_layout Standard
24791 To use a function that is not predefined, like for example the sign function
24792 sgn(x), there are two possibilities:
24795 \begin_layout Itemize
24796 Define the function by inserting the following line to the LaTeX-preamble
24800 \begin_layout Plain Layout
24805 DeclareMathOperator
24808 \begin_inset CommandInset ref
24810 reference "sub:Self-defined-Operators"
24820 \begin_inset Newline newline
24824 \begin_inset VSpace -3mm
24828 \begin_inset Newline newline
24835 DeclareMathOperator{
24843 \begin_layout Plain Layout
24848 DeclareMathOperator
24854 \begin_inset Newline newline
24858 \begin_inset VSpace -2mm
24862 \begin_inset Newline newline
24865 Now the new defined function can be called with the command
24874 \begin_layout Itemize
24875 Write the the formula as usual, mark the formula name, in our example the
24880 , and change it to mathematical text.
24881 At last a space is inserted between prefactor and function.
24884 \begin_layout Standard
24885 The result is the same with both methods as with a predefined function
24889 \begin_layout Plain Layout
24890 In LyX self-defined functions are displayed red, predefined ones black.
24898 \begin_layout Standard
24900 \begin_inset Tabular
24901 <lyxtabular version="3" rows="3" columns="2">
24903 <column alignment="center" valignment="top" width="0pt">
24904 <column alignment="center" valignment="top" width="0pt">
24906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24909 \begin_layout Plain Layout
24915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24918 \begin_layout Plain Layout
24926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24929 \begin_layout Plain Layout
24937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24940 \begin_layout Plain Layout
24941 \begin_inset Formula $A\sgn(x)+B$
24951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24954 \begin_layout Plain Layout
24958 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24969 \begin_layout Plain Layout
24970 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24986 \begin_layout Standard
24987 The first method is more suitable when the self-defined function should
24988 be used several times.
24991 \begin_layout Subsection
24996 \begin_layout Plain Layout
25005 \begin_layout Standard
25006 For limits there are defined besides
25016 \begin_layout Plain Layout
25036 furthermore the following functions:
25039 \begin_layout Standard
25041 \begin_inset Tabular
25042 <lyxtabular version="3" rows="5" columns="2">
25044 <column alignment="center" valignment="top" width="0">
25045 <column alignment="center" valignment="top" width="0">
25047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25050 \begin_layout Plain Layout
25056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25059 \begin_layout Plain Layout
25061 \begin_inset Note Note
25064 \begin_layout Plain Layout
25071 is only used as spacer.
25083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25086 \begin_layout Plain Layout
25094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25097 \begin_layout Plain Layout
25098 \begin_inset Formula $\varliminf$
25108 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25111 \begin_layout Plain Layout
25119 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25122 \begin_layout Plain Layout
25123 \begin_inset Formula $\varlimsup$
25133 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25136 \begin_layout Plain Layout
25144 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25147 \begin_layout Plain Layout
25148 \begin_inset Formula $\varprojlim$
25158 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25161 \begin_layout Plain Layout
25169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25172 \begin_layout Plain Layout
25173 \begin_inset Formula $\varinjlim$
25177 \begin_inset Formula $\raisebox{-2.5mm}{}$
25193 \begin_layout Standard
25194 \begin_inset VSpace medskip
25197 The limit is created by inserting a subscript.
25198 It is set right beside the function in an inline formula:
25201 \begin_layout Standard
25203 \begin_inset Tabular
25204 <lyxtabular version="3" rows="2" columns="2">
25206 <column alignment="center" valignment="top" width="0pt">
25207 <column alignment="center" valignment="top" width="0pt">
25209 <cell alignment="center" valignment="top" usebox="none">
25212 \begin_layout Plain Layout
25218 <cell alignment="center" valignment="top" usebox="none">
25221 \begin_layout Plain Layout
25222 \begin_inset space \hspace{}
25227 \begin_inset Note Note
25230 \begin_layout Plain Layout
25243 are used here as spacer.
25255 <cell alignment="center" valignment="top" usebox="none">
25258 \begin_layout Plain Layout
25267 \begin_layout Plain Layout
25280 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" usebox="none">
25297 \begin_layout Plain Layout
25298 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25314 \begin_layout Standard
25315 In a displayed formula the limit is set below the formula, as usual:
25316 \begin_inset Formula \[
25324 \begin_layout Subsection
25329 \begin_layout Plain Layout
25330 Functions ! modulo-
25338 \begin_layout Standard
25339 The modulo-function is special, because it exists in four variants.
25342 \begin_layout Standard
25343 The variants in a displayed formula:
25344 \begin_inset Formula \begin{align*}
25345 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25346 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25347 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25348 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25349 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25356 \begin_layout Standard
25357 In an inline formula less space is set before the function names for all
25361 \begin_layout Section
25366 \begin_layout Plain Layout
25375 \begin_layout Subsection
25376 Special Characters in Mathematical Text
25379 \begin_layout Standard
25380 The following commands can only be used in mathematical text or in TeX-mode:
25383 \begin_layout Standard
25384 \begin_inset space \hfill{}
25388 \begin_inset Tabular
25389 <lyxtabular version="3" rows="8" columns="2">
25391 <column alignment="block" valignment="top" width="0">
25392 <column alignment="block" valignment="top" width="0">
25394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25397 \begin_layout Plain Layout
25403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25406 \begin_layout Plain Layout
25414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25417 \begin_layout Plain Layout
25425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25428 \begin_layout Plain Layout
25429 \begin_inset Formula $\textrm{œ}$
25439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25442 \begin_layout Plain Layout
25450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25453 \begin_layout Plain Layout
25454 \begin_inset Formula $\textrm{Œ}$
25464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25467 \begin_layout Plain Layout
25475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25478 \begin_layout Plain Layout
25479 \begin_inset Formula $\textrm{æ}$
25489 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25492 \begin_layout Plain Layout
25500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25504 \begin_inset Formula $\textrm{Æ}$
25514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25517 \begin_layout Plain Layout
25525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25528 \begin_layout Plain Layout
25529 \begin_inset Formula $\textrm{\aa}$
25539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25542 \begin_layout Plain Layout
25549 \begin_layout Plain Layout
25556 \begin_layout Plain Layout
25577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25580 \begin_layout Plain Layout
25581 \begin_inset Formula $\textrm{Å}$
25591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25594 \begin_layout Plain Layout
25602 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25605 \begin_layout Plain Layout
25606 \begin_inset Formula $\textrm{ı}$
25620 \begin_inset space \hfill{}
25624 \begin_inset Tabular
25625 <lyxtabular version="3" rows="8" columns="2">
25627 <column alignment="block" valignment="top" width="0">
25628 <column alignment="center" valignment="top" width="0">
25630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25633 \begin_layout Plain Layout
25635 \begin_inset Note Note
25638 \begin_layout Plain Layout
25645 is used for separation, because otherwise the output will be ¡ and ¿ respective
25656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25659 \begin_layout Plain Layout
25667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25670 \begin_layout Plain Layout
25678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25681 \begin_layout Plain Layout
25682 \begin_inset Formula $\textrm{ø}$
25692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25695 \begin_layout Plain Layout
25703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25706 \begin_layout Plain Layout
25707 \begin_inset Formula $\textrm{Ø}$
25717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25720 \begin_layout Plain Layout
25728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25731 \begin_layout Plain Layout
25732 \begin_inset Formula $\textrm{ł}$
25742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25745 \begin_layout Plain Layout
25753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25756 \begin_layout Plain Layout
25757 \begin_inset Formula $\textrm{Ł}$
25767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25770 \begin_layout Plain Layout
25772 \begin_inset space \hspace{}
25780 \begin_layout Plain Layout
25794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25797 \begin_layout Plain Layout
25798 \begin_inset Formula $\textrm{!`}$
25808 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25811 \begin_layout Plain Layout
25813 \begin_inset space \hspace{}
25821 \begin_layout Plain Layout
25835 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25838 \begin_layout Plain Layout
25839 \begin_inset Formula $\textrm{?`}$
25849 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25852 \begin_layout Plain Layout
25860 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25863 \begin_layout Plain Layout
25864 \begin_inset Formula $\textrm{ȷ}$
25878 \begin_inset space \hfill{}
25884 \begin_layout Standard
25886 \begin_inset Formula $\textrm{\textrm{Å}}$
25890 \begin_inset Formula $\textrm{\textrm{Ø}}$
25893 can also be inserted via the math toolbar button
25894 \begin_inset Graphics
25895 filename ../images/math/digamma.png
25903 \begin_layout Standard
25904 An exception are the commands
25907 \begin_inset space \hspace{}
25916 \begin_inset space \hspace{}
25922 , because they can be inserted in LyX directly to text.
25925 \begin_layout Subsection
25927 \begin_inset CommandInset label
25929 name "sub:Accents-in-Text"
25937 \begin_layout Plain Layout
25946 \begin_layout Standard
25947 With the following commands all letters can be accented.
25948 The commands must be inserted in TeX-mode.
25951 \begin_layout Standard
25952 \begin_inset space \hfill{}
25956 \begin_inset Tabular
25957 <lyxtabular version="3" rows="8" columns="2">
25959 <column alignment="block" valignment="top" width="0">
25960 <column alignment="block" valignment="top" width="0">
25962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25965 \begin_layout Plain Layout
25971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25974 \begin_layout Plain Layout
25982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25985 \begin_layout Plain Layout
25989 \begin_inset Quotes grd
25997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26000 \begin_layout Plain Layout
26004 \begin_layout Plain Layout
26020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26023 \begin_layout Plain Layout
26031 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26034 \begin_layout Plain Layout
26038 \begin_layout Plain Layout
26054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26057 \begin_layout Plain Layout
26064 \begin_layout Plain Layout
26078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26081 \begin_layout Plain Layout
26085 \begin_layout Plain Layout
26101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26104 \begin_layout Plain Layout
26112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26115 \begin_layout Plain Layout
26119 \begin_layout Plain Layout
26135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26138 \begin_layout Plain Layout
26145 \begin_layout Plain Layout
26159 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26162 \begin_layout Plain Layout
26166 \begin_layout Plain Layout
26182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26185 \begin_layout Plain Layout
26192 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26209 \begin_layout Plain Layout
26213 \begin_layout Plain Layout
26229 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26232 \begin_layout Plain Layout
26239 \begin_layout Plain Layout
26253 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26256 \begin_layout Plain Layout
26260 \begin_layout Plain Layout
26280 \begin_inset space \hfill{}
26284 \begin_inset Tabular
26285 <lyxtabular version="3" rows="8" columns="2">
26287 <column alignment="block" valignment="top" width="0">
26288 <column alignment="center" valignment="top" width="0">
26290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26293 \begin_layout Plain Layout
26299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26302 \begin_layout Plain Layout
26310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26313 \begin_layout Plain Layout
26320 \begin_layout Plain Layout
26334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26337 \begin_layout Plain Layout
26341 \begin_layout Plain Layout
26357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26360 \begin_layout Plain Layout
26368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26371 \begin_layout Plain Layout
26375 \begin_layout Plain Layout
26391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26394 \begin_layout Plain Layout
26401 \begin_layout Plain Layout
26412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26415 \begin_layout Plain Layout
26419 \begin_layout Plain Layout
26435 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26438 \begin_layout Plain Layout
26446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26449 \begin_layout Plain Layout
26453 \begin_layout Plain Layout
26469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26472 \begin_layout Plain Layout
26479 \begin_layout Plain Layout
26493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26496 \begin_layout Plain Layout
26500 \begin_layout Plain Layout
26516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26519 \begin_layout Plain Layout
26526 \begin_layout Plain Layout
26540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26543 \begin_layout Plain Layout
26547 \begin_layout Plain Layout
26563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26566 \begin_layout Plain Layout
26573 \begin_layout Plain Layout
26587 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26590 \begin_layout Plain Layout
26594 \begin_layout Plain Layout
26614 \begin_inset space \hfill{}
26620 \begin_layout Standard
26621 \begin_inset VSpace medskip
26630 also two different characters can be accented.
26639 \begin_layout Plain Layout
26654 \begin_layout Plain Layout
26666 \begin_layout Standard
26679 can in combination with vowels directly be inserted with the keyboard without
26681 The same applies for the tilde
26685 \begin_layout Plain Layout
26686 This only applies for keyboards where the tilde is defined as accent.
26695 in combination with
26710 \begin_layout Standard
26753 , and accents inserted directly with the keyboard are also available in
26755 For the other accents there are special math commands to be used in formulas,
26757 \begin_inset CommandInset ref
26759 reference "sub:Accents-for-one"
26766 \begin_layout Standard
26767 \begin_inset VSpace bigskip
26770 Furthermore, with the command
26780 \begin_layout Plain Layout
26788 all numbers and letters can be set into a circle, quasi accented with a
26789 circle, similar to the the copyright symbol.
26792 \begin_layout Standard
26794 \begin_inset Tabular
26795 <lyxtabular version="3" rows="3" columns="2">
26797 <column alignment="center" valignment="top" width="0">
26798 <column alignment="center" valignment="top" width="0">
26800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26803 \begin_layout Plain Layout
26809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26812 \begin_layout Plain Layout
26814 \begin_inset Note Note
26817 \begin_layout Plain Layout
26824 is only used as spacer.
26836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26839 \begin_layout Plain Layout
26847 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26850 \begin_layout Plain Layout
26854 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26873 \begin_layout Plain Layout
26884 raisebox{-1.5pt}{W}}
26889 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26892 \begin_layout Plain Layout
26893 \begin_inset Formula $\raisebox{4.5mm}{}$
26900 \begin_layout Plain Layout
26918 \begin_inset Formula $\raisebox{-2mm}{}$
26934 \begin_layout Standard
26935 One has to take care that the character fits in the circle.
26946 \begin_layout Plain Layout
26948 \begin_inset CommandInset ref
26950 reference "sub:Font-Sizes"
26959 specifies thereby the size of the circle.
26970 \begin_layout Plain Layout
26972 \begin_inset CommandInset ref
26974 reference "sub:Boxes-without-Frame"
26983 the character can be centered.
26986 \begin_layout Subsection
26991 \begin_layout Plain Layout
27000 \begin_layout Standard
27001 Minuscule numbers are created with the command
27011 \begin_layout Plain Layout
27020 The command can be used in formulas and in TeX-mode.
27021 The command scheme is:
27024 \begin_layout Standard
27029 oldstylenums{number}
27032 \begin_layout Standard
27037 oldstylenums{0123456789
27040 \begin_inset Formula $\oldstylenums{0123456789}$
27046 \begin_layout Subsection
27047 Miscellaneous special Characters
27048 \begin_inset CommandInset label
27050 name "sub:Miscellaneous-special-Characters"
27058 \begin_layout Plain Layout
27059 Special characters ! miscellaneous
27067 \begin_layout Standard
27068 The following characters can only be inserted to formulas by using commands:
27071 \begin_layout Standard
27073 \begin_inset Tabular
27074 <lyxtabular version="3" rows="4" columns="2">
27076 <column alignment="center" valignment="top" width="0">
27077 <column alignment="center" valignment="top" width="0">
27079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27082 \begin_layout Plain Layout
27088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27091 \begin_layout Plain Layout
27099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27102 \begin_layout Plain Layout
27109 \begin_layout Plain Layout
27123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27126 \begin_layout Plain Layout
27127 \begin_inset Formula $\mathcircumflex$
27137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27140 \begin_layout Plain Layout
27148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27151 \begin_layout Plain Layout
27152 \begin_inset Formula $\_$
27162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27165 \begin_layout Plain Layout
27170 \begin_layout Plain Layout
27185 \begin_layout Plain Layout
27198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27201 \begin_layout Plain Layout
27202 \begin_inset Formula $^{\circ}$
27218 \begin_layout Standard
27219 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27220 contains the following line
27224 \begin_layout Plain Layout
27225 More about this is described in
27226 \begin_inset CommandInset ref
27228 reference "sub:Text-Characters-in"
27240 \begin_layout Standard
27245 DeclareInputtext{176}{
27258 \begin_layout Section
27260 \begin_inset CommandInset label
27262 name "sec:Formula-Styles"
27270 \begin_layout Plain Layout
27279 \begin_layout Itemize
27280 There are two different alignment styles:
27284 \begin_layout Description
27285 Centered is the predefined standard
27288 \begin_layout Description
27289 Indented for this the option
27293 must be inserted in the menu
27295 Document\SpecialChar \menuseparator
27301 \begin_inset space ~
27307 \begin_layout Standard
27312 is used, the indentation can be adjusted with the length
27322 \begin_layout Plain Layout
27331 Should the distance be 15
27332 \begin_inset space \thinspace{}
27335 mm, the following command line is inserted in the LaTeX-preamble
27338 \begin_layout Standard
27348 \begin_layout Standard
27349 When no length is specified, the predefined value of 30
27350 \begin_inset space \thinspace{}
27357 \begin_layout Itemize
27358 And two different numbering styles:
27362 \begin_layout Description
27363 Right is the predefined standard
27366 \begin_layout Description
27367 Left for this the option
27371 must be inserted in the menu
27373 Document\SpecialChar \menuseparator
27379 \begin_inset space ~
27386 \begin_layout Standard
27395 can also be used together.
27396 In this case both options are inserted, separated by a comma.
27399 \begin_layout Standard
27400 The chosen styles are used for all displayed formulas of the document.
27401 When both, centered and indented formulas should be created in a document,
27407 The indented formulas are then set in a flalign environment, see
27408 \begin_inset CommandInset ref
27410 reference "sub:Flalign-Environment"
27417 \begin_layout Section
27419 \begin_inset CommandInset label
27421 name "sec:Multiline-Formulas"
27429 \begin_layout Plain Layout
27430 Formula ! multiline
27438 \begin_layout Subsection
27442 \begin_layout Standard
27443 In LyX multiline formulas are created by pressing
27448 arg "newline-insert newline"
27454 This creates either an
27456 eqnarray environment
27458 that is described in
27459 \begin_inset CommandInset ref
27461 reference "sub:Eqnarray-Environment"
27465 or, when the option
27467 Use AMS math package
27469 in the document settings is selected, an
27473 that is described in
27474 \begin_inset CommandInset ref
27476 reference "sub:Standard-align-Environment"
27483 \begin_layout Standard
27484 There are other multiline formula environments that can be created via the
27487 Insert\SpecialChar \menuseparator
27491 These environments are described in the following sections.
27494 \begin_layout Standard
27495 In all multiline formula environments a new line is created by pressing
27499 arg "newline-insert newline"
27503 To add or delete lines, the math toolbar buttons
27504 \begin_inset Graphics
27505 filename ../images/tabular-feature_append-row.png
27511 \begin_inset Graphics
27512 filename ../images/tabular-feature_delete-row.png
27517 , respectively, or the menu
27519 Edit\SpecialChar \menuseparator
27525 \begin_layout Subsubsection
27527 \begin_inset CommandInset label
27529 name "sub:Line-Separation"
27537 \begin_layout Plain Layout
27538 Formula ! multiline ! Line separation
27546 \begin_layout Standard
27547 There is sometimes not enough space in multiline formulas between the lines:
27548 \begin_inset Formula \begin{eqnarray*}
27549 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}\\
27550 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*}
27557 \begin_layout Standard
27558 In LaTeX additional line space is specified as optional argument of the
27560 This is not yet possible in LyX
27564 \begin_layout Plain Layout
27566 \begin_inset CommandInset href
27568 name "LyX-bug #1505"
27569 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27578 , therefore the whole formula must be inserted in TeX-mode.
27579 To add in our example space, the command
27587 is inserted at the end of the first line.
27592 \begin_layout Plain Layout
27599 \begin_layout Plain Layout
27601 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27604 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27611 \begin_layout Plain Layout
27615 left(B^{2}+x_{0}^{2}
27623 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27628 \begin_layout Plain Layout
27640 \begin_layout Standard
27641 \begin_inset VSpace bigskip
27644 To set the the line separation for all lines in a formula, the length
27654 \begin_layout Plain Layout
27664 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27675 \begin_inset space \thinspace{}
27680 \begin_inset space \thinspace{}
27683 mm additional line separation as in the previous example, the command
27686 \begin_layout Standard
27696 \begin_layout Standard
27697 is inserted in TeX-mode before the formula.
27698 This requires that the LaTeX-package
27706 \begin_layout Plain Layout
27711 is part of every LaTeX standard installation.
27720 \begin_layout Plain Layout
27726 was loaded in LaTeX-preamble with the line
27729 \begin_layout Standard
27737 \begin_layout Standard
27742 \begin_layout Plain Layout
27754 \begin_inset Formula \begin{eqnarray*}
27755 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}\\
27756 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*}
27763 \begin_layout Standard
27767 \begin_layout Plain Layout
27778 To get back to the predefined distance,
27784 is set to the value 3
27785 \begin_inset space \thinspace{}
27791 \begin_layout Subsubsection
27793 \begin_inset CommandInset label
27795 name "sub:Column-Separation"
27803 \begin_layout Plain Layout
27804 Formula ! multiline ! Column separation
27812 \begin_layout Standard
27813 Multiline formulas form a matrix.
27814 A formula in the eqnarray environment is for example a matrix with three
27816 By changing the column separation in this environment, the space beside
27817 the relation sign can be changed.
27820 \begin_layout Standard
27821 The column separation is specified with the length
27831 \begin_layout Plain Layout
27840 \begin_inset Newline newline
27843 column separation = 2
27844 \begin_inset space \thinspace{}
27854 \begin_inset Newline newline
27860 \begin_layout Standard
27870 \begin_layout Standard
27871 inserted in TeX-mode, sets for all following formulas a column separation
27873 \begin_inset space \thinspace{}
27877 To get back to the predefined distance,
27884 \begin_inset space \thinspace{}
27890 \begin_layout Standard
27892 \begin_inset space \thinspace{}
27895 cm column separation:
27899 \begin_layout Plain Layout
27911 \begin_inset Formula \begin{eqnarray*}
27913 C & \ne & A\end{eqnarray*}
27917 A formula with the predefined column separation for matrices of 10
27918 \begin_inset space \thinspace{}
27925 \begin_layout Plain Layout
27937 \begin_inset Formula \begin{eqnarray*}
27939 C & \ne & A\end{eqnarray*}
27946 \begin_layout Subsubsection
27951 \begin_layout Plain Layout
27960 \begin_layout Standard
27961 Long formulas can be typeset using these methods:
27964 \begin_layout Itemize
27965 When one side of the equation is much shorther than the line width, this
27966 one is chosen for the left side and the right side is typeset over two
27971 \begin_layout Plain Layout
27981 \begin_inset Formula \begin{eqnarray}
27982 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 \\
27983 & & -\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}
27991 \begin_layout Plain Layout
28001 \begin_inset Newline newline
28004 The minus sign at the beginning of the second line does normally not appear
28005 as operator because it is the first character of the line.
28006 Thus it would not be surrounded by space and could not be distinguished
28007 from the fraction bar.
28008 To avoid this, space was inserted behind the minus sign with the command
28019 \begin_layout Plain Layout
28027 \begin_inset CommandInset ref
28029 reference "sub:Variable-Space"
28042 \begin_layout Plain Layout
28053 \begin_layout Itemize
28054 When both sides of the equation are too long, the command
28064 \begin_layout Plain Layout
28073 It is inserted to the first column of the first line and effects that all
28074 further insertions overwrite the following columns:
28078 \begin_layout Plain Layout
28088 \begin_inset Formula \begin{eqnarray}
28089 \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 \\
28090 & & -\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 \\
28091 & & =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}
28099 \begin_layout Plain Layout
28109 \begin_inset Newline newline
28112 After the insertion of
28118 , the cursor is in a purple box that is a bit shifted to the left from the
28120 In this the formula is inserted.
28124 \begin_layout Plain Layout
28134 \begin_inset Newline newline
28137 The content of the further lines is inserted to the second or another formula
28139 The greater the column number where it was inserted, the larger the indentation.
28143 \begin_layout Plain Layout
28153 \begin_inset Newline newline
28157 \begin_inset Note Greyedout
28160 \begin_layout Plain Layout
28161 Note the following when using
28170 \begin_layout Itemize
28171 The formula doesn't use the full page width.
28173 \begin_inset space \thinspace{}
28177 \begin_inset space ~
28181 \begin_inset Formula $-B^{2}$
28184 is added to the first line in the above example, it would have been outside
28186 To better use the width, negative space can be inserted at the beginning
28190 \begin_layout Itemize
28191 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28196 \begin_layout Plain Layout
28197 \begin_inset CommandInset href
28199 name "LyX-bug #1429"
28200 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28209 One can only set the cursor at the beginning of the line and move it with
28218 \begin_layout Itemize
28219 Other methods to set long formulas are offered by the environments described
28221 \begin_inset CommandInset ref
28223 reference "sub:Multline-Environment"
28228 \begin_inset CommandInset ref
28230 reference "sub:Multiline-Formula-Parts"
28237 \begin_layout Subsubsection
28239 \begin_inset CommandInset label
28241 name "sub:Multiline-Brackets"
28249 \begin_layout Plain Layout
28250 Brackets ! for multiline expressions
28258 \begin_layout Standard
28259 For brackets spanning multiple lines the following problem occurs:
28260 \begin_inset Formula \begin{eqnarray*}
28261 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28262 & & \left.\cdots+B-D\right]\end{eqnarray*}
28269 \begin_layout Standard
28270 The closing bracket is smaller than the opening bracket because brackets
28271 with variable size may not span multiple lines.
28274 \begin_layout Standard
28275 To set the bracket size for the second line correctly, the first line is
28286 \begin_layout Plain Layout
28294 and the second line with
28302 \begin_layout Plain Layout
28316 \begin_inset CommandInset ref
28318 reference "sub:Automatic-Bracket-Size"
28333 \begin_layout Plain Layout
28359 \begin_layout Plain Layout
28378 \begin_layout Plain Layout
28397 \begin_layout Plain Layout
28409 \begin_inset Formula $\downarrow$
28418 \begin_layout Plain Layout
28426 is inserted, because the multiplication operator with its limits is the
28427 largest symbol in the first line and this should be the size for the bracket
28428 in the second line.
28431 \begin_layout Standard
28432 The result is this:
28433 \begin_inset Formula \begin{eqnarray*}
28434 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28435 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28442 \begin_layout Subsection
28446 \begin_layout Standard
28447 Align environments can be used for every kind of multiline formulas.
28448 They are specially useful to set several formulas side by side.
28451 \begin_layout Standard
28452 Align environments consist of columns.
28453 The odd columns are right aligned, the even ones left aligned.
28454 Every line in an Align environment can be numbered.
28457 \begin_layout Standard
28458 Align environments are created via the menu
28460 Insert\SpecialChar \menuseparator
28466 Edit\SpecialChar \menuseparator
28467 Math\SpecialChar \menuseparator
28468 Change Formula Type
28470 already existing formulas can be converted to Align environments.
28473 \begin_layout Standard
28474 To add or delete columns, the math toolbar buttons
28475 \begin_inset Graphics
28476 filename ../images/tabular-feature_append-column.png
28482 \begin_inset Graphics
28483 filename ../images/tabular-feature_delete-column.png
28488 , respectively, or the menu
28490 Edit\SpecialChar \menuseparator
28496 \begin_layout Subsubsection
28497 Standard align Environment
28498 \begin_inset CommandInset label
28500 name "sub:Standard-align-Environment"
28508 \begin_layout Plain Layout
28509 Formula ! multiline ! align environment
28517 \begin_layout Standard
28518 This Align environment is created by presssing
28521 arg "newline-insert newline"
28524 in a formula or by the menu
28526 Insert\SpecialChar \menuseparator
28527 Math\SpecialChar \menuseparator
28528 AMS align Environment
28533 \begin_layout Standard
28534 An example for two formulas set side by side, that are created with a four
28535 column align environment:
28536 \begin_inset Formula \begin{align*}
28537 A & =\sin(B) & C & =D\\
28538 C & \ne A & B & \ne D\end{align*}
28542 As it can be seen, the formulas in this environment are placed so as if
28551 \begin_layout Plain Layout
28559 \begin_inset CommandInset ref
28561 reference "sub:Variable-Space"
28572 before the first and after every even column.
28573 When the formula style
28579 \begin_layout Plain Layout
28581 \begin_inset CommandInset ref
28583 reference "sec:Formula-Styles"
28594 is used, the formula is set without the
28600 before the first column.
28603 \begin_layout Subsubsection
28604 Alignat Environment
28608 \begin_layout Plain Layout
28609 Formula ! multiline ! alignat environment
28617 \begin_layout Standard
28618 The alignat environment has no predefined column separation.
28619 It can be inserted manually with the spaces that are described
28620 \begin_inset CommandInset ref
28622 reference "sub:Space"
28629 \begin_layout Standard
28630 The above example in the alignat environment where 1
28631 \begin_inset space \thinspace{}
28634 cm space was inserted at the beginning of the second formula:
28635 \begin_inset Formula \begin{alignat*}{2}
28636 A & =\sin(B) & \hspace{1cm}C & =D\\
28637 C & \ne A & B & \ne D\end{alignat*}
28641 Because the column separation can be set separately for every column, this
28642 environment is especially suitable to set three and more formulas side
28646 \begin_layout Subsubsection
28647 Flalign Environment
28648 \begin_inset CommandInset label
28650 name "sub:Flalign-Environment"
28658 \begin_layout Plain Layout
28659 Formula ! multiline ! flalign environment
28667 \begin_layout Standard
28668 In this environment the first two columns are always set as much as possible
28669 to the left and the last two ones to the right.
28671 \begin_inset Formula \begin{flalign*}
28672 A & =1 & B & =2 & C & =3\\
28673 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28680 \begin_layout Standard
28681 By creating a flalign environment with an odd number of columns where an
28682 empty TeX-brace is inserted to the last column, several formulas in a document
28683 can be set to the left, although the formula style
28688 As example the indented formula
28689 \begin_inset CommandInset ref
28691 reference "eq:VolInt"
28696 \begin_inset Formula \begin{flalign}
28697 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28701 The first two columns contain the formula.
28702 To indent it as with the formula style
28707 \begin_inset space \thinspace{}
28710 pt space was inserted at the beginning of the first column.
28713 \begin_layout Subsection
28714 Eqnarray Environment
28715 \begin_inset CommandInset label
28717 name "sub:Eqnarray-Environment"
28725 \begin_layout Plain Layout
28726 Formula ! multiline ! eqnarray environment
28734 \begin_layout Standard
28735 When this environment has been created, three blue boxes appear.
28736 The content of the first box is right aligned, the content of the last
28738 The content of the middle box appears centered and a bit smaller, because
28739 it is designed to insert there only relation characters.
28740 \begin_inset Formula \begin{eqnarray*}
28741 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28743 A & = & A\end{eqnarray*}
28750 \begin_layout Subsection
28755 \begin_layout Plain Layout
28756 Formula ! multiline ! gather environment
28764 \begin_layout Standard
28765 This environment consists of only one centered column.
28766 Every line can be numbered.
28767 \begin_inset Formula \begin{gather}
28769 X=\textrm{-}1\end{gather}
28776 \begin_layout Subsection
28777 Multline Environment
28778 \begin_inset CommandInset label
28780 name "sub:Multline-Environment"
28788 \begin_layout Plain Layout
28789 Formula ! multiline ! multline environment
28797 \begin_layout Standard
28798 The multline environment consists, like the gather environment, of only
28800 But the first line is left aligned, the last one right aligned.
28801 All other lines are centered.
28802 Therefore this environment is suitable for long formulas.
28804 \begin_inset CommandInset ref
28806 reference "eq:lefteqn"
28810 in the multline environment:
28811 \begin_inset Formula \begin{multline}
28812 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}\\
28813 -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}\\
28814 =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}
28821 \begin_layout Standard
28822 In the output only the last (first) line of a multline environment appears
28823 numbered when the document numbering is right (left).
28827 \begin_layout Plain Layout
28828 numbering styles see
28829 \begin_inset CommandInset ref
28831 reference "sec:Formula-Styles"
28843 \begin_layout Standard
28852 \begin_layout Plain Layout
28870 \begin_layout Plain Layout
28880 a centered line can be right or left aligned, respectively.
28881 The commands are used as follows:
28884 \begin_layout Standard
28889 shoveright{line content}
28895 shoveleft{line content}
28898 \begin_layout Standard
28899 \begin_inset VSpace medskip
28910 \begin_layout Plain Layout
28920 specifies the distance of the first line from the left page margin.
28921 Predefined is the length 0
28922 \begin_inset space \thinspace{}
28928 \begin_layout Standard
28929 As example the above formula where the command
28932 \begin_layout Standard
28942 \begin_layout Standard
28943 was inserted in TeX-mode before:
28947 \begin_layout Plain Layout
28959 \begin_inset Formula \begin{multline}
28960 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}\\
28961 \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}}\\
28962 =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}
28970 \begin_layout Plain Layout
28981 The second line was left aligned using
28990 \begin_layout Subsection
28991 Multiline Formula Parts
28992 \begin_inset CommandInset label
28994 name "sub:Multiline-Formula-Parts"
29002 \begin_layout Plain Layout
29003 Formula ! multiline ! formula parts
29011 \begin_layout Standard
29012 To display only parts of a formula with multiple lines, one of the following
29013 environments are used:
29030 They can be inserted via the menu
29032 Insert\SpecialChar \menuseparator
29035 or by using the commands described in this section.
29038 \begin_layout Standard
29039 The first three have the same properties as the corresponding multiline
29040 formula environments, but it is possible to set further formula parts beside
29043 \begin_inset Formula \[
29044 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29045 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29046 \right\} \textrm{Uncertainty relations}\]
29053 \begin_layout Standard
29054 To get this formula, a displayed formula is created where the command
29062 \begin_layout Plain Layout
29073 A purple box appears around the blue formula box where now columns and
29074 lines can be added.
29075 Outside the multiline environment other formula parts can be set, like
29079 \begin_layout Standard
29080 The aligned environment is also suitable for long formulas whose lines are
29081 horizontally aligned.
29082 Using aligned in a displayed formula has the advantage that the formula
29083 number is vertically centered behind the lines.
29085 \begin_inset CommandInset ref
29087 reference "eq:kurzlang"
29091 in the aligned environment:
29092 \begin_inset Formula \begin{equation}
29093 \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}|}\\
29094 & -\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}
29102 \begin_layout Standard
29103 To use the environments
29125 \begin_layout Plain Layout
29143 \begin_layout Plain Layout
29161 \begin_layout Plain Layout
29169 are inserted, respectively.
29170 The split environment has the same properties as the aligned environment
29171 but it can only have two columns.
29174 \begin_layout Subsection
29175 Text in multiline Formulas
29176 \begin_inset CommandInset label
29178 name "sub:Text-in-multiline"
29186 \begin_layout Plain Layout
29196 \begin_layout Plain Layout
29197 Formula ! multiline ! text
29205 \begin_layout Standard
29206 In the Align environments, and the multline and gather environment, text
29207 can be inserted that will appear in a separate line and doesn't affect
29208 the column alignment.
29209 To do this, the command
29217 \begin_layout Plain Layout
29227 is used in the following scheme:
29230 \begin_layout Standard
29238 \begin_layout Standard
29239 The text should not be longer than a line because it cannot be hyphenated.
29240 As LyX doesn't yet support
29246 directly, the text is written as mathematical text.
29253 must hereby be at the beginning of a line and appears in the output above
29255 An example where the text was inserted at the beginning of the second line:
29256 \begin_inset Formula \begin{align}
29257 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29258 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29265 \begin_layout Section
29270 \begin_layout Plain Layout
29280 \begin_layout Plain Layout
29281 Formula ! numbering|see
29285 \begin_layout Plain Layout
29296 \begin_layout Plain Layout
29311 \begin_layout Subsection
29315 \begin_layout Standard
29316 Numbered formulas can be created with the menu
29318 Insert\SpecialChar \menuseparator
29319 Math\SpecialChar \menuseparator
29321 \begin_inset space ~
29329 \begin_inset space ~
29335 Existing formulas can be numbered with the menu
29337 Edit\SpecialChar \menuseparator
29338 Math\SpecialChar \menuseparator
29340 \begin_inset space ~
29348 arg "math-number-toggle"
29352 The formula number is displayed in LyX behind the formula as number sign
29354 The number sign is replaced in the output by the formula number.
29357 \begin_layout Standard
29358 When numbering is turned on in multiline formulas, all lines will be numbered.
29359 But the numbering can be controlled with the menu
29361 Edit\SpecialChar \menuseparator
29362 Math\SpecialChar \menuseparator
29364 \begin_inset space ~
29368 \begin_inset space ~
29372 \begin_inset space ~
29380 arg "math-number-line-toggle"
29386 \begin_layout Standard
29387 Except of inline formulas, all formulas can be numbered with two different
29389 \begin_inset CommandInset ref
29391 reference "sec:Formula-Styles"
29398 \begin_layout Subsection
29403 \begin_layout Plain Layout
29404 Cross-references ! to formulas
29412 \begin_layout Standard
29413 All labeled formulas can be cross-referenced.
29414 A label is added by the menu
29416 Insert\SpecialChar \menuseparator
29419 or the toolbar button
29420 \begin_inset Graphics
29421 filename ../images/label-insert.png
29427 The cursor must hereby be inside a displayed formula.
29428 A dialog pops up displaying the prefix
29433 The label is inserted there behind the prefix.
29434 The predefined prefix means
29435 \begin_inset Quotes eld
29439 \begin_inset Quotes erd
29442 and makes it easier to find labels in large documents because it marks
29443 it as formula label to divide it from e.
29444 \begin_inset space \thinspace{}
29448 \begin_inset space ~
29452 To change a label, the menu
29454 Insert\SpecialChar \menuseparator
29460 \begin_layout Standard
29461 The name of the label is displayed in LyX within two parentheses behind
29463 A formula with a label is always numbered.
29466 \begin_layout Standard
29467 Cross-references are inserted via the menu
29469 Insert\SpecialChar \menuseparator
29472 or with the toolbar button
29473 \begin_inset Graphics
29474 filename ../images/dialog-show-new-inset_ref.png
29480 A formula cross-reference appears in the output as formula number.
29481 When in the cross-reference dialog window the format
29485 is chosen, the cross-reference appears in the output as formula number
29487 \begin_inset Newline newline
29490 By right-clicking on a cross-reference in LyX, one jumps to the formula
29491 that is referenced.
29494 \begin_layout Standard
29495 Here are as examples cross-references to formulas of the following subsections:
29496 \begin_inset Note Note
29499 \begin_layout Plain Layout
29500 Note the different cross-reference types.
29508 \begin_layout Standard
29510 \begin_inset CommandInset ref
29517 \begin_inset CommandInset ref
29525 \begin_inset CommandInset ref
29531 ) big Latin letters are used for the numbering in contrary to (
29532 \begin_inset CommandInset ref
29541 \begin_layout Standard
29542 \begin_inset VSpace medskip
29545 When the argument of
29553 \begin_layout Plain Layout
29561 \begin_inset CommandInset ref
29563 reference "sub:User-defined-Numbering"
29574 contains a box like in
29575 \begin_inset CommandInset ref
29577 reference "sub:Paragraph-Boxes"
29581 , the formula cannot be referenced.
29584 \begin_layout Subsection
29589 \begin_layout Plain Layout
29590 Formula numbering ! subnumbering
29598 \begin_layout Standard
29599 With the help of the commands
29603 begin{subequations}
29611 formulas can be subnumbered.
29612 Both commands are inserted in TeX-mode.
29615 \begin_layout Standard
29617 \begin_inset Formula \begin{equation}
29618 A=C-B\label{eq:a}\end{equation}
29626 \begin_layout Plain Layout
29630 addtocounter{equation}{-1}
29639 \begin_layout Plain Layout
29643 begin{subequations}
29649 \begin_inset VSpace -5mm
29653 \begin_inset Formula \begin{equation}
29654 B=C-A\label{eq:b}\end{equation}
29659 \begin_inset Formula \begin{equation}
29660 C=A+B\label{eq:c}\end{equation}
29667 \begin_layout Standard
29671 \begin_layout Plain Layout
29683 \begin_layout Standard
29684 To create the example, the following is done:
29687 \begin_layout Enumerate
29688 first formula is inserted
29691 \begin_layout Enumerate
29696 addtocounter{equation}{-1}
29698 begin{subequations}
29702 \begin_layout Plain Layout
29711 \begin_inset Newline newline
29716 is inserted after the first formula
29719 \begin_layout Enumerate
29720 second formula is inserted
29723 \begin_layout Enumerate
29724 third formula is inserted
29727 \begin_layout Enumerate
29734 is inserted after the third formula
29737 \begin_layout Standard
29738 Every formula between the commands
29750 is subnumbered as a, b,
29751 \begin_inset Newline linebreak
29754 c, \SpecialChar \ldots{}
29755 For multiline formulas every line will be subnumbered.
29756 All subnumbered formulas are treated as
29761 But as every numbered formula increases the counter
29765 by one, the command
29771 is needed to decrease it.
29772 Otherwise the formulas
29773 \begin_inset CommandInset ref
29780 \begin_inset CommandInset ref
29787 \begin_inset CommandInset ref
29793 would be numbered as
29794 \begin_inset CommandInset ref
29801 \begin_inset CommandInset ref
29808 \begin_inset CommandInset ref
29817 \begin_layout Standard
29818 By inserting the commands in TeX-mode, a space is created between the first
29821 \begin_inset space \thinspace{}
29824 mm vertical space is inserted after the command
29828 begin{subequations}
29831 When the formula style
29837 \begin_layout Plain Layout
29839 \begin_inset CommandInset ref
29841 reference "sec:Formula-Styles"
29853 \begin_inset space \thinspace{}
29856 mm space is inserted instead.
29859 \begin_layout Standard
29860 Here is an example for a multiline formula where the numbering was turned
29861 off for the second line:
29865 \begin_layout Plain Layout
29869 begin{subequations}
29875 \begin_inset Formula \begin{eqnarray}
29876 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29877 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29878 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29886 \begin_layout Plain Layout
29898 \begin_layout Subsection
29899 User-defined Numbering
29900 \begin_inset CommandInset label
29902 name "sub:User-defined-Numbering"
29910 \begin_layout Plain Layout
29911 Formula numbering ! user-defined
29919 \begin_layout Standard
29923 \begin_layout Plain Layout
29924 Formula numbering ! self-defined delimiters
29929 With the standard numbering parentheses are set around the formula number.
29930 To replace the parentheses for example by vertical bars, the following
29931 line is added to the LaTeX-preamble:
29934 \begin_layout Standard
29946 \begin_inset Note Note
29949 \begin_layout Plain Layout
29950 This macro is already declared in the LaTeX-preamble for testing.
29951 To activate it, remove the percent sign at the beginning.
29959 \begin_layout Standard
29960 To use other characters, the vertical bars besides the
29964 are replaced by one ore more characters.
29965 To get only the formula number the vertical bars are omitted.
29968 \begin_layout Standard
29969 \begin_inset VSpace bigskip
29972 When there should be an expression of your choice instead of the consecutive
29973 formula number in parentheses behind the formula, the command
29983 \begin_layout Plain Layout
29992 \begin_inset Formula \begin{equation}
29993 A+B=C\tag{something}\label{eq:tag}\end{equation}
29997 In this example the command
30005 \begin_layout Plain Layout
30016 was inserted to the formula.
30019 \begin_layout Standard
30028 \begin_layout Plain Layout
30039 is inserted instead, the star prevents the parentheses around the expression:
30040 \begin_inset Formula \[
30041 A+B=C\tag*{something}\]
30048 \begin_layout Standard
30049 \begin_inset VSpace bigskip
30052 To restart the formula numbering with new document parts or sections, the
30053 following command is used:
30056 \begin_layout Standard
30061 @addtoreset{equation}{part}
30067 \begin_layout Plain Layout
30072 \begin_layout Plain Layout
30083 \begin_layout Plain Layout
30096 \begin_layout Plain Layout
30107 \begin_layout Plain Layout
30120 \begin_inset Newline newline
30124 \begin_inset Newline newline
30131 @addtoreset{equation}{section}
30134 \begin_layout Standard
30135 To be able to use these commands in TeX-mode, the
30136 \begin_inset Quotes eld
30140 \begin_inset Quotes erd
30143 character has to be made
30144 \begin_inset Quotes eld
30148 \begin_inset Quotes erd
30151 for LaTeX using the command
30165 So the command sequence in TeX-mode is:
30168 \begin_layout Standard
30174 \begin_inset Newline newline
30179 @addtoreset{equation}{section}
30180 \begin_inset Newline newline
30188 \begin_layout Standard
30189 In the LaTeX-preamble
30201 can be omitted as they are automatically internally inserted by LyX.
30204 \begin_layout Standard
30219 \begin_layout Plain Layout
30224 is part of the LaTeX-package
30232 \begin_layout Plain Layout
30233 Packages ! carlisle
30238 that is part of every LaTeX standard installation.
30247 \begin_layout Plain Layout
30248 Packages ! remreset
30253 has to be loaded in the LaTeX-preamble with the line
30256 \begin_layout Standard
30261 usepackage{remreset}
30264 \begin_layout Standard
30275 \begin_layout Plain Layout
30280 \begin_layout Plain Layout
30291 \begin_layout Plain Layout
30304 \begin_layout Plain Layout
30315 \begin_layout Plain Layout
30327 can be used with the same scheme as
30336 \begin_layout Standard
30337 \begin_inset VSpace bigskip
30340 Sometimes formulas should be numbered in the following form:
30343 \begin_layout Standard
30346 (section number.formula number)
30349 \begin_layout Standard
30350 The formula number should start with every section with
30351 \begin_inset Quotes eld
30355 \begin_inset Quotes erd
30361 \begin_layout Standard
30362 For this case there is the command
30372 \begin_layout Plain Layout
30380 , which is used with the following scheme:
30383 \begin_layout Standard
30388 numberwithin{counter}{sectioning}
30391 \begin_layout Standard
30392 Counter denotes what kind of numbering is affected, sectioning denotes what
30393 number is before the dot.
30396 \begin_layout Standard
30397 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30400 \begin_layout Standard
30405 numberwithin{equation}{section}
30408 \begin_layout Standard
30409 This is the result:
30413 \begin_layout Plain Layout
30417 numberwithin{equation}{section}
30423 \begin_inset Formula \begin{equation}
30424 A+B=C\end{equation}
30431 \begin_layout Standard
30433 \begin_inset space \thinspace{}
30437 \begin_inset space ~
30440 tables so that the number of the part is the sectioning,
30441 \begin_inset Newline newline
30448 numberwithin{table}{part}
30453 \begin_layout Standard
30454 To go back to the standard numbering or to prevent this kind of numbering
30455 when it is defined by the document class, the following command is inserted
30456 as TeX-Code or to the LaTeX-preamble:
30459 \begin_layout Standard
30472 \begin_layout Plain Layout
30486 \begin_layout Plain Layout
30502 \begin_inset Newline newline
30510 \begin_inset Newline newline
30522 \begin_layout Standard
30529 uses internally the command
30535 , described above, that also needs to be reverted.
30539 \begin_layout Plain Layout
30546 \begin_layout Plain Layout
30550 @removefromreset{equation}{section}
30553 \begin_layout Plain Layout
30565 \begin_layout Subsection
30566 Numbering with Roman Numbers and Letters
30570 \begin_layout Plain Layout
30571 Formula numbering ! with letters
30580 \begin_layout Plain Layout
30581 Formula numbering ! with Roman numbers
30589 \begin_layout Standard
30590 Formulas can also be numbered with Roman numbers and Latin letters.
30591 To number for example with small Roman numbers, the command
30594 \begin_layout Standard
30606 \begin_layout Standard
30607 is inserted before the formula in TeX-mode.
30618 \begin_layout Plain Layout
30626 redefines the predefined command
30642 \begin_layout Plain Layout
30649 has the same scheme like the command
30655 that is described in
30656 \begin_inset CommandInset ref
30658 reference "sec:User-defined-Commands"
30672 is the formula counter.
30679 is used as prefix for a counter, the value of the counter is output as
30681 When a formula is numbered, LaTeX sets internally the command
30687 behind the formula.
30696 \begin_layout Plain Layout
30706 outputs the counter as small Roman number.
30709 \begin_layout Standard
30710 All formulas behind the command
30720 are now numbered Roman.
30721 To switch to numbering with big Roman numbers, the command is inserted
30738 \begin_layout Plain Layout
30750 \begin_inset Quotes eld
30754 \begin_inset Quotes erd
30757 with small Latin letters there is the command
30767 \begin_layout Plain Layout
30775 , for big ones there is the command
30785 \begin_layout Plain Layout
30798 \begin_layout Standard
30799 \begin_inset Note Greyedout
30802 \begin_layout Plain Layout
30807 Only maximal 26 formulas can be numbered with Latin letters in one document.
30815 \begin_layout Standard
30819 \begin_layout Plain Layout
30835 \begin_layout Standard
30836 \begin_inset Formula \begin{equation}
30837 A=\textrm{small roman}\label{eq:rom}\end{equation}
30845 \begin_layout Plain Layout
30859 \begin_inset Formula \begin{equation}
30860 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30868 \begin_layout Plain Layout
30882 \begin_inset Formula \begin{equation}
30883 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30891 \begin_layout Plain Layout
30905 \begin_inset Formula \begin{equation}
30906 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30913 \begin_layout Standard
30914 To switch back to the default numbering, insert the command:
30917 \begin_layout Standard
30930 \begin_layout Plain Layout
30941 \begin_layout Standard
30945 \begin_layout Plain Layout
30959 \begin_inset Formula \begin{equation}
30960 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30967 \begin_layout Standard
30968 \begin_inset VSpace medskip
30971 As you see, formulas are numbered serially independent from the numbering
30973 When then numbering should start with
30974 \begin_inset Quotes eld
30978 \begin_inset Quotes erd
30981 when the style is changed, new equation counters have to be defined.
30982 A description about this can be found in the file
30983 \begin_inset CommandInset href
30985 target "Formula-numbering.lyx"
30992 \begin_layout Section
30993 User-defined Commands
30994 \begin_inset CommandInset label
30996 name "sec:User-defined-Commands"
31004 \begin_layout Plain Layout
31005 User-defined commands
31013 \begin_layout Standard
31014 Many LaTeX-commands are too long to be used frequently.
31015 But it is possible to define with the command
31025 \begin_layout Plain Layout
31033 new shorter commands.
31036 \begin_layout Standard
31037 The command scheme of
31046 \begin_layout Standard
31051 newcommand{new command name}[number of arguments][optional
31056 \begin_inset Newline newline
31063 \begin_layout Plain Layout
31078 \begin_layout Plain Layout
31085 {command definition}
31088 \begin_layout Standard
31089 \begin_inset Note Greyedout
31092 \begin_layout Plain Layout
31097 Assure that the name of the new command is not already used in your document
31098 or by LaTeX-packages that you use.
31099 When you for example define the command
31111 , you get an error message because
31117 is already defined as command for
31118 \begin_inset Quotes eld
31122 \begin_inset Formula $\le$
31126 \begin_inset Quotes erd
31137 \begin_layout Standard
31138 \begin_inset Note Greyedout
31141 \begin_layout Plain Layout
31146 The names of user-defined commands may only consist of Latin letters.
31154 \begin_layout Standard
31155 The number of arguments is an integer in the range 0
31156 \begin_inset space \thinspace{}
31160 \begin_inset space \thinspace{}
31163 9 and specifies how many arguments the new command should have.
31164 With the optional value a value for an optional argument can be predefined.
31165 When this is done, the
31173 rgument of the new command is automatically an optional one.
31176 \begin_layout Standard
31177 Here are some examples:
31180 \begin_layout Itemize
31181 To define the command
31193 , the LaTeX-preamble line is:
31197 \begin_layout Plain Layout
31209 \begin_inset Newline newline
31221 \begin_layout Itemize
31222 To define the command
31234 , the argument (that should be underlined) must be taken into account.
31235 For this the preamble line is:
31239 \begin_layout Plain Layout
31251 \begin_inset Newline newline
31266 \begin_layout Plain Layout
31278 \begin_inset Newline newline
31287 acts as argument placeholder, the
31291 behind it denotes that it is the placeholder for the first argument.
31294 \begin_layout Itemize
31302 \begin_inset space \thinspace{}
31306 \begin_inset space ~
31319 \begin_layout Plain Layout
31331 \begin_inset Newline newline
31340 framebox#1#2{$#3$}}
31346 \begin_layout Plain Layout
31358 \begin_inset Newline newline
31363 The two Dollar signs creates the extra formula needed for
31370 \begin_inset CommandInset ref
31372 reference "sub:Boxes-with-Frame"
31379 \begin_layout Itemize
31380 To create a new command for
31386 where the color for the box needn't to be specified, the argument for the
31387 color is defined optional:
31391 \begin_layout Plain Layout
31403 \begin_inset Newline newline
31412 fcolorbox{#2}{#1}{$#3$}}
31418 \begin_layout Plain Layout
31428 \begin_inset Newline newline
31431 When the color is not specified when using
31437 , the predefined color
31444 \begin_layout Standard
31445 A test of the new defined commands:
31448 \begin_layout Standard
31450 \begin_inset Tabular
31451 <lyxtabular version="3" rows="6" columns="2">
31453 <column alignment="center" valignment="top" width="0">
31454 <column alignment="center" valignment="top" width="0">
31456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31459 \begin_layout Plain Layout
31465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31468 \begin_layout Plain Layout
31470 \begin_inset Note Note
31473 \begin_layout Plain Layout
31480 is only used as spacer.
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31495 \begin_layout Plain Layout
31502 \begin_layout Plain Layout
31516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31519 \begin_layout Plain Layout
31520 \begin_inset Formula $A\gr B$
31530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31533 \begin_layout Plain Layout
31541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31544 \begin_layout Plain Layout
31545 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31558 \begin_layout Plain Layout
31562 \begin_inset Formula $\to$
31568 \begin_inset Formula $\to$
31579 \begin_layout Plain Layout
31593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31596 \begin_layout Plain Layout
31597 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31610 \begin_layout Plain Layout
31614 \begin_inset Formula $\to$
31625 \begin_layout Plain Layout
31639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31642 \begin_layout Plain Layout
31643 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31656 \begin_layout Plain Layout
31662 \begin_inset Formula $\to$
31673 \begin_layout Plain Layout
31687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31690 \begin_layout Plain Layout
31691 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31707 \begin_layout Section
31711 \begin_layout Standard
31712 LyX supports two types of commutative diagrams:
31720 that are explained in the following.
31723 \begin_layout Subsection
31728 \begin_layout Plain Layout
31737 \begin_layout Standard
31738 Diagrams of this type visualize relations by vertical and horizontal lines
31740 \begin_inset Formula \[
31741 \begin{CD}A@>>>B@>>>C\\
31743 F@<<<E@<<<D\end{CD}\]
31750 \begin_layout Standard
31751 To get them, the command
31759 \begin_layout Plain Layout
31769 is inserted to a formula.
31770 A blue box appears with two dashed lines where further commands can be
31775 arg "newline-insert newline"
31778 a new line is created.
31779 Horizontal relations are inserted in odd, vertical in even formula lines.
31782 \begin_layout Standard
31783 To create the relations there are the following commands:
31786 \begin_layout Itemize
31791 creates a left arrow,
31802 \begin_layout Itemize
31807 creates an up arrow,
31815 a vertical equal sign
31818 \begin_layout Itemize
31824 is a placeholder for non-existent relations
31827 \begin_layout Standard
31828 All arrows can be labeled as follows:
31831 \begin_layout Itemize
31832 Is text inserted between the first and second < or >, resp., it is placed
31834 When it is inserted between the second and third one, it appears under
31838 \begin_layout Itemize
31839 When text for vertical arrows is inserted between the first and second A
31840 or V, resp., it is placed left beside the arrow.
31841 When it is inserted between the second and third one, it appears right
31843 If the text contains an A or V, these letters must be set into a TeX-brace.
31846 \begin_layout Standard
31847 As example a diagram with all possible relations:
31850 \begin_layout Standard
31851 \begin_inset Formula \[
31852 \begin{CD}A@>j>>B@>>k>C@=F\\
31854 D@<<j<E@>k>>F@=C\end{CD}\]
31861 \begin_layout Standard
31862 The command for this is:
31863 \begin_inset Newline newline
31874 \begin_layout Plain Layout
31883 A@>j>>B@>>k>C@=F Ctrl+Return
31884 \begin_inset Newline newline
31891 \begin_layout Plain Layout
31906 \begin_layout Plain Layout
31919 \begin_layout Plain Layout
31931 \begin_inset Formula $\to$
31937 \begin_inset Newline newline
31944 \begin_layout Plain Layout
31959 \begin_layout Plain Layout
31972 \begin_layout Plain Layout
31982 \begin_layout Subsection
31987 \begin_layout Plain Layout
31988 Diagrams ! xymatrix
31996 \begin_layout Standard
31997 To be able to use xymatrices, the LaTeX-package
32002 A xymatrix is created by inserting the command
32009 Then you are able to add new matrix columns and rows like for normal matrices,
32011 \begin_inset CommandInset ref
32013 reference "sec:Matrices"
32020 \begin_layout Standard
32021 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32023 All possibilities to create commutative diagrams and decorations are explained
32024 in detail in this manual:
32025 \begin_inset CommandInset href
32027 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
32034 \begin_layout Standard
32035 \begin_inset Newpage newpage
32041 \begin_layout Section
32046 \begin_layout Plain Layout
32059 \begin_layout Plain Layout
32060 Other useful math tips can be found in
32061 \begin_inset CommandInset citation
32076 \begin_layout Plain Layout
32084 \begin_inset Note Note
32087 \begin_layout Plain Layout
32090 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32093 \begin_layout Plain Layout
32096 texorpdfstring is in section
32097 \begin_inset CommandInset ref
32099 reference "sub:Formulas-in-Section"
32112 \begin_layout Plain Layout
32122 \begin_layout Plain Layout
32127 \begin_layout Plain Layout
32134 Chemical characters
32138 \begin_layout Plain Layout
32153 \begin_layout Subsection
32154 Chemical Symbols and Equations
32155 \begin_inset CommandInset label
32157 name "sub:Chemical-Symbols-and"
32165 \begin_layout Plain Layout
32166 Chemical characters ! Symbols
32175 \begin_layout Plain Layout
32185 \begin_layout Plain Layout
32194 \begin_layout Standard
32195 An example text from chemistry:
32198 \begin_layout Quote
32200 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32203 -ion reacts with two
32204 \begin_inset Formula $\mathrm{Na^{+}}$
32207 -ions to sodium sulfate
32208 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32212 The chemical equation for this is:
32213 \begin_inset Formula \[
32214 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32221 \begin_layout Standard
32222 This chemical equation can directly be created as formula.
32223 To avoid that the symbols appear italic, everything is highlighted and
32224 changed by the shortcut
32230 to the upright font style.
32234 \begin_layout Plain Layout
32240 \begin_inset CommandInset ref
32242 reference "sub:Font-Styles"
32254 \begin_layout Subsection
32259 \begin_layout Plain Layout
32268 \begin_layout Standard
32269 Negative numbers often look ugly in formulas because the minus sign before
32270 the number is set with the same length as the minus operator sign.
32271 When writing the negative number in normal text, the minus sign appears
32275 \begin_layout Standard
32276 Thus, the problem disappears when converting the minus sign to mathematical
32280 \begin_layout Standard
32281 An example to visualize the problem:
32284 \begin_layout Standard
32286 \begin_inset Tabular
32287 <lyxtabular version="3" rows="3" columns="2">
32289 <column alignment="right" valignment="top" width="0">
32290 <column alignment="left" valignment="top" width="0">
32292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32295 \begin_layout Plain Layout
32301 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32304 \begin_layout Plain Layout
32312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32315 \begin_layout Plain Layout
32321 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32324 \begin_layout Plain Layout
32325 \begin_inset Formula $x=-2$
32335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32338 \begin_layout Plain Layout
32344 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32347 \begin_layout Plain Layout
32348 \begin_inset Formula $x=\textrm{-}2$
32364 \begin_layout Subsection
32365 Comma as decimal Separator
32369 \begin_layout Plain Layout
32378 \begin_layout Standard
32379 In LaTeX a comma inside a formula is used, according to the English convention,
32380 as number group separator.
32381 So there will be space added behind all commas in formulas.
32384 \begin_layout Standard
32385 To avoid this, the comma is highlighted and changed to mathematical text
32395 \begin_layout Standard
32396 To use all formula commas in the document as decimal separator, the file
32405 \begin_layout Plain Layout
32410 is part of the LaTeX-package
32418 \begin_layout Plain Layout
32423 \begin_layout Plain Layout
32446 \begin_layout Plain Layout
32452 is loaded with the LaTeX-preamble line
32455 \begin_layout Standard
32463 \begin_layout Subsection
32465 \begin_inset CommandInset label
32467 name "sub:Physical-Vectors"
32475 \begin_layout Plain Layout
32484 \begin_layout Standard
32485 Predefined vectors are offered by the LaTeX-package
32493 \begin_layout Plain Layout
32498 should be part of every LaTeX standard installation.
32507 \begin_layout Plain Layout
32513 that is loaded with the LaTeX-preamble line
32516 \begin_layout Standard
32524 \begin_layout Standard
32528 \begin_layout Plain Layout
32538 \begin_inset Note Note
32541 \begin_layout Plain Layout
32542 The following table will only be displayed when the LaTeX-package
32551 The following commands are defined:
32554 \begin_layout Standard
32556 \begin_inset Tabular
32557 <lyxtabular version="3" rows="4" columns="2">
32559 <column alignment="center" valignment="top" width="0">
32560 <column alignment="center" valignment="top" width="0">
32562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32565 \begin_layout Plain Layout
32571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32574 \begin_layout Plain Layout
32582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32585 \begin_layout Plain Layout
32595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32598 \begin_layout Plain Layout
32599 \begin_inset Formula $\Bra{\psi}$
32609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32612 \begin_layout Plain Layout
32622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32625 \begin_layout Plain Layout
32626 \begin_inset Formula $\Ket{\psi}$
32636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32639 \begin_layout Plain Layout
32651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32654 \begin_layout Plain Layout
32655 \begin_inset Formula $\Braket{\psi|\phi}$
32671 \begin_layout Standard
32678 assures that all vertical bars are set in the size of the surrounding brackets:
32679 \begin_inset Formula \[
32680 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32688 \begin_layout Plain Layout
32698 \begin_inset Note Note
32701 \begin_layout Plain Layout
32702 The following will be displayed when the LaTeX-package
32714 \begin_layout Standard
32715 You need to install the LaTeX-package
32719 to see the rest of this subsection in the output.
32722 \begin_layout Standard
32726 \begin_layout Plain Layout
32738 \begin_layout Standard
32745 can also be achieved using the command
32751 , that is described in
32752 \begin_inset CommandInset ref
32754 reference "sub:Automatic-Bracket-Size"
32761 \begin_layout Subsection
32762 Self-defined Fractions
32763 \begin_inset CommandInset label
32765 name "sub:Self-defined-Fractions"
32773 \begin_layout Plain Layout
32774 Fractions ! self-defined
32782 \begin_layout Standard
32783 To define custom commands for fractions, the command
32793 \begin_layout Plain Layout
32801 is used in the following scheme:
32804 \begin_layout Standard
32817 bracket}{fraction bar thickness}{style}
32818 \begin_inset Newline newline
32825 \begin_layout Plain Layout
32840 \begin_layout Plain Layout
32847 {numerator}{denominator}
32850 \begin_layout Standard
32851 The style is a number in the range of 0
32852 \begin_inset space \thinspace{}
32856 \begin_inset space \thinspace{}
32862 \begin_layout Standard
32864 \begin_inset Tabular
32865 <lyxtabular version="3" rows="5" columns="2">
32867 <column alignment="center" valignment="top" width="0">
32868 <column alignment="center" valignment="top" width="0">
32870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32873 \begin_layout Plain Layout
32879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32882 \begin_layout Plain Layout
32890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32893 \begin_layout Plain Layout
32899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32902 \begin_layout Plain Layout
32903 display style formula
32910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32913 \begin_layout Plain Layout
32919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32922 \begin_layout Plain Layout
32930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32933 \begin_layout Plain Layout
32939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32942 \begin_layout Plain Layout
32950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32953 \begin_layout Plain Layout
32959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32962 \begin_layout Plain Layout
32976 \begin_layout Standard
32977 When no style is given, the size is adjusted to the surrounding environment
32978 like for the command
32987 \begin_layout Standard
32988 When no fraction bar thickness is given, the predefined value of 0.4
32989 \begin_inset space \thinspace{}
32995 \begin_layout Standard
32996 \begin_inset VSpace medskip
32999 For example, the commands
33012 \begin_inset CommandInset ref
33014 reference "sub:Fractions"
33018 are defined with the commands
33021 \begin_layout Standard
33030 genfrac{}{}{}{0}{#1}{#2}}
33033 \begin_layout Standard
33037 \begin_layout Standard
33046 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33049 \begin_layout Standard
33050 \begin_inset VSpace medskip
33053 To define a fraction where the fraction bar thickness can be given as optional
33054 argument, the following line is inserted to the LaTeX-preamble:
33057 \begin_layout Standard
33066 genfrac{}{}{#1}{}{#2}{#3}}
33069 \begin_layout Standard
33071 \begin_inset Formula \begin{align*}
33072 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33073 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33077 As one can see, the distance of the numerator and the denominator to the
33078 fraction bar is round about three times the bar thickness.
33081 \begin_layout Subsection
33086 \begin_layout Plain Layout
33095 \begin_layout Standard
33096 To cancel formulas or formula parts, the LaTeX-package
33104 \begin_layout Plain Layout
33109 is part of every LaTeX standard installation.
33118 \begin_layout Plain Layout
33124 has to be loaded with the LaTeX-preamble line
33127 \begin_layout Standard
33132 usepackage[samesize]{cancel}
33135 \begin_layout Standard
33136 There are four ways to cancel formulas:
33139 \begin_layout Standard
33141 \begin_inset Tabular
33142 <lyxtabular version="3" rows="5" columns="2">
33144 <column alignment="center" valignment="top" width="0">
33145 <column alignment="center" valignment="top" width="0">
33147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33150 \begin_layout Plain Layout
33156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33159 \begin_layout Plain Layout
33161 \begin_inset Note Note
33164 \begin_layout Plain Layout
33177 are used here as spacer.
33189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33192 \begin_layout Plain Layout
33201 \begin_layout Plain Layout
33215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33218 \begin_layout Plain Layout
33219 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33232 \begin_layout Plain Layout
33241 \begin_layout Plain Layout
33255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33258 \begin_layout Plain Layout
33259 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33272 \begin_layout Plain Layout
33281 \begin_layout Plain Layout
33295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33298 \begin_layout Plain Layout
33299 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33312 \begin_layout Plain Layout
33316 \begin_inset Formula $\to$
33327 \begin_layout Plain Layout
33341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33344 \begin_layout Plain Layout
33345 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33361 \begin_layout Standard
33368 is especially suitable to visualize the reduction of fractions within formulas:
33369 \begin_inset Formula \[
33370 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33377 \begin_layout Subsection
33378 Formulas in Section Headings
33379 \begin_inset CommandInset label
33381 name "sub:Formulas-in-Section"
33389 \begin_layout Plain Layout
33390 Formula ! in section headings
33398 \begin_layout Standard
33399 When formulas are used in section headings, the following has to be taken
33403 \begin_layout Standard
33404 \begin_inset Note Greyedout
33407 \begin_layout Plain Layout
33416 \begin_layout Plain Layout
33417 Packages ! hyperref
33422 support is enabled in the document settings dialog under
33425 \begin_inset space ~
33430 , PDF-bookmarks are created for every section heading in the table of contents.
33431 If a section heading contains formulas, they are incorrectly displayed
33432 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33441 \begin_layout Standard
33442 Both problems can be solved by inserting at the end of the section heading
33443 a short title with the menu
33445 Insert\SpecialChar \menuseparator
33447 \begin_inset space ~
33453 Short titles are used as alternative for multiline section headings to
33454 keep the table of contents clearly arranged.
33455 Only the short title appears in the table of contents and therefore also
33456 in the PDF-bookmark.
33459 \begin_layout Standard
33460 When formulas should be used in the table of contents but
33464 is used, one can use the following command in TeX-mode:
33467 \begin_layout Standard
33472 texorpdfstring{part}{alternative}
33476 \begin_layout Plain Layout
33487 \begin_layout Standard
33488 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33489 This can be characters, formulas, footnotes, but also cross-references.
33490 The alternative is used instead of the part for the bookmark.
33493 \begin_layout Standard
33494 Here are two example headings:
33495 \begin_inset VSpace -3mm
33502 \begin_layout Plain Layout
33514 \begin_layout Subsubsection
33515 Heading without formula in table of contents
33516 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33520 \begin_inset OptArg
33523 \begin_layout Plain Layout
33524 Heading without formula in table of contents
33532 \begin_layout Subsubsection
33533 Heading with formula in table of contents
33537 \begin_layout Plain Layout
33547 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33554 \begin_layout Plain Layout
33564 \begin_layout Standard
33568 \begin_layout Plain Layout
33577 In the first heading a short title was used, in the second one
33586 \begin_layout Standard
33587 To get the same formatting as for the other headings, the complete heading
33596 \begin_layout Plain Layout
33598 \begin_inset CommandInset ref
33600 reference "sub:Bold-Formulas"
33612 \begin_layout Subsection
33613 Formulas in multi-column Text
33617 \begin_layout Plain Layout
33618 Formula ! in multi-column text
33626 \begin_layout Standard
33627 Formulas in multi-column text are often too wide to fit into a column and
33628 thus need to be set over the whole page width.
33629 This is done by using the LaTeX-package
33637 \begin_layout Plain Layout
33642 is part of every LaTeX standard installation.
33651 \begin_layout Plain Layout
33652 Packages ! multicol
33657 , that is loaded with the LaTeX-preamble line
33660 \begin_layout Standard
33665 usepackage{multicol}
33668 \begin_layout Standard
33669 \begin_inset Note Greyedout
33672 \begin_layout Plain Layout
33673 Note herby that the setting
33676 \begin_inset space ~
33683 Document\SpecialChar \menuseparator
33689 \begin_inset space ~
33709 \begin_layout Standard
33710 Before the multi-column text the command
33713 \begin_layout Standard
33718 begin{multicols}{column number}
33721 \begin_layout Standard
33722 is written in TeX-mode.
33723 The column number is a number in the range of 2
33724 \begin_inset space \thinspace{}
33728 \begin_inset space \thinspace{}
33732 Before the formula the multi-column text is ended by inserting the command
33735 \begin_layout Standard
33743 \begin_layout Standard
33747 \begin_layout Standard
33748 Due to the command some space is automatically added before the formula.
33750 \begin_inset space \thinspace{}
33753 mm vertical space is inserted before the formula.
33754 When the formula style
33760 \begin_layout Plain Layout
33762 \begin_inset CommandInset ref
33764 reference "sec:Formula-Styles"
33776 \begin_inset space \thinspace{}
33779 mm space is inserted instead.
33782 \begin_layout Standard
33783 As example a multi-column text with a displayed formula:
33786 \begin_layout Standard
33790 \begin_layout Plain Layout
33794 begin{multicols}{2}
33799 Das Spektrum wird fouriertransformiert.
33800 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33801 , Lösungsmittel) zu trennen.
33802 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33803 nun das Aussehen des Ausgangssignals.
33804 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33805 über alle Phasen integrieren muss.
33807 \begin_inset Formula $S$
33810 unser normiertes Ausgangssignal and
33811 \begin_inset Formula $P$
33814 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33818 \begin_layout Plain Layout
33828 \begin_inset VSpace -6mm
33832 \begin_inset Formula \begin{equation}
33833 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33841 \begin_layout Plain Layout
33845 begin{multicols}{2}
33851 \begin_inset Formula $S_{0}$
33854 das Signal ohne Gradient ist and the Normierungsbedingung
33855 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33859 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33861 \begin_inset Formula $\nicefrac{\pi}{2}$
33865 \begin_inset space \thinspace{}
33868 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33869 das Signal zusätzlich abschwächt.
33870 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33872 \begin_inset Formula $T_{2}$
33878 \begin_layout Standard
33882 \begin_layout Plain Layout
33894 \begin_layout Subsection
33895 Formulas with Description of Variables
33899 \begin_layout Plain Layout
33900 Formula ! with description of variables
33908 \begin_layout Standard
33909 To describe variables within a formula, like in formula
33910 \begin_inset CommandInset ref
33912 reference "eq:within"
33921 \begin_inset Formula $n$
33925 \begin_inset space ~
33928 matrix is used with left aligned columns for the
33929 \begin_inset Formula $n$
33936 \begin_layout Plain Layout
33938 \begin_inset CommandInset ref
33940 reference "sec:Matrices"
33949 To set the description in a smaller size, before the matrix e.
33950 \begin_inset space \thinspace{}
33954 \begin_inset space ~
33967 \begin_layout Plain Layout
33969 \begin_inset CommandInset ref
33971 reference "sub:Font-Sizes"
33983 \begin_layout Standard
33984 When the formula style
33990 \begin_layout Plain Layout
33992 \begin_inset CommandInset ref
33994 reference "sec:Formula-Styles"
34015 \begin_layout Plain Layout
34022 only works in formulas with the style
34027 \begin_inset CommandInset ref
34029 reference "sub:Variable-Space"
34038 is inserted before and after the matrix to have the same separation of
34039 the matrix from the equation and the side margin.
34042 \begin_layout Standard
34043 When the formula style
34047 is used, the method described in
34048 \begin_inset CommandInset ref
34050 reference "sub:Flalign-Environment"
34054 is used to indent formulas.
34056 \begin_inset CommandInset ref
34058 reference "eq:within"
34062 consists of five columns whereas in the first two columns contain the equation,
34063 the third the matrix, and the last one an empty TeX-brace.
34064 \begin_inset Formula \begin{flalign}
34065 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34066 \rho & \textrm{density}\\
34067 V & \textrm{volume}\\
34068 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34075 \begin_layout Subsection
34076 Upright small Greek Letters
34077 \begin_inset CommandInset label
34079 name "sub:Upright-small-Greek"
34087 \begin_layout Plain Layout
34088 Greek letters ! upright
34096 \begin_layout Standard
34097 Most of the math fonts only provide italic small Greek letters.
34098 But for symbols of elementary particles like pions and neutrinos, upright
34099 Greek letters are needed.
34108 \begin_layout Plain Layout
34113 is part of the LaTeX-package
34121 \begin_layout Plain Layout
34126 \begin_layout Plain Layout
34149 \begin_layout Plain Layout
34155 that is loaded with the LaTeX-preamble line
34158 \begin_layout Standard
34163 usepackage{upgreek}
34166 \begin_layout Standard
34172 \begin_layout Plain Layout
34182 \begin_inset Note Note
34185 \begin_layout Plain Layout
34186 The following table will only be displayed when the LaTeX-package
34195 They are created when the command for a small Greek letters is started
34201 For example the command
34208 \begin_inset Formula $\uptau$
34214 \begin_layout Standard
34215 With these commands reactions of elementary particles can be typeset:
34216 \begin_inset Formula \[
34217 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34224 \begin_layout Standard
34225 The upright letters are more bold and wider than the italic ones.
34226 They should therefore not be used for units like
34227 \begin_inset Quotes eld
34231 \begin_inset Quotes erd
34237 \begin_layout Standard
34241 \begin_layout Plain Layout
34251 \begin_inset Note Note
34254 \begin_layout Plain Layout
34255 The following will be displayed when the LaTeX-package
34267 \begin_layout Standard
34268 You need to install the LaTeX-package
34272 to see the rest of this subsection in the output.
34275 \begin_layout Standard
34279 \begin_layout Plain Layout
34291 \begin_layout Subsection
34292 Text Characters in Formulas
34293 \begin_inset CommandInset label
34295 name "sub:Text-Characters-in"
34303 \begin_layout Plain Layout
34312 \begin_layout Standard
34313 In some cases you might want to insert text characters directly into formulas.
34314 When for example the centered dot · is often used in formulas like
34315 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34318 , one would have to insert the command
34328 \begin_layout Plain Layout
34330 \begin_inset CommandInset ref
34332 reference "sub:Binary-Operators"
34341 all the time, because this character is defined in all encodings as text
34343 But the encoding can be changed by this LaTeX-preamble line:
34346 \begin_layout Standard
34351 Declare Inputtext{183}{
34361 f\SpecialChar \textcompwordmark{}
34365 \begin_layout Standard
34366 The character encoding (menu
34368 Document\SpecialChar \menuseparator
34369 Settings\SpecialChar \menuseparator
34372 ) specifies what character appears when a keyboard key is pressed.
34373 When the key for the character '·' is pressed, internally the command
34380 But this command is not available in a formula so that you would get LaTeX-erro
34382 With the changed encoding the right command is chosen automatically, depending
34383 on if the character was inserted into a formula or not.
34386 \begin_layout Standard
34387 The encoding of several characters is saved in definition files.
34388 Fore example the encoding
34392 is defined in the file
34396 that is in the installation folder of LaTeX.
34397 Encodings should only be changed via the LaTeX-preamble and not in the
34399 Otherwise own documents could not be edited by other LyX users working
34400 on other computers.
34403 \begin_layout Standard
34404 \begin_inset VSpace medskip
34407 Besides the centered dot, in this document the degree sign ° is defined
34408 with the following LaTeX-preamble line so that it can directly be inserted
34412 \begin_layout Standard
34417 DeclareInputtext{176}{
34427 f\SpecialChar \textcompwordmark{}
34431 \begin_layout Standard
34432 \begin_inset Newpage newpage
34438 \begin_layout Section
34444 \begin_layout Plain Layout
34453 \begin_layout Standard
34454 This section is a summary of the most important typographic rules, listed
34459 \begin_layout Plain Layout
34460 This collection was partly taken from the German semi-official dictionary
34462 \begin_inset Quotes eld
34466 \begin_inset Quotes erd
34470 \begin_inset CommandInset citation
34476 that lists some of the ISO rules.
34484 \begin_layout Itemize
34493 \begin_layout Plain Layout
34494 done with font styles, see
34495 \begin_inset CommandInset ref
34497 reference "sub:Font-Styles"
34507 \begin_inset space \thinspace{}
34511 \begin_inset Newline newline
34514 Between the value and the unit is the smallest space, see
34515 \begin_inset CommandInset ref
34517 reference "sub:Predefined-Space"
34522 \begin_inset Newline newline
34525 This convention is automatically fulfilled when the command
34532 When it is entered to a formula, two boxes appear.
34533 In the first one the value is inserted, in the second one the unit, and
34535 \begin_inset Formula $\unit[30]{km/h}$
34539 \begin_inset space \thinspace{}
34549 is not a real LaTeX command but the command
34555 , therefore you cannot use it in TeX code.
34558 \begin_layout Itemize
34559 Percent and perthousand signs are set like physical units:
34560 \begin_inset Newline newline
34564 \begin_inset space \thinspace{}
34570 \begin_layout Itemize
34571 The degree sign follows directly on the value: 15°, but not when it is used
34573 \begin_inset space \thinspace{}
34579 \begin_layout Itemize
34580 In numbers with more than four digits the smallest space is inserted before
34581 every third digit to group them:
34591 \begin_inset space \thinspace{}
34595 \begin_inset space \thinspace{}
34601 \begin_layout Itemize
34602 For dimensions like 120×90×40
34603 \begin_inset space \thinspace{}
34606 cm the multiplication sign
34607 \begin_inset Quotes eld
34611 \begin_inset Quotes erd
34615 It is available with the LaTeX-command
34621 , but can also directly be inserted with some keyboard definitions.
34624 \begin_layout Itemize
34625 Functions with names consisting of several letters are set upright to avoid
34627 \begin_inset CommandInset ref
34629 reference "sub:Predefined-Functions"
34636 \begin_layout Itemize
34637 Indices consisting of several letters, are set upright:
34638 \begin_inset Formula $E_{\mathrm{kin}}$
34642 \begin_inset Newline newline
34645 Components of matrices are set italic:
34646 \begin_inset Formula $\hat{H}_{kl}$
34652 \begin_layout Itemize
34653 The differentiation/integration operator 'd', the Euler's number 'e', and
34654 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34658 \begin_layout Standard
34659 \begin_inset Newpage newpage
34665 \begin_layout Section
34670 \begin_layout Plain Layout
34679 \begin_layout Standard
34680 Some characters and symbols can be created with several commands.
34681 Here is a list of the synonym commands:
34684 \begin_layout Standard
34685 \begin_inset VSpace bigskip
34689 \begin_inset space \hfill{}
34693 \begin_inset Tabular
34694 <lyxtabular version="3" rows="12" columns="2">
34696 <column alignment="center" valignment="top" width="0pt">
34697 <column alignment="center" valignment="top" width="0pt">
34699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34702 \begin_layout Plain Layout
34708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34711 \begin_layout Plain Layout
34713 \begin_inset Note Note
34716 \begin_layout Plain Layout
34723 is only used as spacer.
34735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34738 \begin_layout Plain Layout
34746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34749 \begin_layout Plain Layout
34753 \begin_layout Plain Layout
34766 \begin_layout Plain Layout
34780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34783 \begin_layout Plain Layout
34791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34794 \begin_layout Plain Layout
34804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34807 \begin_layout Plain Layout
34815 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34818 \begin_layout Plain Layout
34828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34831 \begin_layout Plain Layout
34839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34842 \begin_layout Plain Layout
34850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34853 \begin_layout Plain Layout
34861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34864 \begin_layout Plain Layout
34872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34875 \begin_layout Plain Layout
34883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34886 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34910 \begin_layout Plain Layout
34920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34923 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34934 \begin_layout Plain Layout
34944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34947 \begin_layout Plain Layout
34955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34958 \begin_layout Plain Layout
34968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34971 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34982 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34993 \begin_layout Plain Layout
35001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35004 \begin_layout Plain Layout
35016 \begin_inset space \hfill{}
35020 \begin_inset Tabular
35021 <lyxtabular version="3" rows="12" columns="2">
35023 <column alignment="center" valignment="top" width="0pt">
35024 <column alignment="center" valignment="top" width="0pt">
35026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35029 \begin_layout Plain Layout
35035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35038 \begin_layout Plain Layout
35046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35049 \begin_layout Plain Layout
35057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35060 \begin_layout Plain Layout
35072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35075 \begin_layout Plain Layout
35083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35086 \begin_layout Plain Layout
35096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35099 \begin_layout Plain Layout
35107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35110 \begin_layout Plain Layout
35120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35123 \begin_layout Plain Layout
35131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35134 \begin_layout Plain Layout
35142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35145 \begin_layout Plain Layout
35153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35156 \begin_layout Plain Layout
35164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35167 \begin_layout Plain Layout
35175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35178 \begin_layout Plain Layout
35188 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35191 \begin_layout Plain Layout
35199 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35202 \begin_layout Plain Layout
35212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35215 \begin_layout Plain Layout
35223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35226 \begin_layout Plain Layout
35236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35239 \begin_layout Plain Layout
35247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35250 \begin_layout Plain Layout
35260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35263 \begin_layout Plain Layout
35271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35274 \begin_layout Plain Layout
35284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35287 \begin_layout Plain Layout
35295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35298 \begin_layout Plain Layout
35312 \begin_inset space \hfill{}
35318 \begin_layout Standard
35319 \begin_inset Newpage newpage
35325 \begin_layout Bibliography
35326 \begin_inset CommandInset bibitem
35327 LatexCommand bibitem
35339 The LaTeX Companion
35342 Addison Wesley, 2004
35345 \begin_layout Bibliography
35346 \begin_inset CommandInset bibitem
35347 LatexCommand bibitem
35353 \begin_inset CommandInset href
35356 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35360 of LaTeX's math abilities
35363 \begin_layout Bibliography
35364 \begin_inset CommandInset bibitem
35365 LatexCommand bibitem
35370 LaTeX tips and tricks-
35371 \begin_inset CommandInset href
35374 target "http://tug.org/TeXnik/"
35381 \begin_layout Bibliography
35382 \begin_inset CommandInset bibitem
35383 LatexCommand bibitem
35389 \begin_inset CommandInset href
35392 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35400 \begin_layout Plain Layout
35412 \begin_layout Bibliography
35413 \begin_inset CommandInset bibitem
35414 LatexCommand bibitem
35420 \begin_inset CommandInset href
35423 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35427 of all symbols available with LaTeX-packages
35430 \begin_layout Bibliography
35431 \begin_inset CommandInset bibitem
35432 LatexCommand bibitem
35438 \begin_inset CommandInset href
35440 name "Documentation"
35441 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35445 of the LaTeX-package
35453 \begin_layout Plain Layout
35454 Packages ! hyperref
35462 \begin_layout Bibliography
35463 \begin_inset CommandInset bibitem
35464 LatexCommand bibitem
35470 \begin_inset CommandInset href
35473 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35484 \begin_inset CommandInset ref
35486 reference "sub:Operator-Limits"
35494 \begin_layout Plain Layout
35505 \begin_layout Bibliography
35506 \begin_inset CommandInset bibitem
35507 LatexCommand bibitem
35518 Auflage, Duden 2001
35521 \begin_layout Subsubsection*
35522 \begin_inset CommandInset index_print
35523 LatexCommand printindex