1 #LyX 1.6.0rc5 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 \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{}
4245 \begin_inset space \space{}
4257 \begin_layout Standard
4258 It is possible to place up to 6 lines above or below characters.
4261 \begin_layout Standard
4262 \begin_inset VSpace bigskip
4265 Custom lines can be created using the command
4275 \begin_layout Plain Layout
4283 which has the following scheme:
4286 \begin_layout Standard
4291 rule[vertical offset]{length}{thickness}
4294 \begin_layout Standard
4295 The optional vertical offset shifts the line upwards (or downwards, when
4296 the value is negative).
4298 \begin_inset CommandInset ref
4300 reference "tab:Available-units"
4304 can be used for the values.
4305 Here are two example lines created with the commands
4306 \begin_inset Newline newline
4313 rule[-2ex]{3cm}{2pt}
4324 \begin_layout Standard
4326 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4332 \begin_layout Standard
4339 can also be used for text when it is inserted in TeX-mode.
4342 \begin_layout Subsection
4344 \begin_inset CommandInset label
4354 \begin_layout Plain Layout
4363 \begin_layout Standard
4364 There are different types of ellipses available.
4368 \begin_layout Plain Layout
4369 In the math toolbar in the submenu of the button
4370 \begin_inset Graphics
4371 filename ../images/math/ldots.png
4381 For listings dots at the baseline are used (
4391 \begin_layout Plain Layout
4399 ), while for operations dots are needed that are on the same height as the
4410 \begin_layout Plain Layout
4419 When using the command
4429 \begin_layout Plain Layout
4437 , LaTeX decides on the basis of the next character what type is used.
4440 \begin_layout Standard
4442 \begin_inset Tabular
4443 <lyxtabular version="3" rows="8" columns="2">
4445 <column alignment="center" valignment="top" width="0pt">
4446 <column alignment="center" valignment="top" width="0pt">
4448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4451 \begin_layout Plain Layout
4457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4460 \begin_layout Plain Layout
4468 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4471 \begin_layout Plain Layout
4476 \begin_layout Plain Layout
4491 \begin_layout Plain Layout
4505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4508 \begin_layout Plain Layout
4509 \begin_inset Formula $A_{1},\dots,A_{n}$
4519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4522 \begin_layout Plain Layout
4527 \begin_layout Plain Layout
4542 \begin_layout Plain Layout
4556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4559 \begin_layout Plain Layout
4560 \begin_inset Formula $A_{1}+\dots+A_{n}$
4570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4573 \begin_layout Plain Layout
4578 \begin_layout Plain Layout
4593 \begin_layout Plain Layout
4607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4610 \begin_layout Plain Layout
4611 \begin_inset Formula $A_{1},\ldots,A_{n}$
4621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4624 \begin_layout Plain Layout
4629 \begin_layout Plain Layout
4644 \begin_layout Plain Layout
4658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4661 \begin_layout Plain Layout
4662 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4675 \begin_layout Plain Layout
4683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4686 \begin_layout Plain Layout
4687 \begin_inset Formula $\vdots$
4697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4700 \begin_layout Plain Layout
4708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4711 \begin_layout Plain Layout
4712 \begin_inset Formula $\ddots$
4722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4725 \begin_layout Plain Layout
4727 \begin_inset space \thinspace{}
4730 matrix with the different dots
4735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4738 \begin_layout Plain Layout
4739 \begin_inset Formula $\begin{array}{ccc}
4740 A_{11} & \cdots & A_{1m}\\
4741 \vdots & \ddots & \vdots\\
4742 A_{n1} & \cdots & A_{nm}\end{array}$
4758 \begin_layout Standard
4759 The ellipses available in menu
4761 Insert\SpecialChar \menuseparator
4763 \begin_inset space ~
4777 \begin_layout Standard
4778 \begin_inset VSpace medskip
4781 Specially for matrices there are ellipses that span over several columns.
4782 They are created with the command
4792 \begin_layout Plain Layout
4800 , that has the following scheme:
4803 \begin_layout Standard
4808 hdotsfor[distance]{number of columns}
4811 \begin_layout Standard
4812 The number of columns specifies how many columns should be spanned.
4813 Distance is a factor for the distance between the dots.
4816 \begin_layout Standard
4817 In the following matrix the command
4823 was inserted in the first box of the second line, to get an ellipsis with
4824 a dot distance twice as long as with the command
4831 \begin_inset Formula \[
4832 \left(\begin{array}{cccc}
4835 q & w & e & r\end{array}\right)\]
4839 Note that the matrix fields that should be spanned must be empty, otherwise
4840 you get LaTeX-errors.
4843 \begin_layout Standard
4844 \begin_inset VSpace bigskip
4847 Furthermore you can fill with the command
4857 \begin_layout Plain Layout
4865 the rest of a line with dots.
4866 The effect of these commands is the same like with
4873 \begin_inset CommandInset ref
4875 reference "sub:Variable-Space"
4882 \begin_layout Standard
4883 For example the command
4891 \begin_layout Plain Layout
4905 \begin_layout Standard
4906 \begin_inset Formula $A\dotfill B$
4912 \begin_layout Standard
4919 there is for a line the command
4929 \begin_layout Plain Layout
4940 \begin_layout Standard
4941 \begin_inset Formula $A\hrulefill B$
4947 \begin_layout Standard
4948 To use the commands for text, they have to be inserted in TeX-mode.
4951 \begin_layout Section
4953 \begin_inset CommandInset label
4963 \begin_layout Plain Layout
4972 \begin_layout Standard
4973 Matrices can be inserted via the math toolbar button
4974 \begin_inset Graphics
4975 filename ../images/dialog-show_mathmatrix.png
4982 Insert\SpecialChar \menuseparator
4983 Math\SpecialChar \menuseparator
4987 You will be asked for the number of matrix columns and rows, and the alignment.
4988 The vertical alignment is hereby only of importance for matrices in inline
4992 \begin_layout Standard
4993 The first matrix is top
4994 \begin_inset Formula $\begin{array}[t]{cccc}
4997 C & F & I & L\end{array}$
5001 \begin_inset Formula $\begin{array}{cccc}
5004 C & F & I & L\end{array}$
5007 , and the third bottom
5008 \begin_inset Formula $\begin{array}[b]{cccc}
5011 C & F & I & L\end{array}$
5017 \begin_layout Standard
5018 The horizontal alignment specifies how the column entries should be aligned.
5019 It is set by entering a letter for every column.
5024 denotes left aligned,
5033 To create for example a 4
5038 \begin_inset space ~
5041 matrix where the first column is left aligned, the second and third are
5042 centered, and the last one is right aligned, one enters for the horizontal
5048 Normally are in a matrix all columns centered, therefore the default is
5049 for every column is a
5056 \begin_layout Standard
5057 Horizontal alignment:
5060 \begin_layout Standard
5066 \begin_inset Formula $\begin{array}{lll}
5069 C & F & 10000\end{array}$
5077 \begin_inset Formula $\begin{array}{ccc}
5080 C & F & 10000\end{array}$
5088 \begin_inset Formula $\begin{array}{rrr}
5091 C & F & 10000\end{array}$
5097 \begin_layout Standard
5098 To add or delete rows and columns subsequently, the math toolbar buttons
5100 \begin_inset Graphics
5101 filename ../images/tabular-feature_append-row.png
5107 \begin_inset Graphics
5108 filename ../images/tabular-feature_delete-row.png
5114 \begin_inset space \thinspace{}
5119 Edit\SpecialChar \menuseparator
5123 New rows can also be created with
5126 arg "newline-insert newline"
5132 \begin_layout Standard
5133 \begin_inset VSpace bigskip
5136 Parentheses around a matrix can can either be created with the commands
5147 \begin_layout Plain Layout
5165 \begin_layout Plain Layout
5176 \begin_inset space ~
5182 \begin_inset CommandInset ref
5184 reference "sub:Automatic-Bracket-Size"
5188 , or by using the following commands:
5189 \begin_inset VSpace medskip
5195 \begin_layout Standard
5196 \begin_inset space \hfill{}
5200 \begin_inset Tabular
5201 <lyxtabular version="3" rows="4" columns="2">
5203 <column alignment="center" valignment="top" width="0">
5204 <column alignment="center" valignment="top" width="0">
5206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5209 \begin_layout Plain Layout
5215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5218 \begin_layout Plain Layout
5220 \begin_inset Note Note
5223 \begin_layout Plain Layout
5230 is only used as spacer.
5242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5245 \begin_layout Plain Layout
5252 \begin_layout Plain Layout
5266 \begin_inset space \thinspace{}
5274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5277 \begin_layout Plain Layout
5278 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5279 0 & \textrm{-}\mathrm{i}\\
5280 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5293 \begin_layout Plain Layout
5300 \begin_layout Plain Layout
5314 \begin_inset space \thinspace{}
5322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5325 \begin_layout Plain Layout
5326 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5327 0 & \textrm{-}\mathrm{i}\\
5328 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5341 \begin_layout Plain Layout
5348 \begin_layout Plain Layout
5362 \begin_inset space \thinspace{}
5370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5373 \begin_layout Plain Layout
5374 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5375 0 & \textrm{-}\mathrm{i}\\
5376 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5390 \begin_inset space \hfill{}
5394 \begin_inset Tabular
5395 <lyxtabular version="3" rows="4" columns="2">
5397 <column alignment="center" valignment="top" width="0">
5398 <column alignment="center" valignment="top" width="0">
5400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5403 \begin_layout Plain Layout
5409 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5412 \begin_layout Plain Layout
5420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5423 \begin_layout Plain Layout
5430 \begin_layout Plain Layout
5444 \begin_inset space \thinspace{}
5452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5455 \begin_layout Plain Layout
5456 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5457 0 & \textrm{-}\mathrm{i}\\
5458 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5471 \begin_layout Plain Layout
5478 \begin_layout Plain Layout
5492 \begin_inset space \thinspace{}
5500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5503 \begin_layout Plain Layout
5504 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5505 0 & \textrm{-}\mathrm{i}\\
5506 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5519 \begin_layout Plain Layout
5526 \begin_layout Plain Layout
5540 \begin_inset space \thinspace{}
5548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5551 \begin_layout Plain Layout
5552 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5553 0 & \textrm{-}\mathrm{i}\\
5554 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5568 \begin_inset space \hfill{}
5574 \begin_layout Standard
5575 \begin_inset VSpace medskip
5579 \begin_inset space \thinspace{}
5583 \begin_inset space \space{}
5592 is inserted, a blue box appears between two vertical lines where the matrix
5596 \begin_layout Standard
5597 \begin_inset VSpace bigskip
5600 As all multiline formulas are matrices, the length
5610 \begin_layout Plain Layout
5618 that is described in
5619 \begin_inset CommandInset ref
5621 reference "sub:Column-Separation"
5625 can also be used to change the column separation of matrices.
5628 \begin_layout Standard
5629 To change the row separation, the command
5639 \begin_layout Plain Layout
5648 It is used as follows:
5651 \begin_layout Standard
5658 arraystretch}{stretch factor}
5662 \begin_layout Plain Layout
5673 \begin_layout Standard
5680 assigns the stretch factor to the predefined command
5688 \begin_inset space \thinspace{}
5692 \begin_inset space \space{}
5695 the row separation, use the factor 2.
5696 This is then used for all following matrices.
5697 To go back to the original separation, assign the factor 1 to
5706 \begin_layout Standard
5707 To set matrices into a text line, the command
5717 \begin_layout Plain Layout
5726 When it is inserted a blue box with two dashed lines appears.
5727 In this box the matrix is inserted.
5730 \begin_layout Standard
5732 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5733 C & D\end{smallmatrix}\right)$
5739 \begin_layout Section
5740 Brackets and Delimiters
5744 \begin_layout Plain Layout
5754 \begin_layout Plain Layout
5763 \begin_layout Subsection
5764 Vertical Brackets and Delimiters
5768 \begin_layout Plain Layout
5777 \begin_layout Standard
5778 \begin_inset space \hfill{}
5782 \begin_inset Tabular
5783 <lyxtabular version="3" rows="9" columns="2">
5785 <column alignment="center" valignment="top" width="0pt">
5786 <column alignment="center" valignment="top" width="0pt">
5788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5791 \begin_layout Plain Layout
5797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5800 \begin_layout Plain Layout
5808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5811 \begin_layout Plain Layout
5817 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5820 \begin_layout Plain Layout
5821 \begin_inset Formula $($
5831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5834 \begin_layout Plain Layout
5840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5843 \begin_layout Plain Layout
5844 \begin_inset Formula $\{$
5854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5857 \begin_layout Plain Layout
5863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5866 \begin_layout Plain Layout
5867 \begin_inset Formula $[$
5877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5880 \begin_layout Plain Layout
5888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5891 \begin_layout Plain Layout
5892 \begin_inset Formula $\langle$
5902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5905 \begin_layout Plain Layout
5913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5916 \begin_layout Plain Layout
5917 \begin_inset Formula $\lceil$
5927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5930 \begin_layout Plain Layout
5938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5941 \begin_layout Plain Layout
5942 \begin_inset Formula $\lfloor$
5952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5955 \begin_layout Plain Layout
5961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5964 \begin_layout Plain Layout
5965 \begin_inset Formula $/$
5975 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5978 \begin_layout Plain Layout
5984 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5987 \begin_layout Plain Layout
5988 \begin_inset Formula $|$
6002 \begin_inset space \hfill{}
6006 \begin_inset Tabular
6007 <lyxtabular version="3" rows="9" columns="2">
6009 <column alignment="center" valignment="top" width="0pt">
6010 <column alignment="center" valignment="top" width="0pt">
6012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6015 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6024 \begin_layout Plain Layout
6032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6035 \begin_layout Plain Layout
6041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6044 \begin_layout Plain Layout
6045 \begin_inset Formula $)$
6055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6058 \begin_layout Plain Layout
6064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6067 \begin_layout Plain Layout
6068 \begin_inset Formula $\}$
6078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6081 \begin_layout Plain Layout
6087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6090 \begin_layout Plain Layout
6091 \begin_inset Formula $]$
6101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6104 \begin_layout Plain Layout
6112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6115 \begin_layout Plain Layout
6116 \begin_inset Formula $\rangle$
6126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6129 \begin_layout Plain Layout
6137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6140 \begin_layout Plain Layout
6141 \begin_inset Formula $\rceil$
6151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6154 \begin_layout Plain Layout
6162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6165 \begin_layout Plain Layout
6166 \begin_inset Formula $\rfloor$
6176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6179 \begin_layout Plain Layout
6189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6192 \begin_layout Plain Layout
6193 \begin_inset Formula $\backslash$
6203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6206 \begin_layout Plain Layout
6214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6217 \begin_layout Plain Layout
6218 \begin_inset Formula $\|$
6232 \begin_inset space \hfill{}
6238 \begin_layout Standard
6241 \begin_inset Note Greyedout
6244 \begin_layout Plain Layout
6249 In TeX-mode the command
6259 \begin_layout Plain Layout
6267 must be used for the backslash, because the command
6275 produces there a line break.
6283 \begin_layout Standard
6284 For all characters listed above the size can be adjusted with the commands
6285 described in the following two subsections.
6286 When using these commands, the characters < and > can directly be used
6287 instead of the commands
6302 \begin_layout Subsubsection
6304 \begin_inset CommandInset label
6306 name "sub:Manual-Bracket-Size"
6314 \begin_layout Plain Layout
6315 Bracket size ! manual
6323 \begin_layout Standard
6324 The bracket size can be specified manually by the LaTeX-commands
6334 \begin_layout Plain Layout
6367 denotes the smallest and
6373 the largest bracket size.
6376 \begin_layout Standard
6377 These commands are used to emphasize levels of brackets:
6380 \begin_layout Standard
6382 \begin_inset Tabular
6383 <lyxtabular version="3" rows="2" columns="2">
6385 <column alignment="center" valignment="top" width="0pt">
6386 <column alignment="center" valignment="top" width="0pt">
6388 <cell alignment="center" valignment="top" usebox="none">
6391 \begin_layout Plain Layout
6392 all brackets in the same size:
6397 <cell alignment="center" valignment="top" usebox="none">
6400 \begin_layout Plain Layout
6401 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6411 <cell alignment="center" valignment="top" usebox="none">
6414 \begin_layout Plain Layout
6420 <cell alignment="center" valignment="top" usebox="none">
6423 \begin_layout Plain Layout
6424 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6438 \begin_inset Note Note
6441 \begin_layout Plain Layout
6448 is only used as spacer.
6456 \begin_layout Standard
6457 For the second formula the command
6467 \begin_layout Plain Layout
6481 \begin_layout Standard
6482 Here is an overview about all bracket sizes:
6485 \begin_layout Standard
6505 \begin_layout Plain Layout
6522 \begin_layout Plain Layout
6535 \begin_layout Plain Layout
6551 \begin_layout Standard
6553 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6559 \begin_layout Standard
6566 -commands there is the variant
6576 \begin_layout Plain Layout
6584 that adds a bit more space between the bracket and its content, and the
6601 \begin_layout Plain Layout
6611 , that don't add additional space.
6616 at the end of the command
6622 is for a left bracket; for a right bracket this will be replaced by an
6628 A left or right bracket can each be an opening or closing bracket.
6631 \begin_layout Standard
6632 In the following table is a comparison of the variants:
6635 \begin_layout Standard
6637 \begin_inset Tabular
6638 <lyxtabular version="3" rows="5" columns="2">
6640 <column alignment="center" valignment="middle" width="0">
6641 <column alignment="center" valignment="middle" width="0">
6643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6646 \begin_layout Plain Layout
6652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6655 \begin_layout Plain Layout
6657 \begin_inset Note Note
6660 \begin_layout Plain Layout
6667 is only used as spacer.
6679 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6682 \begin_layout Plain Layout
6697 \begin_layout Plain Layout
6715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6718 \begin_layout Plain Layout
6719 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6732 \begin_layout Plain Layout
6747 \begin_layout Plain Layout
6765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6768 \begin_layout Plain Layout
6769 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6782 \begin_layout Plain Layout
6797 \begin_layout Plain Layout
6815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6818 \begin_layout Plain Layout
6819 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6832 \begin_layout Plain Layout
6844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6847 \begin_layout Plain Layout
6848 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6864 \begin_layout Subsubsection
6865 Automatic Bracket Size
6866 \begin_inset CommandInset label
6868 name "sub:Automatic-Bracket-Size"
6876 \begin_layout Plain Layout
6877 Bracket size ! automatic
6885 \begin_layout Standard
6886 Brackets with variable size can be inserted with the commands
6896 \begin_layout Plain Layout
6914 \begin_layout Plain Layout
6922 or via the math toolbar button
6923 \begin_inset Graphics
6924 filename ../images/dialog-show_mathdelimiter.png
6942 the wanted bracket must be inserted.
6943 The bracket size will then automatically be calculated for the output.
6946 \begin_layout Standard
6948 normal bracket: The command
6958 \begin_layout Plain Layout
6968 \begin_inset Formula $\downarrow$
6975 \begin_layout Plain Layout
6987 \begin_inset Formula \[
6995 \begin_layout Standard
6997 multiline bracket: The command
7009 \begin_layout Plain Layout
7019 \begin_inset Formula $\downarrow$
7026 \begin_layout Plain Layout
7040 \begin_inset Formula \[
7041 \ln\left(\frac{A}{C}\right)\]
7048 \begin_layout Standard
7064 \begin_inset space ~
7070 This has the advantage that you can see in LyX immediately the real bracket
7071 size and that the matching right bracket will be created too.
7072 \begin_inset Newline newline
7075 The command for the last example would then be:
7089 \begin_layout Plain Layout
7099 \begin_inset Formula $\downarrow$
7105 \begin_layout Standard
7106 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7107 For example the command
7117 \begin_layout Plain Layout
7127 \begin_inset Formula $\downarrow$
7134 \begin_layout Plain Layout
7150 \begin_inset Formula \[
7151 \left.\frac{A}{B}\right\} \]
7169 will be converted by LyX to brackets in the right size when the document
7170 is reloaded and an omitted bracket will appear as dashed line.
7173 \begin_layout Standard
7174 \begin_inset VSpace bigskip
7177 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7188 \begin_layout Plain Layout
7196 is additionally available for all brackets and limits.
7197 With this command the height of the following character is adapted to the
7198 one of the surrounding brackets, what is e.
7199 \begin_inset space \thinspace{}
7203 \begin_inset space \space{}
7206 needed for physical vectors:
7207 \begin_inset Formula \[
7208 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7212 For physical vectors there is a special LaTeX-package, described in
7213 \begin_inset CommandInset ref
7215 reference "sub:Physical-Vectors"
7222 \begin_layout Subsection
7227 \begin_layout Plain Layout
7228 Brackets ! horizontal
7236 \begin_layout Standard
7238 \begin_inset Tabular
7239 <lyxtabular version="3" rows="4" columns="2">
7241 <column alignment="center" valignment="top" width="0pt">
7242 <column alignment="center" valignment="top" width="0pt">
7244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7247 \begin_layout Plain Layout
7249 \begin_inset Note Note
7252 \begin_layout Plain Layout
7259 is only used as spacer.
7269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7272 \begin_layout Plain Layout
7280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7283 \begin_layout Plain Layout
7287 \begin_layout Plain Layout
7302 \begin_layout Plain Layout
7315 \begin_layout Plain Layout
7328 \begin_layout Plain Layout
7341 \begin_layout Plain Layout
7352 \begin_layout Plain Layout
7365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7368 \begin_layout Plain Layout
7369 \begin_inset Formula $\overbrace{A+B}^{3}$
7379 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7382 \begin_layout Plain Layout
7386 \begin_layout Plain Layout
7401 \begin_layout Plain Layout
7414 \begin_layout Plain Layout
7427 \begin_layout Plain Layout
7438 \begin_layout Plain Layout
7451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7454 \begin_layout Plain Layout
7455 \begin_inset Formula $\underbrace{A+B}_{5}$
7465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7468 \begin_layout Plain Layout
7475 \begin_layout Plain Layout
7490 \begin_layout Plain Layout
7503 \begin_layout Plain Layout
7516 \begin_layout Plain Layout
7529 \begin_layout Plain Layout
7542 \begin_layout Plain Layout
7555 \begin_layout Plain Layout
7569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7572 \begin_layout Plain Layout
7573 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7589 \begin_layout Standard
7590 In the last example it doesn't matter if
7602 is inserted at first.
7605 \begin_layout Standard
7606 \begin_inset VSpace bigskip
7609 When brackets are needed that overlap each other, multiline formulas, as
7611 \begin_inset CommandInset ref
7613 reference "sec:Multiline-Formulas"
7618 \begin_inset Formula \begin{eqnarray*}
7619 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7620 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7624 In the first row the formula is inserted together with the first brace.
7625 It is hereby important that the space command
7629 \begin_layout Plain Layout
7630 Space commands are explained in
7631 \begin_inset CommandInset ref
7633 reference "sub:Predefined-Space"
7648 is inserted before the first
7649 \begin_inset Formula $d$
7652 , because the brace that ends behind the
7653 \begin_inset Formula $q$
7656 prevents that the following
7657 \begin_inset Quotes eld
7661 \begin_inset Quotes erd
7664 is surrounded by space.
7668 \begin_layout Plain Layout
7669 because a bracket is not handled as character, see
7670 \begin_inset CommandInset ref
7672 reference "sub:Binary-Operators"
7681 In the second row the second brace is inserted.
7682 As it should begin before the
7683 \begin_inset Formula $b$
7698 \begin_layout Plain Layout
7706 \begin_inset CommandInset ref
7708 reference "sub:Placeholders"
7717 This space is needed because the
7718 \begin_inset Quotes eld
7722 \begin_inset Quotes erd
7725 is also surrounded by space in the formula.
7726 The brace is placed under the command
7735 \begin_layout Standard
7736 It gets more complicated when brackets overlap each other, like in the following
7741 \begin_layout Plain Layout
7753 \begin_inset Formula \begin{eqnarray*}
7754 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7755 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7763 \begin_layout Plain Layout
7774 The first formula row is the same as the second row of the previous example,
7775 with the difference that the brace is above.
7776 The second row contains the formula together with the second brace.
7777 To avoid that there is space between the upper brace in the first row and
7778 the formula, the row spacing need to be reduced.
7779 This is not easily possible due to a bug in LyX
7783 \begin_layout Plain Layout
7784 \begin_inset CommandInset href
7786 name "LyX-bug #1505"
7787 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7797 As solution for the problem, the global formula row separation
7807 \begin_layout Plain Layout
7815 must be changed to -6
7816 \begin_inset space \thinspace{}
7819 pt before the formula with the command
7834 is set back after the formula to the standard value of 3
7835 \begin_inset space \thinspace{}
7838 pt using the same command.
7839 More about the row separation in formulas is explained in
7840 \begin_inset CommandInset ref
7842 reference "sub:Line-Separation"
7849 \begin_layout Section
7854 \begin_layout Plain Layout
7863 \begin_layout Standard
7864 Arrows can be inserted via the math toolbar button
7865 \begin_inset Graphics
7866 filename ../images/math/leftarrow.png
7871 or the commands listed in the following subsections.
7874 \begin_layout Standard
7875 \begin_inset Newpage newpage
7881 \begin_layout Subsection
7886 \begin_layout Plain Layout
7895 \begin_layout Standard
7896 \begin_inset space \hfill{}
7900 \begin_inset Tabular
7901 <lyxtabular version="3" rows="8" columns="2">
7903 <column alignment="center" valignment="top" width="0pt">
7904 <column alignment="center" valignment="top" width="0pt">
7906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7909 \begin_layout Plain Layout
7915 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7918 \begin_layout Plain Layout
7926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7929 \begin_layout Plain Layout
7937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7940 \begin_layout Plain Layout
7941 \begin_inset Formula $\gets$
7951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7954 \begin_layout Plain Layout
7962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7965 \begin_layout Plain Layout
7966 \begin_inset Formula $\Leftarrow$
7976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7979 \begin_layout Plain Layout
7987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7990 \begin_layout Plain Layout
7991 \begin_inset Formula $\longleftarrow$
8001 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8004 \begin_layout Plain Layout
8012 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8015 \begin_layout Plain Layout
8016 \begin_inset Formula $\Longleftarrow$
8026 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8029 \begin_layout Plain Layout
8037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8040 \begin_layout Plain Layout
8041 \begin_inset Formula $\leftharpoonup$
8051 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8054 \begin_layout Plain Layout
8062 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8065 \begin_layout Plain Layout
8066 \begin_inset Formula $\leftharpoondown$
8076 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8079 \begin_layout Plain Layout
8087 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8090 \begin_layout Plain Layout
8091 \begin_inset Formula $\hookleftarrow$
8105 \begin_inset space \hfill{}
8109 \begin_inset Tabular
8110 <lyxtabular version="3" rows="8" columns="2">
8112 <column alignment="center" valignment="top" width="0pt">
8113 <column alignment="center" valignment="top" width="0pt">
8115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8118 \begin_layout Plain Layout
8124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8127 \begin_layout Plain Layout
8135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8138 \begin_layout Plain Layout
8146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8149 \begin_layout Plain Layout
8150 \begin_inset Formula $\to$
8160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8163 \begin_layout Plain Layout
8171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8174 \begin_layout Plain Layout
8175 \begin_inset Formula $\Rightarrow$
8185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8188 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8199 \begin_layout Plain Layout
8200 \begin_inset Formula $\longrightarrow$
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8213 \begin_layout Plain Layout
8221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8224 \begin_layout Plain Layout
8225 \begin_inset Formula $\Longrightarrow$
8235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8238 \begin_layout Plain Layout
8246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8249 \begin_layout Plain Layout
8250 \begin_inset Formula $\rightharpoonup$
8260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8263 \begin_layout Plain Layout
8271 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8274 \begin_layout Plain Layout
8275 \begin_inset Formula $\rightharpoondown$
8285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8288 \begin_layout Plain Layout
8296 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8299 \begin_layout Plain Layout
8300 \begin_inset Formula $\hookrightarrow$
8314 \begin_inset space \hfill{}
8320 \begin_layout Standard
8321 \begin_inset space \hfill{}
8325 \begin_inset Tabular
8326 <lyxtabular version="3" rows="6" columns="2">
8328 <column alignment="center" valignment="top" width="0pt">
8329 <column alignment="center" valignment="top" width="0pt">
8331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8334 \begin_layout Plain Layout
8340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8343 \begin_layout Plain Layout
8351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8354 \begin_layout Plain Layout
8362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8365 \begin_layout Plain Layout
8366 \begin_inset Formula $\leftrightarrow$
8376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8379 \begin_layout Plain Layout
8387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8390 \begin_layout Plain Layout
8391 \begin_inset Formula $\Leftrightarrow$
8401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8404 \begin_layout Plain Layout
8412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8415 \begin_layout Plain Layout
8416 \begin_inset Formula $\longleftrightarrow$
8426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8429 \begin_layout Plain Layout
8437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8440 \begin_layout Plain Layout
8441 \begin_inset Formula $\Longleftrightarrow$
8451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8454 \begin_layout Plain Layout
8462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8465 \begin_layout Plain Layout
8466 \begin_inset Formula $\rightleftharpoons$
8480 \begin_inset space \hspace{}
8485 \begin_inset space \hfill{}
8489 \begin_inset Tabular
8490 <lyxtabular version="3" rows="5" columns="2">
8492 <column alignment="center" valignment="top" width="0pt">
8493 <column alignment="center" valignment="top" width="0pt">
8495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8498 \begin_layout Plain Layout
8504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8507 \begin_layout Plain Layout
8515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8518 \begin_layout Plain Layout
8526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8529 \begin_layout Plain Layout
8530 \begin_inset Formula $\mapsto$
8540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8543 \begin_layout Plain Layout
8551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8554 \begin_layout Plain Layout
8555 \begin_inset Formula $\longmapsto$
8565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8568 \begin_layout Plain Layout
8576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8579 \begin_layout Plain Layout
8580 \begin_inset Formula $\leadsto$
8590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8593 \begin_layout Plain Layout
8601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8604 \begin_layout Plain Layout
8605 \begin_inset Formula $\dasharrow$
8619 \begin_inset space \hfill{}
8625 \begin_layout Standard
8626 \begin_inset VSpace medskip
8629 Arrows used as accent like e.
8630 \begin_inset space \thinspace{}
8634 \begin_inset space \space{}
8637 vector arrows are listed in
8638 \begin_inset CommandInset ref
8640 reference "sec:Accents"
8647 \begin_layout Standard
8648 \begin_inset VSpace bigskip
8651 Furthermore there are the labeled arrows
8655 \begin_layout Plain Layout
8671 \begin_layout Plain Layout
8689 \begin_layout Plain Layout
8696 \begin_layout Plain Layout
8711 When inserting one of these commands in a formula, an arrow with two blue
8712 boxes appear where the label can be inserted.
8713 The length of the arrow adapts to the label width.
8716 \begin_layout Standard
8718 \begin_inset Tabular
8719 <lyxtabular version="3" rows="3" columns="2">
8721 <column alignment="center" valignment="top" width="0pt">
8722 <column alignment="center" valignment="top" width="0pt">
8724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8727 \begin_layout Plain Layout
8733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8736 \begin_layout Plain Layout
8738 \begin_inset Note Note
8741 \begin_layout Plain Layout
8748 is only used as spacer.
8760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8763 \begin_layout Plain Layout
8770 \begin_layout Plain Layout
8780 \begin_inset Formula $\downarrow$
8784 \begin_inset Formula $\to$
8792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8795 \begin_layout Plain Layout
8796 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8809 \begin_layout Plain Layout
8816 \begin_layout Plain Layout
8826 \begin_inset Formula $\downarrow$
8830 \begin_inset Formula $\to$
8838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8841 \begin_layout Plain Layout
8842 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8858 \begin_layout Subsection
8859 Vertical and diagonal Arrows
8863 \begin_layout Plain Layout
8873 \begin_layout Plain Layout
8882 \begin_layout Standard
8883 \begin_inset space \hfill{}
8887 \begin_inset Tabular
8888 <lyxtabular version="3" rows="7" columns="2">
8890 <column alignment="center" valignment="top" width="0pt">
8891 <column alignment="center" valignment="top" width="0pt">
8893 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8896 \begin_layout Plain Layout
8902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8905 \begin_layout Plain Layout
8913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8916 \begin_layout Plain Layout
8924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8927 \begin_layout Plain Layout
8928 \begin_inset Formula $\uparrow$
8938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8941 \begin_layout Plain Layout
8949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8952 \begin_layout Plain Layout
8953 \begin_inset Formula $\Uparrow$
8963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8966 \begin_layout Plain Layout
8974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8977 \begin_layout Plain Layout
8978 \begin_inset Formula $\updownarrow$
8988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8991 \begin_layout Plain Layout
8999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9002 \begin_layout Plain Layout
9003 \begin_inset Formula $\Updownarrow$
9013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9016 \begin_layout Plain Layout
9024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9027 \begin_layout Plain Layout
9028 \begin_inset Formula $\Downarrow$
9038 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9041 \begin_layout Plain Layout
9049 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9052 \begin_layout Plain Layout
9053 \begin_inset Formula $\downarrow$
9067 \begin_inset space \hfill{}
9071 \begin_inset Tabular
9072 <lyxtabular version="3" rows="5" columns="2">
9074 <column alignment="center" valignment="top" width="0pt">
9075 <column alignment="center" valignment="top" width="0pt">
9077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9080 \begin_layout Plain Layout
9086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9089 \begin_layout Plain Layout
9097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9100 \begin_layout Plain Layout
9108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9111 \begin_layout Plain Layout
9112 \begin_inset Formula $\nearrow$
9122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9125 \begin_layout Plain Layout
9133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9136 \begin_layout Plain Layout
9137 \begin_inset Formula $\searrow$
9147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9150 \begin_layout Plain Layout
9158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9161 \begin_layout Plain Layout
9162 \begin_inset Formula $\swarrow$
9172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9175 \begin_layout Plain Layout
9183 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9186 \begin_layout Plain Layout
9187 \begin_inset Formula $\nwarrow$
9201 \begin_inset space \hfill{}
9207 \begin_layout Standard
9208 \begin_inset VSpace medskip
9211 Vertical arrows can be used also as delimiter together with the commands
9213 \begin_inset CommandInset ref
9215 reference "sub:Manual-Bracket-Size"
9220 \begin_inset CommandInset ref
9222 reference "sub:Automatic-Bracket-Size"
9229 \begin_layout Standard
9230 \begin_inset Newpage newpage
9236 \begin_layout Section
9238 \begin_inset CommandInset label
9248 \begin_layout Plain Layout
9257 \begin_layout Standard
9258 Accents can be inserted via the math toolbar button
9259 \begin_inset Graphics
9260 filename ../images/math/hat.png
9265 or the commands listed in the following subsections.
9268 \begin_layout Subsection
9269 Accents for one Character
9273 \begin_layout Plain Layout
9286 \begin_layout Plain Layout
9288 \begin_inset CommandInset ref
9290 reference "sub:Accents-in-Text"
9303 \begin_layout Plain Layout
9311 \begin_inset Note Note
9314 \begin_layout Plain Layout
9317 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9320 \begin_layout Plain Layout
9323 texorpdfstring is in section
9324 \begin_inset CommandInset ref
9326 reference "sub:Formulas-in-Section"
9336 \begin_inset CommandInset label
9338 name "sub:Accents-for-one"
9346 \begin_layout Plain Layout
9347 Accents ! for one character
9355 \begin_layout Standard
9356 \begin_inset space \hfill{}
9360 \begin_inset Tabular
9361 <lyxtabular version="3" rows="8" columns="2">
9363 <column alignment="center" valignment="top" width="0pt">
9364 <column alignment="center" valignment="top" width="0pt">
9366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9369 \begin_layout Plain Layout
9375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9378 \begin_layout Plain Layout
9380 \begin_inset Note Note
9383 \begin_layout Plain Layout
9390 is only used as spacer.
9402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9405 \begin_layout Plain Layout
9412 \begin_layout Plain Layout
9426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9429 \begin_layout Plain Layout
9430 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9443 \begin_layout Plain Layout
9450 \begin_layout Plain Layout
9464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9467 \begin_layout Plain Layout
9468 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9481 \begin_layout Plain Layout
9488 \begin_layout Plain Layout
9502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9505 \begin_layout Plain Layout
9506 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9519 \begin_layout Plain Layout
9527 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9530 \begin_layout Plain Layout
9531 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9541 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9544 \begin_layout Plain Layout
9551 \begin_layout Plain Layout
9564 \begin_layout Plain Layout
9575 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9578 \begin_layout Plain Layout
9579 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9589 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9592 \begin_layout Plain Layout
9599 \begin_layout Plain Layout
9613 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9616 \begin_layout Plain Layout
9617 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9627 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9630 \begin_layout Plain Layout
9637 \begin_layout Plain Layout
9651 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9654 \begin_layout Plain Layout
9655 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9669 \begin_inset space \hfill{}
9673 \begin_inset Tabular
9674 <lyxtabular version="3" rows="7" columns="2">
9676 <column alignment="center" valignment="top" width="0pt">
9677 <column alignment="center" valignment="top" width="0pt">
9679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9682 \begin_layout Plain Layout
9688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9691 \begin_layout Plain Layout
9699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9702 \begin_layout Plain Layout
9709 \begin_layout Plain Layout
9723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9726 \begin_layout Plain Layout
9727 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9737 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9740 \begin_layout Plain Layout
9747 \begin_layout Plain Layout
9761 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9764 \begin_layout Plain Layout
9765 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9775 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9778 \begin_layout Plain Layout
9785 \begin_layout Plain Layout
9799 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9802 \begin_layout Plain Layout
9803 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9816 \begin_layout Plain Layout
9823 \begin_layout Plain Layout
9837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9840 \begin_layout Plain Layout
9841 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9854 \begin_layout Plain Layout
9861 \begin_layout Plain Layout
9875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9878 \begin_layout Plain Layout
9879 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9892 \begin_layout Plain Layout
9899 \begin_layout Plain Layout
9913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9916 \begin_layout Plain Layout
9917 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9931 \begin_inset space \hfill{}
9937 \begin_layout Standard
9938 \begin_inset VSpace bigskip
9944 \begin_layout Standard
9945 You can directly insert accents like é to formulas.
9946 LyX will transform them to the corresponding accent command.
9951 \begin_layout Plain Layout
9957 it is better to insert a quotation mark before the vowel.
9958 These two characters are then treated by LaTeX as
9962 character when the formula part with the umlaut is marked as German.
9970 \begin_inset Quotes eld
9974 \begin_inset Quotes erd
9977 umlauts are created as demonstrated in the following example:
9980 \begin_layout Standard
9981 \begin_inset VSpace -2mm
9987 \begin_layout Standard
9989 \begin_inset Tabular
9990 <lyxtabular version="3" rows="3" columns="2">
9992 <column alignment="center" valignment="top" width="0">
9993 <column alignment="center" valignment="top" width="0">
9995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9998 \begin_layout Plain Layout
10004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10007 \begin_layout Plain Layout
10009 \begin_inset Note Note
10012 \begin_layout Plain Layout
10020 \begin_inset space \thinspace{}
10023 pt space are only used as spacer.
10035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10038 \begin_layout Plain Layout
10041 \begin_inset Quotes grd
10049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10052 \begin_layout Plain Layout
10053 \begin_inset space \hspace{}
10060 \begin_inset Formula $"i$
10070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10073 \begin_layout Plain Layout
10080 \begin_layout Plain Layout
10094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10097 \begin_layout Plain Layout
10098 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10114 \begin_layout Standard
10115 Another advantage to
10121 is that umlauts can directly be converted to mathematical text because
10122 the accent commands above are
10128 in mathematical text
10131 To convert an accented character to mathematical text, only the character
10132 under the accent may be converted.
10133 This applies also for all other conversions, e.
10134 \begin_inset space \thinspace{}
10138 \begin_inset space \space{}
10144 \begin_layout Standard
10145 In mathematical text, umlauts and other accented characters can directly
10149 \begin_layout Subsection
10150 Accents for Operators
10154 \begin_layout Plain Layout
10155 Accents ! for operators
10163 \begin_layout Standard
10174 \begin_layout Plain Layout
10192 \begin_layout Plain Layout
10200 characters can be placed above or below an operator, respectively, to accent
10212 \begin_layout Plain Layout
10220 characters can be set before and behind an operator.
10221 The command scheme is:
10224 \begin_layout Standard
10240 \begin_layout Standard
10247 must always be before the operator that should be accented.
10248 You can accent with several characters and even with other operators and
10256 for example only characters behind an operator, write nothing between the
10257 first braces but don't omit the braces.
10260 \begin_layout Standard
10261 For example the command
10266 \begin_inset Formula $\to$
10276 \begin_inset Formula $\to$
10285 \begin_layout Plain Layout
10301 \begin_inset Formula \[
10302 \sideset{}{'}\sum_{k=1}^{n}\]
10309 \begin_layout Standard
10318 \begin_layout Plain Layout
10333 \begin_layout Plain Layout
10345 \begin_inset Formula $\uparrow$
10353 \begin_inset Formula \[
10354 \overset{a}{\maltese}\]
10358 As seen in the last example, with
10370 also symbols and characters can be accented; with
10376 this is not possible.
10379 \begin_layout Subsection
10380 Accents for several Characters
10384 \begin_layout Plain Layout
10385 Accents ! for several characters
10393 \begin_layout Standard
10394 \begin_inset space \hfill{}
10398 \begin_inset Tabular
10399 <lyxtabular version="3" rows="5" columns="2">
10401 <column alignment="center" valignment="top" width="0pt">
10402 <column alignment="center" valignment="top" width="0pt">
10404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10407 \begin_layout Plain Layout
10413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10416 \begin_layout Plain Layout
10418 \begin_inset Note Note
10421 \begin_layout Plain Layout
10428 is only used as spacer.
10440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10443 \begin_layout Plain Layout
10450 \begin_layout Plain Layout
10464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10467 \begin_layout Plain Layout
10468 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10478 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10481 \begin_layout Plain Layout
10488 \begin_layout Plain Layout
10502 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10505 \begin_layout Plain Layout
10506 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10516 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10519 \begin_layout Plain Layout
10526 \begin_layout Plain Layout
10540 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10543 \begin_layout Plain Layout
10544 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10554 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10557 \begin_layout Plain Layout
10560 underleftrightarrow
10564 \begin_layout Plain Layout
10578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10581 \begin_layout Plain Layout
10582 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10596 \begin_inset space \hfill{}
10600 \begin_inset Tabular
10601 <lyxtabular version="3" rows="5" columns="2">
10603 <column alignment="center" valignment="top" width="0pt">
10604 <column alignment="center" valignment="top" width="0pt">
10606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10609 \begin_layout Plain Layout
10615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10618 \begin_layout Plain Layout
10626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10629 \begin_layout Plain Layout
10636 \begin_layout Plain Layout
10650 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10653 \begin_layout Plain Layout
10654 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10664 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10667 \begin_layout Plain Layout
10674 \begin_layout Plain Layout
10688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10691 \begin_layout Plain Layout
10692 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10705 \begin_layout Plain Layout
10712 \begin_layout Plain Layout
10726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10729 \begin_layout Plain Layout
10730 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10740 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10743 \begin_layout Plain Layout
10750 \begin_layout Plain Layout
10764 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10767 \begin_layout Plain Layout
10768 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10782 \begin_inset space \hfill{}
10788 \begin_layout Standard
10789 \begin_inset VSpace medskip
10792 With these commands as many characters as you like can be accented.
10805 will only be set in the output with a length of three characters, as shown
10806 in the following example:
10807 \begin_inset Formula \[
10808 \widetilde{A+B=C-D}\]
10815 \begin_layout Standard
10826 \begin_layout Plain Layout
10844 \begin_layout Plain Layout
10852 described in the previous subsection it is also possible to accent several
10862 \begin_layout Plain Layout
10872 \begin_inset Formula $\downarrow$
10878 \begin_inset Formula \[
10879 \underset{***}{A=B}\]
10886 \begin_layout Section
10888 \begin_inset CommandInset label
10898 \begin_layout Plain Layout
10907 \begin_layout Subsection
10909 \begin_inset CommandInset label
10911 name "sub:Predefined-Space"
10919 \begin_layout Plain Layout
10920 Space ! horizontal ! predefined
10928 \begin_layout Standard
10929 Sometimes it is necessary to insert horizontal space to a formula.
10930 This is done by inserting a protected space (shortcut
10936 \begin_inset Quotes eld
10946 \begin_layout Plain Layout
10959 \begin_inset Quotes erd
10962 appears and by pressing
10966 several times one can select one of eight different space sizes.
10967 The spaces can also be inserted using the math toolbar button
10968 \begin_inset Graphics
10969 filename ../images/math/space.png
10974 or special commands.
10975 Independent from the inserted command, one can select the size again by
10983 \begin_layout Standard
10986 \begin_inset VSpace -5mm
10990 \begin_inset Tabular
10991 <lyxtabular version="3" rows="3" columns="7">
10993 <column alignment="center" valignment="middle" width="6.8cm">
10994 <column alignment="center" valignment="top" width="0">
10995 <column alignment="center" valignment="top" width="0">
10996 <column alignment="center" valignment="top" width="0">
10997 <column alignment="center" valignment="top" width="0">
10998 <column alignment="center" valignment="top" width="0">
10999 <column alignment="center" valignment="top" width="0">
11001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11004 \begin_layout Plain Layout
11010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11013 \begin_layout Plain Layout
11021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11024 \begin_layout Plain Layout
11032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11035 \begin_layout Plain Layout
11043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11046 \begin_layout Plain Layout
11054 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11057 \begin_layout Plain Layout
11065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11068 \begin_layout Plain Layout
11078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11081 \begin_layout Plain Layout
11086 keystrokes after inserting the protected space
11091 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11094 \begin_layout Plain Layout
11100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11103 \begin_layout Plain Layout
11109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11112 \begin_layout Plain Layout
11118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11121 \begin_layout Plain Layout
11127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11130 \begin_layout Plain Layout
11136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11139 \begin_layout Plain Layout
11147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11150 \begin_layout Plain Layout
11156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11159 \begin_layout Plain Layout
11160 \begin_inset Formula $A\, B$
11168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11171 \begin_layout Plain Layout
11172 \begin_inset Formula $A\: B$
11180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11183 \begin_layout Plain Layout
11184 \begin_inset Formula $A\; B$
11192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11195 \begin_layout Plain Layout
11196 \begin_inset Formula $A\quad B$
11204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11207 \begin_layout Plain Layout
11208 \begin_inset Formula $A\qquad B$
11216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11219 \begin_layout Plain Layout
11220 \begin_inset Formula $A\! B$
11236 \begin_layout Standard
11237 The last size seem to produce no space.
11238 It is displayed red in LyX contrary to the other sizes, because it is a
11240 There are two more negative spaces:
11243 \begin_layout Standard
11245 \begin_inset Tabular
11246 <lyxtabular version="3" rows="3" columns="3">
11248 <column alignment="center" valignment="middle" width="6.8cm">
11249 <column alignment="center" valignment="top" width="0pt">
11250 <column alignment="center" valignment="top" width="0pt">
11252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11255 \begin_layout Plain Layout
11261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11264 \begin_layout Plain Layout
11272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11275 \begin_layout Plain Layout
11285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11288 \begin_layout Plain Layout
11293 keystrokes after inserting the protected space
11298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11301 \begin_layout Plain Layout
11307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11310 \begin_layout Plain Layout
11318 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11321 \begin_layout Plain Layout
11327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11330 \begin_layout Plain Layout
11331 \begin_inset Formula $A\negmedspace B$
11339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11342 \begin_layout Plain Layout
11343 \begin_inset Formula $A\negthickspace B$
11359 \begin_layout Standard
11360 Negative spaces can lead to characters overlapping each other.
11361 Thus they can be used to enforce ligatures, what is e.
11362 \begin_inset space \thinspace{}
11366 \begin_inset space \space{}
11369 useful for summation operators:
11372 \begin_layout Standard
11374 \begin_inset Tabular
11375 <lyxtabular version="3" rows="3" columns="2">
11377 <column alignment="center" valignment="top" width="0">
11378 <column alignment="center" valignment="top" width="0">
11380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11383 \begin_layout Plain Layout
11389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11392 \begin_layout Plain Layout
11394 \begin_inset Note Note
11397 \begin_layout Plain Layout
11404 is only used as spacer.
11416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11419 \begin_layout Plain Layout
11428 \begin_layout Plain Layout
11442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11445 \begin_layout Plain Layout
11446 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11459 \begin_layout Plain Layout
11470 \begin_layout Plain Layout
11484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11487 \begin_layout Plain Layout
11488 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11504 \begin_layout Standard
11505 Relations like for example equal signs, are always surrounded by space.
11506 To suppress this, the equal sign is placed into a TeX-brace.
11507 The following example demonstrates this:
11510 \begin_layout Standard
11512 \begin_inset Tabular
11513 <lyxtabular version="3" rows="2" columns="2">
11515 <column alignment="center" valignment="top" width="0pt">
11516 <column alignment="center" valignment="top" width="0pt">
11518 <cell alignment="center" valignment="top" usebox="none">
11521 \begin_layout Plain Layout
11527 <cell alignment="center" valignment="top" usebox="none">
11530 \begin_layout Plain Layout
11531 \begin_inset Formula $A=B$
11541 <cell alignment="center" valignment="top" usebox="none">
11544 \begin_layout Plain Layout
11545 \begin_inset Note Note
11548 \begin_layout Plain Layout
11555 is only used as spacer.
11561 \begin_inset Formula $\raisebox{5mm}{}$
11564 equation without space
11569 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11572 \begin_layout Plain Layout
11573 \begin_inset Formula $A{=}B$
11589 \begin_layout Standard
11591 The command for the last formula is:
11596 \begin_inset Formula $\to$
11602 \begin_layout Standard
11603 \begin_inset VSpace bigskip
11606 Spaces are needed for physical units, because the space between the value
11607 and the unit is the smallest one and not a normal space.
11608 For units in text, the smallest space is inserted via the menu
11610 Insert\SpecialChar \menuseparator
11611 Formatting\SpecialChar \menuseparator
11613 \begin_inset space ~
11621 arg "space-insert thin"
11627 \begin_layout Standard
11628 An example to visualize the difference:
11631 \begin_layout Standard
11632 \begin_inset Tabular
11633 <lyxtabular version="3" rows="2" columns="2">
11635 <column alignment="left" valignment="top" width="0">
11636 <column alignment="left" valignment="top" width="0">
11638 <cell alignment="center" valignment="top" usebox="none">
11641 \begin_layout Plain Layout
11643 \begin_inset Formula $\cdot$
11651 <cell alignment="center" valignment="top" usebox="none">
11654 \begin_layout Plain Layout
11655 space between value and unit
11662 <cell alignment="center" valignment="top" usebox="none">
11665 \begin_layout Plain Layout
11667 \begin_inset space \thinspace{}
11671 \begin_inset Formula $\cdot$
11679 <cell alignment="center" valignment="top" usebox="none">
11682 \begin_layout Plain Layout
11683 smallest space between value and unit
11696 \begin_layout Subsection
11701 \begin_layout Plain Layout
11714 \begin_layout Plain Layout
11715 for vertical space in formulas see
11716 \begin_inset CommandInset ref
11718 reference "sub:Line-Separation"
11731 \begin_layout Plain Layout
11739 \begin_inset Note Note
11742 \begin_layout Plain Layout
11745 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11748 \begin_layout Plain Layout
11751 texorpdfstring is in section
11752 \begin_inset CommandInset ref
11754 reference "sub:Formulas-in-Section"
11764 \begin_inset CommandInset label
11766 name "sub:Variable-Space"
11774 \begin_layout Plain Layout
11775 Space ! horizontal ! variable
11783 \begin_layout Standard
11784 Space with a defined length can be inserted in LyX with the command
11785 \begin_inset Newline newline
11798 \begin_layout Plain Layout
11807 For the length all units listed in
11808 \begin_inset CommandInset ref
11810 reference "tab:Available-units"
11814 are allowed, except of the unit
11815 \begin_inset Quotes eld
11819 \begin_inset Quotes erd
11823 The length may also be negative.
11824 To insert so many space that the formula uses all available space, the
11835 \begin_layout Plain Layout
11846 \begin_layout Standard
11847 \begin_inset VSpace -1mm
11853 \begin_layout Standard
11855 \begin_inset Tabular
11856 <lyxtabular version="3" rows="4" columns="2">
11858 <column alignment="center" valignment="top" width="0">
11859 <column alignment="center" valignment="top" width="0">
11861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11864 \begin_layout Plain Layout
11870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11873 \begin_layout Plain Layout
11881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11884 \begin_layout Plain Layout
11888 \begin_inset Formula $\to$
11898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11901 \begin_layout Plain Layout
11902 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11915 \begin_layout Plain Layout
11919 \begin_inset Formula $\to$
11929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11932 \begin_layout Plain Layout
11933 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11946 \begin_layout Plain Layout
11953 \begin_layout Plain Layout
11967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11970 \begin_layout Plain Layout
11971 \begin_inset Formula $A=A\hfill B=B$
11987 \begin_layout Standard
11988 In the last example the available space is given by the longest column entry
11990 In an inline formula the space depends on the length of the line in which
11998 Thus, when the line uses the full width, no space will be created.
12005 only has an effect on displayed formulas when the formula style
12010 (Formula styles are explained in
12011 \begin_inset CommandInset ref
12013 reference "sec:Formula-Styles"
12020 \begin_layout Standard
12027 , there are the commands
12039 that fill the space with a pattern, see
12040 \begin_inset CommandInset ref
12042 reference "sub:Ellipses"
12049 \begin_layout Standard
12050 For text, variable space can be inserted via the menu
12052 Insert\SpecialChar \menuseparator
12053 Formatting\SpecialChar \menuseparator
12055 \begin_inset space ~
12060 , what is not possible in formulas:
12063 \begin_layout Standard
12064 This is a line with
12065 \begin_inset space \hspace{}
12070 \begin_inset space \thinspace{}
12076 \begin_layout Standard
12077 This is a line with
12078 \begin_inset space \hfill{}
12084 \begin_layout Subsection
12085 Space besides inline Formulas
12089 \begin_layout Plain Layout
12090 Space ! besides inline formulas
12098 \begin_layout Standard
12099 The space that surrounds inline formulas can be adjusted with the length
12108 \begin_layout Plain Layout
12119 The value of a length is set with the command
12127 \begin_layout Plain Layout
12137 that has the following scheme:
12140 \begin_layout Standard
12145 setlength{length name}{value}
12148 \begin_layout Standard
12156 \begin_inset space \thinspace{}
12162 \begin_layout Standard
12172 \begin_layout Standard
12173 is inserted in TeX-mode.
12175 \begin_inset space \thinspace{}
12178 mm space will now be set around all inline formulas:
12182 \begin_layout Plain Layout
12196 \begin_layout Standard
12197 This is a line with an inline formula
12198 \begin_inset Formula $A=B$
12202 \begin_inset space \thinspace{}
12205 mm surrounding space.
12209 \begin_layout Plain Layout
12223 \begin_layout Standard
12224 To return to the predefined value,
12230 is set to the value 0
12231 \begin_inset space \thinspace{}
12237 \begin_layout Section
12242 \begin_layout Plain Layout
12252 \begin_layout Plain Layout
12257 \begin_layout Plain Layout
12268 \begin_layout Plain Layout
12283 \begin_layout Standard
12284 Boxes for text are described in chapter
12291 \begin_inset space ~
12299 \begin_layout Subsection
12301 \begin_inset CommandInset label
12303 name "sub:Boxes-with-Frame"
12311 \begin_layout Plain Layout
12320 \begin_layout Standard
12321 It is possible to frame formulas or parts of it with the commands
12331 \begin_layout Plain Layout
12349 \begin_layout Plain Layout
12360 \begin_layout Standard
12361 When one of these commands is inserted to a formula, a blue box appears
12362 within a frame to enter formula parts.
12369 an additional formula has to be created by
12377 \begin_layout Plain Layout
12378 Due to a bug in LyX it is not possible to create a new formula with
12383 \begin_inset CommandInset href
12385 name "LyX-bug #1435"
12386 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12395 , because the box content will otherwise be treated as mathematical text.
12402 is used, a new formula is automatically created inside the frame.
12405 \begin_layout Standard
12412 is not suitable to frame displayed formulas, because the formula will always
12413 be set in the size of the text.
12420 is in contrary not suitable to frame inline formulas, because the formula
12421 will always be set in the size of a displayed formula.
12424 \begin_layout Standard
12431 there is the command
12441 \begin_layout Plain Layout
12449 where additionally the frame width and the alignment can be specified.
12456 is used in the following scheme:
12459 \begin_layout Standard
12464 framebox[frame width][position]{box content}
12467 \begin_layout Standard
12468 The position can either be
12485 right aligns the formula in the box.
12486 When no position is given, the formula will be centered.
12487 \begin_inset Newline newline
12490 Is no width given, also no position can be given.
12491 In this case the frame width is adjusted to the box content like for
12500 \begin_layout Standard
12507 is inserted, a box appears containing three blue boxes.
12508 The first two boxes are surrounded by brackets and denote the two optional
12510 The third box is for formula parts like for
12519 \begin_layout Standard
12521 \begin_inset Note Note
12524 \begin_layout Plain Layout
12525 The table has been set into a minipage to make the footnote appearing.
12526 Otherwise the footnote text would not be displayed.
12532 \begin_inset Box Frameless
12541 height_special "totalheight"
12544 \begin_layout Plain Layout
12546 \begin_inset Tabular
12547 <lyxtabular version="3" rows="5" columns="2">
12549 <column alignment="center" valignment="top" width="0">
12550 <column alignment="center" valignment="top" width="0">
12552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12555 \begin_layout Plain Layout
12560 \begin_layout Plain Layout
12561 Due to a bug in LyX it is not possible to create a new formula with
12566 \begin_inset CommandInset href
12568 name "LyX-bug #1435"
12569 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12586 \begin_layout Plain Layout
12588 \begin_inset Note Note
12591 \begin_layout Plain Layout
12598 is only used as spacer.
12610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12613 \begin_layout Plain Layout
12620 \begin_layout Plain Layout
12639 \begin_layout Plain Layout
12653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12656 \begin_layout Plain Layout
12657 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12670 \begin_layout Plain Layout
12677 \begin_layout Plain Layout
12692 \begin_layout Plain Layout
12706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12709 \begin_layout Plain Layout
12710 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12723 \begin_layout Plain Layout
12730 \begin_layout Plain Layout
12744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12747 \begin_layout Plain Layout
12748 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12761 \begin_layout Plain Layout
12768 \begin_layout Plain Layout
12778 \begin_inset Formula $\to$
12782 \begin_inset Formula $\to$
12795 \begin_layout Plain Layout
12805 \begin_inset Formula $\downarrow$
12813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12816 \begin_layout Plain Layout
12817 \begin_inset Formula $\raisebox{6mm}{}$
12821 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12825 \begin_inset Formula $\raisebox{-4mm}{}$
12846 \begin_layout Standard
12847 The frame thickness can also be adjusted.
12848 To do this the following commands have to be inserted in TeX-mode before
12852 \begin_layout Standard
12862 \begin_inset Quotes eld
12866 \begin_inset Quotes erd
12880 \begin_inset Quotes eld
12884 \begin_inset Quotes erd
12890 \begin_layout Standard
12891 \begin_inset Quotes eld
12895 \begin_inset Quotes erd
12898 specifies the minimal distance between the frame and the first character
12900 An example for this is the following framed formula:
12904 \begin_layout Plain Layout
12916 \begin_inset Formula \[
12921 Before this formula the commands
12924 \begin_layout Standard
12946 \begin_layout Standard
12947 were inserted in TeX-mode.
12948 The given values are used for all following boxes.
12951 \begin_layout Standard
12952 To return to the standard frame size, the command
12955 \begin_layout Standard
12980 \begin_layout Plain Layout
12994 \begin_layout Standard
12995 is inserted in TeX-mode before the next formula.
12998 \begin_layout Subsection
12999 Boxes without Frame
13000 \begin_inset CommandInset label
13002 name "sub:Boxes-without-Frame"
13010 \begin_layout Plain Layout
13011 Boxes ! without frame
13019 \begin_layout Standard
13020 For boxes without a frame there are the following box commands:
13030 \begin_layout Plain Layout
13048 \begin_layout Plain Layout
13066 \begin_layout Plain Layout
13077 \begin_layout Standard
13084 a box can be super- or subscripted.
13085 But in contrary to normal super- and subscripting, the characters in the
13086 box keep their font size.
13093 is used in the following scheme:
13096 \begin_layout Standard
13101 raisebox{height}{box content}
13104 \begin_layout Standard
13105 When the box should contain a formula, an extra formula is needed like for
13115 \begin_layout Standard
13117 \begin_inset Tabular
13118 <lyxtabular version="3" rows="4" columns="2">
13120 <column alignment="center" valignment="top" width="0">
13121 <column alignment="center" valignment="top" width="0">
13123 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13126 \begin_layout Plain Layout
13132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13135 \begin_layout Plain Layout
13143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13146 \begin_layout Plain Layout
13150 \begin_inset Formula $\to$
13156 \begin_inset Formula $\to$
13164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13167 \begin_layout Plain Layout
13168 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13181 \begin_layout Plain Layout
13185 \begin_inset Formula $\to$
13191 \begin_inset Formula $\to$
13199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13202 \begin_layout Plain Layout
13203 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13216 \begin_layout Plain Layout
13220 \begin_inset Formula $\to$
13235 \begin_layout Plain Layout
13249 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13252 \begin_layout Plain Layout
13256 \begin_layout Plain Layout
13280 \begin_layout Standard
13281 The last formula can currently only be created using TeX-mode because LyX
13282 inserts a box instead of the needed extra formula.
13286 \begin_layout Plain Layout
13288 \begin_inset CommandInset href
13290 name "LyX-bug #1435"
13291 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13303 \begin_layout Standard
13328 , with the difference that there is no frame.
13331 \begin_layout Subsection
13333 \begin_inset CommandInset label
13335 name "sub:Colored-Boxes"
13343 \begin_layout Plain Layout
13352 \begin_layout Standard
13353 To be able to use all commands explained in this section, the LaTeX-package
13362 \begin_layout Plain Layout
13367 is part of every LaTeX standard installation.
13376 \begin_layout Plain Layout
13382 has to be loaded in the LaTeX-preamble with the line
13386 \begin_layout Plain Layout
13387 When text is colored somewhere in the document with a predefined color,
13388 LyX loads the LaTeX-package
13393 Thus it is possible that the package is loaded twice, but this doesn't
13400 \begin_inset Note Note
13403 \begin_layout Plain Layout
13404 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13413 \begin_layout Standard
13421 \begin_layout Standard
13422 \begin_inset VSpace medskip
13425 To color boxes, the command
13435 \begin_layout Plain Layout
13443 is used in the following scheme:
13446 \begin_layout Standard
13451 colorbox{color}{box content}
13454 \begin_layout Standard
13455 The box content can also be a box and a
13461 can also be part of another box (see the 2nd and 3rd example).
13462 When the box should contain a formula, an extra formula has to be created,
13473 \begin_layout Plain Layout
13474 This also applies for the command
13482 \begin_inset CommandInset href
13484 name "LyX-bug #1435"
13485 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13497 \begin_layout Standard
13498 One of the following predefined colors can be chosen:
13501 \begin_layout Standard
13535 \begin_layout Standard
13537 \begin_inset Tabular
13538 <lyxtabular version="3" rows="4" columns="2">
13540 <column alignment="center" valignment="top" width="0">
13541 <column alignment="center" valignment="top" width="0">
13543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13546 \begin_layout Plain Layout
13552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13555 \begin_layout Plain Layout
13557 \begin_inset Note Note
13560 \begin_layout Plain Layout
13567 is only used as spacer.
13579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13582 \begin_layout Plain Layout
13586 \begin_inset Formula $\to$
13596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13599 \begin_layout Plain Layout
13600 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13613 \begin_layout Plain Layout
13617 \begin_inset Formula $\to$
13628 \begin_layout Plain Layout
13642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13645 \begin_layout Plain Layout
13646 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13659 \begin_layout Plain Layout
13666 \begin_layout Plain Layout
13678 \begin_inset Formula $\to$
13688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13691 \begin_layout Plain Layout
13692 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13708 \begin_layout Standard
13715 only colors the box but not the characters in the box.
13716 To color all characters, the whole formula is highlighted and the wanted
13717 color is chosen in the
13720 \begin_inset space ~
13726 The dialog can be called with the toolbar button
13727 \begin_inset Graphics
13728 filename ../images/dialog-show_character.png
13735 Edit\SpecialChar \menuseparator
13737 \begin_inset space ~
13740 Style\SpecialChar \menuseparator
13744 The formula number has then the same color as the formula.
13745 When the formula number should get another color than the formula characters,
13746 the color must be changed within the formula.
13749 \begin_layout Standard
13753 \begin_layout Standard
13756 \begin_inset Formula \begin{equation}
13757 \int A=B\label{eq:red}\end{equation}
13764 \begin_inset Formula \begin{equation}
13765 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13772 \begin_layout Standard
13774 \begin_inset CommandInset ref
13780 is completely colored red.
13781 \begin_inset Newline newline
13785 \begin_inset CommandInset ref
13787 reference "eq:redgreen"
13791 was first completely colored green to set the color for the formula number.
13792 Subsequently the formula characters were colored red.
13795 \begin_layout Standard
13796 \begin_inset VSpace bigskip
13799 To color the frame different than the rest of the box, the command
13809 \begin_layout Plain Layout
13817 is used in the following scheme:
13820 \begin_layout Standard
13825 fcolorbox{frame color}{color}{box content}
13828 \begin_layout Standard
13835 is an extension of the command
13842 The frame width is set, like for
13865 \begin_layout Plain Layout
13877 \begin_inset Formula \[
13878 \fcolorbox{cyan}{magenta}{A=B}\]
13886 \begin_layout Plain Layout
13900 \begin_layout Standard
13901 This formula was created with the command
13902 \begin_inset Newline newline
13910 \begin_inset Formula $\to$
13916 \begin_inset Formula $\to$
13926 \begin_layout Standard
13927 \begin_inset VSpace bigskip
13930 To use other colors than the predefined ones, they have to be defined first.
13933 \begin_layout Standard
13934 One can for example define the color
13935 \begin_inset Quotes eld
13943 \begin_inset Quotes erd
13946 with the LaTeX-preamble line:
13949 \begin_layout Standard
13954 definecolor{darkgreen}{cmyk}{0.5,
13972 \begin_layout Plain Layout
13983 \begin_layout Standard
13988 is the color space that denotes the colors
14005 The four comma separated numbers are the portion factor for the corresponding
14006 colors of the color space.
14007 The factors can be in the range of 0
14008 \begin_inset space \thinspace{}
14012 \begin_inset space \thinspace{}
14020 also the color space
14024 can be used for definitions.
14041 , so that there are in this case three portion factors for the corresponding
14043 Furthermore there is the color space
14047 with one portion factor for the gray value.
14050 \begin_layout Standard
14051 As example a framed box with the new defined color
14055 where the characters have been colored
14060 \begin_inset Formula \begin{equation}
14061 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14068 \begin_layout Standard
14069 Self-defined colors can also be used for text with the help of the command
14080 \begin_layout Plain Layout
14089 \begin_layout Standard
14093 \begin_layout Plain Layout
14097 textcolor{darkgreen}{
14103 \begin_inset Quotes eld
14107 \begin_inset Quotes erd
14114 \begin_layout Plain Layout
14124 \begin_layout Standard
14135 \begin_layout Plain Layout
14143 is used in the scheme
14147 textcolor{color}{characters to color}
14152 \begin_layout Subsection
14154 \begin_inset CommandInset label
14156 name "sub:Paragraph-Boxes"
14164 \begin_layout Plain Layout
14165 Boxes ! as paragraph
14173 \begin_layout Standard
14174 A box that can contain several lines and paragraphs, a so called paragraph
14175 box (parbox), can be created with the menu
14177 Insert\SpecialChar \menuseparator
14180 or the toolbar button
14181 \begin_inset Graphics
14182 filename ../images/box-insert.png
14190 \begin_layout Standard
14191 The following example shows a framed parbox in a line:
14194 \begin_layout Standard
14195 \begin_inset VSpace medskip
14199 \begin_inset Box Boxed
14208 height_special "totalheight"
14211 \begin_layout Plain Layout
14212 This is a paragraph box.
14214 \begin_inset space \thinspace{}
14217 cm long and can also contain formulas:
14218 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14229 \begin_layout Standard
14230 \begin_inset VSpace medskip
14236 \begin_layout Standard
14237 Such a box is created by right-clicking on the gray box inset.
14238 A dialog pops up showing the box properties.
14252 \begin_inset space \thinspace{}
14257 Vertical Box Alignment
14262 \begin_layout Standard
14263 \begin_inset VSpace medskip
14266 In LaTeX a parbox is created with the command
14276 \begin_layout Plain Layout
14284 that has the following scheme:
14287 \begin_layout Standard
14292 parbox[position]{width}{box content}
14295 \begin_layout Standard
14309 for bottom means that the box is aligned within the surrounding text with
14315 for top this is done with the first line.
14316 When no position is given, the box will be vertically centered, see section
14324 \begin_inset space ~
14329 manual for examples.
14332 \begin_layout Standard
14333 \begin_inset VSpace bigskip
14336 To frame formulas completely, including the formula number, the formula
14337 must be set into a parbox.
14338 To do this, the command
14352 is inserted in TeX-mode before the formula.
14361 \begin_layout Plain Layout
14371 is hereby the line width set for the document.
14372 Because the frame is outside the parbox, 2
14373 \begin_inset space \thinspace{}
14376 times the frame separation and the frame thickness must be subtracted from
14378 As this is not automatically done by LyX due to a bug
14382 \begin_layout Plain Layout
14383 \begin_inset CommandInset href
14385 name "LyX-bug #4483"
14386 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14395 , TeX-mode has to be used.
14396 To be able to multiply and subtract in arguments, the LaTeX-package
14404 \begin_layout Plain Layout
14409 is part of every LaTeX standard installation.
14418 \begin_layout Plain Layout
14424 must be loaded in the LaTeX-preamble with the line
14427 \begin_layout Standard
14435 \begin_layout Standard
14436 Behind the formula both boxes are closed by entering
14441 Here is an example:
14445 \begin_layout Plain Layout
14459 \begin_layout Standard
14463 \begin_layout Plain Layout
14481 \begin_inset Formula \begin{equation}
14482 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14490 \begin_layout Plain Layout
14501 \begin_layout Plain Layout
14515 \begin_layout Standard
14516 \begin_inset VSpace medskip
14519 As a parbox is used as argument of
14525 , there is in this case no difference between
14540 \begin_layout Standard
14541 \begin_inset VSpace bigskip
14544 Paragraph boxes are very useful to comment formulas directly.
14551 is used in combination with the command
14565 \begin_inset CommandInset ref
14567 reference "sub:User-defined-Numbering"
14574 \begin_layout Standard
14575 An example of a formula commented with
14584 \begin_layout Standard
14588 \begin_layout Plain Layout
14601 This is a description.
14602 It is distinctly separated from the formula and multiline.
14606 \begin_layout Plain Layout
14618 \begin_layout Standard
14619 Such a formula must be inserted completely in TeX-mode because LyX does
14620 not yet support the command
14627 The formula is created with the following command sequence:
14630 \begin_layout Standard
14643 is inserted in TeX-mode.
14647 \begin_layout Plain Layout
14648 When the formula style
14660 can also be replaced by
14667 (formula styles see
14668 \begin_inset CommandInset ref
14670 reference "sec:Formula-Styles"
14679 Then the description follows as normal text, and finally
14685 is inserted in TeX-mode.
14698 hereby create a displayed formula.
14701 \begin_layout Standard
14708 can be seen in this example that was
14709 \begin_inset Quotes eld
14713 \begin_inset Quotes erd
14716 using the mathematical textmode:
14717 \begin_inset Formula \[
14718 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14725 \begin_layout Section
14730 \begin_layout Plain Layout
14739 \begin_layout Subsection
14741 \begin_inset CommandInset label
14743 name "sub:Big-Operators"
14751 \begin_layout Plain Layout
14761 \begin_layout Plain Layout
14771 \begin_layout Plain Layout
14780 \begin_layout Standard
14781 To be able to use all integral operators listed here, the option
14783 Use esint package automatically
14785 must be set in the document settings under
14788 \begin_inset space ~
14796 \begin_layout Standard
14797 \begin_inset space \hfill{}
14801 \begin_inset Tabular
14802 <lyxtabular version="3" rows="11" columns="2">
14804 <column alignment="center" valignment="top" width="0pt">
14805 <column alignment="center" valignment="top" width="0pt">
14807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14810 \begin_layout Plain Layout
14816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14819 \begin_layout Plain Layout
14827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14830 \begin_layout Plain Layout
14837 \begin_layout Plain Layout
14850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14853 \begin_layout Plain Layout
14854 \begin_inset Formula $\sum$
14864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14867 \begin_layout Plain Layout
14874 \begin_layout Plain Layout
14887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14890 \begin_layout Plain Layout
14891 \begin_inset Formula $\int$
14901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14904 \begin_layout Plain Layout
14912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14915 \begin_layout Plain Layout
14916 \begin_inset Formula $\intop$
14926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14929 \begin_layout Plain Layout
14937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14940 \begin_layout Plain Layout
14941 \begin_inset Formula $\oint$
14951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14954 \begin_layout Plain Layout
14962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14965 \begin_layout Plain Layout
14966 \begin_inset Formula $\ointop$
14976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14979 \begin_layout Plain Layout
14987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14990 \begin_layout Plain Layout
14991 \begin_inset Formula $\ointctrclockwise$
15001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15004 \begin_layout Plain Layout
15012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15015 \begin_layout Plain Layout
15016 \begin_inset Formula $\ointclockwise$
15026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15029 \begin_layout Plain Layout
15037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15040 \begin_layout Plain Layout
15041 \begin_inset Formula $\sqint$
15051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15054 \begin_layout Plain Layout
15062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15065 \begin_layout Plain Layout
15066 \begin_inset Formula $\bigcap$
15076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15079 \begin_layout Plain Layout
15087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15090 \begin_layout Plain Layout
15091 \begin_inset Formula $\bigcup$
15105 \begin_inset space \hfill{}
15109 \begin_inset Tabular
15110 <lyxtabular version="3" rows="10" columns="2">
15112 <column alignment="center" valignment="top" width="0pt">
15113 <column alignment="center" valignment="top" width="0pt">
15115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15118 \begin_layout Plain Layout
15124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15127 \begin_layout Plain Layout
15135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15138 \begin_layout Plain Layout
15145 \begin_layout Plain Layout
15158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15161 \begin_layout Plain Layout
15162 \begin_inset Formula $\prod$
15172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15175 \begin_layout Plain Layout
15183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15186 \begin_layout Plain Layout
15187 \begin_inset Formula $\coprod$
15197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15200 \begin_layout Plain Layout
15208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15211 \begin_layout Plain Layout
15212 \begin_inset Formula $\bigodot$
15222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15225 \begin_layout Plain Layout
15233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15236 \begin_layout Plain Layout
15237 \begin_inset Formula $\bigotimes$
15247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15250 \begin_layout Plain Layout
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15261 \begin_layout Plain Layout
15262 \begin_inset Formula $\bigoplus$
15272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15275 \begin_layout Plain Layout
15283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15286 \begin_layout Plain Layout
15287 \begin_inset Formula $\bigwedge$
15297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15300 \begin_layout Plain Layout
15308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15311 \begin_layout Plain Layout
15312 \begin_inset Formula $\bigvee$
15322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15325 \begin_layout Plain Layout
15333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15336 \begin_layout Plain Layout
15337 \begin_inset Formula $\bigsqcup$
15347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15350 \begin_layout Plain Layout
15358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15361 \begin_layout Plain Layout
15362 \begin_inset Formula $\biguplus$
15376 \begin_inset space \hfill{}
15382 \begin_layout Standard
15383 All big operators can also be inserted via the math toolbar button
15384 \begin_inset Graphics
15385 filename ../images/math/intop.png
15393 \begin_layout Standard
15394 The operators are called big because they are bigger than the sometimes
15395 equal looking binary operators.
15396 All big operators can have limits as described in the next subsection.
15399 \begin_layout Standard
15425 \begin_inset space ~
15428 in the style the operator limits are displayed, see
15429 \begin_inset CommandInset ref
15431 reference "sub:Operator-Limits"
15439 \begin_layout Subsubsection*
15440 Advices for Integrals
15443 \begin_layout Standard
15448 in an integral is an operator, that therefore has to be set upright.
15449 This is done by highlighting the
15453 and using the keyboard shortcut
15463 \begin_layout Plain Layout
15469 \begin_inset CommandInset ref
15471 reference "sub:Font-Styles"
15481 Finally the smallest space is inserted before the
15485 , as this is usual for operators.
15489 \begin_layout Standard
15491 \begin_inset Formula $\int A(x)dx$
15495 \begin_inset Newline newline
15502 \begin_layout Plain Layout
15512 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15518 \begin_layout Standard
15519 For multiple integrals there are the following commands:
15520 \begin_inset VSpace medskip
15526 \begin_layout Standard
15527 \begin_inset space \hfill{}
15531 \begin_inset Tabular
15532 <lyxtabular version="3" rows="4" columns="2">
15534 <column alignment="center" valignment="top" width="0">
15535 <column alignment="center" valignment="top" width="0">
15537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15540 \begin_layout Plain Layout
15546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15549 \begin_layout Plain Layout
15551 \begin_inset Note Note
15554 \begin_layout Plain Layout
15561 is only used as spacer.
15573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15576 \begin_layout Plain Layout
15584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15587 \begin_layout Plain Layout
15588 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15601 \begin_layout Plain Layout
15609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15612 \begin_layout Plain Layout
15613 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15626 \begin_layout Plain Layout
15634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15637 \begin_layout Plain Layout
15638 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15652 \begin_inset space \hfill{}
15656 \begin_inset Tabular
15657 <lyxtabular version="3" rows="4" columns="2">
15659 <column alignment="center" valignment="top" width="0">
15660 <column alignment="center" valignment="top" width="0">
15662 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15665 \begin_layout Plain Layout
15671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15674 \begin_layout Plain Layout
15682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15685 \begin_layout Plain Layout
15693 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15696 \begin_layout Plain Layout
15697 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15710 \begin_layout Plain Layout
15718 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15721 \begin_layout Plain Layout
15722 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15735 \begin_layout Plain Layout
15743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15746 \begin_layout Plain Layout
15747 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15761 \begin_inset space \hfill{}
15767 \begin_layout Subsection
15769 \begin_inset CommandInset label
15771 name "sub:Operator-Limits"
15779 \begin_layout Plain Layout
15788 \begin_layout Standard
15789 Limits are created by super- and subscripts:
15792 \begin_layout Standard
15794 \begin_inset Tabular
15795 <lyxtabular version="3" rows="2" columns="2">
15797 <column alignment="center" valignment="top" width="0pt">
15798 <column alignment="center" valignment="top" width="0pt">
15800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15803 \begin_layout Plain Layout
15809 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15812 \begin_layout Plain Layout
15814 \begin_inset Note Note
15817 \begin_layout Plain Layout
15824 is only used as spacer.
15836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15839 \begin_layout Plain Layout
15848 \begin_layout Plain Layout
15858 \begin_inset Formula $\to$
15862 \begin_inset Formula $\to$
15870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15873 \begin_layout Plain Layout
15874 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15890 \begin_layout Standard
15891 Limits of inline formulas are set right beside the operator.
15892 Limits in displayed formulas are set above or below the operator, except
15893 of integral limits.
15896 \begin_layout Standard
15897 To force that the limits are set beside the operator, the cursor is set
15898 directly behind the operator and the limits type is changed with the menu
15901 Edit\SpecialChar \menuseparator
15902 Math\SpecialChar \menuseparator
15921 \begin_layout Standard
15922 The default limits type is this:
15923 \begin_inset Formula \[
15924 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15928 This is how it looks when the limits type was changed to
15935 \begin_inset Formula \[
15936 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15940 For integrals, except of
15952 , the limits are by default set beside the operator.
15953 But for multiple integrals the limits are often set below the operator.
15954 In the following example the limits type was therefore set to
15958 and so set below the integrals:
15959 \begin_inset Formula \begin{equation}
15960 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15967 \begin_layout Standard
15968 \begin_inset VSpace medskip
15971 To specify conditions for limits, the commands
15981 \begin_layout Plain Layout
15999 \begin_layout Plain Layout
16008 To create for example this expression
16009 \begin_inset Formula \begin{equation}
16010 \sum_{\begin{subarray}{c}
16012 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16019 \begin_layout Standard
16020 the following has to be done:
16021 \begin_inset Newline newline
16036 \begin_layout Plain Layout
16048 One is now in a blue box under the summation operator and insert there
16057 \begin_layout Plain Layout
16069 The blue box is now within a purple box and now several lines can be written
16071 A new line is created by inserting a line break (
16074 arg "newline-insert newline"
16079 \begin_inset Newline newline
16084 0<k<1000 Ctrl+Return
16085 \begin_inset Newline newline
16090 is typed in, a new box appears below for the new line.
16093 \begin_layout Standard
16094 The alignment of the lines can be changed to left aligned with the
16104 Edit\SpecialChar \menuseparator
16108 To get right alignment,
16116 \begin_layout Plain Layout
16127 is inserted at the beginning of the line.
16130 \begin_layout Standard
16143 with the difference that the lines are always centered.
16146 \begin_layout Standard
16147 \begin_inset VSpace bigskip
16151 \begin_inset CommandInset ref
16153 reference "eq:substack"
16157 there can be too much space beside an operator, because the characters
16158 following the operator are set beside the limits.
16161 \begin_layout Standard
16162 To avoid this, the following macro can be used in the LaTeX-preamble:
16165 \begin_layout Standard
16179 \begin_inset Newline newline
16191 \begin_inset Newline newline
16198 mathclapinternal #1#2{
16202 mathsurround =0pt #1{#2}$}}
16205 \begin_layout Standard
16206 This defines the command
16216 \begin_layout Plain Layout
16224 that sets the width of the limit to 0
16225 \begin_inset space \thinspace{}
16229 The command scheme is
16232 \begin_layout Standard
16240 \begin_layout Standard
16241 where the limit can consist of several conditions.
16244 \begin_layout Standard
16246 \begin_inset CommandInset ref
16248 reference "eq:substack"
16252 , one uses the command
16255 \begin_layout Standard
16268 \begin_layout Plain Layout
16277 0<k<1000 Ctrl+Return
16280 \begin_layout Standard
16281 to create the lower limit.
16282 The summand is now directly behind the summation operator:
16283 \begin_inset Formula \[
16284 \sum_{\mathclap{\substack{0<k<1000\\
16285 \\k\,\in\,\mathbb{N}}
16293 \begin_layout Standard
16294 \begin_inset VSpace bigskip
16297 How to use one limit for several operators is described in
16298 \begin_inset CommandInset ref
16300 reference "sub:Self-defined-Operators"
16307 \begin_layout Standard
16308 \begin_inset Newpage newpage
16314 \begin_layout Subsection
16316 \begin_inset CommandInset label
16318 name "sub:Binary-Operators"
16326 \begin_layout Plain Layout
16335 \begin_layout Standard
16336 Binary operators are surrounded by space when there is a character before
16338 \begin_inset VSpace medskip
16344 \begin_layout Standard
16345 \begin_inset space \hfill{}
16349 \begin_inset Tabular
16350 <lyxtabular version="3" rows="13" columns="2">
16352 <column alignment="center" valignment="top" width="0pt">
16353 <column alignment="center" valignment="top" width="0pt">
16355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16358 \begin_layout Plain Layout
16360 \begin_inset Note Note
16363 \begin_layout Plain Layout
16370 is only used as spacer.
16380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16383 \begin_layout Plain Layout
16391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16394 \begin_layout Plain Layout
16400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16403 \begin_layout Plain Layout
16404 \begin_inset Formula $+$
16414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16417 \begin_layout Plain Layout
16423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16426 \begin_layout Plain Layout
16427 \begin_inset Formula $-$
16437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16440 \begin_layout Plain Layout
16448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16451 \begin_layout Plain Layout
16452 \begin_inset Formula $\pm$
16462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16465 \begin_layout Plain Layout
16473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16476 \begin_layout Plain Layout
16477 \begin_inset Formula $\mp$
16487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16490 \begin_layout Plain Layout
16498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16501 \begin_layout Plain Layout
16502 \begin_inset Formula $\cdot$
16512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16515 \begin_layout Plain Layout
16523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16526 \begin_layout Plain Layout
16527 \begin_inset Formula $\times$
16537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16540 \begin_layout Plain Layout
16548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16551 \begin_layout Plain Layout
16552 \begin_inset Formula $\div$
16562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16565 \begin_layout Plain Layout
16569 \begin_layout Plain Layout
16582 \begin_layout Plain Layout
16594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16597 \begin_layout Plain Layout
16598 \begin_inset Formula $*$
16608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16611 \begin_layout Plain Layout
16619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16622 \begin_layout Plain Layout
16623 \begin_inset Formula $\star$
16633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16636 \begin_layout Plain Layout
16644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16647 \begin_layout Plain Layout
16648 \begin_inset Formula $\circ$
16658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16661 \begin_layout Plain Layout
16669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16672 \begin_layout Plain Layout
16673 \begin_inset Formula $\diamond$
16683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16686 \begin_layout Plain Layout
16694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16697 \begin_layout Plain Layout
16698 \begin_inset Formula $\bullet$
16712 \begin_inset space \hfill{}
16716 \begin_inset Tabular
16717 <lyxtabular version="3" rows="13" columns="2">
16719 <column alignment="center" valignment="top" width="0pt">
16720 <column alignment="center" valignment="top" width="0pt">
16722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16725 \begin_layout Plain Layout
16731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16734 \begin_layout Plain Layout
16742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16745 \begin_layout Plain Layout
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16756 \begin_layout Plain Layout
16757 \begin_inset Formula $\nabla$
16767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16770 \begin_layout Plain Layout
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16781 \begin_layout Plain Layout
16782 \begin_inset Formula $\bigtriangledown$
16792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16795 \begin_layout Plain Layout
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16806 \begin_layout Plain Layout
16807 \begin_inset Formula $\bigtriangleup$
16817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16820 \begin_layout Plain Layout
16828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16831 \begin_layout Plain Layout
16832 \begin_inset Formula $\Box$
16842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16845 \begin_layout Plain Layout
16853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16856 \begin_layout Plain Layout
16857 \begin_inset Formula $\cap$
16867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16870 \begin_layout Plain Layout
16878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16881 \begin_layout Plain Layout
16882 \begin_inset Formula $\cup$
16892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16895 \begin_layout Plain Layout
16903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16906 \begin_layout Plain Layout
16907 \begin_inset Formula $\dagger$
16917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16920 \begin_layout Plain Layout
16928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16931 \begin_layout Plain Layout
16932 \begin_inset Formula $\ddagger$
16942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16945 \begin_layout Plain Layout
16953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16956 \begin_layout Plain Layout
16957 \begin_inset Formula $\wr$
16967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16970 \begin_layout Plain Layout
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16981 \begin_layout Plain Layout
16982 \begin_inset Formula $\bigcirc$
16992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16995 \begin_layout Plain Layout
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17006 \begin_layout Plain Layout
17007 \begin_inset Formula $\wedge$
17017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17020 \begin_layout Plain Layout
17028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17031 \begin_layout Plain Layout
17032 \begin_inset Formula $\vee$
17046 \begin_inset space \hfill{}
17050 \begin_inset Tabular
17051 <lyxtabular version="3" rows="13" columns="2">
17053 <column alignment="center" valignment="top" width="0pt">
17054 <column alignment="center" valignment="top" width="0pt">
17056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17059 \begin_layout Plain Layout
17065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17068 \begin_layout Plain Layout
17076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17079 \begin_layout Plain Layout
17087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17090 \begin_layout Plain Layout
17091 \begin_inset Formula $\oplus$
17101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17104 \begin_layout Plain Layout
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17115 \begin_layout Plain Layout
17116 \begin_inset Formula $\ominus$
17126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17129 \begin_layout Plain Layout
17137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17140 \begin_layout Plain Layout
17141 \begin_inset Formula $\otimes$
17151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17154 \begin_layout Plain Layout
17162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17165 \begin_layout Plain Layout
17166 \begin_inset Formula $\oslash$
17176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17179 \begin_layout Plain Layout
17187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17190 \begin_layout Plain Layout
17191 \begin_inset Formula $\odot$
17201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17204 \begin_layout Plain Layout
17212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17215 \begin_layout Plain Layout
17216 \begin_inset Formula $\amalg$
17226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17229 \begin_layout Plain Layout
17237 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17240 \begin_layout Plain Layout
17241 \begin_inset Formula $\uplus$
17251 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17254 \begin_layout Plain Layout
17262 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17265 \begin_layout Plain Layout
17266 \begin_inset Formula $\setminus$
17276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17279 \begin_layout Plain Layout
17287 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17290 \begin_layout Plain Layout
17291 \begin_inset Formula $\sqcap$
17301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17304 \begin_layout Plain Layout
17312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17315 \begin_layout Plain Layout
17316 \begin_inset Formula $\sqcup$
17326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17329 \begin_layout Plain Layout
17337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17340 \begin_layout Plain Layout
17341 \begin_inset Formula $\triangleleft$
17351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17354 \begin_layout Plain Layout
17362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17365 \begin_layout Plain Layout
17366 \begin_inset Formula $\triangleright$
17380 \begin_inset space \hfill{}
17386 \begin_layout Standard
17387 All binary operators can also be inserted via the math toolbar button
17388 \begin_inset Graphics
17389 filename ../images/math/pm.png
17397 \begin_layout Standard
17398 To typeset the Laplace operator also
17415 \begin_inset Formula $\nabla^{2}$
17418 ) can be used instead of
17427 \begin_layout Standard
17434 Insert\SpecialChar \menuseparator
17446 \begin_layout Subsection
17447 Self-defined Operators
17448 \begin_inset CommandInset label
17450 name "sub:Self-defined-Operators"
17458 \begin_layout Plain Layout
17459 Operators ! self-defined
17467 \begin_layout Standard
17468 With the help of the command
17472 DeclareMathOperator
17478 \begin_layout Plain Layout
17483 DeclareMathOperator
17488 custom operators can be defined in the LaTeX-preamble.
17489 Its command scheme is:
17492 \begin_layout Standard
17497 DeclareMathOperator{new command}{display}
17500 \begin_layout Standard
17501 Display can be characters or symbols that define how the operator looks
17503 To define a big operator a * is set behind the command.
17504 All self-defined big operators can have limits as described in
17505 \begin_inset CommandInset ref
17507 reference "sub:Operator-Limits"
17514 \begin_layout Standard
17515 For example the LaTeX-preamble line
17518 \begin_layout Standard
17523 DeclareMathOperator*{
17530 \begin_layout Standard
17531 defines the command
17537 , that inserts a big operator consisting of the lozenge symbol from
17538 \begin_inset CommandInset ref
17540 reference "sub:Miscellaneous-Symbols"
17545 \begin_inset Formula \[
17546 \Lozenge_{n=1}^{\infty}\]
17550 The command for this formula is:
17561 \begin_inset Formula $\to$
17567 \begin_layout Standard
17568 \begin_inset VSpace bigskip
17571 When self-defined operators are not used several times in the document,
17572 they can also be defined with the commands
17582 \begin_layout Plain Layout
17600 \begin_layout Plain Layout
17608 , which have the following scheme:
17611 \begin_layout Standard
17625 \begin_layout Standard
17632 defines big operators,
17641 \begin_layout Standard
17649 \begin_inset space \thinspace{}
17653 \begin_inset space \space{}
17656 be used to use one limit for several operators:
17659 \begin_layout Standard
17660 \begin_inset Formula \[
17661 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17668 \begin_layout Standard
17669 The command for the formula above is:
17670 \begin_inset Newline newline
17689 \begin_layout Plain Layout
17701 \begin_inset Formula $\to$
17710 \begin_layout Plain Layout
17724 \begin_layout Section
17729 \begin_layout Plain Layout
17738 \begin_layout Subsection
17740 \begin_inset CommandInset label
17742 name "sub:Font-Styles"
17750 \begin_layout Plain Layout
17759 \begin_layout Standard
17760 Latin letters in formulas can be set in one of the following font styles:
17761 \begin_inset VSpace -2mm
17767 \begin_layout Standard
17769 \begin_inset Tabular
17770 <lyxtabular version="3" rows="6" columns="3">
17772 <column alignment="center" valignment="top" width="0">
17773 <column alignment="center" valignment="top" width="0">
17774 <column alignment="center" valignment="top" width="0">
17776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17779 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17797 \begin_layout Plain Layout
17805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17808 \begin_layout Plain Layout
17817 \begin_layout Plain Layout
17833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17836 \begin_layout Plain Layout
17837 \begin_inset Formula $\mathbb{ABC}$
17845 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17848 \begin_layout Plain Layout
17861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17864 \begin_layout Plain Layout
17873 \begin_layout Plain Layout
17889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17892 \begin_layout Plain Layout
17893 \begin_inset Formula $\mathbf{AbC}$
17901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17904 \begin_layout Plain Layout
17917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17920 \begin_layout Plain Layout
17929 \begin_layout Plain Layout
17945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17948 \begin_layout Plain Layout
17949 \begin_inset Formula $\boldsymbol{AbC}$
17957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17960 \begin_layout Plain Layout
17963 arg "font-boldsymbol"
17973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17976 \begin_layout Plain Layout
17985 \begin_layout Plain Layout
18001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18004 \begin_layout Plain Layout
18005 \begin_inset Formula $\mathcal{ABC}$
18013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18016 \begin_layout Plain Layout
18029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18032 \begin_layout Plain Layout
18041 \begin_layout Plain Layout
18057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18060 \begin_layout Plain Layout
18061 \begin_inset Formula $\mathfrak{AbC}$
18069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18072 \begin_layout Plain Layout
18086 \begin_layout Standard
18088 \begin_inset Tabular
18089 <lyxtabular version="3" rows="5" columns="3">
18091 <column alignment="center" valignment="top" width="0">
18092 <column alignment="center" valignment="top" width="0">
18093 <column alignment="center" valignment="top" width="0">
18095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18098 \begin_layout Plain Layout
18104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18107 \begin_layout Plain Layout
18113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18116 \begin_layout Plain Layout
18124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18127 \begin_layout Plain Layout
18136 \begin_layout Plain Layout
18152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18155 \begin_layout Plain Layout
18156 \begin_inset Formula $\mathit{AbC}$
18164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18167 \begin_layout Plain Layout
18175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18178 \begin_layout Plain Layout
18187 \begin_layout Plain Layout
18203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18206 \begin_layout Plain Layout
18207 \begin_inset Formula $\mathrm{AbC}$
18215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18218 \begin_layout Plain Layout
18231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18234 \begin_layout Plain Layout
18243 \begin_layout Plain Layout
18259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18262 \begin_layout Plain Layout
18263 \begin_inset Formula $\mathsf{AbC}$
18271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18274 \begin_layout Plain Layout
18287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18290 \begin_layout Plain Layout
18299 \begin_layout Plain Layout
18315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18318 \begin_layout Plain Layout
18319 \begin_inset Formula $\mathtt{AbC}$
18327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18330 \begin_layout Plain Layout
18333 arg "font-typewriter"
18349 \begin_layout Standard
18350 \begin_inset Note Greyedout
18353 \begin_layout Plain Layout
18370 can only be used for big letters.
18378 \begin_layout Standard
18379 Predefined is the style
18388 \begin_layout Standard
18389 The style commands work also for letters in mathematical constructs:
18390 \begin_inset Formula \[
18391 \mathfrak{A=\frac{b}{C}}\]
18398 \begin_layout Standard
18399 Characters in mathematical text don't appear in a math font style but in
18400 the text font style
18407 That their style can't be set correctly via the text style dialog is a
18412 \begin_layout Plain Layout
18413 \begin_inset CommandInset href
18415 name "LyX-bug #4091"
18416 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18428 \begin_layout Standard
18429 Instead of the style commands the dialog
18431 Edit\SpecialChar \menuseparator
18432 Math\SpecialChar \menuseparator
18435 or the toolbar button
18436 \begin_inset Graphics
18437 filename ../images/math/font.png
18445 \begin_layout Subsection
18447 \begin_inset CommandInset label
18449 name "sub:Bold-Formulas"
18457 \begin_layout Plain Layout
18466 \begin_layout Standard
18467 To make a complete formula bold, the command
18473 from the previous subsection cannot be used, because it doesn't work for
18474 small Greek letters.
18475 Furthermore it prints Latin letters always upright, like in the following
18479 \begin_layout Standard
18480 \begin_inset Formula \[
18481 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18488 \begin_layout Standard
18489 To display the formula correctly, the command
18496 \begin_inset Formula \[
18497 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18501 It is also possible to set the formula in a
18503 boldmath environment
18506 This environment is created by inserting the command
18514 \begin_layout Plain Layout
18525 To end the environment, the command
18533 \begin_layout Plain Layout
18543 is inserted in TeX-mode.
18547 \begin_layout Plain Layout
18557 \begin_inset Formula \[
18558 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18566 \begin_layout Plain Layout
18578 \begin_layout Subsection
18583 \begin_layout Plain Layout
18592 \begin_layout Standard
18593 Formulas can be colored like normal text: Highlight a formula or a formula
18599 Here is a formula in magenta:
18600 \begin_inset Formula \[
18601 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18608 \begin_layout Standard
18609 You can also define your own colors as described in
18610 \begin_inset CommandInset ref
18612 reference "sub:Colored-Boxes"
18617 They can be used with the TeX code command
18627 \begin_layout Plain Layout
18638 \begin_layout Standard
18643 textcolor{color}{characters or formula}
18646 \begin_layout Standard
18647 The following example was colored completely dark green and partly red:
18650 \begin_layout Standard
18654 \begin_layout Plain Layout
18658 textcolor{darkgreen}{
18664 \begin_inset Formula \[
18665 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18673 \begin_layout Plain Layout
18683 \begin_layout Standard
18684 Due to a bug in LyX only complete formulas can be colored with self-defined
18689 \begin_layout Plain Layout
18690 \begin_inset CommandInset href
18692 name "LyX-bug #5269"
18693 target "http://bugzilla.lyx.org/show_bug.cgi?id=5269"
18705 \begin_layout Subsection
18707 \begin_inset CommandInset label
18709 name "sub:Font-Sizes"
18717 \begin_layout Plain Layout
18726 \begin_layout Standard
18727 For characters in formulas there are, analog to characters in text, the
18728 following size commands:
18731 \begin_layout Standard
18775 \begin_inset Newline newline
18797 \begin_layout Standard
18798 The size produced by the commands depends on the document font size, that
18799 corresponds with the command
18806 The other commands produce smaller or larger sizes than
18813 The font size can however not exceed a certain value.
18814 Is for example the document font size 12
18815 \begin_inset space \thinspace{}
18824 switches to the same size as
18834 \begin_layout Standard
18835 A size command is inserted in TeX-mode before the formula and sets the size
18836 for all following formula and text characters.
18837 To switch back to the initial size, the command
18843 is inserted behind the formula in TeX-mode.
18846 \begin_layout Standard
18847 Within a formula the size can only be changed for symbols or letters in
18849 To do this, the size command is inserted in mathematical text.
18850 All following characters until the end of the mathematical text or until
18851 another size command will have the selected size.
18853 \begin_inset VSpace -2mm
18859 \begin_layout Standard
18863 \begin_layout Plain Layout
18873 \begin_inset Formula \[
18874 A=\frac{B}{c}\cdot\maltese\]
18879 \begin_inset Formula \[
18880 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18888 \begin_layout Plain Layout
18900 \begin_layout Standard
18901 \begin_inset VSpace medskip
18904 Before both formulas the command
18911 The command for the second formula is:
18912 \begin_inset Newline newline
18923 \begin_layout Plain Layout
18938 \begin_layout Plain Layout
18953 \begin_layout Plain Layout
18968 \begin_layout Plain Layout
18978 \begin_inset Formula $\to$
18982 \begin_inset Formula $\to$
18986 \begin_inset Newline newline
18990 \begin_inset space \hspace*{}
19004 \begin_layout Plain Layout
19019 \begin_layout Plain Layout
19034 \begin_layout Plain Layout
19046 \begin_layout Standard
19047 If a symbol cannot be displayed in different sizes, it will always be displayed
19048 in the default size.
19051 \begin_layout Section
19056 \begin_layout Plain Layout
19065 \begin_layout Standard
19066 All Greek letters can also be inserted via the toolbar button
19067 \begin_inset Graphics
19068 filename ../images/math/alpha.png
19076 \begin_layout Subsection
19081 \begin_layout Plain Layout
19082 Greek letters ! small
19090 \begin_layout Standard
19091 \begin_inset space \hfill{}
19095 \begin_inset Tabular
19096 <lyxtabular version="3" rows="11" columns="2">
19098 <column alignment="center" valignment="top" width="0pt">
19099 <column alignment="center" valignment="top" width="0pt">
19101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19104 \begin_layout Plain Layout
19110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19113 \begin_layout Plain Layout
19121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19124 \begin_layout Plain Layout
19132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19135 \begin_layout Plain Layout
19136 \begin_inset Formula $\alpha$
19146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19149 \begin_layout Plain Layout
19157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19160 \begin_layout Plain Layout
19161 \begin_inset Formula $\beta$
19171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19174 \begin_layout Plain Layout
19182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19185 \begin_layout Plain Layout
19186 \begin_inset Formula $\gamma$
19196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19199 \begin_layout Plain Layout
19207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19210 \begin_layout Plain Layout
19211 \begin_inset Formula $\delta$
19221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19224 \begin_layout Plain Layout
19232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19235 \begin_layout Plain Layout
19236 \begin_inset Formula $\epsilon$
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19249 \begin_layout Plain Layout
19257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19260 \begin_layout Plain Layout
19261 \begin_inset Formula $\varepsilon$
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19274 \begin_layout Plain Layout
19282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19285 \begin_layout Plain Layout
19286 \begin_inset Formula $\zeta$
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19299 \begin_layout Plain Layout
19307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19310 \begin_layout Plain Layout
19311 \begin_inset Formula $\eta$
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19324 \begin_layout Plain Layout
19332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19335 \begin_layout Plain Layout
19336 \begin_inset Formula $\theta$
19346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19349 \begin_layout Plain Layout
19357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19360 \begin_layout Plain Layout
19361 \begin_inset Formula $\vartheta$
19375 \begin_inset space \hfill{}
19379 \begin_inset Tabular
19380 <lyxtabular version="3" rows="12" columns="2">
19382 <column alignment="center" valignment="top" width="0pt">
19383 <column alignment="center" valignment="top" width="0pt">
19385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19408 \begin_layout Plain Layout
19416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19419 \begin_layout Plain Layout
19420 \begin_inset Formula $\iota$
19430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19433 \begin_layout Plain Layout
19441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19444 \begin_layout Plain Layout
19445 \begin_inset Formula $\kappa$
19455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19458 \begin_layout Plain Layout
19466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19469 \begin_layout Plain Layout
19470 \begin_inset Formula $\varkappa$
19480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19483 \begin_layout Plain Layout
19491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19494 \begin_layout Plain Layout
19495 \begin_inset Formula $\lambda$
19505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19508 \begin_layout Plain Layout
19516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19519 \begin_layout Plain Layout
19520 \begin_inset Formula $\mu$
19530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19533 \begin_layout Plain Layout
19541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19544 \begin_layout Plain Layout
19545 \begin_inset Formula $\nu$
19555 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19558 \begin_layout Plain Layout
19566 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19569 \begin_layout Plain Layout
19570 \begin_inset Formula $\xi$
19580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19583 \begin_layout Plain Layout
19589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19592 \begin_layout Plain Layout
19593 \begin_inset Formula $o$
19603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19606 \begin_layout Plain Layout
19614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19617 \begin_layout Plain Layout
19618 \begin_inset Formula $\pi$
19628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19631 \begin_layout Plain Layout
19639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19642 \begin_layout Plain Layout
19643 \begin_inset Formula $\varpi$
19653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19656 \begin_layout Plain Layout
19664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19667 \begin_layout Plain Layout
19668 \begin_inset Formula $\rho$
19682 \begin_inset space \hfill{}
19686 \begin_inset Tabular
19687 <lyxtabular version="3" rows="11" columns="2">
19689 <column alignment="center" valignment="top" width="0pt">
19690 <column alignment="center" valignment="top" width="0pt">
19692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19695 \begin_layout Plain Layout
19701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19704 \begin_layout Plain Layout
19712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19715 \begin_layout Plain Layout
19723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19726 \begin_layout Plain Layout
19727 \begin_inset Formula $\varrho$
19737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19740 \begin_layout Plain Layout
19748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19751 \begin_layout Plain Layout
19752 \begin_inset Formula $\sigma$
19762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19765 \begin_layout Plain Layout
19773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19776 \begin_layout Plain Layout
19777 \begin_inset Formula $\varsigma$
19787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19790 \begin_layout Plain Layout
19798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19801 \begin_layout Plain Layout
19802 \begin_inset Formula $\tau$
19812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19815 \begin_layout Plain Layout
19823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19826 \begin_layout Plain Layout
19827 \begin_inset Formula $\upsilon$
19837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19840 \begin_layout Plain Layout
19848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19851 \begin_layout Plain Layout
19852 \begin_inset Formula $\phi$
19862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19865 \begin_layout Plain Layout
19873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19876 \begin_layout Plain Layout
19877 \begin_inset Formula $\varphi$
19887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19890 \begin_layout Plain Layout
19898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19901 \begin_layout Plain Layout
19902 \begin_inset Formula $\chi$
19912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19915 \begin_layout Plain Layout
19923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19926 \begin_layout Plain Layout
19927 \begin_inset Formula $\psi$
19937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19940 \begin_layout Plain Layout
19948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19951 \begin_layout Plain Layout
19952 \begin_inset Formula $\omega$
19966 \begin_inset space \hfill{}
19972 \begin_layout Standard
19973 \begin_inset VSpace medskip
19979 \begin_layout Standard
19980 How to create upright Greek letters is explained in
19981 \begin_inset CommandInset ref
19983 reference "sub:Upright-small-Greek"
19990 \begin_layout Subsection
19995 \begin_layout Plain Layout
19996 Greek letters ! big
20004 \begin_layout Standard
20005 \begin_inset space \hfill{}
20009 \begin_inset Tabular
20010 <lyxtabular version="3" rows="7" columns="2">
20012 <column alignment="center" valignment="top" width="0pt">
20013 <column alignment="center" valignment="top" width="0pt">
20015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20018 \begin_layout Plain Layout
20024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20027 \begin_layout Plain Layout
20035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20038 \begin_layout Plain Layout
20046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20049 \begin_layout Plain Layout
20050 \begin_inset Formula $\Gamma$
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20063 \begin_layout Plain Layout
20071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20074 \begin_layout Plain Layout
20075 \begin_inset Formula $\Delta$
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20088 \begin_layout Plain Layout
20096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20099 \begin_layout Plain Layout
20100 \begin_inset Formula $\Theta$
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20113 \begin_layout Plain Layout
20121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20124 \begin_layout Plain Layout
20125 \begin_inset Formula $\Lambda$
20135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20138 \begin_layout Plain Layout
20146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20149 \begin_layout Plain Layout
20150 \begin_inset Formula $\Xi$
20160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20163 \begin_layout Plain Layout
20171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20174 \begin_layout Plain Layout
20175 \begin_inset Formula $\Pi$
20189 \begin_inset space \hfill{}
20193 \begin_inset Tabular
20194 <lyxtabular version="3" rows="6" columns="2">
20196 <column alignment="center" valignment="top" width="0pt">
20197 <column alignment="center" valignment="top" width="0pt">
20199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20202 \begin_layout Plain Layout
20208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20211 \begin_layout Plain Layout
20219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20222 \begin_layout Plain Layout
20230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20233 \begin_layout Plain Layout
20234 \begin_inset Formula $\Sigma$
20244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20247 \begin_layout Plain Layout
20255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20258 \begin_layout Plain Layout
20259 \begin_inset Formula $\Upsilon$
20269 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20272 \begin_layout Plain Layout
20280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20283 \begin_layout Plain Layout
20284 \begin_inset Formula $\Phi$
20294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20297 \begin_layout Plain Layout
20305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20308 \begin_layout Plain Layout
20309 \begin_inset Formula $\Psi$
20319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20322 \begin_layout Plain Layout
20330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20333 \begin_layout Plain Layout
20334 \begin_inset Formula $\Omega$
20348 \begin_inset space \hfill{}
20354 \begin_layout Standard
20355 \begin_inset VSpace medskip
20358 That the big Greek letters appear upright is caused by a design bug when
20360 To get correct italic big letters, begin every command with
20365 For example the command
20372 \begin_inset Formula $\varGamma$
20378 \begin_layout Subsection
20383 \begin_layout Plain Layout
20384 Greek letters ! bold
20392 \begin_layout Standard
20393 Greek letters cannot be set with different font styles like Latin letters.
20394 They can only be made bold with the command
20404 \begin_layout Plain Layout
20415 \begin_layout Standard
20417 \begin_inset Tabular
20418 <lyxtabular version="3" rows="3" columns="2">
20420 <column alignment="center" valignment="top" width="0">
20421 <column alignment="center" valignment="top" width="0">
20423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20426 \begin_layout Plain Layout
20432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20435 \begin_layout Plain Layout
20443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20446 \begin_layout Plain Layout
20458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20461 \begin_layout Plain Layout
20462 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20475 \begin_layout Plain Layout
20487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20490 \begin_layout Plain Layout
20491 \begin_inset Formula $\theta\boldsymbol{\theta}$
20507 \begin_layout Section
20512 \begin_layout Plain Layout
20525 \begin_layout Plain Layout
20526 A list with all symbols of most of the LaTeX-packages can be found in
20527 \begin_inset CommandInset citation
20542 \begin_layout Plain Layout
20550 \begin_inset Note Note
20553 \begin_layout Plain Layout
20556 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20559 \begin_layout Plain Layout
20562 texorpdfstring is in section
20563 \begin_inset CommandInset ref
20565 reference "sub:Formulas-in-Section"
20578 \begin_layout Plain Layout
20587 \begin_layout Standard
20588 Many of the symbols listed in this section can also be inserted via the
20590 \begin_inset Graphics
20591 filename ../images/math/nabla.png
20597 \begin_inset Graphics
20598 filename ../images/math/digamma.png
20606 \begin_layout Subsection
20607 Mathematical Symbols
20608 \begin_inset CommandInset label
20610 name "sub:Mathematical-Symbols"
20618 \begin_layout Plain Layout
20619 Symbols ! mathematical
20627 \begin_layout Standard
20628 \begin_inset space \hfill{}
20632 \begin_inset Tabular
20633 <lyxtabular version="3" rows="10" columns="2">
20635 <column alignment="center" valignment="top" width="0pt">
20636 <column alignment="center" valignment="top" width="0pt">
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20661 \begin_layout Plain Layout
20669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20672 \begin_layout Plain Layout
20673 \begin_inset Formula $\neg$
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20686 \begin_layout Plain Layout
20694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20697 \begin_layout Plain Layout
20698 \begin_inset Formula $\Im$
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20711 \begin_layout Plain Layout
20719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20722 \begin_layout Plain Layout
20723 \begin_inset Formula $\Re$
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20736 \begin_layout Plain Layout
20744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20747 \begin_layout Plain Layout
20748 \begin_inset Formula $\aleph$
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20772 \begin_layout Plain Layout
20773 \begin_inset Formula $\partial$
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20786 \begin_layout Plain Layout
20794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20797 \begin_layout Plain Layout
20798 \begin_inset Formula $\infty$
20808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20811 \begin_layout Plain Layout
20819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20822 \begin_layout Plain Layout
20823 \begin_inset Formula $\wp$
20833 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20836 \begin_layout Plain Layout
20844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20847 \begin_layout Plain Layout
20848 \begin_inset Formula $\imath$
20858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20861 \begin_layout Plain Layout
20869 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20872 \begin_layout Plain Layout
20873 \begin_inset Formula $\jmath$
20887 \begin_inset space \hfill{}
20891 \begin_inset Tabular
20892 <lyxtabular version="3" rows="10" columns="2">
20894 <column alignment="center" valignment="top" width="0pt">
20895 <column alignment="center" valignment="top" width="0pt">
20897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20900 \begin_layout Plain Layout
20906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20909 \begin_layout Plain Layout
20911 \begin_inset Note Note
20914 \begin_layout Plain Layout
20921 is only used as spacer.
20933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20936 \begin_layout Plain Layout
20944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20947 \begin_layout Plain Layout
20948 \begin_inset Formula $\forall$
20958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20961 \begin_layout Plain Layout
20969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20972 \begin_layout Plain Layout
20973 \begin_inset Formula $\exists$
20983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20986 \begin_layout Plain Layout
20994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20997 \begin_layout Plain Layout
20998 \begin_inset Formula $\nexists$
21008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21011 \begin_layout Plain Layout
21019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21022 \begin_layout Plain Layout
21023 \begin_inset Formula $\emptyset$
21033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21036 \begin_layout Plain Layout
21044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21047 \begin_layout Plain Layout
21048 \begin_inset Formula $\varnothing$
21058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21061 \begin_layout Plain Layout
21069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21072 \begin_layout Plain Layout
21073 \begin_inset Formula $\dag$
21083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21086 \begin_layout Plain Layout
21094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21097 \begin_layout Plain Layout
21098 \begin_inset Formula $\ddag$
21108 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21111 \begin_layout Plain Layout
21119 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21122 \begin_layout Plain Layout
21126 \begin_layout Plain Layout
21136 \begin_inset Formula $\complement$
21143 \begin_layout Plain Layout
21157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21160 \begin_layout Plain Layout
21168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21171 \begin_layout Plain Layout
21172 \begin_inset Formula $\Bbbk$
21186 \begin_inset space \hfill{}
21190 \begin_inset Tabular
21191 <lyxtabular version="3" rows="10" columns="2">
21193 <column alignment="center" valignment="top" width="0pt">
21194 <column alignment="center" valignment="top" width="0pt">
21196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21199 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21219 \begin_layout Plain Layout
21227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21230 \begin_layout Plain Layout
21231 \begin_inset Formula $\prime$
21241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21244 \begin_layout Plain Layout
21252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21255 \begin_layout Plain Layout
21256 \begin_inset Formula $\backprime$
21266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21269 \begin_layout Plain Layout
21277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21280 \begin_layout Plain Layout
21281 \begin_inset Formula $\mho$
21291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21294 \begin_layout Plain Layout
21302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21305 \begin_layout Plain Layout
21306 \begin_inset Formula $\triangle$
21316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21319 \begin_layout Plain Layout
21327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21330 \begin_layout Plain Layout
21331 \begin_inset Formula $\angle$
21341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21344 \begin_layout Plain Layout
21352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21355 \begin_layout Plain Layout
21356 \begin_inset Formula $\measuredangle$
21366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21369 \begin_layout Plain Layout
21377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21380 \begin_layout Plain Layout
21381 \begin_inset Formula $\sphericalangle$
21391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21394 \begin_layout Plain Layout
21402 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21405 \begin_layout Plain Layout
21406 \begin_inset Formula $\top$
21416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21419 \begin_layout Plain Layout
21427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21430 \begin_layout Plain Layout
21431 \begin_inset Formula $\bot$
21445 \begin_inset space \hfill{}
21451 \begin_layout Subsection
21452 Miscellaneous Symbols
21453 \begin_inset CommandInset label
21455 name "sub:Miscellaneous-Symbols"
21463 \begin_layout Plain Layout
21464 Symbols ! miscellaneous
21472 \begin_layout Standard
21475 \begin_inset Tabular
21476 <lyxtabular version="3" rows="10" columns="2">
21478 <column alignment="center" valignment="top" width="0pt">
21479 <column alignment="center" valignment="top" width="0pt">
21481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21484 \begin_layout Plain Layout
21490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21493 \begin_layout Plain Layout
21501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21504 \begin_layout Plain Layout
21512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21515 \begin_layout Plain Layout
21516 \begin_inset Formula $\flat$
21526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21529 \begin_layout Plain Layout
21537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21540 \begin_layout Plain Layout
21541 \begin_inset Formula $\natural$
21551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21554 \begin_layout Plain Layout
21562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21565 \begin_layout Plain Layout
21566 \begin_inset Formula $\sharp$
21576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21579 \begin_layout Plain Layout
21587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21590 \begin_layout Plain Layout
21591 \begin_inset Formula $\surd$
21601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21604 \begin_layout Plain Layout
21612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21615 \begin_layout Plain Layout
21616 \begin_inset Formula $\checkmark$
21626 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21629 \begin_layout Plain Layout
21637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21640 \begin_layout Plain Layout
21641 \begin_inset Formula $\yen$
21651 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21654 \begin_layout Plain Layout
21662 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21665 \begin_layout Plain Layout
21666 \begin_inset Formula $\pounds$
21676 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21679 \begin_layout Plain Layout
21685 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21688 \begin_layout Plain Layout
21689 \begin_inset Formula $\$$
21699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21702 \begin_layout Plain Layout
21708 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21711 \begin_layout Plain Layout
21712 \begin_inset Formula $§$
21726 \begin_inset Tabular
21727 <lyxtabular version="3" rows="10" columns="2">
21729 <column alignment="center" valignment="top" width="0">
21730 <column alignment="center" valignment="top" width="0">
21732 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21735 \begin_layout Plain Layout
21741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21744 \begin_layout Plain Layout
21752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21755 \begin_layout Plain Layout
21763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21766 \begin_layout Plain Layout
21767 \begin_inset Formula $\hbar$
21777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21780 \begin_layout Plain Layout
21788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21791 \begin_layout Plain Layout
21792 \begin_inset Formula $\hslash$
21802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21805 \begin_layout Plain Layout
21813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21816 \begin_layout Plain Layout
21817 \begin_inset Formula $\clubsuit$
21827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21830 \begin_layout Plain Layout
21838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21841 \begin_layout Plain Layout
21842 \begin_inset Formula $\spadesuit$
21852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21855 \begin_layout Plain Layout
21863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21866 \begin_layout Plain Layout
21867 \begin_inset Formula $\bigstar$
21877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21880 \begin_layout Plain Layout
21888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21891 \begin_layout Plain Layout
21892 \begin_inset Formula $\blacklozenge$
21902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21905 \begin_layout Plain Layout
21913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21916 \begin_layout Plain Layout
21917 \begin_inset Formula $\blacktriangle$
21927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21930 \begin_layout Plain Layout
21938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21941 \begin_layout Plain Layout
21942 \begin_inset Formula $\blacktriangledown$
21952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21955 \begin_layout Plain Layout
21963 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21966 \begin_layout Plain Layout
21967 \begin_inset Formula $\bullet$
21981 \begin_inset Tabular
21982 <lyxtabular version="3" rows="10" columns="2">
21984 <column alignment="center" valignment="top" width="0pt">
21985 <column alignment="center" valignment="top" width="0pt">
21987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21990 \begin_layout Plain Layout
21996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22010 \begin_layout Plain Layout
22018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22021 \begin_layout Plain Layout
22022 \begin_inset Formula $\diamondsuit$
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22035 \begin_layout Plain Layout
22043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22046 \begin_layout Plain Layout
22047 \begin_inset Formula $\Diamond$
22057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22060 \begin_layout Plain Layout
22068 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22071 \begin_layout Plain Layout
22072 \begin_inset Formula $\heartsuit$
22082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22085 \begin_layout Plain Layout
22093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22096 \begin_layout Plain Layout
22097 \begin_inset Formula $\P$
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22110 \begin_layout Plain Layout
22118 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22121 \begin_layout Plain Layout
22122 \begin_inset Formula $\copyright$
22132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22135 \begin_layout Plain Layout
22143 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22146 \begin_layout Plain Layout
22147 \begin_inset Formula $\circledR$
22157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22160 \begin_layout Plain Layout
22168 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22171 \begin_layout Plain Layout
22172 \begin_inset Formula $\maltese$
22182 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22185 \begin_layout Plain Layout
22193 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22196 \begin_layout Plain Layout
22197 \begin_inset Formula $\diagup$
22207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22210 \begin_layout Plain Layout
22218 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22221 \begin_layout Plain Layout
22222 \begin_inset Formula $\diagdown$
22238 \begin_layout Standard
22239 \begin_inset VSpace medskip
22242 More symbols are listed in
22243 \begin_inset CommandInset ref
22245 reference "sub:Miscellaneous-special-Characters"
22252 \begin_layout Standard
22253 Some symbols can be displayed in different sizes, see
22254 \begin_inset CommandInset ref
22256 reference "sub:Font-Sizes"
22263 \begin_layout Subsection
22268 \begin_layout Plain Layout
22269 Symbols ! Euro-symbol
22278 \begin_layout Plain Layout
22285 \begin_layout Plain Layout
22302 \begin_layout Standard
22303 To use the Euro symbol in formulas, the LaTeX-package
22311 \begin_layout Plain Layout
22317 must be installed and loaded with the LaTeX-preamble line
22320 \begin_layout Standard
22325 usepackage[gennarrow]{eurosym}
22328 \begin_layout Standard
22329 The Euro symbol can now be inserted with the command
22339 \begin_layout Plain Layout
22350 \begin_layout Standard
22351 The Euro symbol can directly be inserted with the € key in mathematical
22352 text, without having
22367 can also be inserted in TeX-mode.
22368 The official currency symbol can then be inserted with the command
22378 \begin_layout Plain Layout
22386 , that is only available in TeX-mode.
22389 \begin_layout Standard
22393 \begin_layout Plain Layout
22403 \begin_inset Note Note
22406 \begin_layout Plain Layout
22407 The following table will only be displayed when the LaTeX-package
22419 \begin_layout Standard
22420 An overview about the different Euro symbols:
22423 \begin_layout Standard
22425 \begin_inset Tabular
22426 <lyxtabular version="3" rows="4" columns="3">
22428 <column alignment="center" valignment="top" width="0pt">
22429 <column alignment="center" valignment="top" width="0pt">
22430 <column alignment="center" valignment="top" width="0pt">
22432 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22435 \begin_layout Plain Layout
22441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22444 \begin_layout Plain Layout
22450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22464 \begin_layout Plain Layout
22470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22473 \begin_layout Plain Layout
22481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22484 \begin_layout Plain Layout
22485 \begin_inset Formula $\euro$
22495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22498 \begin_layout Plain Layout
22504 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22507 \begin_layout Plain Layout
22513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22516 \begin_layout Plain Layout
22517 \begin_inset Formula $\mbox{€}$
22527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22530 \begin_layout Plain Layout
22536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22539 \begin_layout Plain Layout
22547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22550 \begin_layout Plain Layout
22554 \begin_layout Plain Layout
22576 \begin_layout Standard
22580 \begin_layout Plain Layout
22590 \begin_inset Note Note
22593 \begin_layout Plain Layout
22594 The following will be displayed when the LaTeX-package
22606 \begin_layout Standard
22607 You need to install the LaTeX-package
22611 to see the rest of this subsection in the output.
22614 \begin_layout Standard
22618 \begin_layout Plain Layout
22630 \begin_layout Section
22632 \begin_inset CommandInset label
22634 name "sec:Relations"
22642 \begin_layout Plain Layout
22652 \begin_layout Plain Layout
22657 \begin_layout Plain Layout
22668 \begin_layout Plain Layout
22683 \begin_layout Standard
22684 All relations can also be inserted via the toolbar button
22685 \begin_inset Graphics
22686 filename ../images/math/leq.png
22694 \begin_layout Standard
22695 \begin_inset space \hfill{}
22699 \begin_inset Tabular
22700 <lyxtabular version="3" rows="17" columns="2">
22702 <column alignment="center" valignment="top" width="0pt">
22703 <column alignment="center" valignment="top" width="0pt">
22705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22708 \begin_layout Plain Layout
22714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22717 \begin_layout Plain Layout
22725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22728 \begin_layout Plain Layout
22734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22737 \begin_layout Plain Layout
22738 \begin_inset Formula $<$
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22751 \begin_layout Plain Layout
22759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22762 \begin_layout Plain Layout
22763 \begin_inset Formula $\le$
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22776 \begin_layout Plain Layout
22784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22787 \begin_layout Plain Layout
22788 \begin_inset Formula $\ll$
22798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22801 \begin_layout Plain Layout
22809 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22812 \begin_layout Plain Layout
22813 \begin_inset Formula $\prec$
22823 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22826 \begin_layout Plain Layout
22834 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22837 \begin_layout Plain Layout
22838 \begin_inset Formula $\preceq$
22848 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22851 \begin_layout Plain Layout
22859 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22862 \begin_layout Plain Layout
22863 \begin_inset Formula $\subset$
22873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22876 \begin_layout Plain Layout
22884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22887 \begin_layout Plain Layout
22888 \begin_inset Formula $\subseteq$
22898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22901 \begin_layout Plain Layout
22909 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22912 \begin_layout Plain Layout
22913 \begin_inset Formula $\sqsubseteq$
22923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22926 \begin_layout Plain Layout
22934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22937 \begin_layout Plain Layout
22938 \begin_inset Formula $\in$
22948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22951 \begin_layout Plain Layout
22959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22962 \begin_layout Plain Layout
22963 \begin_inset Formula $\vdash$
22973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22976 \begin_layout Plain Layout
22984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22987 \begin_layout Plain Layout
22988 \begin_inset Formula $\smile$
22998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23001 \begin_layout Plain Layout
23009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23012 \begin_layout Plain Layout
23013 \begin_inset Formula $\lhd$
23023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23026 \begin_layout Plain Layout
23034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23037 \begin_layout Plain Layout
23038 \begin_inset Formula $\unlhd$
23048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23051 \begin_layout Plain Layout
23059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23062 \begin_layout Plain Layout
23063 \begin_inset Formula $\gtrless$
23073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23076 \begin_layout Plain Layout
23084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23087 \begin_layout Plain Layout
23088 \begin_inset Formula $\mid$
23098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23101 \begin_layout Plain Layout
23109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23112 \begin_layout Plain Layout
23113 \begin_inset Formula $\nmid$
23127 \begin_inset space \hfill{}
23131 \begin_inset Tabular
23132 <lyxtabular version="3" rows="17" columns="2">
23134 <column alignment="center" valignment="top" width="0pt">
23135 <column alignment="center" valignment="top" width="0pt">
23137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23140 \begin_layout Plain Layout
23146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23149 \begin_layout Plain Layout
23157 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23160 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23169 \begin_layout Plain Layout
23170 \begin_inset Formula $=$
23180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23183 \begin_layout Plain Layout
23191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23194 \begin_layout Plain Layout
23195 \begin_inset Formula $\not=$
23205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23208 \begin_layout Plain Layout
23216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23219 \begin_layout Plain Layout
23220 \begin_inset Formula $\equiv$
23230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23233 \begin_layout Plain Layout
23241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23244 \begin_layout Plain Layout
23245 \begin_inset Formula $\sim$
23255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23258 \begin_layout Plain Layout
23266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23269 \begin_layout Plain Layout
23270 \begin_inset Formula $\simeq$
23280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23283 \begin_layout Plain Layout
23291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23294 \begin_layout Plain Layout
23295 \begin_inset Formula $\approx$
23305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23308 \begin_layout Plain Layout
23316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23319 \begin_layout Plain Layout
23320 \begin_inset Formula $\cong$
23330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23333 \begin_layout Plain Layout
23341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23344 \begin_layout Plain Layout
23345 \begin_inset Formula $\bowtie$
23355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23358 \begin_layout Plain Layout
23366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23369 \begin_layout Plain Layout
23370 \begin_inset Formula $\notin$
23380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23383 \begin_layout Plain Layout
23391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23394 \begin_layout Plain Layout
23395 \begin_inset Formula $\perp$
23405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23408 \begin_layout Plain Layout
23416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23419 \begin_layout Plain Layout
23420 \begin_inset Formula $\propto$
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23433 \begin_layout Plain Layout
23441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23444 \begin_layout Plain Layout
23445 \begin_inset Formula $\asymp$
23455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23458 \begin_layout Plain Layout
23466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23469 \begin_layout Plain Layout
23470 \begin_inset Formula $\doteq$
23480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23483 \begin_layout Plain Layout
23491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23494 \begin_layout Plain Layout
23495 \begin_inset Formula $\circeq$
23505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23508 \begin_layout Plain Layout
23516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23519 \begin_layout Plain Layout
23520 \begin_inset Formula $\models$
23530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23533 \begin_layout Plain Layout
23541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23544 \begin_layout Plain Layout
23545 \begin_inset Formula $\widehat{=}$
23559 \begin_inset space \hfill{}
23563 \begin_inset Tabular
23564 <lyxtabular version="3" rows="17" columns="2">
23566 <column alignment="center" valignment="top" width="0pt">
23567 <column alignment="center" valignment="top" width="0pt">
23569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23572 \begin_layout Plain Layout
23578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23592 \begin_layout Plain Layout
23598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23601 \begin_layout Plain Layout
23602 \begin_inset Formula $>$
23612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23615 \begin_layout Plain Layout
23623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23626 \begin_layout Plain Layout
23627 \begin_inset Formula $\ge$
23637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23640 \begin_layout Plain Layout
23648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23651 \begin_layout Plain Layout
23652 \begin_inset Formula $\gg$
23662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23665 \begin_layout Plain Layout
23673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23676 \begin_layout Plain Layout
23677 \begin_inset Formula $\succ$
23687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23690 \begin_layout Plain Layout
23698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23701 \begin_layout Plain Layout
23702 \begin_inset Formula $\succeq$
23712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23715 \begin_layout Plain Layout
23723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23726 \begin_layout Plain Layout
23727 \begin_inset Formula $\supset$
23737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23740 \begin_layout Plain Layout
23748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23751 \begin_layout Plain Layout
23752 \begin_inset Formula $\supseteq$
23762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23765 \begin_layout Plain Layout
23773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23776 \begin_layout Plain Layout
23777 \begin_inset Formula $\sqsupseteq$
23787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23790 \begin_layout Plain Layout
23798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23801 \begin_layout Plain Layout
23802 \begin_inset Formula $\ni$
23812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23815 \begin_layout Plain Layout
23823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23826 \begin_layout Plain Layout
23827 \begin_inset Formula $\dashv$
23837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23840 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23851 \begin_layout Plain Layout
23852 \begin_inset Formula $\frown$
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23865 \begin_layout Plain Layout
23873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23876 \begin_layout Plain Layout
23877 \begin_inset Formula $\rhd$
23887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23890 \begin_layout Plain Layout
23898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23901 \begin_layout Plain Layout
23902 \begin_inset Formula $\unrhd$
23912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23915 \begin_layout Plain Layout
23923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23926 \begin_layout Plain Layout
23927 \begin_inset Formula $\lessgtr$
23937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23940 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23951 \begin_layout Plain Layout
23952 \begin_inset Formula $\parallel$
23962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23965 \begin_layout Plain Layout
23973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23976 \begin_layout Plain Layout
23977 \begin_inset Formula $\nparallel$
23991 \begin_inset space \hfill{}
23997 \begin_layout Standard
23998 \begin_inset VSpace medskip
24013 are bigger than the equal looking operators
24028 \begin_layout Standard
24029 Relations are, in contrary to symbols, always surrounded by space.
24032 \begin_layout Standard
24033 Relations with labels can be created with the command
24043 \begin_layout Plain Layout
24054 \begin_layout Standard
24056 \begin_inset Tabular
24057 <lyxtabular version="3" rows="2" columns="2">
24059 <column alignment="center" valignment="top" width="0">
24060 <column alignment="center" valignment="top" width="0">
24062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24076 \begin_inset Note Note
24079 \begin_layout Plain Layout
24086 is only used as spacer.
24098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24101 \begin_layout Plain Layout
24108 \begin_layout Plain Layout
24125 \begin_layout Plain Layout
24135 \begin_inset Formula $\downarrow$
24144 \begin_layout Plain Layout
24157 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24175 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24191 \begin_layout Section
24195 \begin_layout Subsection
24196 Predefined Functions
24197 \begin_inset CommandInset label
24199 name "sub:Predefined-Functions"
24207 \begin_layout Plain Layout
24208 Functions ! predefined
24216 \begin_layout Standard
24217 In general, variables are set
24221 in mathematical expressions, but not function names, because
24222 \begin_inset Formula $sin$
24225 could be misunderstood as
24226 \begin_inset Formula $s\cdot i\cdot n$
24230 Therefore there are predefined functions, that are additionally a bit separated
24232 They are inserted as commands starting with a backslash before their name.
24235 \begin_layout Standard
24237 \begin_inset Tabular
24238 <lyxtabular version="3" rows="2" columns="4">
24240 <column alignment="center" valignment="top" width="0pt">
24241 <column alignment="center" valignment="top" width="0pt">
24242 <column alignment="center" valignment="top" width="0pt">
24243 <column alignment="center" valignment="top" width="0pt">
24245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24248 \begin_layout Plain Layout
24254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24257 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24266 \begin_layout Plain Layout
24272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24275 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24286 \begin_layout Plain Layout
24292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24295 \begin_layout Plain Layout
24296 \begin_inset Formula $Asin(x)+B$
24304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24307 \begin_layout Plain Layout
24315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24318 \begin_layout Plain Layout
24319 \begin_inset Formula $A\sin(x)+B$
24335 \begin_layout Standard
24336 The following functions are predefined:
24339 \begin_layout Standard
24340 \begin_inset VSpace -2mm
24346 \begin_layout Standard
24348 \begin_inset Tabular
24349 <lyxtabular version="3" rows="9" columns="4">
24351 <column alignment="center" valignment="top" width="0pt">
24352 <column alignment="center" valignment="top" width="0pt">
24353 <column alignment="center" valignment="top" width="0pt">
24354 <column alignment="center" valignment="top" width="0pt">
24356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24359 \begin_layout Plain Layout
24365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24368 \begin_layout Plain Layout
24374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24377 \begin_layout Plain Layout
24383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24386 \begin_layout Plain Layout
24394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24397 \begin_layout Plain Layout
24405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24419 \begin_layout Plain Layout
24427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24430 \begin_layout Plain Layout
24440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24443 \begin_layout Plain Layout
24451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24454 \begin_layout Plain Layout
24462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24465 \begin_layout Plain Layout
24473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24476 \begin_layout Plain Layout
24486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24489 \begin_layout Plain Layout
24497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24500 \begin_layout Plain Layout
24508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24511 \begin_layout Plain Layout
24519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24522 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24535 \begin_layout Plain Layout
24543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24546 \begin_layout Plain Layout
24554 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24557 \begin_layout Plain Layout
24565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24568 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24581 \begin_layout Plain Layout
24589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24592 \begin_layout Plain Layout
24600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24603 \begin_layout Plain Layout
24611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24614 \begin_layout Plain Layout
24624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24627 \begin_layout Plain Layout
24635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24638 \begin_layout Plain Layout
24646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24649 \begin_layout Plain Layout
24657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24660 \begin_layout Plain Layout
24670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24673 \begin_layout Plain Layout
24681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24695 \begin_layout Plain Layout
24703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24706 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24719 \begin_layout Plain Layout
24727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24730 \begin_layout Plain Layout
24738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24741 \begin_layout Plain Layout
24749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24752 \begin_layout Plain Layout
24768 \begin_layout Standard
24769 They can also be inserted with the math toolbar button
24770 \begin_inset Graphics
24771 filename ../images/math/functions.png
24779 \begin_layout Subsection
24780 Self-defined Functions
24784 \begin_layout Plain Layout
24785 Functions ! self-defined
24793 \begin_layout Standard
24794 To use a function that is not predefined, like for example the sign function
24795 sgn(x), there are two possibilities:
24798 \begin_layout Itemize
24799 Define the function by inserting the following line to the LaTeX-preamble
24803 \begin_layout Plain Layout
24808 DeclareMathOperator
24811 \begin_inset CommandInset ref
24813 reference "sub:Self-defined-Operators"
24823 \begin_inset Newline newline
24827 \begin_inset VSpace -3mm
24831 \begin_inset Newline newline
24838 DeclareMathOperator{
24846 \begin_layout Plain Layout
24851 DeclareMathOperator
24857 \begin_inset Newline newline
24861 \begin_inset VSpace -2mm
24865 \begin_inset Newline newline
24868 Now the new defined function can be called with the command
24877 \begin_layout Itemize
24878 Write the the formula as usual, mark the formula name, in our example the
24883 , and change it to mathematical text.
24884 At last a space is inserted between prefactor and function.
24887 \begin_layout Standard
24888 The result is the same with both methods as with a predefined function
24892 \begin_layout Plain Layout
24893 In LyX self-defined functions are displayed red, predefined ones black.
24901 \begin_layout Standard
24903 \begin_inset Tabular
24904 <lyxtabular version="3" rows="3" columns="2">
24906 <column alignment="center" valignment="top" width="0pt">
24907 <column alignment="center" valignment="top" width="0pt">
24909 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24912 \begin_layout Plain Layout
24918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24921 \begin_layout Plain Layout
24929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24932 \begin_layout Plain Layout
24940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24943 \begin_layout Plain Layout
24944 \begin_inset Formula $A\sgn(x)+B$
24954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24957 \begin_layout Plain Layout
24961 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24972 \begin_layout Plain Layout
24973 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24989 \begin_layout Standard
24990 The first method is more suitable when the self-defined function should
24991 be used several times.
24994 \begin_layout Subsection
24999 \begin_layout Plain Layout
25008 \begin_layout Standard
25009 For limits there are defined besides
25019 \begin_layout Plain Layout
25039 furthermore the following functions:
25042 \begin_layout Standard
25044 \begin_inset Tabular
25045 <lyxtabular version="3" rows="5" columns="2">
25047 <column alignment="center" valignment="top" width="0">
25048 <column alignment="center" valignment="top" width="0">
25050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25053 \begin_layout Plain Layout
25059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25062 \begin_layout Plain Layout
25064 \begin_inset Note Note
25067 \begin_layout Plain Layout
25074 is only used as spacer.
25086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25089 \begin_layout Plain Layout
25097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25100 \begin_layout Plain Layout
25101 \begin_inset Formula $\varliminf$
25111 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25114 \begin_layout Plain Layout
25122 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25125 \begin_layout Plain Layout
25126 \begin_inset Formula $\varlimsup$
25136 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25139 \begin_layout Plain Layout
25147 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25150 \begin_layout Plain Layout
25151 \begin_inset Formula $\varprojlim$
25161 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25164 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25175 \begin_layout Plain Layout
25176 \begin_inset Formula $\varinjlim$
25180 \begin_inset Formula $\raisebox{-2.5mm}{}$
25196 \begin_layout Standard
25197 \begin_inset VSpace medskip
25200 The limit is created by inserting a subscript.
25201 It is set right beside the function in an inline formula:
25204 \begin_layout Standard
25206 \begin_inset Tabular
25207 <lyxtabular version="3" rows="2" columns="2">
25209 <column alignment="center" valignment="top" width="0pt">
25210 <column alignment="center" valignment="top" width="0pt">
25212 <cell alignment="center" valignment="top" usebox="none">
25215 \begin_layout Plain Layout
25221 <cell alignment="center" valignment="top" usebox="none">
25224 \begin_layout Plain Layout
25225 \begin_inset space \hspace{}
25230 \begin_inset Note Note
25233 \begin_layout Plain Layout
25246 are used here as spacer.
25258 <cell alignment="center" valignment="top" usebox="none">
25261 \begin_layout Plain Layout
25270 \begin_layout Plain Layout
25283 \begin_layout Plain Layout
25297 <cell alignment="center" valignment="top" usebox="none">
25300 \begin_layout Plain Layout
25301 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25317 \begin_layout Standard
25318 In a displayed formula the limit is set below the formula, as usual:
25319 \begin_inset Formula \[
25327 \begin_layout Subsection
25332 \begin_layout Plain Layout
25333 Functions ! modulo-
25341 \begin_layout Standard
25342 The modulo-function is special, because it exists in four variants.
25345 \begin_layout Standard
25346 The variants in a displayed formula:
25347 \begin_inset Formula \begin{align*}
25348 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25349 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25350 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25351 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25352 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25359 \begin_layout Standard
25360 In an inline formula less space is set before the function names for all
25364 \begin_layout Section
25369 \begin_layout Plain Layout
25378 \begin_layout Subsection
25379 Special Characters in Mathematical Text
25382 \begin_layout Standard
25383 The following commands can only be used in mathematical text or in TeX-mode:
25386 \begin_layout Standard
25387 \begin_inset space \hfill{}
25391 \begin_inset Tabular
25392 <lyxtabular version="3" rows="8" columns="2">
25394 <column alignment="block" valignment="top" width="0">
25395 <column alignment="block" valignment="top" width="0">
25397 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25400 \begin_layout Plain Layout
25406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25409 \begin_layout Plain Layout
25417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25420 \begin_layout Plain Layout
25428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25431 \begin_layout Plain Layout
25432 \begin_inset Formula $\textrm{œ}$
25442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25445 \begin_layout Plain Layout
25453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25456 \begin_layout Plain Layout
25457 \begin_inset Formula $\textrm{Œ}$
25467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25470 \begin_layout Plain Layout
25478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25481 \begin_layout Plain Layout
25482 \begin_inset Formula $\textrm{æ}$
25492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25495 \begin_layout Plain Layout
25503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25506 \begin_layout Plain Layout
25507 \begin_inset Formula $\textrm{Æ}$
25517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25520 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25531 \begin_layout Plain Layout
25532 \begin_inset Formula $\textrm{\aa}$
25542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25545 \begin_layout Plain Layout
25552 \begin_layout Plain Layout
25559 \begin_layout Plain Layout
25580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25583 \begin_layout Plain Layout
25584 \begin_inset Formula $\textrm{Å}$
25594 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25597 \begin_layout Plain Layout
25605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25608 \begin_layout Plain Layout
25609 \begin_inset Formula $\textrm{ı}$
25623 \begin_inset space \hfill{}
25627 \begin_inset Tabular
25628 <lyxtabular version="3" rows="8" columns="2">
25630 <column alignment="block" valignment="top" width="0">
25631 <column alignment="center" valignment="top" width="0">
25633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25636 \begin_layout Plain Layout
25638 \begin_inset Note Note
25641 \begin_layout Plain Layout
25648 is used for separation, because otherwise the output will be ¡ and ¿ respective
25659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25662 \begin_layout Plain Layout
25670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25673 \begin_layout Plain Layout
25681 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25684 \begin_layout Plain Layout
25685 \begin_inset Formula $\textrm{ø}$
25695 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25698 \begin_layout Plain Layout
25706 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25709 \begin_layout Plain Layout
25710 \begin_inset Formula $\textrm{Ø}$
25720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25723 \begin_layout Plain Layout
25731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25734 \begin_layout Plain Layout
25735 \begin_inset Formula $\textrm{ł}$
25745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25748 \begin_layout Plain Layout
25756 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25759 \begin_layout Plain Layout
25760 \begin_inset Formula $\textrm{Ł}$
25770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25773 \begin_layout Plain Layout
25775 \begin_inset space \hspace{}
25783 \begin_layout Plain Layout
25797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25800 \begin_layout Plain Layout
25801 \begin_inset Formula $\textrm{!`}$
25811 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25814 \begin_layout Plain Layout
25816 \begin_inset space \hspace{}
25824 \begin_layout Plain Layout
25838 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25841 \begin_layout Plain Layout
25842 \begin_inset Formula $\textrm{?`}$
25852 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25855 \begin_layout Plain Layout
25863 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25866 \begin_layout Plain Layout
25867 \begin_inset Formula $\textrm{ȷ}$
25881 \begin_inset space \hfill{}
25887 \begin_layout Standard
25889 \begin_inset Formula $\textrm{\textrm{Å}}$
25893 \begin_inset Formula $\textrm{\textrm{Ø}}$
25896 can also be inserted via the math toolbar button
25897 \begin_inset Graphics
25898 filename ../images/math/digamma.png
25906 \begin_layout Standard
25907 An exception are the commands
25910 \begin_inset space \hspace{}
25919 \begin_inset space \hspace{}
25925 , because they can be inserted in LyX directly to text.
25928 \begin_layout Subsection
25930 \begin_inset CommandInset label
25932 name "sub:Accents-in-Text"
25940 \begin_layout Plain Layout
25949 \begin_layout Standard
25950 With the following commands all letters can be accented.
25951 The commands must be inserted in TeX-mode.
25954 \begin_layout Standard
25955 \begin_inset space \hfill{}
25959 \begin_inset Tabular
25960 <lyxtabular version="3" rows="8" columns="2">
25962 <column alignment="block" valignment="top" width="0">
25963 <column alignment="block" valignment="top" width="0">
25965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25968 \begin_layout Plain Layout
25974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25977 \begin_layout Plain Layout
25985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25988 \begin_layout Plain Layout
25992 \begin_inset Quotes grd
26000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26003 \begin_layout Plain Layout
26007 \begin_layout Plain Layout
26023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26026 \begin_layout Plain Layout
26034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26037 \begin_layout Plain Layout
26041 \begin_layout Plain Layout
26057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26060 \begin_layout Plain Layout
26067 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26084 \begin_layout Plain Layout
26088 \begin_layout Plain Layout
26104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26107 \begin_layout Plain Layout
26115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26118 \begin_layout Plain Layout
26122 \begin_layout Plain Layout
26138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26141 \begin_layout Plain Layout
26148 \begin_layout Plain Layout
26162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26165 \begin_layout Plain Layout
26169 \begin_layout Plain Layout
26185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26188 \begin_layout Plain Layout
26195 \begin_layout Plain Layout
26209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26212 \begin_layout Plain Layout
26216 \begin_layout Plain Layout
26232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26235 \begin_layout Plain Layout
26242 \begin_layout Plain Layout
26256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26259 \begin_layout Plain Layout
26263 \begin_layout Plain Layout
26283 \begin_inset space \hfill{}
26287 \begin_inset Tabular
26288 <lyxtabular version="3" rows="8" columns="2">
26290 <column alignment="block" valignment="top" width="0">
26291 <column alignment="center" valignment="top" width="0">
26293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26296 \begin_layout Plain Layout
26302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26305 \begin_layout Plain Layout
26313 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26316 \begin_layout Plain Layout
26323 \begin_layout Plain Layout
26337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26340 \begin_layout Plain Layout
26344 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26363 \begin_layout Plain Layout
26371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26374 \begin_layout Plain Layout
26378 \begin_layout Plain Layout
26394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26397 \begin_layout Plain Layout
26404 \begin_layout Plain Layout
26415 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26418 \begin_layout Plain Layout
26422 \begin_layout Plain Layout
26438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26441 \begin_layout Plain Layout
26449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26452 \begin_layout Plain Layout
26456 \begin_layout Plain Layout
26472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26475 \begin_layout Plain Layout
26482 \begin_layout Plain Layout
26496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26499 \begin_layout Plain Layout
26503 \begin_layout Plain Layout
26519 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26522 \begin_layout Plain Layout
26529 \begin_layout Plain Layout
26543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26546 \begin_layout Plain Layout
26550 \begin_layout Plain Layout
26566 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26569 \begin_layout Plain Layout
26576 \begin_layout Plain Layout
26590 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26593 \begin_layout Plain Layout
26597 \begin_layout Plain Layout
26617 \begin_inset space \hfill{}
26623 \begin_layout Standard
26624 \begin_inset VSpace medskip
26633 also two different characters can be accented.
26642 \begin_layout Plain Layout
26657 \begin_layout Plain Layout
26669 \begin_layout Standard
26682 can in combination with vowels directly be inserted with the keyboard without
26684 The same applies for the tilde
26688 \begin_layout Plain Layout
26689 This only applies for keyboards where the tilde is defined as accent.
26698 in combination with
26713 \begin_layout Standard
26756 , and accents inserted directly with the keyboard are also available in
26758 For the other accents there are special math commands to be used in formulas,
26760 \begin_inset CommandInset ref
26762 reference "sub:Accents-for-one"
26769 \begin_layout Standard
26770 \begin_inset VSpace bigskip
26773 Furthermore, with the command
26783 \begin_layout Plain Layout
26791 all numbers and letters can be set into a circle, quasi accented with a
26792 circle, similar to the the copyright symbol.
26795 \begin_layout Standard
26797 \begin_inset Tabular
26798 <lyxtabular version="3" rows="3" columns="2">
26800 <column alignment="center" valignment="top" width="0">
26801 <column alignment="center" valignment="top" width="0">
26803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26806 \begin_layout Plain Layout
26812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26815 \begin_layout Plain Layout
26817 \begin_inset Note Note
26820 \begin_layout Plain Layout
26827 is only used as spacer.
26839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26842 \begin_layout Plain Layout
26850 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26853 \begin_layout Plain Layout
26857 \begin_layout Plain Layout
26873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26876 \begin_layout Plain Layout
26887 raisebox{-1.5pt}{W}}
26892 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26895 \begin_layout Plain Layout
26896 \begin_inset Formula $\raisebox{4.5mm}{}$
26903 \begin_layout Plain Layout
26921 \begin_inset Formula $\raisebox{-2mm}{}$
26937 \begin_layout Standard
26938 One has to take care that the character fits in the circle.
26949 \begin_layout Plain Layout
26951 \begin_inset CommandInset ref
26953 reference "sub:Font-Sizes"
26962 specifies thereby the size of the circle.
26973 \begin_layout Plain Layout
26975 \begin_inset CommandInset ref
26977 reference "sub:Boxes-without-Frame"
26986 the character can be centered.
26989 \begin_layout Subsection
26994 \begin_layout Plain Layout
27003 \begin_layout Standard
27004 Minuscule numbers are created with the command
27014 \begin_layout Plain Layout
27023 The command can be used in formulas and in TeX-mode.
27024 The command scheme is:
27027 \begin_layout Standard
27032 oldstylenums{number}
27035 \begin_layout Standard
27040 oldstylenums{0123456789
27043 \begin_inset Formula $\oldstylenums{0123456789}$
27049 \begin_layout Subsection
27050 Miscellaneous special Characters
27051 \begin_inset CommandInset label
27053 name "sub:Miscellaneous-special-Characters"
27061 \begin_layout Plain Layout
27062 Special characters ! miscellaneous
27070 \begin_layout Standard
27071 The following characters can only be inserted to formulas by using commands:
27074 \begin_layout Standard
27076 \begin_inset Tabular
27077 <lyxtabular version="3" rows="4" columns="2">
27079 <column alignment="center" valignment="top" width="0">
27080 <column alignment="center" valignment="top" width="0">
27082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27085 \begin_layout Plain Layout
27091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27094 \begin_layout Plain Layout
27102 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27105 \begin_layout Plain Layout
27112 \begin_layout Plain Layout
27126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27129 \begin_layout Plain Layout
27130 \begin_inset Formula $\mathcircumflex$
27140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27143 \begin_layout Plain Layout
27151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27154 \begin_layout Plain Layout
27155 \begin_inset Formula $\_$
27165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27168 \begin_layout Plain Layout
27173 \begin_layout Plain Layout
27188 \begin_layout Plain Layout
27201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27204 \begin_layout Plain Layout
27205 \begin_inset Formula $^{\circ}$
27221 \begin_layout Standard
27222 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27223 contains the following line
27227 \begin_layout Plain Layout
27228 More about this is described in
27229 \begin_inset CommandInset ref
27231 reference "sub:Text-Characters-in"
27243 \begin_layout Standard
27248 DeclareInputtext{176}{
27261 \begin_layout Section
27263 \begin_inset CommandInset label
27265 name "sec:Formula-Styles"
27273 \begin_layout Plain Layout
27282 \begin_layout Itemize
27283 There are two different alignment styles:
27287 \begin_layout Description
27288 Centered is the predefined standard
27291 \begin_layout Description
27292 Indented for this the option
27296 must be inserted in the menu
27298 Document\SpecialChar \menuseparator
27304 \begin_inset space ~
27310 \begin_layout Standard
27315 is used, the indentation can be adjusted with the length
27325 \begin_layout Plain Layout
27334 Should the distance be 15
27335 \begin_inset space \thinspace{}
27338 mm, the following command line is inserted in the LaTeX-preamble
27341 \begin_layout Standard
27351 \begin_layout Standard
27352 When no length is specified, the predefined value of 30
27353 \begin_inset space \thinspace{}
27360 \begin_layout Itemize
27361 And two different numbering styles:
27365 \begin_layout Description
27366 Right is the predefined standard
27369 \begin_layout Description
27370 Left for this the option
27374 must be inserted in the menu
27376 Document\SpecialChar \menuseparator
27382 \begin_inset space ~
27389 \begin_layout Standard
27398 can also be used together.
27399 In this case both options are inserted, separated by a comma.
27402 \begin_layout Standard
27403 The chosen styles are used for all displayed formulas of the document.
27404 When both, centered and indented formulas should be created in a document,
27410 The indented formulas are then set in a flalign environment, see
27411 \begin_inset CommandInset ref
27413 reference "sub:Flalign-Environment"
27420 \begin_layout Section
27422 \begin_inset CommandInset label
27424 name "sec:Multiline-Formulas"
27432 \begin_layout Plain Layout
27433 Formula ! multiline
27441 \begin_layout Subsection
27445 \begin_layout Standard
27446 In LyX multiline formulas are created by pressing
27451 arg "newline-insert newline"
27457 This creates either an
27459 eqnarray environment
27461 that is described in
27462 \begin_inset CommandInset ref
27464 reference "sub:Eqnarray-Environment"
27468 or, when the option
27470 Use AMS math package
27472 in the document settings is selected, an
27476 that is described in
27477 \begin_inset CommandInset ref
27479 reference "sub:Standard-align-Environment"
27486 \begin_layout Standard
27487 There are other multiline formula environments that can be created via the
27490 Insert\SpecialChar \menuseparator
27494 These environments are described in the following sections.
27497 \begin_layout Standard
27498 In all multiline formula environments a new line is created by pressing
27502 arg "newline-insert newline"
27506 To add or delete lines, the math toolbar buttons
27507 \begin_inset Graphics
27508 filename ../images/tabular-feature_append-row.png
27514 \begin_inset Graphics
27515 filename ../images/tabular-feature_delete-row.png
27520 , respectively, or the menu
27522 Edit\SpecialChar \menuseparator
27528 \begin_layout Subsubsection
27530 \begin_inset CommandInset label
27532 name "sub:Line-Separation"
27540 \begin_layout Plain Layout
27541 Formula ! multiline ! Line separation
27549 \begin_layout Standard
27550 There is sometimes not enough space in multiline formulas between the lines:
27551 \begin_inset Formula \begin{eqnarray*}
27552 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}\\
27553 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*}
27560 \begin_layout Standard
27561 In LaTeX additional line space is specified as optional argument of the
27563 This is not yet possible in LyX
27567 \begin_layout Plain Layout
27569 \begin_inset CommandInset href
27571 name "LyX-bug #1505"
27572 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27581 , therefore the whole formula must be inserted in TeX-mode.
27582 To add in our example space, the command
27590 is inserted at the end of the first line.
27595 \begin_layout Plain Layout
27602 \begin_layout Plain Layout
27604 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27607 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27614 \begin_layout Plain Layout
27618 left(B^{2}+x_{0}^{2}
27626 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27631 \begin_layout Plain Layout
27643 \begin_layout Standard
27644 \begin_inset VSpace bigskip
27647 To set the the line separation for all lines in a formula, the length
27657 \begin_layout Plain Layout
27667 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27678 \begin_inset space \thinspace{}
27683 \begin_inset space \thinspace{}
27686 mm additional line separation as in the previous example, the command
27689 \begin_layout Standard
27699 \begin_layout Standard
27700 is inserted in TeX-mode before the formula.
27701 This requires that the LaTeX-package
27709 \begin_layout Plain Layout
27714 is part of every LaTeX standard installation.
27723 \begin_layout Plain Layout
27729 was loaded in LaTeX-preamble with the line
27732 \begin_layout Standard
27740 \begin_layout Standard
27745 \begin_layout Plain Layout
27757 \begin_inset Formula \begin{eqnarray*}
27758 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}\\
27759 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*}
27766 \begin_layout Standard
27770 \begin_layout Plain Layout
27781 To get back to the predefined distance,
27787 is set to the value 3
27788 \begin_inset space \thinspace{}
27794 \begin_layout Subsubsection
27796 \begin_inset CommandInset label
27798 name "sub:Column-Separation"
27806 \begin_layout Plain Layout
27807 Formula ! multiline ! Column separation
27815 \begin_layout Standard
27816 Multiline formulas form a matrix.
27817 A formula in the eqnarray environment is for example a matrix with three
27819 By changing the column separation in this environment, the space beside
27820 the relation sign can be changed.
27823 \begin_layout Standard
27824 The column separation is specified with the length
27834 \begin_layout Plain Layout
27843 \begin_inset Newline newline
27846 column separation = 2
27847 \begin_inset space \thinspace{}
27857 \begin_inset Newline newline
27863 \begin_layout Standard
27873 \begin_layout Standard
27874 inserted in TeX-mode, sets for all following formulas a column separation
27876 \begin_inset space \thinspace{}
27880 To get back to the predefined distance,
27887 \begin_inset space \thinspace{}
27893 \begin_layout Standard
27895 \begin_inset space \thinspace{}
27898 cm column separation:
27902 \begin_layout Plain Layout
27914 \begin_inset Formula \begin{eqnarray*}
27916 C & \ne & A\end{eqnarray*}
27920 A formula with the predefined column separation for matrices of 10
27921 \begin_inset space \thinspace{}
27928 \begin_layout Plain Layout
27940 \begin_inset Formula \begin{eqnarray*}
27942 C & \ne & A\end{eqnarray*}
27949 \begin_layout Subsubsection
27954 \begin_layout Plain Layout
27963 \begin_layout Standard
27964 Long formulas can be typeset using these methods:
27967 \begin_layout Itemize
27968 When one side of the equation is much shorther than the line width, this
27969 one is chosen for the left side and the right side is typeset over two
27974 \begin_layout Plain Layout
27984 \begin_inset Formula \begin{eqnarray}
27985 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 \\
27986 & & -\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}
27994 \begin_layout Plain Layout
28004 \begin_inset Newline newline
28007 The minus sign at the beginning of the second line does normally not appear
28008 as operator because it is the first character of the line.
28009 Thus it would not be surrounded by space and could not be distinguished
28010 from the fraction bar.
28011 To avoid this, space was inserted behind the minus sign with the command
28022 \begin_layout Plain Layout
28030 \begin_inset CommandInset ref
28032 reference "sub:Variable-Space"
28045 \begin_layout Plain Layout
28056 \begin_layout Itemize
28057 When both sides of the equation are too long, the command
28067 \begin_layout Plain Layout
28076 It is inserted to the first column of the first line and effects that all
28077 further insertions overwrite the following columns:
28081 \begin_layout Plain Layout
28091 \begin_inset Formula \begin{eqnarray}
28092 \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 \\
28093 & & -\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 \\
28094 & & =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}
28102 \begin_layout Plain Layout
28112 \begin_inset Newline newline
28115 After the insertion of
28121 , the cursor is in a purple box that is a bit shifted to the left from the
28123 In this the formula is inserted.
28127 \begin_layout Plain Layout
28137 \begin_inset Newline newline
28140 The content of the further lines is inserted to the second or another formula
28142 The greater the column number where it was inserted, the larger the indentation.
28146 \begin_layout Plain Layout
28156 \begin_inset Newline newline
28160 \begin_inset Note Greyedout
28163 \begin_layout Plain Layout
28164 Note the following when using
28173 \begin_layout Itemize
28174 The formula doesn't use the full page width.
28176 \begin_inset space \thinspace{}
28180 \begin_inset space \space{}
28184 \begin_inset Formula $-B^{2}$
28187 is added to the first line in the above example, it would have been outside
28189 To better use the width, negative space can be inserted at the beginning
28193 \begin_layout Itemize
28194 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28199 \begin_layout Plain Layout
28200 \begin_inset CommandInset href
28202 name "LyX-bug #1429"
28203 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28212 One can only set the cursor at the beginning of the line and move it with
28221 \begin_layout Itemize
28222 Other methods to set long formulas are offered by the environments described
28224 \begin_inset CommandInset ref
28226 reference "sub:Multline-Environment"
28231 \begin_inset CommandInset ref
28233 reference "sub:Multiline-Formula-Parts"
28240 \begin_layout Subsubsection
28242 \begin_inset CommandInset label
28244 name "sub:Multiline-Brackets"
28252 \begin_layout Plain Layout
28253 Brackets ! for multiline expressions
28261 \begin_layout Standard
28262 For brackets spanning multiple lines the following problem occurs:
28263 \begin_inset Formula \begin{eqnarray*}
28264 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28265 & & \left.\cdots+B-D\right]\end{eqnarray*}
28272 \begin_layout Standard
28273 The closing bracket is smaller than the opening bracket because brackets
28274 with variable size may not span multiple lines.
28277 \begin_layout Standard
28278 To set the bracket size for the second line correctly, the first line is
28289 \begin_layout Plain Layout
28297 and the second line with
28305 \begin_layout Plain Layout
28319 \begin_inset CommandInset ref
28321 reference "sub:Automatic-Bracket-Size"
28336 \begin_layout Plain Layout
28362 \begin_layout Plain Layout
28381 \begin_layout Plain Layout
28400 \begin_layout Plain Layout
28412 \begin_inset Formula $\downarrow$
28421 \begin_layout Plain Layout
28429 is inserted, because the multiplication operator with its limits is the
28430 largest symbol in the first line and this should be the size for the bracket
28431 in the second line.
28434 \begin_layout Standard
28435 The result is this:
28436 \begin_inset Formula \begin{eqnarray*}
28437 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28438 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28445 \begin_layout Subsection
28449 \begin_layout Standard
28450 Align environments can be used for every kind of multiline formulas.
28451 They are specially useful to set several formulas side by side.
28454 \begin_layout Standard
28455 Align environments consist of columns.
28456 The odd columns are right aligned, the even ones left aligned.
28457 Every line in an Align environment can be numbered.
28460 \begin_layout Standard
28461 Align environments are created via the menu
28463 Insert\SpecialChar \menuseparator
28469 Edit\SpecialChar \menuseparator
28470 Math\SpecialChar \menuseparator
28471 Change Formula Type
28473 already existing formulas can be converted to Align environments.
28476 \begin_layout Standard
28477 To add or delete columns, the math toolbar buttons
28478 \begin_inset Graphics
28479 filename ../images/tabular-feature_append-column.png
28485 \begin_inset Graphics
28486 filename ../images/tabular-feature_delete-column.png
28491 , respectively, or the menu
28493 Edit\SpecialChar \menuseparator
28499 \begin_layout Subsubsection
28500 Standard align Environment
28501 \begin_inset CommandInset label
28503 name "sub:Standard-align-Environment"
28511 \begin_layout Plain Layout
28512 Formula ! multiline ! align environment
28520 \begin_layout Standard
28521 This Align environment is created by presssing
28524 arg "newline-insert newline"
28527 in a formula or by the menu
28529 Insert\SpecialChar \menuseparator
28530 Math\SpecialChar \menuseparator
28531 AMS align Environment
28536 \begin_layout Standard
28537 An example for two formulas set side by side, that are created with a four
28538 column align environment:
28539 \begin_inset Formula \begin{align*}
28540 A & =\sin(B) & C & =D\\
28541 C & \ne A & B & \ne D\end{align*}
28545 As it can be seen, the formulas in this environment are placed so as if
28554 \begin_layout Plain Layout
28562 \begin_inset CommandInset ref
28564 reference "sub:Variable-Space"
28575 before the first and after every even column.
28576 When the formula style
28582 \begin_layout Plain Layout
28584 \begin_inset CommandInset ref
28586 reference "sec:Formula-Styles"
28597 is used, the formula is set without the
28603 before the first column.
28606 \begin_layout Subsubsection
28607 Alignat Environment
28611 \begin_layout Plain Layout
28612 Formula ! multiline ! alignat environment
28620 \begin_layout Standard
28621 The alignat environment has no predefined column separation.
28622 It can be inserted manually with the spaces that are described
28623 \begin_inset CommandInset ref
28625 reference "sub:Space"
28632 \begin_layout Standard
28633 The above example in the alignat environment where 1
28634 \begin_inset space \thinspace{}
28637 cm space was inserted at the beginning of the second formula:
28638 \begin_inset Formula \begin{alignat*}{2}
28639 A & =\sin(B) & \hspace{1cm}C & =D\\
28640 C & \ne A & B & \ne D\end{alignat*}
28644 Because the column separation can be set separately for every column, this
28645 environment is especially suitable to set three and more formulas side
28649 \begin_layout Subsubsection
28650 Flalign Environment
28651 \begin_inset CommandInset label
28653 name "sub:Flalign-Environment"
28661 \begin_layout Plain Layout
28662 Formula ! multiline ! flalign environment
28670 \begin_layout Standard
28671 In this environment the first two columns are always set as much as possible
28672 to the left and the last two ones to the right.
28674 \begin_inset Formula \begin{flalign*}
28675 A & =1 & B & =2 & C & =3\\
28676 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28683 \begin_layout Standard
28684 By creating a flalign environment with an odd number of columns where an
28685 empty TeX-brace is inserted to the last column, several formulas in a document
28686 can be set to the left, although the formula style
28691 As example the indented formula
28692 \begin_inset CommandInset ref
28694 reference "eq:VolInt"
28699 \begin_inset Formula \begin{flalign}
28700 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28704 The first two columns contain the formula.
28705 To indent it as with the formula style
28710 \begin_inset space \thinspace{}
28713 pt space was inserted at the beginning of the first column.
28716 \begin_layout Subsection
28717 Eqnarray Environment
28718 \begin_inset CommandInset label
28720 name "sub:Eqnarray-Environment"
28728 \begin_layout Plain Layout
28729 Formula ! multiline ! eqnarray environment
28737 \begin_layout Standard
28738 When this environment has been created, three blue boxes appear.
28739 The content of the first box is right aligned, the content of the last
28741 The content of the middle box appears centered and a bit smaller, because
28742 it is designed to insert there only relation characters.
28743 \begin_inset Formula \begin{eqnarray*}
28744 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28746 A & = & A\end{eqnarray*}
28753 \begin_layout Subsection
28758 \begin_layout Plain Layout
28759 Formula ! multiline ! gather environment
28767 \begin_layout Standard
28768 This environment consists of only one centered column.
28769 Every line can be numbered.
28770 \begin_inset Formula \begin{gather}
28772 X=\textrm{-}1\end{gather}
28779 \begin_layout Subsection
28780 Multline Environment
28781 \begin_inset CommandInset label
28783 name "sub:Multline-Environment"
28791 \begin_layout Plain Layout
28792 Formula ! multiline ! multline environment
28800 \begin_layout Standard
28801 The multline environment consists, like the gather environment, of only
28803 But the first line is left aligned, the last one right aligned.
28804 All other lines are centered.
28805 Therefore this environment is suitable for long formulas.
28807 \begin_inset CommandInset ref
28809 reference "eq:lefteqn"
28813 in the multline environment:
28814 \begin_inset Formula \begin{multline}
28815 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}\\
28816 -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}\\
28817 =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}
28824 \begin_layout Standard
28825 In the output only the last (first) line of a multline environment appears
28826 numbered when the document numbering is right (left).
28830 \begin_layout Plain Layout
28831 numbering styles see
28832 \begin_inset CommandInset ref
28834 reference "sec:Formula-Styles"
28846 \begin_layout Standard
28855 \begin_layout Plain Layout
28873 \begin_layout Plain Layout
28883 a centered line can be right or left aligned, respectively.
28884 The commands are used as follows:
28887 \begin_layout Standard
28892 shoveright{line content}
28898 shoveleft{line content}
28901 \begin_layout Standard
28902 \begin_inset VSpace medskip
28913 \begin_layout Plain Layout
28923 specifies the distance of the first line from the left page margin.
28924 Predefined is the length 0
28925 \begin_inset space \thinspace{}
28931 \begin_layout Standard
28932 As example the above formula where the command
28935 \begin_layout Standard
28945 \begin_layout Standard
28946 was inserted in TeX-mode before:
28950 \begin_layout Plain Layout
28962 \begin_inset Formula \begin{multline}
28963 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}\\
28964 \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}}\\
28965 =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}
28973 \begin_layout Plain Layout
28984 The second line was left aligned using
28993 \begin_layout Subsection
28994 Multiline Formula Parts
28995 \begin_inset CommandInset label
28997 name "sub:Multiline-Formula-Parts"
29005 \begin_layout Plain Layout
29006 Formula ! multiline ! formula parts
29014 \begin_layout Standard
29015 To display only parts of a formula with multiple lines, one of the following
29016 environments are used:
29033 They can be inserted via the menu
29035 Insert\SpecialChar \menuseparator
29038 or by using the commands described in this section.
29041 \begin_layout Standard
29042 The first three have the same properties as the corresponding multiline
29043 formula environments, but it is possible to set further formula parts beside
29046 \begin_inset Formula \[
29047 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29048 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29049 \right\} \textrm{Uncertainty relations}\]
29056 \begin_layout Standard
29057 To get this formula, a displayed formula is created where the command
29065 \begin_layout Plain Layout
29076 A purple box appears around the blue formula box where now columns and
29077 lines can be added.
29078 Outside the multiline environment other formula parts can be set, like
29082 \begin_layout Standard
29083 The aligned environment is also suitable for long formulas whose lines are
29084 horizontally aligned.
29085 Using aligned in a displayed formula has the advantage that the formula
29086 number is vertically centered behind the lines.
29088 \begin_inset CommandInset ref
29090 reference "eq:kurzlang"
29094 in the aligned environment:
29095 \begin_inset Formula \begin{equation}
29096 \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}|}\\
29097 & -\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}
29105 \begin_layout Standard
29106 To use the environments
29128 \begin_layout Plain Layout
29146 \begin_layout Plain Layout
29164 \begin_layout Plain Layout
29172 are inserted, respectively.
29173 The split environment has the same properties as the aligned environment
29174 but it can only have two columns.
29177 \begin_layout Subsection
29178 Text in multiline Formulas
29179 \begin_inset CommandInset label
29181 name "sub:Text-in-multiline"
29189 \begin_layout Plain Layout
29199 \begin_layout Plain Layout
29200 Formula ! multiline ! text
29208 \begin_layout Standard
29209 In the Align environments, and the multline and gather environment, text
29210 can be inserted that will appear in a separate line and doesn't affect
29211 the column alignment.
29212 To do this, the command
29220 \begin_layout Plain Layout
29230 is used in the following scheme:
29233 \begin_layout Standard
29241 \begin_layout Standard
29242 The text should not be longer than a line because it cannot be hyphenated.
29243 As LyX doesn't yet support
29249 directly, the text is written as mathematical text.
29256 must hereby be at the beginning of a line and appears in the output above
29258 An example where the text was inserted at the beginning of the second line:
29259 \begin_inset Formula \begin{align}
29260 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29261 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29268 \begin_layout Section
29273 \begin_layout Plain Layout
29283 \begin_layout Plain Layout
29284 Formula ! numbering|see
29288 \begin_layout Plain Layout
29299 \begin_layout Plain Layout
29314 \begin_layout Subsection
29318 \begin_layout Standard
29319 Numbered formulas can be created with the menu
29321 Insert\SpecialChar \menuseparator
29322 Math\SpecialChar \menuseparator
29324 \begin_inset space ~
29332 \begin_inset space ~
29338 Existing formulas can be numbered with the menu
29340 Edit\SpecialChar \menuseparator
29341 Math\SpecialChar \menuseparator
29343 \begin_inset space ~
29351 arg "math-number-toggle"
29355 The formula number is displayed in LyX behind the formula as number sign
29357 The number sign is replaced in the output by the formula number.
29360 \begin_layout Standard
29361 When numbering is turned on in multiline formulas, all lines will be numbered.
29362 But the numbering can be controlled with the menu
29364 Edit\SpecialChar \menuseparator
29365 Math\SpecialChar \menuseparator
29367 \begin_inset space ~
29371 \begin_inset space ~
29375 \begin_inset space ~
29383 arg "math-number-line-toggle"
29389 \begin_layout Standard
29390 Except of inline formulas, all formulas can be numbered with two different
29392 \begin_inset CommandInset ref
29394 reference "sec:Formula-Styles"
29401 \begin_layout Subsection
29406 \begin_layout Plain Layout
29407 Cross-references ! to formulas
29415 \begin_layout Standard
29416 All labeled formulas can be cross-referenced.
29417 A label is added by the menu
29419 Insert\SpecialChar \menuseparator
29422 or the toolbar button
29423 \begin_inset Graphics
29424 filename ../images/label-insert.png
29430 The cursor must hereby be inside a displayed formula.
29431 A dialog pops up displaying the prefix
29436 The label is inserted there behind the prefix.
29437 The predefined prefix means
29438 \begin_inset Quotes eld
29442 \begin_inset Quotes erd
29445 and makes it easier to find labels in large documents because it marks
29446 it as formula label to divide it from e.
29447 \begin_inset space \thinspace{}
29451 \begin_inset space \space{}
29455 To change a label, the menu
29457 Insert\SpecialChar \menuseparator
29463 \begin_layout Standard
29464 The name of the label is displayed in LyX within two parentheses behind
29466 A formula with a label is always numbered.
29469 \begin_layout Standard
29470 Cross-references are inserted via the menu
29472 Insert\SpecialChar \menuseparator
29475 or with the toolbar button
29476 \begin_inset Graphics
29477 filename ../images/dialog-show-new-inset_ref.png
29483 A formula cross-reference appears in the output as formula number.
29484 When in the cross-reference dialog window the format
29488 is chosen, the cross-reference appears in the output as formula number
29490 \begin_inset Newline newline
29493 By right-clicking on a cross-reference in LyX, one jumps to the formula
29494 that is referenced.
29497 \begin_layout Standard
29498 Here are as examples cross-references to formulas of the following subsections:
29499 \begin_inset Note Note
29502 \begin_layout Plain Layout
29503 Note the different cross-reference types.
29511 \begin_layout Standard
29513 \begin_inset CommandInset ref
29520 \begin_inset CommandInset ref
29528 \begin_inset CommandInset ref
29534 ) big Latin letters are used for the numbering in contrary to (
29535 \begin_inset CommandInset ref
29544 \begin_layout Standard
29545 \begin_inset VSpace medskip
29548 When the argument of
29556 \begin_layout Plain Layout
29564 \begin_inset CommandInset ref
29566 reference "sub:User-defined-Numbering"
29577 contains a box like in
29578 \begin_inset CommandInset ref
29580 reference "sub:Paragraph-Boxes"
29584 , the formula cannot be referenced.
29587 \begin_layout Subsection
29592 \begin_layout Plain Layout
29593 Formula numbering ! subnumbering
29601 \begin_layout Standard
29602 With the help of the commands
29606 begin{subequations}
29614 formulas can be subnumbered.
29615 Both commands are inserted in TeX-mode.
29618 \begin_layout Standard
29620 \begin_inset Formula \begin{equation}
29621 A=C-B\label{eq:a}\end{equation}
29629 \begin_layout Plain Layout
29633 addtocounter{equation}{-1}
29642 \begin_layout Plain Layout
29646 begin{subequations}
29652 \begin_inset VSpace -5mm
29656 \begin_inset Formula \begin{equation}
29657 B=C-A\label{eq:b}\end{equation}
29662 \begin_inset Formula \begin{equation}
29663 C=A+B\label{eq:c}\end{equation}
29670 \begin_layout Standard
29674 \begin_layout Plain Layout
29686 \begin_layout Standard
29687 To create the example, the following is done:
29690 \begin_layout Enumerate
29691 first formula is inserted
29694 \begin_layout Enumerate
29699 addtocounter{equation}{-1}
29701 begin{subequations}
29705 \begin_layout Plain Layout
29714 \begin_inset Newline newline
29719 is inserted after the first formula
29722 \begin_layout Enumerate
29723 second formula is inserted
29726 \begin_layout Enumerate
29727 third formula is inserted
29730 \begin_layout Enumerate
29737 is inserted after the third formula
29740 \begin_layout Standard
29741 Every formula between the commands
29753 is subnumbered as a, b,
29754 \begin_inset Newline linebreak
29757 c, \SpecialChar \ldots{}
29758 For multiline formulas every line will be subnumbered.
29759 All subnumbered formulas are treated as
29764 But as every numbered formula increases the counter
29768 by one, the command
29774 is needed to decrease it.
29775 Otherwise the formulas
29776 \begin_inset CommandInset ref
29783 \begin_inset CommandInset ref
29790 \begin_inset CommandInset ref
29796 would be numbered as
29797 \begin_inset CommandInset ref
29804 \begin_inset CommandInset ref
29811 \begin_inset CommandInset ref
29820 \begin_layout Standard
29821 By inserting the commands in TeX-mode, a space is created between the first
29824 \begin_inset space \thinspace{}
29827 mm vertical space is inserted after the command
29831 begin{subequations}
29834 When the formula style
29840 \begin_layout Plain Layout
29842 \begin_inset CommandInset ref
29844 reference "sec:Formula-Styles"
29856 \begin_inset space \thinspace{}
29859 mm space is inserted instead.
29862 \begin_layout Standard
29863 Here is an example for a multiline formula where the numbering was turned
29864 off for the second line:
29868 \begin_layout Plain Layout
29872 begin{subequations}
29878 \begin_inset Formula \begin{eqnarray}
29879 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29880 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29881 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29889 \begin_layout Plain Layout
29901 \begin_layout Subsection
29902 User-defined Numbering
29903 \begin_inset CommandInset label
29905 name "sub:User-defined-Numbering"
29913 \begin_layout Plain Layout
29914 Formula numbering ! user-defined
29922 \begin_layout Standard
29926 \begin_layout Plain Layout
29927 Formula numbering ! self-defined delimiters
29932 With the standard numbering parentheses are set around the formula number.
29933 To replace the parentheses for example by vertical bars, the following
29934 line is added to the LaTeX-preamble:
29937 \begin_layout Standard
29949 \begin_inset Note Note
29952 \begin_layout Plain Layout
29953 This macro is already declared in the LaTeX-preamble for testing.
29954 To activate it, remove the percent sign at the beginning.
29962 \begin_layout Standard
29963 To use other characters, the vertical bars besides the
29967 are replaced by one ore more characters.
29968 To get only the formula number the vertical bars are omitted.
29971 \begin_layout Standard
29972 \begin_inset VSpace bigskip
29975 When there should be an expression of your choice instead of the consecutive
29976 formula number in parentheses behind the formula, the command
29986 \begin_layout Plain Layout
29995 \begin_inset Formula \begin{equation}
29996 A+B=C\tag{something}\label{eq:tag}\end{equation}
30000 In this example the command
30008 \begin_layout Plain Layout
30019 was inserted to the formula.
30022 \begin_layout Standard
30031 \begin_layout Plain Layout
30042 is inserted instead, the star prevents the parentheses around the expression:
30043 \begin_inset Formula \[
30044 A+B=C\tag*{something}\]
30051 \begin_layout Standard
30052 \begin_inset VSpace bigskip
30055 To restart the formula numbering with new document parts or sections, the
30056 following command is used:
30059 \begin_layout Standard
30064 @addtoreset{equation}{part}
30070 \begin_layout Plain Layout
30075 \begin_layout Plain Layout
30086 \begin_layout Plain Layout
30099 \begin_layout Plain Layout
30110 \begin_layout Plain Layout
30123 \begin_inset Newline newline
30127 \begin_inset Newline newline
30134 @addtoreset{equation}{section}
30137 \begin_layout Standard
30138 To be able to use these commands in TeX-mode, the
30139 \begin_inset Quotes eld
30143 \begin_inset Quotes erd
30146 character has to be made
30147 \begin_inset Quotes eld
30151 \begin_inset Quotes erd
30154 for LaTeX using the command
30168 So the command sequence in TeX-mode is:
30171 \begin_layout Standard
30177 \begin_inset Newline newline
30182 @addtoreset{equation}{section}
30183 \begin_inset Newline newline
30191 \begin_layout Standard
30192 In the LaTeX-preamble
30204 can be omitted as they are automatically internally inserted by LyX.
30207 \begin_layout Standard
30222 \begin_layout Plain Layout
30227 is part of the LaTeX-package
30235 \begin_layout Plain Layout
30236 Packages ! carlisle
30241 that is part of every LaTeX standard installation.
30250 \begin_layout Plain Layout
30251 Packages ! remreset
30256 has to be loaded in the LaTeX-preamble with the line
30259 \begin_layout Standard
30264 usepackage{remreset}
30267 \begin_layout Standard
30278 \begin_layout Plain Layout
30283 \begin_layout Plain Layout
30294 \begin_layout Plain Layout
30307 \begin_layout Plain Layout
30318 \begin_layout Plain Layout
30330 can be used with the same scheme as
30339 \begin_layout Standard
30340 \begin_inset VSpace bigskip
30343 Sometimes formulas should be numbered in the following form:
30346 \begin_layout Standard
30349 (section number.formula number)
30352 \begin_layout Standard
30353 The formula number should start with every section with
30354 \begin_inset Quotes eld
30358 \begin_inset Quotes erd
30364 \begin_layout Standard
30365 For this case there is the command
30375 \begin_layout Plain Layout
30383 , which is used with the following scheme:
30386 \begin_layout Standard
30391 numberwithin{counter}{sectioning}
30394 \begin_layout Standard
30395 Counter denotes what kind of numbering is affected, sectioning denotes what
30396 number is before the dot.
30399 \begin_layout Standard
30400 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30403 \begin_layout Standard
30408 numberwithin{equation}{section}
30411 \begin_layout Standard
30412 This is the result:
30416 \begin_layout Plain Layout
30420 numberwithin{equation}{section}
30426 \begin_inset Formula \begin{equation}
30427 A+B=C\end{equation}
30434 \begin_layout Standard
30436 \begin_inset space \thinspace{}
30440 \begin_inset space \space{}
30443 tables so that the number of the part is the sectioning,
30444 \begin_inset Newline newline
30451 numberwithin{table}{part}
30456 \begin_layout Standard
30457 To go back to the standard numbering or to prevent this kind of numbering
30458 when it is defined by the document class, the following command is inserted
30459 as TeX-Code or to the LaTeX-preamble:
30462 \begin_layout Standard
30475 \begin_layout Plain Layout
30489 \begin_layout Plain Layout
30505 \begin_inset Newline newline
30513 \begin_inset Newline newline
30525 \begin_layout Standard
30532 uses internally the command
30538 , described above, that also needs to be reverted.
30542 \begin_layout Plain Layout
30549 \begin_layout Plain Layout
30553 @removefromreset{equation}{section}
30556 \begin_layout Plain Layout
30568 \begin_layout Subsection
30569 Numbering with Roman Numbers and Letters
30573 \begin_layout Plain Layout
30574 Formula numbering ! with letters
30583 \begin_layout Plain Layout
30584 Formula numbering ! with Roman numbers
30592 \begin_layout Standard
30593 Formulas can also be numbered with Roman numbers and Latin letters.
30594 To number for example with small Roman numbers, the command
30597 \begin_layout Standard
30609 \begin_layout Standard
30610 is inserted before the formula in TeX-mode.
30621 \begin_layout Plain Layout
30629 redefines the predefined command
30645 \begin_layout Plain Layout
30652 has the same scheme like the command
30658 that is described in
30659 \begin_inset CommandInset ref
30661 reference "sec:User-defined-Commands"
30675 is the formula counter.
30682 is used as prefix for a counter, the value of the counter is output as
30684 When a formula is numbered, LaTeX sets internally the command
30690 behind the formula.
30699 \begin_layout Plain Layout
30709 outputs the counter as small Roman number.
30712 \begin_layout Standard
30713 All formulas behind the command
30723 are now numbered Roman.
30724 To switch to numbering with big Roman numbers, the command is inserted
30741 \begin_layout Plain Layout
30753 \begin_inset Quotes eld
30757 \begin_inset Quotes erd
30760 with small Latin letters there is the command
30770 \begin_layout Plain Layout
30778 , for big ones there is the command
30788 \begin_layout Plain Layout
30801 \begin_layout Standard
30802 \begin_inset Note Greyedout
30805 \begin_layout Plain Layout
30810 Only maximal 26 formulas can be numbered with Latin letters in one document.
30818 \begin_layout Standard
30822 \begin_layout Plain Layout
30838 \begin_layout Standard
30839 \begin_inset Formula \begin{equation}
30840 A=\textrm{small roman}\label{eq:rom}\end{equation}
30848 \begin_layout Plain Layout
30862 \begin_inset Formula \begin{equation}
30863 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30871 \begin_layout Plain Layout
30885 \begin_inset Formula \begin{equation}
30886 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30894 \begin_layout Plain Layout
30908 \begin_inset Formula \begin{equation}
30909 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30916 \begin_layout Standard
30917 To switch back to the default numbering, insert the command:
30920 \begin_layout Standard
30933 \begin_layout Plain Layout
30944 \begin_layout Standard
30948 \begin_layout Plain Layout
30962 \begin_inset Formula \begin{equation}
30963 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30970 \begin_layout Standard
30971 \begin_inset VSpace medskip
30974 As you see, formulas are numbered serially independent from the numbering
30976 When then numbering should start with
30977 \begin_inset Quotes eld
30981 \begin_inset Quotes erd
30984 when the style is changed, new equation counters have to be defined.
30985 A description about this can be found in the file
30986 \begin_inset CommandInset href
30988 target "Formula-numbering.lyx"
30995 \begin_layout Section
30996 User-defined Commands
30997 \begin_inset CommandInset label
30999 name "sec:User-defined-Commands"
31007 \begin_layout Plain Layout
31008 User-defined commands
31016 \begin_layout Standard
31017 Many LaTeX-commands are too long to be used frequently.
31018 But it is possible to define with the command
31028 \begin_layout Plain Layout
31036 new shorter commands.
31039 \begin_layout Standard
31040 The command scheme of
31049 \begin_layout Standard
31054 newcommand{new command name}[number of arguments][optional
31059 \begin_inset Newline newline
31066 \begin_layout Plain Layout
31081 \begin_layout Plain Layout
31088 {command definition}
31091 \begin_layout Standard
31092 \begin_inset Note Greyedout
31095 \begin_layout Plain Layout
31100 Assure that the name of the new command is not already used in your document
31101 or by LaTeX-packages that you use.
31102 When you for example define the command
31114 , you get an error message because
31120 is already defined as command for
31121 \begin_inset Quotes eld
31125 \begin_inset Formula $\le$
31129 \begin_inset Quotes erd
31140 \begin_layout Standard
31141 \begin_inset Note Greyedout
31144 \begin_layout Plain Layout
31149 The names of user-defined commands may only consist of Latin letters.
31157 \begin_layout Standard
31158 The number of arguments is an integer in the range 0
31159 \begin_inset space \thinspace{}
31163 \begin_inset space \thinspace{}
31166 9 and specifies how many arguments the new command should have.
31167 With the optional value a value for an optional argument can be predefined.
31168 When this is done, the
31176 rgument of the new command is automatically an optional one.
31179 \begin_layout Standard
31180 Here are some examples:
31183 \begin_layout Itemize
31184 To define the command
31196 , the LaTeX-preamble line is:
31200 \begin_layout Plain Layout
31212 \begin_inset Newline newline
31224 \begin_layout Itemize
31225 To define the command
31237 , the argument (that should be underlined) must be taken into account.
31238 For this the preamble line is:
31242 \begin_layout Plain Layout
31254 \begin_inset Newline newline
31269 \begin_layout Plain Layout
31281 \begin_inset Newline newline
31290 acts as argument placeholder, the
31294 behind it denotes that it is the placeholder for the first argument.
31297 \begin_layout Itemize
31305 \begin_inset space \thinspace{}
31309 \begin_inset space \space{}
31322 \begin_layout Plain Layout
31334 \begin_inset Newline newline
31343 framebox#1#2{$#3$}}
31349 \begin_layout Plain Layout
31361 \begin_inset Newline newline
31366 The two Dollar signs creates the extra formula needed for
31373 \begin_inset CommandInset ref
31375 reference "sub:Boxes-with-Frame"
31382 \begin_layout Itemize
31383 To create a new command for
31389 where the color for the box needn't to be specified, the argument for the
31390 color is defined optional:
31394 \begin_layout Plain Layout
31406 \begin_inset Newline newline
31415 fcolorbox{#2}{#1}{$#3$}}
31421 \begin_layout Plain Layout
31431 \begin_inset Newline newline
31434 When the color is not specified when using
31440 , the predefined color
31447 \begin_layout Standard
31448 A test of the new defined commands:
31451 \begin_layout Standard
31453 \begin_inset Tabular
31454 <lyxtabular version="3" rows="6" columns="2">
31456 <column alignment="center" valignment="top" width="0">
31457 <column alignment="center" valignment="top" width="0">
31459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31462 \begin_layout Plain Layout
31468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31471 \begin_layout Plain Layout
31473 \begin_inset Note Note
31476 \begin_layout Plain Layout
31483 is only used as spacer.
31495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31498 \begin_layout Plain Layout
31505 \begin_layout Plain Layout
31519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31522 \begin_layout Plain Layout
31523 \begin_inset Formula $A\gr B$
31533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31536 \begin_layout Plain Layout
31544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31547 \begin_layout Plain Layout
31548 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31561 \begin_layout Plain Layout
31565 \begin_inset Formula $\to$
31571 \begin_inset Formula $\to$
31582 \begin_layout Plain Layout
31596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31599 \begin_layout Plain Layout
31600 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31613 \begin_layout Plain Layout
31617 \begin_inset Formula $\to$
31628 \begin_layout Plain Layout
31642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31645 \begin_layout Plain Layout
31646 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31659 \begin_layout Plain Layout
31665 \begin_inset Formula $\to$
31676 \begin_layout Plain Layout
31690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31693 \begin_layout Plain Layout
31694 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31710 \begin_layout Section
31714 \begin_layout Standard
31715 LyX supports two types of commutative diagrams:
31723 that are explained in the following.
31726 \begin_layout Subsection
31731 \begin_layout Plain Layout
31740 \begin_layout Standard
31741 Diagrams of this type visualize relations by vertical and horizontal lines
31743 \begin_inset Formula \[
31744 \begin{CD}A@>>>B@>>>C\\
31746 F@<<<E@<<<D\end{CD}\]
31753 \begin_layout Standard
31754 To get them, the command
31762 \begin_layout Plain Layout
31772 is inserted to a formula.
31773 A blue box appears with two dashed lines where further commands can be
31778 arg "newline-insert newline"
31781 a new line is created.
31782 Horizontal relations are inserted in odd, vertical in even formula lines.
31785 \begin_layout Standard
31786 To create the relations there are the following commands:
31789 \begin_layout Itemize
31794 creates a left arrow,
31805 \begin_layout Itemize
31810 creates an up arrow,
31818 a vertical equal sign
31821 \begin_layout Itemize
31827 is a placeholder for non-existent relations
31830 \begin_layout Standard
31831 All arrows can be labeled as follows:
31834 \begin_layout Itemize
31835 Is text inserted between the first and second < or >, resp., it is placed
31837 When it is inserted between the second and third one, it appears under
31841 \begin_layout Itemize
31842 When text for vertical arrows is inserted between the first and second A
31843 or V, resp., it is placed left beside the arrow.
31844 When it is inserted between the second and third one, it appears right
31846 If the text contains an A or V, these letters must be set into a TeX-brace.
31849 \begin_layout Standard
31850 As example a diagram with all possible relations:
31853 \begin_layout Standard
31854 \begin_inset Formula \[
31855 \begin{CD}A@>j>>B@>>k>C@=F\\
31857 D@<<j<E@>k>>F@=C\end{CD}\]
31864 \begin_layout Standard
31865 The command for this is:
31866 \begin_inset Newline newline
31877 \begin_layout Plain Layout
31886 A@>j>>B@>>k>C@=F Ctrl+Return
31887 \begin_inset Newline newline
31894 \begin_layout Plain Layout
31909 \begin_layout Plain Layout
31922 \begin_layout Plain Layout
31934 \begin_inset Formula $\to$
31940 \begin_inset Newline newline
31947 \begin_layout Plain Layout
31962 \begin_layout Plain Layout
31975 \begin_layout Plain Layout
31985 \begin_layout Subsection
31990 \begin_layout Plain Layout
31991 Diagrams ! xymatrix
31999 \begin_layout Standard
32000 To be able to use xymatrices, the LaTeX-package
32005 A xymatrix is created by inserting the command
32012 Then you are able to add new matrix columns and rows like for normal matrices,
32014 \begin_inset CommandInset ref
32016 reference "sec:Matrices"
32023 \begin_layout Standard
32024 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32026 All possibilities to create commutative diagrams and decorations are explained
32027 in detail in this manual:
32028 \begin_inset CommandInset href
32030 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
32037 \begin_layout Standard
32038 \begin_inset Newpage newpage
32044 \begin_layout Section
32049 \begin_layout Plain Layout
32062 \begin_layout Plain Layout
32063 Other useful math tips can be found in
32064 \begin_inset CommandInset citation
32079 \begin_layout Plain Layout
32087 \begin_inset Note Note
32090 \begin_layout Plain Layout
32093 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
32096 \begin_layout Plain Layout
32099 texorpdfstring is in section
32100 \begin_inset CommandInset ref
32102 reference "sub:Formulas-in-Section"
32115 \begin_layout Plain Layout
32125 \begin_layout Plain Layout
32130 \begin_layout Plain Layout
32137 Chemical characters
32141 \begin_layout Plain Layout
32156 \begin_layout Subsection
32157 Chemical Symbols and Equations
32158 \begin_inset CommandInset label
32160 name "sub:Chemical-Symbols-and"
32168 \begin_layout Plain Layout
32169 Chemical characters ! Symbols
32178 \begin_layout Plain Layout
32188 \begin_layout Plain Layout
32197 \begin_layout Standard
32198 An example text from chemistry:
32201 \begin_layout Quote
32203 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32206 -ion reacts with two
32207 \begin_inset Formula $\mathrm{Na^{+}}$
32210 -ions to sodium sulfate
32211 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32215 The chemical equation for this is:
32216 \begin_inset Formula \[
32217 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32224 \begin_layout Standard
32225 This chemical equation can directly be created as formula.
32226 To avoid that the symbols appear italic, everything is highlighted and
32227 changed by the shortcut
32233 to the upright font style.
32237 \begin_layout Plain Layout
32243 \begin_inset CommandInset ref
32245 reference "sub:Font-Styles"
32257 \begin_layout Subsection
32262 \begin_layout Plain Layout
32271 \begin_layout Standard
32272 Negative numbers often look ugly in formulas because the minus sign before
32273 the number is set with the same length as the minus operator sign.
32274 When writing the negative number in normal text, the minus sign appears
32278 \begin_layout Standard
32279 Thus, the problem disappears when converting the minus sign to mathematical
32283 \begin_layout Standard
32284 An example to visualize the problem:
32287 \begin_layout Standard
32289 \begin_inset Tabular
32290 <lyxtabular version="3" rows="3" columns="2">
32292 <column alignment="right" valignment="top" width="0">
32293 <column alignment="left" valignment="top" width="0">
32295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32298 \begin_layout Plain Layout
32304 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32307 \begin_layout Plain Layout
32315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32318 \begin_layout Plain Layout
32324 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32327 \begin_layout Plain Layout
32328 \begin_inset Formula $x=-2$
32338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32341 \begin_layout Plain Layout
32347 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32350 \begin_layout Plain Layout
32351 \begin_inset Formula $x=\textrm{-}2$
32367 \begin_layout Subsection
32368 Comma as decimal Separator
32372 \begin_layout Plain Layout
32381 \begin_layout Standard
32382 In LaTeX a comma inside a formula is used, according to the English convention,
32383 as number group separator.
32384 So there will be space added behind all commas in formulas.
32387 \begin_layout Standard
32388 To avoid this, the comma is highlighted and changed to mathematical text
32398 \begin_layout Standard
32399 To use all formula commas in the document as decimal separator, the file
32408 \begin_layout Plain Layout
32413 is part of the LaTeX-package
32421 \begin_layout Plain Layout
32426 \begin_layout Plain Layout
32449 \begin_layout Plain Layout
32455 is loaded with the LaTeX-preamble line
32458 \begin_layout Standard
32466 \begin_layout Subsection
32468 \begin_inset CommandInset label
32470 name "sub:Physical-Vectors"
32478 \begin_layout Plain Layout
32487 \begin_layout Standard
32488 Predefined vectors are offered by the LaTeX-package
32496 \begin_layout Plain Layout
32501 should be part of every LaTeX standard installation.
32510 \begin_layout Plain Layout
32516 that is loaded with the LaTeX-preamble line
32519 \begin_layout Standard
32527 \begin_layout Standard
32531 \begin_layout Plain Layout
32541 \begin_inset Note Note
32544 \begin_layout Plain Layout
32545 The following table will only be displayed when the LaTeX-package
32554 The following commands are defined:
32557 \begin_layout Standard
32559 \begin_inset Tabular
32560 <lyxtabular version="3" rows="4" columns="2">
32562 <column alignment="center" valignment="top" width="0">
32563 <column alignment="center" valignment="top" width="0">
32565 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32568 \begin_layout Plain Layout
32574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32577 \begin_layout Plain Layout
32585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32588 \begin_layout Plain Layout
32598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32601 \begin_layout Plain Layout
32602 \begin_inset Formula $\Bra{\psi}$
32612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32615 \begin_layout Plain Layout
32625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32628 \begin_layout Plain Layout
32629 \begin_inset Formula $\Ket{\psi}$
32639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32642 \begin_layout Plain Layout
32654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32657 \begin_layout Plain Layout
32658 \begin_inset Formula $\Braket{\psi|\phi}$
32674 \begin_layout Standard
32681 assures that all vertical bars are set in the size of the surrounding brackets:
32682 \begin_inset Formula \[
32683 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32691 \begin_layout Plain Layout
32701 \begin_inset Note Note
32704 \begin_layout Plain Layout
32705 The following will be displayed when the LaTeX-package
32717 \begin_layout Standard
32718 You need to install the LaTeX-package
32722 to see the rest of this subsection in the output.
32725 \begin_layout Standard
32729 \begin_layout Plain Layout
32741 \begin_layout Standard
32748 can also be achieved using the command
32754 , that is described in
32755 \begin_inset CommandInset ref
32757 reference "sub:Automatic-Bracket-Size"
32764 \begin_layout Subsection
32765 Self-defined Fractions
32766 \begin_inset CommandInset label
32768 name "sub:Self-defined-Fractions"
32776 \begin_layout Plain Layout
32777 Fractions ! self-defined
32785 \begin_layout Standard
32786 To define custom commands for fractions, the command
32796 \begin_layout Plain Layout
32804 is used in the following scheme:
32807 \begin_layout Standard
32820 bracket}{fraction bar thickness}{style}
32821 \begin_inset Newline newline
32828 \begin_layout Plain Layout
32843 \begin_layout Plain Layout
32850 {numerator}{denominator}
32853 \begin_layout Standard
32854 The style is a number in the range of 0
32855 \begin_inset space \thinspace{}
32859 \begin_inset space \thinspace{}
32865 \begin_layout Standard
32867 \begin_inset Tabular
32868 <lyxtabular version="3" rows="5" columns="2">
32870 <column alignment="center" valignment="top" width="0">
32871 <column alignment="center" valignment="top" width="0">
32873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32876 \begin_layout Plain Layout
32882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32885 \begin_layout Plain Layout
32893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32896 \begin_layout Plain Layout
32902 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32905 \begin_layout Plain Layout
32906 display style formula
32913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32916 \begin_layout Plain Layout
32922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32925 \begin_layout Plain Layout
32933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32936 \begin_layout Plain Layout
32942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32945 \begin_layout Plain Layout
32953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32956 \begin_layout Plain Layout
32962 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32965 \begin_layout Plain Layout
32979 \begin_layout Standard
32980 When no style is given, the size is adjusted to the surrounding environment
32981 like for the command
32990 \begin_layout Standard
32991 When no fraction bar thickness is given, the predefined value of 0.4
32992 \begin_inset space \thinspace{}
32998 \begin_layout Standard
32999 \begin_inset VSpace medskip
33002 For example, the commands
33015 \begin_inset CommandInset ref
33017 reference "sub:Fractions"
33021 are defined with the commands
33024 \begin_layout Standard
33033 genfrac{}{}{}{0}{#1}{#2}}
33036 \begin_layout Standard
33040 \begin_layout Standard
33049 genfrac{(}{)}{0pt}{1}{#1}{#2}}
33052 \begin_layout Standard
33053 \begin_inset VSpace medskip
33056 To define a fraction where the fraction bar thickness can be given as optional
33057 argument, the following line is inserted to the LaTeX-preamble:
33060 \begin_layout Standard
33069 genfrac{}{}{#1}{}{#2}{#3}}
33072 \begin_layout Standard
33074 \begin_inset Formula \begin{align*}
33075 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
33076 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
33080 As one can see, the distance of the numerator and the denominator to the
33081 fraction bar is round about three times the bar thickness.
33084 \begin_layout Subsection
33089 \begin_layout Plain Layout
33098 \begin_layout Standard
33099 To cancel formulas or formula parts, the LaTeX-package
33107 \begin_layout Plain Layout
33112 is part of every LaTeX standard installation.
33121 \begin_layout Plain Layout
33127 has to be loaded with the LaTeX-preamble line
33130 \begin_layout Standard
33135 usepackage[samesize]{cancel}
33138 \begin_layout Standard
33139 There are four ways to cancel formulas:
33142 \begin_layout Standard
33144 \begin_inset Tabular
33145 <lyxtabular version="3" rows="5" columns="2">
33147 <column alignment="center" valignment="top" width="0">
33148 <column alignment="center" valignment="top" width="0">
33150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33153 \begin_layout Plain Layout
33159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33162 \begin_layout Plain Layout
33164 \begin_inset Note Note
33167 \begin_layout Plain Layout
33180 are used here as spacer.
33192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33195 \begin_layout Plain Layout
33204 \begin_layout Plain Layout
33218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33221 \begin_layout Plain Layout
33222 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33235 \begin_layout Plain Layout
33244 \begin_layout Plain Layout
33258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33261 \begin_layout Plain Layout
33262 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33275 \begin_layout Plain Layout
33284 \begin_layout Plain Layout
33298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33301 \begin_layout Plain Layout
33302 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33312 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33315 \begin_layout Plain Layout
33319 \begin_inset Formula $\to$
33330 \begin_layout Plain Layout
33344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33347 \begin_layout Plain Layout
33348 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33364 \begin_layout Standard
33371 is especially suitable to visualize the reduction of fractions within formulas:
33372 \begin_inset Formula \[
33373 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33380 \begin_layout Subsection
33381 Formulas in Section Headings
33382 \begin_inset CommandInset label
33384 name "sub:Formulas-in-Section"
33392 \begin_layout Plain Layout
33393 Formula ! in section headings
33401 \begin_layout Standard
33402 When formulas are used in section headings, the following has to be taken
33406 \begin_layout Standard
33407 \begin_inset Note Greyedout
33410 \begin_layout Plain Layout
33419 \begin_layout Plain Layout
33420 Packages ! hyperref
33425 support is enabled in the document settings dialog under
33428 \begin_inset space ~
33433 , PDF-bookmarks are created for every section heading in the table of contents.
33434 If a section heading contains formulas, they are incorrectly displayed
33435 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33444 \begin_layout Standard
33445 Both problems can be solved by inserting at the end of the section heading
33446 a short title with the menu
33448 Insert\SpecialChar \menuseparator
33450 \begin_inset space ~
33456 Short titles are used as alternative for multiline section headings to
33457 keep the table of contents clearly arranged.
33458 Only the short title appears in the table of contents and therefore also
33459 in the PDF-bookmark.
33462 \begin_layout Standard
33463 When formulas should be used in the table of contents but
33467 is used, one can use the following command in TeX-mode:
33470 \begin_layout Standard
33475 texorpdfstring{part}{alternative}
33479 \begin_layout Plain Layout
33490 \begin_layout Standard
33491 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33492 This can be characters, formulas, footnotes, but also cross-references.
33493 The alternative is used instead of the part for the bookmark.
33496 \begin_layout Standard
33497 Here are two example headings:
33498 \begin_inset VSpace -3mm
33505 \begin_layout Plain Layout
33517 \begin_layout Subsubsection
33518 Heading without formula in table of contents
33519 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33523 \begin_inset OptArg
33526 \begin_layout Plain Layout
33527 Heading without formula in table of contents
33535 \begin_layout Subsubsection
33536 Heading with formula in table of contents
33540 \begin_layout Plain Layout
33550 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33557 \begin_layout Plain Layout
33567 \begin_layout Standard
33571 \begin_layout Plain Layout
33580 In the first heading a short title was used, in the second one
33589 \begin_layout Standard
33590 To get the same formatting as for the other headings, the complete heading
33599 \begin_layout Plain Layout
33601 \begin_inset CommandInset ref
33603 reference "sub:Bold-Formulas"
33615 \begin_layout Subsection
33616 Formulas in multi-column Text
33620 \begin_layout Plain Layout
33621 Formula ! in multi-column text
33629 \begin_layout Standard
33630 Formulas in multi-column text are often too wide to fit into a column and
33631 thus need to be set over the whole page width.
33632 This is done by using the LaTeX-package
33640 \begin_layout Plain Layout
33645 is part of every LaTeX standard installation.
33654 \begin_layout Plain Layout
33655 Packages ! multicol
33660 , that is loaded with the LaTeX-preamble line
33663 \begin_layout Standard
33668 usepackage{multicol}
33671 \begin_layout Standard
33672 \begin_inset Note Greyedout
33675 \begin_layout Plain Layout
33676 Note herby that the setting
33679 \begin_inset space ~
33686 Document\SpecialChar \menuseparator
33692 \begin_inset space ~
33712 \begin_layout Standard
33713 Before the multi-column text the command
33716 \begin_layout Standard
33721 begin{multicols}{column number}
33724 \begin_layout Standard
33725 is written in TeX-mode.
33726 The column number is a number in the range of 2
33727 \begin_inset space \thinspace{}
33731 \begin_inset space \thinspace{}
33735 Before the formula the multi-column text is ended by inserting the command
33738 \begin_layout Standard
33746 \begin_layout Standard
33750 \begin_layout Standard
33751 Due to the command some space is automatically added before the formula.
33753 \begin_inset space \thinspace{}
33756 mm vertical space is inserted before the formula.
33757 When the formula style
33763 \begin_layout Plain Layout
33765 \begin_inset CommandInset ref
33767 reference "sec:Formula-Styles"
33779 \begin_inset space \thinspace{}
33782 mm space is inserted instead.
33785 \begin_layout Standard
33786 As example a multi-column text with a displayed formula:
33789 \begin_layout Standard
33793 \begin_layout Plain Layout
33797 begin{multicols}{2}
33802 Das Spektrum wird fouriertransformiert.
33803 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33804 , Lösungsmittel) zu trennen.
33805 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33806 nun das Aussehen des Ausgangssignals.
33807 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33808 über alle Phasen integrieren muss.
33810 \begin_inset Formula $S$
33813 unser normiertes Ausgangssignal and
33814 \begin_inset Formula $P$
33817 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33821 \begin_layout Plain Layout
33831 \begin_inset VSpace -6mm
33835 \begin_inset Formula \begin{equation}
33836 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33844 \begin_layout Plain Layout
33848 begin{multicols}{2}
33854 \begin_inset Formula $S_{0}$
33857 das Signal ohne Gradient ist and the Normierungsbedingung
33858 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33862 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33864 \begin_inset Formula $\nicefrac{\pi}{2}$
33868 \begin_inset space \thinspace{}
33871 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33872 das Signal zusätzlich abschwächt.
33873 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33875 \begin_inset Formula $T_{2}$
33881 \begin_layout Standard
33885 \begin_layout Plain Layout
33897 \begin_layout Subsection
33898 Formulas with Description of Variables
33902 \begin_layout Plain Layout
33903 Formula ! with description of variables
33911 \begin_layout Standard
33912 To describe variables within a formula, like in formula
33913 \begin_inset CommandInset ref
33915 reference "eq:within"
33924 \begin_inset Formula $n$
33928 \begin_inset space ~
33931 matrix is used with left aligned columns for the
33932 \begin_inset Formula $n$
33939 \begin_layout Plain Layout
33941 \begin_inset CommandInset ref
33943 reference "sec:Matrices"
33952 To set the description in a smaller size, before the matrix e.
33953 \begin_inset space \thinspace{}
33957 \begin_inset space \space{}
33970 \begin_layout Plain Layout
33972 \begin_inset CommandInset ref
33974 reference "sub:Font-Sizes"
33986 \begin_layout Standard
33987 When the formula style
33993 \begin_layout Plain Layout
33995 \begin_inset CommandInset ref
33997 reference "sec:Formula-Styles"
34018 \begin_layout Plain Layout
34025 only works in formulas with the style
34030 \begin_inset CommandInset ref
34032 reference "sub:Variable-Space"
34041 is inserted before and after the matrix to have the same separation of
34042 the matrix from the equation and the side margin.
34045 \begin_layout Standard
34046 When the formula style
34050 is used, the method described in
34051 \begin_inset CommandInset ref
34053 reference "sub:Flalign-Environment"
34057 is used to indent formulas.
34059 \begin_inset CommandInset ref
34061 reference "eq:within"
34065 consists of five columns whereas in the first two columns contain the equation,
34066 the third the matrix, and the last one an empty TeX-brace.
34067 \begin_inset Formula \begin{flalign}
34068 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
34069 \rho & \textrm{density}\\
34070 V & \textrm{volume}\\
34071 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
34078 \begin_layout Subsection
34079 Upright small Greek Letters
34080 \begin_inset CommandInset label
34082 name "sub:Upright-small-Greek"
34090 \begin_layout Plain Layout
34091 Greek letters ! upright
34099 \begin_layout Standard
34100 Most of the math fonts only provide italic small Greek letters.
34101 But for symbols of elementary particles like pions and neutrinos, upright
34102 Greek letters are needed.
34111 \begin_layout Plain Layout
34116 is part of the LaTeX-package
34124 \begin_layout Plain Layout
34129 \begin_layout Plain Layout
34152 \begin_layout Plain Layout
34158 that is loaded with the LaTeX-preamble line
34161 \begin_layout Standard
34166 usepackage{upgreek}
34169 \begin_layout Standard
34175 \begin_layout Plain Layout
34185 \begin_inset Note Note
34188 \begin_layout Plain Layout
34189 The following table will only be displayed when the LaTeX-package
34198 They are created when the command for a small Greek letters is started
34204 For example the command
34211 \begin_inset Formula $\uptau$
34217 \begin_layout Standard
34218 With these commands reactions of elementary particles can be typeset:
34219 \begin_inset Formula \[
34220 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34227 \begin_layout Standard
34228 The upright letters are more bold and wider than the italic ones.
34229 They should therefore not be used for units like
34230 \begin_inset Quotes eld
34234 \begin_inset Quotes erd
34240 \begin_layout Standard
34244 \begin_layout Plain Layout
34254 \begin_inset Note Note
34257 \begin_layout Plain Layout
34258 The following will be displayed when the LaTeX-package
34270 \begin_layout Standard
34271 You need to install the LaTeX-package
34275 to see the rest of this subsection in the output.
34278 \begin_layout Standard
34282 \begin_layout Plain Layout
34294 \begin_layout Subsection
34295 Text Characters in Formulas
34296 \begin_inset CommandInset label
34298 name "sub:Text-Characters-in"
34306 \begin_layout Plain Layout
34315 \begin_layout Standard
34316 In some cases you might want to insert text characters directly into formulas.
34317 When for example the centered dot · is often used in formulas like
34318 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34321 , one would have to insert the command
34331 \begin_layout Plain Layout
34333 \begin_inset CommandInset ref
34335 reference "sub:Binary-Operators"
34344 all the time, because this character is defined in all encodings as text
34346 But the encoding can be changed by this LaTeX-preamble line:
34349 \begin_layout Standard
34354 Declare Inputtext{183}{
34364 f\SpecialChar \textcompwordmark{}
34368 \begin_layout Standard
34369 The character encoding (menu
34371 Document\SpecialChar \menuseparator
34372 Settings\SpecialChar \menuseparator
34375 ) specifies what character appears when a keyboard key is pressed.
34376 When the key for the character '·' is pressed, internally the command
34383 But this command is not available in a formula so that you would get LaTeX-erro
34385 With the changed encoding the right command is chosen automatically, depending
34386 on if the character was inserted into a formula or not.
34389 \begin_layout Standard
34390 The encoding of several characters is saved in definition files.
34391 Fore example the encoding
34395 is defined in the file
34399 that is in the installation folder of LaTeX.
34400 Encodings should only be changed via the LaTeX-preamble and not in the
34402 Otherwise own documents could not be edited by other LyX users working
34403 on other computers.
34406 \begin_layout Standard
34407 \begin_inset VSpace medskip
34410 Besides the centered dot, in this document the degree sign ° is defined
34411 with the following LaTeX-preamble line so that it can directly be inserted
34415 \begin_layout Standard
34420 DeclareInputtext{176}{
34430 f\SpecialChar \textcompwordmark{}
34434 \begin_layout Standard
34435 \begin_inset Newpage newpage
34441 \begin_layout Section
34447 \begin_layout Plain Layout
34456 \begin_layout Standard
34457 This section is a summary of the most important typographic rules, listed
34462 \begin_layout Plain Layout
34463 This collection was partly taken from the German semi-official dictionary
34465 \begin_inset Quotes eld
34469 \begin_inset Quotes erd
34473 \begin_inset CommandInset citation
34479 that lists some of the ISO rules.
34487 \begin_layout Itemize
34496 \begin_layout Plain Layout
34497 done with font styles, see
34498 \begin_inset CommandInset ref
34500 reference "sub:Font-Styles"
34510 \begin_inset space \thinspace{}
34514 \begin_inset Newline newline
34517 Between the value and the unit is the smallest space, see
34518 \begin_inset CommandInset ref
34520 reference "sub:Predefined-Space"
34525 \begin_inset Newline newline
34528 This convention is automatically fulfilled when the command
34535 When it is entered to a formula, two boxes appear.
34536 In the first one the value is inserted, in the second one the unit, and
34538 \begin_inset Formula $\unit[30]{km/h}$
34542 \begin_inset space \thinspace{}
34552 is not a real LaTeX command but the command
34558 , therefore you cannot use it in TeX code.
34561 \begin_layout Itemize
34562 Percent and perthousand signs are set like physical units:
34563 \begin_inset Newline newline
34567 \begin_inset space \thinspace{}
34573 \begin_layout Itemize
34574 The degree sign follows directly on the value: 15°, but not when it is used
34576 \begin_inset space \thinspace{}
34582 \begin_layout Itemize
34583 In numbers with more than four digits the smallest space is inserted before
34584 every third digit to group them:
34594 \begin_inset space \thinspace{}
34598 \begin_inset space \thinspace{}
34604 \begin_layout Itemize
34605 For dimensions like 120×90×40
34606 \begin_inset space \thinspace{}
34609 cm the multiplication sign
34610 \begin_inset Quotes eld
34614 \begin_inset Quotes erd
34618 It is available via the menu
34620 Insert\SpecialChar \menuseparator
34621 Special Character\SpecialChar \menuseparator
34625 With some keyboard definitions it can also be inserted directly.
34628 \begin_layout Itemize
34629 Functions with names consisting of several letters are set upright to avoid
34631 \begin_inset CommandInset ref
34633 reference "sub:Predefined-Functions"
34640 \begin_layout Itemize
34641 Indices consisting of several letters, are set upright:
34642 \begin_inset Formula $E_{\mathrm{kin}}$
34646 \begin_inset Newline newline
34649 Components of matrices are set italic:
34650 \begin_inset Formula $\hat{H}_{kl}$
34656 \begin_layout Itemize
34657 The differentiation/integration operator 'd', the Euler's number 'e', and
34658 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34662 \begin_layout Standard
34663 \begin_inset Newpage newpage
34669 \begin_layout Section
34674 \begin_layout Plain Layout
34683 \begin_layout Standard
34684 Some characters and symbols can be created with several commands.
34685 Here is a list of the synonym commands:
34688 \begin_layout Standard
34689 \begin_inset VSpace bigskip
34693 \begin_inset space \hfill{}
34697 \begin_inset Tabular
34698 <lyxtabular version="3" rows="12" columns="2">
34700 <column alignment="center" valignment="top" width="0pt">
34701 <column alignment="center" valignment="top" width="0pt">
34703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34706 \begin_layout Plain Layout
34712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34715 \begin_layout Plain Layout
34717 \begin_inset Note Note
34720 \begin_layout Plain Layout
34727 is only used as spacer.
34739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34742 \begin_layout Plain Layout
34750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34753 \begin_layout Plain Layout
34757 \begin_layout Plain Layout
34770 \begin_layout Plain Layout
34784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34787 \begin_layout Plain Layout
34795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34798 \begin_layout Plain Layout
34808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34811 \begin_layout Plain Layout
34819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34822 \begin_layout Plain Layout
34832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34835 \begin_layout Plain Layout
34843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34846 \begin_layout Plain Layout
34854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34857 \begin_layout Plain Layout
34865 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34868 \begin_layout Plain Layout
34876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34879 \begin_layout Plain Layout
34887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34890 \begin_layout Plain Layout
34900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34903 \begin_layout Plain Layout
34911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34914 \begin_layout Plain Layout
34924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34927 \begin_layout Plain Layout
34935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34938 \begin_layout Plain Layout
34948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34951 \begin_layout Plain Layout
34959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34962 \begin_layout Plain Layout
34972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34975 \begin_layout Plain Layout
34983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34986 \begin_layout Plain Layout
34994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34997 \begin_layout Plain Layout
35005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35008 \begin_layout Plain Layout
35020 \begin_inset space \hfill{}
35024 \begin_inset Tabular
35025 <lyxtabular version="3" rows="12" columns="2">
35027 <column alignment="center" valignment="top" width="0pt">
35028 <column alignment="center" valignment="top" width="0pt">
35030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35033 \begin_layout Plain Layout
35039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35042 \begin_layout Plain Layout
35050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35053 \begin_layout Plain Layout
35061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35064 \begin_layout Plain Layout
35076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35079 \begin_layout Plain Layout
35087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35090 \begin_layout Plain Layout
35100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35103 \begin_layout Plain Layout
35111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35114 \begin_layout Plain Layout
35124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35127 \begin_layout Plain Layout
35135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35138 \begin_layout Plain Layout
35146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35149 \begin_layout Plain Layout
35157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35160 \begin_layout Plain Layout
35168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35171 \begin_layout Plain Layout
35179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35182 \begin_layout Plain Layout
35192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35195 \begin_layout Plain Layout
35203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35206 \begin_layout Plain Layout
35216 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35219 \begin_layout Plain Layout
35227 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35230 \begin_layout Plain Layout
35240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35243 \begin_layout Plain Layout
35251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35254 \begin_layout Plain Layout
35264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35267 \begin_layout Plain Layout
35275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35278 \begin_layout Plain Layout
35288 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35291 \begin_layout Plain Layout
35299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35302 \begin_layout Plain Layout
35316 \begin_inset space \hfill{}
35322 \begin_layout Standard
35323 \begin_inset Newpage newpage
35329 \begin_layout Bibliography
35330 \begin_inset CommandInset bibitem
35331 LatexCommand bibitem
35343 The LaTeX Companion
35346 Addison Wesley, 2004
35349 \begin_layout Bibliography
35350 \begin_inset CommandInset bibitem
35351 LatexCommand bibitem
35357 \begin_inset CommandInset href
35360 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35364 of LaTeX's math abilities
35367 \begin_layout Bibliography
35368 \begin_inset CommandInset bibitem
35369 LatexCommand bibitem
35374 LaTeX tips and tricks-
35375 \begin_inset CommandInset href
35378 target "http://tug.org/TeXnik/"
35385 \begin_layout Bibliography
35386 \begin_inset CommandInset bibitem
35387 LatexCommand bibitem
35393 \begin_inset CommandInset href
35396 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35404 \begin_layout Plain Layout
35416 \begin_layout Bibliography
35417 \begin_inset CommandInset bibitem
35418 LatexCommand bibitem
35424 \begin_inset CommandInset href
35427 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35431 of all symbols available with LaTeX-packages
35434 \begin_layout Bibliography
35435 \begin_inset CommandInset bibitem
35436 LatexCommand bibitem
35442 \begin_inset CommandInset href
35444 name "Documentation"
35445 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35449 of the LaTeX-package
35457 \begin_layout Plain Layout
35458 Packages ! hyperref
35466 \begin_layout Bibliography
35467 \begin_inset CommandInset bibitem
35468 LatexCommand bibitem
35474 \begin_inset CommandInset href
35477 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35488 \begin_inset CommandInset ref
35490 reference "sub:Operator-Limits"
35498 \begin_layout Plain Layout
35509 \begin_layout Bibliography
35510 \begin_inset CommandInset bibitem
35511 LatexCommand bibitem
35522 Auflage, Duden 2001
35525 \begin_layout Subsubsection*
35526 \begin_inset CommandInset index_print
35527 LatexCommand printindex