1 #LyX 1.6.6svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % Folgendes Problem lösen:
27 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
28 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
29 % die Kapitelnummer geschrieben.
30 % Als Lösung wird mehr Platz zwischen Nummer und
31 % Überschrift eingefügt.
32 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
33 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
35 % To be able to enter the character ° and · directly in LyX,
37 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
38 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
40 % increase link area for cross-references and autoname them,
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50 % don't load packages twice
51 % see first footnote in sec. 9.3
52 \@ifundefined{textcolor}{\usepackage{color}}{}
54 % the pages of the TOC are numbered roman
55 % and a PDF-bookmark for the TOC is added
57 \let\myTOC\tableofcontents
58 \renewcommand{\tableofcontents}{%
60 \pdfbookmark[1]{\contentsname}{}
63 \pagenumbering{arabic}}
65 % insert additional vertical space of 1.5 mm between footnotes,
67 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
69 % provides caption formatting
70 \setkomafont{captionlabel}{\bfseries}
73 \usepackage[samesize]{cancel}
75 % enables calculation of values,
78 % for multiple table row and column cells
85 % for the Fourier transformation symbol
88 % center multirows (e.g. in sec. 13.3)
89 \renewcommand{\multirowsetup}{\centering}
91 % define a color, used in sec.9.3
92 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
94 % declare operators (see sec. 10.4 and sec. 15.2)
95 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
96 \DeclareMathOperator{\sgn}{sgn}
98 \newcommand{\spce}{\textvisiblespace}
100 % example definitions for sec. 20.1
101 \newcommand{\gr}{\Longrightarrow}
102 \newcommand{\us}[1]{\underline{#1}}
103 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
104 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
105 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
107 % example macro from sec. 19.4
108 %\def\tagform@#1{\maketag@@@{|#1|}}
110 % macro from sec. 10.2
111 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
112 \def\mathclap {\mathpalette \mathclapinternal}
113 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
115 % redefine the greyed out note
116 \renewenvironment{lyxgreyedout}
117 {\textcolor{blue}\bgroup}{\egroup}
119 % ------------------------------------
120 % used to check for needed LaTeX packages
123 % check for package eurosym
124 % used for the Euro symbol
126 \IfFileExists{eurosym.sty}
127 {\usepackage[gennarrow]{eurosym}
128 \setboolean{eurosym}{true}}
129 {\setboolean{eurosym}{false}}
131 % check for package braket
132 % used for physical vectors
134 \IfFileExists{braket.sty}
136 \setboolean{braket}{true}}
137 {\setboolean{braket}{false}}
139 % check for package upgreek
141 \IfFileExists{upgreek.sty}
142 {\usepackage{upgreek}
143 \setboolean{upgreek}{true}}
144 {\setboolean{upgreek}{false}}
146 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
147 \use_default_options false
152 \font_typewriter default
153 \font_default_family default
163 \pdf_title "LyX's Math Manual"
164 \pdf_author "LyX Team, Uwe Stöhr"
165 \pdf_subject "LyX-documentation about math"
166 \pdf_keywords "LyX, Mathed"
168 \pdf_bookmarksnumbered true
169 \pdf_bookmarksopen true
170 \pdf_bookmarksopenlevel 1
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183 \paperorientation portrait
186 \paragraph_separation skip
188 \quotes_language english
191 \paperpagestyle plain
195 \tracking_changes false
196 \output_changes false
204 LyX's detailed Math manual
212 \begin_layout Plain Layout
214 If you have comments or error corrections, please send them to the LyX Documenta
218 \begin_inset CommandInset href
220 name "lyx-docs@lists.lyx.org"
221 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
232 \begin_inset Note Note
235 \begin_layout Plain Layout
242 \begin_inset Newline newline
246 \begin_inset Newline newline
254 \begin_layout Standard
255 \begin_inset CommandInset toc
256 LatexCommand tableofcontents
263 \begin_layout Standard
264 \begin_inset Note Note
267 \begin_layout Plain Layout
268 To export this document to PDF, PS or DVI the LaTeX-packages
293 are not installed you can export the document anyway but the sections where
294 the packages are required won't appear in the output.
299 is not installed, this file cannot be exported.
302 \begin_layout Plain Layout
303 The latest PDF-version of this document can be found here:
304 \begin_inset Newline newline
309 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
317 \begin_layout Standard
318 \begin_inset Newpage newpage
324 \begin_layout Section
328 \begin_layout Standard
329 This document explains LyX's math features and is furthermore a collection
330 of LaTeX-commands used for mathematical characters and constructs.
331 The explanations are designed for the usage of commands.
332 It is therefore required that you have read the section
343 \begin_layout Standard
344 Most of the characters and many constructs explained in this manual are
345 also accessible via the menu
349 \SpecialChar \menuseparator
365 But everybody who has to write lots of formulas will notice that it is
366 much faster to use commands instead of the math toolbar.
367 Therefore this manual is focused on commands but also mentions the correspondin
368 g toolbar buttons when available.
371 \begin_layout Standard
372 If not specially mentioned the commands are only available within formulas.
373 To be able to use all commands explained in this document, the option
377 must be used in the document settings (menu
379 Document\SpecialChar \menuseparator
380 Settings\SpecialChar \menuseparator
391 \begin_layout Plain Layout
394 Use AMS math package automatically
400 \begin_layout Plain Layout
409 -math when math constructs are found that are supported by LyX.
417 \begin_layout Standard
418 This document doesn't list all
422 \begin_layout Plain Layout
435 \begin_layout Plain Layout
440 \begin_layout Plain Layout
449 -math commands is in the file
452 \begin_inset CommandInset href
455 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
461 , which is part of every LaTeX standard installation.
466 for lucidity reasons.
469 \begin_layout Section
473 \begin_layout Standard
474 To create an inline formula
478 \begin_layout Plain Layout
484 that is embedded into a text line, use one of the shortcuts
490 or the toolbar button
491 \begin_inset Graphics
492 filename ../images/math-mode.png
498 \begin_inset Newline newline
501 To create a display style formula
505 \begin_layout Plain Layout
506 Formula ! display style
511 that will appear bigger and in an own paragraph, use one of these shortcuts:
521 \begin_layout Standard
522 To change a display style formula to an inline formula, set the cursor into
523 the formula and use one of the shortcuts
531 Edit\SpecialChar \menuseparator
532 Math\SpecialChar \menuseparator
536 The same way is used to change an inline formula to a display style formula.
539 \begin_layout Standard
540 To display parts of an inline formula in the size of a display style formula,
551 \begin_layout Plain Layout
560 Then a new blue box appears in which the desired formula part is inserted.
563 \begin_layout Standard
564 Only inline formulas are allowed inside tables.
567 \begin_layout Standard
572 can be turned on in the menu
574 View\SpecialChar \menuseparator
578 When you click there on
579 \begin_inset Quotes eld
583 \begin_inset Quotes erd
586 the toolbar will be shown permanently at the bottom; this state is visualized
591 menu with a checkmark.
592 When you click in this state again on
593 \begin_inset Quotes eld
597 \begin_inset Quotes erd
608 is only shown when the cursor is within a formula; this state is visualized
609 by the renaming of the menu entry from
610 \begin_inset Quotes eld
614 \begin_inset Quotes erd
618 \begin_inset Quotes eld
626 \begin_inset Quotes erd
632 \begin_layout Standard
637 \begin_layout Plain Layout
643 is invoked by pressing the toolbar button
644 \begin_inset Graphics
645 filename ../images/ert-insert.png
652 Insert\SpecialChar \menuseparator
657 \begin_layout Plain Layout
673 \begin_inset Note Note
676 \begin_layout Plain Layout
677 In LyX there are three
678 \begin_inset Quotes eld
682 \begin_inset Quotes erd
685 that appear in the output with sub- and superscript letters: TeX, LaTeX
689 \begin_layout Plain Layout
690 To avoid that these names are recognized as proper names, a TeX-brace pair
699 \begin_layout Standard
700 To change the LaTeX-preamble
704 \begin_layout Plain Layout
712 Document\SpecialChar \menuseparator
713 Settings\SpecialChar \menuseparator
718 \begin_layout Plain Layout
734 \begin_layout Standard
735 To edit matrices, case differentiations and multiline formulas subsequently,
738 Edit\SpecialChar \menuseparator
743 Edit\SpecialChar \menuseparator
745 \begin_inset space \thinspace{}
749 \begin_inset space \thinspace{}
759 When lines and columns are swapped via the menu, the column or line where
760 the cursor is in is exchanged with the column to the right or the line
762 Is the cursor in the last column or row, the exchange is done with the
763 column to the left or the line above.
766 \begin_layout Standard
767 To write text in formulas
771 \begin_layout Plain Layout
772 For multiline formulas the command
779 \begin_inset CommandInset ref
781 reference "sub:Text-in-multiline"
798 \begin_layout Plain Layout
808 \begin_layout Plain Layout
815 This mode is invoked with the the shortcut
821 or by the insertion of the command
831 \begin_layout Plain Layout
840 The text appears black in LyX and can therefore be distinguished from the
841 other formula parts that appear blue.
842 In the output mathematical text is set upright, in contrary to other formula
846 \begin_layout Subsection*
850 \begin_layout Standard
851 Most of the LaTeX-commands for math constructs have the following scheme:
854 \begin_layout Standard
870 \begin_layout Standard
871 A command starts always with a backslash
872 \begin_inset Quotes gld
882 \begin_inset Quotes grd
886 To omit optional arguments, also omit the associated brackets.
887 The braces around the required arguments are named in this document as
892 \begin_layout Plain Layout
899 If you add in a formula a left brace to a command name, LyX creates automatical
901 In all other cases TeX-braces are created in formulas with the command
909 TeX-braces appear red in LyX, in contrary to normal braces that appear
911 In TeX-mode no command is needed to get TeX-braces.
912 TeX-braces don't appear in the output.
915 \begin_layout Standard
916 When commands without arguments, like commands for symbols are entered in
917 TeX-mode, a space character must
921 be behind the command to end it.
922 This space doesn't appear in the output.
923 When the space should appear in the output, the space must be followed
924 by a protected space in normal text.
927 \begin_layout Standard
928 A protected space is inserted with
931 arg "space-insert protected"
937 \begin_layout Subsection*
938 \begin_inset Newpage newpage
944 \begin_layout Itemize
949 \begin_layout Plain Layout
950 This visible space character can be created with the command
960 \begin_layout Plain Layout
968 , inserted in TeX-mode.
977 \begin_layout Plain Layout
990 denotes a space character to be input.
993 \begin_layout Itemize
995 \begin_inset Formula $\to$
998 denotes the usage of the corresponding arrow key on the keyboard.
1001 \begin_layout Subsection*
1005 \begin_layout Standard
1007 \begin_inset Float table
1013 \begin_layout Plain Layout
1015 \begin_inset Caption
1017 \begin_layout Plain Layout
1018 \begin_inset CommandInset label
1020 name "tab:Available-units"
1032 \begin_layout Plain Layout
1034 \begin_inset Tabular
1035 <lyxtabular version="3" rows="13" columns="2">
1037 <column alignment="center" valignment="top" width="0">
1038 <column alignment="center" valignment="top" width="0">
1040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1043 \begin_layout Plain Layout
1049 <cell alignment="center" valignment="top" topline="true" bottomline="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
1100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1103 \begin_layout Plain Layout
1109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1112 \begin_layout Plain Layout
1114 \begin_inset space \thinspace{}
1118 \begin_inset space \thinspace{}
1128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1131 \begin_layout Plain Layout
1137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1140 \begin_layout Plain Layout
1142 \begin_inset space \thinspace{}
1146 \begin_inset space \thinspace{}
1156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1159 \begin_layout Plain Layout
1165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1168 \begin_layout Plain Layout
1170 \begin_inset space \thinspace{}
1174 \begin_inset space \thinspace{}
1184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1187 \begin_layout Plain Layout
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1196 \begin_layout Plain Layout
1198 \begin_inset space \thinspace{}
1202 \begin_inset space \thinspace{}
1212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1215 \begin_layout Plain Layout
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1224 \begin_layout Plain Layout
1226 \begin_inset space \thinspace{}
1230 \begin_inset space \thinspace{}
1240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1243 \begin_layout Plain Layout
1249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1252 \begin_layout Plain Layout
1254 \begin_inset space \thinspace{}
1258 \begin_inset Formula $\approx$
1262 \begin_inset space \thinspace{}
1272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1275 \begin_layout Plain Layout
1281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1284 \begin_layout Plain Layout
1286 \begin_inset space \thinspace{}
1290 \begin_inset space \thinspace{}
1300 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1303 \begin_layout Plain Layout
1309 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1312 \begin_layout Plain Layout
1316 \begin_inset Quotes eld
1322 \begin_inset Quotes erd
1332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1335 \begin_layout Plain Layout
1341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1344 \begin_layout Plain Layout
1346 \begin_inset Quotes eld
1354 \begin_inset Quotes erd
1364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1367 \begin_layout Plain Layout
1373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1376 \begin_layout Plain Layout
1378 \begin_inset space \thinspace{}
1382 \begin_inset Formula $\nicefrac{1}{18}$
1386 \begin_inset space \thinspace{}
1407 \begin_layout Standard
1408 \begin_inset Newpage newpage
1414 \begin_layout Section
1418 \begin_layout Subsection
1423 \begin_layout Plain Layout
1433 \begin_layout Plain Layout
1443 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1459 \begin_layout Plain Layout
1475 \begin_layout Plain Layout
1480 \begin_layout Plain Layout
1491 \begin_layout Plain Layout
1506 \begin_layout Standard
1507 Indices are created with an underscore
1508 \begin_inset Quotes eld
1512 \begin_inset Quotes erd
1515 or via the math toolbar button
1516 \begin_inset Graphics
1517 filename ../images/math-subscript.png
1522 , exponents with a caret
1523 \begin_inset Quotes eld
1527 \begin_inset Quotes erd
1530 or via the math toolbar button
1531 \begin_inset Graphics
1532 filename ../images/math-superscript.png
1540 \begin_layout Standard
1542 \begin_inset Tabular
1543 <lyxtabular version="3" rows="4" columns="2">
1545 <column alignment="center" valignment="top" width="0pt">
1546 <column alignment="center" valignment="top" width="0pt">
1548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1551 \begin_layout Plain Layout
1557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1560 \begin_layout Plain Layout
1562 \begin_inset Note Note
1565 \begin_layout Plain Layout
1572 is only used as spacer.
1584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1587 \begin_layout Plain Layout
1593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1596 \begin_layout Plain Layout
1597 \begin_inset Formula $B_{V}$
1607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1610 \begin_layout Plain Layout
1616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1619 \begin_layout Plain Layout
1620 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1633 \begin_layout Plain Layout
1638 \begin_layout Plain Layout
1652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1655 \begin_layout Plain Layout
1656 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1672 \begin_layout Standard
1673 As the caret is in some languages an accent, vowels will be accentuated
1674 in this case and not set as exponents
1678 \begin_layout Plain Layout
1679 Depending on the used keyboard settings this can also happen for other character
1686 To get in this case exponents, press
1690 after the caret as in the last example.
1693 \begin_layout Subsection
1695 \begin_inset CommandInset label
1697 name "sub:Fractions"
1705 \begin_layout Plain Layout
1714 \begin_layout Standard
1715 Fractions are generated with the command
1725 \begin_layout Plain Layout
1733 or via the math toolbar button
1734 \begin_inset Graphics
1735 filename ../images/math/frac.png
1741 The font size is adjusted automatically, depending on whether the fraction
1742 is in an inline or display style formula.
1743 With the math toolbar button
1744 \begin_inset Graphics
1745 filename ../images/math/frac-square.png
1750 you can select different fraction types.
1753 \begin_layout Standard
1762 \begin_layout Plain Layout
1772 a fraction can be created that has in any case the size of a display style
1782 \begin_layout Plain Layout
1792 the fraction appears always with the size of an inline formula.
1796 \begin_layout Standard
1797 A line with the fraction
1798 \begin_inset Formula $\frac{1}{2}$
1801 that was created with the command
1810 \begin_layout Standard
1811 A line with the fraction
1812 \begin_inset Formula $\dfrac{1}{2}$
1815 that was created with the command
1824 \begin_layout Standard
1826 \begin_inset Tabular
1827 <lyxtabular version="3" rows="4" columns="2">
1829 <column alignment="center" valignment="top" width="0pt">
1830 <column alignment="center" valignment="top" width="0pt">
1832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1835 \begin_layout Plain Layout
1841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1844 \begin_layout Plain Layout
1846 \begin_inset Note Note
1849 \begin_layout Plain Layout
1856 is only used as spacer.
1868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1871 \begin_layout Plain Layout
1878 \begin_layout Plain Layout
1888 \begin_inset Formula $\downarrow$
1896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1899 \begin_layout Plain Layout
1900 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1913 \begin_layout Plain Layout
1920 \begin_layout Plain Layout
1930 \begin_inset Formula $\downarrow$
1938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1941 \begin_layout Plain Layout
1942 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1955 \begin_layout Plain Layout
1962 \begin_layout Plain Layout
1975 \begin_layout Plain Layout
1990 \begin_layout Plain Layout
2000 \begin_inset Formula $\downarrow$
2004 \begin_inset Formula $\downarrow\downarrow$
2012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2015 \begin_layout Plain Layout
2016 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2032 \begin_layout Standard
2033 \begin_inset VSpace bigskip
2037 \begin_inset Newpage newpage
2040 For nested fractions the command
2050 \begin_layout Plain Layout
2060 \begin_inset VSpace -3mm
2066 \begin_layout Standard
2067 \begin_inset Formula \begin{align*}
2068 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2069 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2076 \begin_layout Standard
2077 The command for the example above is:
2080 \begin_layout Standard
2089 \begin_layout Plain Layout
2099 \begin_inset Formula $\downarrow$
2108 \begin_layout Plain Layout
2123 \begin_layout Plain Layout
2133 \begin_inset Formula $\downarrow$
2137 \begin_inset Formula $\downarrow$
2143 \begin_layout Standard
2144 \begin_inset VSpace medskip
2150 \begin_layout Standard
2157 sets the fraction always in the size of a displayed formula, also when
2158 it is part of another fraction.
2161 \begin_layout Standard
2162 It is possible to specify the alignment of the numerator.
2169 is used to left align it, the command
2182 centers the numerator.
2183 These fractions demonstrate the different alignments:
2186 \begin_layout Standard
2187 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2191 \begin_inset Formula $\cfrac{A}{B+C}$
2195 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2201 \begin_layout Standard
2202 \begin_inset Note Greyedout
2205 \begin_layout Plain Layout
2222 are no real LaTeX commands but represent the command
2226 cfrac[alignment]{numerator}{denominator}
2229 Therefore you cannot use them in TeX code.
2237 \begin_layout Standard
2238 \begin_inset VSpace medskip
2241 It is often advantageous to combine
2254 \begin_inset Formula \[
2255 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2262 \begin_layout Standard
2263 For inline fractions with a sloped fraction stroke you can use the command
2274 \begin_layout Plain Layout
2283 \begin_inset Formula $\nicefrac{5}{31}$
2296 \begin_layout Plain Layout
2305 \begin_inset Formula $\unitfrac{5}{31}$
2308 There is furthermore the command
2314 that offers to write a fraction in combination with a number:
2315 \begin_inset Formula $\unitfrac[2]{1}{3}$
2321 \begin_layout Standard
2322 \begin_inset Note Greyedout
2325 \begin_layout Plain Layout
2336 is not a real LaTeX command but the command
2337 \begin_inset Newline newline
2344 unitfrac[number]{numerator}{denominator}
2347 Therefore you cannot use it in TeX code.
2355 \begin_layout Standard
2356 How to define own fractions where the fraction stroke can be changed, is
2358 \begin_inset CommandInset ref
2360 reference "sub:Self-defined-Fractions"
2367 \begin_layout Subsection
2372 \begin_layout Plain Layout
2381 \begin_layout Standard
2382 Square roots are created with
2392 \begin_layout Plain Layout
2400 or the math toolbar button
2401 \begin_inset Graphics
2402 filename ../images/math/sqrt.png
2407 , all other roots with the command
2417 \begin_layout Plain Layout
2425 or with the math toolbar button
2426 \begin_inset Graphics
2427 filename ../images/math/root.png
2435 \begin_layout Standard
2437 \begin_inset Tabular
2438 <lyxtabular version="3" rows="3" columns="2">
2440 <column alignment="center" valignment="top" width="0pt">
2441 <column alignment="center" valignment="top" width="0pt">
2443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2446 \begin_layout Plain Layout
2452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2455 \begin_layout Plain Layout
2457 \begin_inset Note Note
2460 \begin_layout Plain Layout
2467 is only used as spacer.
2479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2482 \begin_layout Plain Layout
2489 \begin_layout Plain Layout
2503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2506 \begin_layout Plain Layout
2507 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2520 \begin_layout Plain Layout
2527 \begin_layout Plain Layout
2537 \begin_inset Formula $\downarrow$
2545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2548 \begin_layout Plain Layout
2549 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2565 \begin_layout Standard
2566 A square root can also be created with
2572 when the root index field is left empty.
2575 \begin_layout Standard
2576 With certain indices the distance to the root is too small, like in this
2578 \begin_inset Formula $\sqrt[\beta]{B}$
2582 \begin_inset Newline newline
2586 \begin_inset Formula $\beta$
2590 To avoid this, the commands
2600 \begin_layout Plain Layout
2618 \begin_layout Plain Layout
2626 are used with the following scheme:
2629 \begin_layout Standard
2643 \begin_layout Standard
2644 Distance is the number of Big Points (unit bp;
2645 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2648 ), that the index should be moved to the left or top, resp..
2649 The commands are written to the index.
2650 This way the command
2651 \begin_inset Newline newline
2661 \begin_inset Formula $\to$
2667 \begin_inset Formula $\to$
2676 \begin_layout Plain Layout
2686 \begin_inset Formula $\to$
2690 \begin_inset Newline newline
2695 produces a correct typeset formula:
2696 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2702 \begin_layout Subsection
2703 Binomial Coefficients
2707 \begin_layout Plain Layout
2708 Binomial coefficients
2716 \begin_layout Standard
2717 Binomial coefficients are inserted with the command
2727 \begin_layout Plain Layout
2735 or with the submenu of the math toolbar button
2736 \begin_inset Graphics
2737 filename ../images/math/frac-square.png
2743 Analog to fractions (
2763 \begin_layout Plain Layout
2783 \begin_layout Plain Layout
2792 For other brackets around binomial coeficients there are the commands
2802 \begin_layout Plain Layout
2820 \begin_layout Plain Layout
2831 \begin_layout Standard
2833 \begin_inset Tabular
2834 <lyxtabular version="3" rows="6" columns="2">
2836 <column alignment="center" valignment="top" width="0pt">
2837 <column alignment="center" valignment="top" width="0pt">
2839 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2842 \begin_layout Plain Layout
2848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2851 \begin_layout Plain Layout
2853 \begin_inset Note Note
2856 \begin_layout Plain Layout
2863 is only used as spacer.
2875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2878 \begin_layout Plain Layout
2885 \begin_layout Plain Layout
2895 \begin_inset Formula $\downarrow$
2903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2906 \begin_layout Plain Layout
2907 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2920 \begin_layout Plain Layout
2927 \begin_layout Plain Layout
2937 \begin_inset Formula $\downarrow$
2945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2948 \begin_layout Plain Layout
2949 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2962 \begin_layout Plain Layout
2969 \begin_layout Plain Layout
2979 \begin_inset Formula $\downarrow$
2987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2990 \begin_layout Plain Layout
2991 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3004 \begin_layout Plain Layout
3011 \begin_layout Plain Layout
3021 \begin_inset Formula $\downarrow$
3029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3032 \begin_layout Plain Layout
3033 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3053 \begin_layout Plain Layout
3063 \begin_inset Formula $\downarrow$
3071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3074 \begin_layout Plain Layout
3075 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3091 \begin_layout Subsection
3092 Case Differentiations
3096 \begin_layout Plain Layout
3097 Case differentiations
3105 \begin_layout Standard
3107 \begin_inset Tabular
3108 <lyxtabular version="3" rows="3" columns="2">
3110 <column alignment="center" valignment="top" width="0pt">
3111 <column alignment="center" valignment="top" width="0pt">
3113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3116 \begin_layout Plain Layout
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3125 \begin_layout Plain Layout
3133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3136 \begin_layout Plain Layout
3143 \begin_layout Plain Layout
3153 \begin_inset Formula $\to$
3160 \begin_layout Plain Layout
3173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3176 \begin_layout Plain Layout
3177 \begin_inset Formula $\begin{cases}
3188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3191 \begin_layout Plain Layout
3198 \begin_layout Plain Layout
3210 arg "newline-insert newline"
3218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3221 \begin_layout Plain Layout
3222 \begin_inset Formula $\begin{cases}
3223 A & \textrm{for }x>0\\
3224 B & \textrm{for }x=0\end{cases}$
3240 \begin_layout Standard
3247 or the usage of the math toolbar button
3248 \begin_inset Graphics
3249 filename ../images/math/cases.png
3254 you can create new lines with the shortcut
3257 arg "newline-insert newline"
3260 or the table toolbar button
3261 \begin_inset Graphics
3262 filename ../images/tabular-feature_append-row.png
3270 \begin_layout Standard
3277 is also available via the menu
3279 Insert\SpecialChar \menuseparator
3280 Math\SpecialChar \menuseparator
3286 \begin_layout Subsection
3291 \begin_layout Plain Layout
3300 \begin_layout Standard
3311 \begin_layout Plain Layout
3319 every character can be displayed canceled.
3320 The characters are quasi accentuated by a slash.
3323 \begin_layout Standard
3325 \begin_inset Tabular
3326 <lyxtabular version="3" rows="4" columns="2">
3328 <column alignment="center" valignment="top" width="0pt">
3329 <column alignment="center" valignment="top" width="0pt">
3331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3334 \begin_layout Plain Layout
3340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3343 \begin_layout Plain Layout
3351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3354 \begin_layout Plain Layout
3362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3365 \begin_layout Plain Layout
3366 \begin_inset Formula $\not=$
3376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3379 \begin_layout Plain Layout
3389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3392 \begin_layout Plain Layout
3393 \begin_inset Formula $\not\le$
3403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3406 \begin_layout Plain Layout
3416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3419 \begin_layout Plain Layout
3420 \begin_inset Formula $\not\parallel$
3436 \begin_layout Standard
3437 The last example shows, that not all negations look good.
3438 Therefore there are for some negations special commands (see
3439 \begin_inset CommandInset ref
3441 reference "sub:Mathematical-Symbols"
3446 \begin_inset CommandInset ref
3448 reference "sec:Relations"
3455 \begin_layout Subsection
3457 \begin_inset CommandInset label
3459 name "sub:Placeholders"
3467 \begin_layout Plain Layout
3477 \begin_layout Plain Layout
3478 Chemical characters ! Isotopes
3487 \begin_layout Plain Layout
3492 \begin_layout Plain Layout
3503 \begin_layout Plain Layout
3518 \begin_layout Standard
3520 \begin_inset space \thinspace{}
3524 \begin_inset space \space{}
3531 \begin_layout Plain Layout
3532 Typesetting isotopes and chemical symbols is described in
3533 \begin_inset CommandInset ref
3535 reference "sub:Chemical-Symbols-and"
3544 the following problem occurs:
3547 \begin_layout Standard
3549 \begin_inset Tabular
3550 <lyxtabular version="3" rows="2" columns="2">
3552 <column alignment="center" valignment="top" width="0pt">
3553 <column alignment="center" valignment="top" width="0pt">
3555 <cell alignment="center" valignment="top" usebox="none">
3558 \begin_layout Plain Layout
3559 Indices created with sub- and superscripts:
3564 <cell alignment="center" valignment="top" usebox="none">
3567 \begin_layout Plain Layout
3568 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3578 <cell alignment="center" valignment="top" usebox="none">
3581 \begin_layout Plain Layout
3587 <cell alignment="center" valignment="top" usebox="none">
3590 \begin_layout Plain Layout
3591 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3605 \begin_inset Note Note
3608 \begin_layout Plain Layout
3615 is only used as spacer.
3623 \begin_layout Standard
3624 The shorter index is by default placed below or above the first character
3625 of the longer index.
3626 To avoid this there is the command
3636 \begin_layout Plain Layout
3644 or the math toolbar button
3645 \begin_inset space \thinspace{}
3652 \begin_layout Plain Layout
3653 can be found in the submenu of the toolbar button
3654 \begin_inset Graphics
3655 filename ../images/math/space.png
3666 \begin_inset Graphics
3667 filename ../images/math/phantom.png
3672 that creates one or more phantom characters.
3679 a small blue box appears that is superposed with two red arrows.
3680 The arrows indicate that the complete width and height of the box content
3681 will be created as placeholder.
3682 Phantom characters are accordingly placeholders with the size of the characters.
3685 \begin_layout Standard
3687 \begin_inset Tabular
3688 <lyxtabular version="3" rows="4" columns="2">
3690 <column alignment="center" valignment="top" width="0">
3691 <column alignment="center" valignment="top" width="0">
3693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3696 \begin_layout Plain Layout
3702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3705 \begin_layout Plain Layout
3707 \begin_inset Note Note
3710 \begin_layout Plain Layout
3717 is only used as spacer.
3729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3732 \begin_layout Plain Layout
3737 \begin_layout Plain Layout
3752 \begin_layout Plain Layout
3762 \begin_inset Formula $\to$
3769 \begin_layout Plain Layout
3783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3786 \begin_layout Plain Layout
3787 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3800 \begin_layout Plain Layout
3805 \begin_layout Plain Layout
3820 \begin_layout Plain Layout
3830 \begin_inset Formula $\to$
3837 \begin_layout Plain Layout
3851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3854 \begin_layout Plain Layout
3855 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3868 \begin_layout Plain Layout
3875 \begin_layout Plain Layout
3890 \begin_layout Plain Layout
3900 \begin_inset Formula $\to$
3907 \begin_layout Plain Layout
3921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3924 \begin_layout Plain Layout
3925 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3941 \begin_layout Standard
3942 Furthermore there are the commands
3952 \begin_layout Plain Layout
3961 \begin_inset space ~
3965 \begin_inset Graphics
3966 filename ../images/math/vphantom.png
3981 \begin_layout Plain Layout
3990 \begin_inset space ~
3994 \begin_inset Graphics
3995 filename ../images/math/hphantom.png
4007 creates only space for the maximal height of the characters in the box
4008 but not for its width.
4015 creates only space for the width of the box content.
4016 Therefore the boxes of both commands have only one red arrow.
4019 \begin_layout Standard
4030 \begin_layout Plain Layout
4045 space for the height of the integral sign,
4049 \begin_layout Plain Layout
4056 creates an integral sign, see
4057 \begin_inset CommandInset ref
4059 reference "sub:Big-Operators"
4068 because this is the larger character.
4069 An example application is in
4070 \begin_inset CommandInset ref
4072 reference "sub:Multiline-Brackets"
4079 \begin_layout Subsection
4084 \begin_layout Plain Layout
4094 \begin_layout Plain Layout
4095 Formula ! underlined
4103 \begin_layout Standard
4105 \begin_inset Tabular
4106 <lyxtabular version="3" rows="4" columns="2">
4108 <column alignment="center" valignment="top" width="0pt">
4109 <column alignment="center" valignment="top" width="0pt">
4111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4114 \begin_layout Plain Layout
4120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4123 \begin_layout Plain Layout
4125 \begin_inset Note Note
4128 \begin_layout Plain Layout
4135 is only used as spacer.
4147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4150 \begin_layout Plain Layout
4157 \begin_layout Plain Layout
4170 \begin_layout Plain Layout
4183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4186 \begin_layout Plain Layout
4187 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4197 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4200 \begin_layout Plain Layout
4207 \begin_layout Plain Layout
4220 \begin_layout Plain Layout
4233 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4236 \begin_layout Plain Layout
4237 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4250 \begin_layout Plain Layout
4257 \begin_layout Plain Layout
4272 \begin_layout Plain Layout
4286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4289 \begin_layout Plain Layout
4290 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4306 \begin_layout Standard
4307 In the last example it doesn't matter if first
4322 \begin_layout Standard
4323 To double underline e.
4324 \begin_inset space \thinspace{}
4328 \begin_inset space \space{}
4340 \begin_layout Standard
4341 It is possible to place up to 6 lines above or below characters.
4344 \begin_layout Standard
4345 \begin_inset VSpace bigskip
4348 Custom lines can be created using the command
4358 \begin_layout Plain Layout
4366 which has the following scheme:
4369 \begin_layout Standard
4374 rule[vertical offset]{length}{thickness}
4377 \begin_layout Standard
4378 The optional vertical offset shifts the line upwards (or downwards, when
4379 the value is negative).
4381 \begin_inset CommandInset ref
4383 reference "tab:Available-units"
4387 can be used for the values.
4388 Here are two example lines created with the commands
4389 \begin_inset Newline newline
4396 rule[-2ex]{3cm}{2pt}
4407 \begin_layout Standard
4409 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4415 \begin_layout Standard
4422 can also be used for text when it is inserted in TeX-mode.
4425 \begin_layout Subsection
4427 \begin_inset CommandInset label
4437 \begin_layout Plain Layout
4446 \begin_layout Standard
4447 There are different types of ellipses available.
4451 \begin_layout Plain Layout
4452 In the math toolbar in the submenu of the button
4453 \begin_inset Graphics
4454 filename ../images/math/ldots.png
4464 For listings dots at the baseline are used (
4474 \begin_layout Plain Layout
4482 ), while for operations dots are needed that are on the same height as the
4493 \begin_layout Plain Layout
4502 When using the command
4512 \begin_layout Plain Layout
4520 , LaTeX decides on the basis of the next character what type is used.
4523 \begin_layout Standard
4525 \begin_inset Tabular
4526 <lyxtabular version="3" rows="8" columns="2">
4528 <column alignment="center" valignment="top" width="0pt">
4529 <column alignment="center" valignment="top" width="0pt">
4531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4534 \begin_layout Plain Layout
4540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4543 \begin_layout Plain Layout
4551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4554 \begin_layout Plain Layout
4559 \begin_layout Plain Layout
4574 \begin_layout Plain Layout
4588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4591 \begin_layout Plain Layout
4592 \begin_inset Formula $A_{1},\dots,A_{n}$
4602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4605 \begin_layout Plain Layout
4610 \begin_layout Plain Layout
4625 \begin_layout Plain Layout
4639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4642 \begin_layout Plain Layout
4643 \begin_inset Formula $A_{1}+\dots+A_{n}$
4653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4656 \begin_layout Plain Layout
4661 \begin_layout Plain Layout
4676 \begin_layout Plain Layout
4690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4693 \begin_layout Plain Layout
4694 \begin_inset Formula $A_{1},\ldots,A_{n}$
4704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4707 \begin_layout Plain Layout
4712 \begin_layout Plain Layout
4727 \begin_layout Plain Layout
4741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4744 \begin_layout Plain Layout
4745 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4758 \begin_layout Plain Layout
4766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4769 \begin_layout Plain Layout
4770 \begin_inset Formula $\vdots$
4780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4783 \begin_layout Plain Layout
4791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4794 \begin_layout Plain Layout
4795 \begin_inset Formula $\ddots$
4805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4808 \begin_layout Plain Layout
4810 \begin_inset space \thinspace{}
4813 matrix with the different dots
4818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4821 \begin_layout Plain Layout
4822 \begin_inset Formula $\begin{array}{ccc}
4823 A_{11} & \cdots & A_{1m}\\
4824 \vdots & \ddots & \vdots\\
4825 A_{n1} & \cdots & A_{nm}\end{array}$
4841 \begin_layout Standard
4842 The ellipses available in menu
4844 Insert\SpecialChar \menuseparator
4846 \begin_inset space ~
4860 \begin_layout Standard
4861 \begin_inset VSpace medskip
4864 Specially for matrices there are ellipses that span over several columns.
4865 They are created with the command
4875 \begin_layout Plain Layout
4883 , that has the following scheme:
4886 \begin_layout Standard
4891 hdotsfor[distance]{number of columns}
4894 \begin_layout Standard
4895 The number of columns specifies how many columns should be spanned.
4896 Distance is a factor for the distance between the dots.
4899 \begin_layout Standard
4900 In the following matrix the command
4906 was inserted in the first box of the second line, to get an ellipsis with
4907 a dot distance twice as long as with the command
4914 \begin_inset Formula \[
4915 \left(\begin{array}{cccc}
4918 q & w & e & r\end{array}\right)\]
4922 Note that the matrix fields that should be spanned must be empty, otherwise
4923 you get LaTeX-errors.
4926 \begin_layout Standard
4927 \begin_inset VSpace bigskip
4930 Furthermore you can fill with the command
4940 \begin_layout Plain Layout
4948 the rest of a line with dots.
4949 The effect of these commands is the same like with
4956 \begin_inset CommandInset ref
4958 reference "sub:Variable-Space"
4965 \begin_layout Standard
4966 For example the command
4974 \begin_layout Plain Layout
4988 \begin_layout Standard
4989 \begin_inset Formula $A\dotfill B$
4995 \begin_layout Standard
5002 there is for a line the command
5012 \begin_layout Plain Layout
5023 \begin_layout Standard
5024 \begin_inset Formula $A\hrulefill B$
5030 \begin_layout Standard
5031 To use the commands for text, they have to be inserted in TeX-mode.
5034 \begin_layout Section
5036 \begin_inset CommandInset label
5046 \begin_layout Plain Layout
5055 \begin_layout Standard
5056 Matrices can be inserted via the math toolbar button
5057 \begin_inset Graphics
5058 filename ../images/dialog-show_mathmatrix.png
5065 Insert\SpecialChar \menuseparator
5066 Math\SpecialChar \menuseparator
5070 You will be asked for the number of matrix columns and rows and the alignment.
5071 The vertical alignment is hereby only of importance for matrices in inline
5075 \begin_layout Standard
5076 The first matrix is top
5077 \begin_inset Formula $\begin{array}[t]{cccc}
5080 C & F & I & L\end{array}$
5084 \begin_inset Formula $\begin{array}{cccc}
5087 C & F & I & L\end{array}$
5090 and the third bottom
5091 \begin_inset Formula $\begin{array}[b]{cccc}
5094 C & F & I & L\end{array}$
5100 \begin_layout Standard
5101 The horizontal alignment specifies how the column entries should be aligned.
5102 It is set by entering a letter for every column.
5107 denotes left aligned,
5116 To create for example a 4
5121 \begin_inset space ~
5124 matrix where the first column is left aligned, the second and third are
5125 centered and the last one is right aligned, one enters for the horizontal
5131 Normally are in a matrix all columns centered, therefore the default is
5132 for every column is a
5139 \begin_layout Standard
5140 Horizontal alignment:
5143 \begin_layout Standard
5149 \begin_inset Formula $\begin{array}{lll}
5152 C & F & 10000\end{array}$
5160 \begin_inset Formula $\begin{array}{ccc}
5163 C & F & 10000\end{array}$
5171 \begin_inset Formula $\begin{array}{rrr}
5174 C & F & 10000\end{array}$
5180 \begin_layout Standard
5181 To add or delete rows and columns subsequently, the math toolbar buttons
5183 \begin_inset Graphics
5184 filename ../images/tabular-feature_append-row.png
5190 \begin_inset Graphics
5191 filename ../images/tabular-feature_delete-row.png
5197 \begin_inset space \thinspace{}
5202 Edit\SpecialChar \menuseparator
5206 New rows can also be created with
5209 arg "newline-insert newline"
5215 \begin_layout Standard
5216 \begin_inset VSpace bigskip
5219 Parentheses around a matrix can can either be created with the commands
5230 \begin_layout Plain Layout
5248 \begin_layout Plain Layout
5259 \begin_inset space ~
5265 \begin_inset CommandInset ref
5267 reference "sub:Automatic-Bracket-Size"
5271 , or by using the following commands:
5272 \begin_inset VSpace medskip
5278 \begin_layout Standard
5279 \begin_inset space \hfill{}
5283 \begin_inset Tabular
5284 <lyxtabular version="3" rows="4" columns="2">
5286 <column alignment="center" valignment="top" width="0">
5287 <column alignment="center" valignment="top" width="0">
5289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5292 \begin_layout Plain Layout
5298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5301 \begin_layout Plain Layout
5303 \begin_inset Note Note
5306 \begin_layout Plain Layout
5313 is only used as spacer.
5325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5328 \begin_layout Plain Layout
5335 \begin_layout Plain Layout
5349 \begin_inset space \thinspace{}
5357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5360 \begin_layout Plain Layout
5361 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5362 0 & \textrm{-}\mathrm{i}\\
5363 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5376 \begin_layout Plain Layout
5383 \begin_layout Plain Layout
5397 \begin_inset space \thinspace{}
5405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5408 \begin_layout Plain Layout
5409 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5410 0 & \textrm{-}\mathrm{i}\\
5411 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5424 \begin_layout Plain Layout
5431 \begin_layout Plain Layout
5445 \begin_inset space \thinspace{}
5453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5456 \begin_layout Plain Layout
5457 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5458 0 & \textrm{-}\mathrm{i}\\
5459 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5473 \begin_inset space \hfill{}
5477 \begin_inset Tabular
5478 <lyxtabular version="3" rows="4" columns="2">
5480 <column alignment="center" valignment="top" width="0">
5481 <column alignment="center" valignment="top" width="0">
5483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5486 \begin_layout Plain Layout
5492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5495 \begin_layout Plain Layout
5503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5506 \begin_layout Plain Layout
5513 \begin_layout Plain Layout
5527 \begin_inset space \thinspace{}
5535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5538 \begin_layout Plain Layout
5539 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5540 0 & \textrm{-}\mathrm{i}\\
5541 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5554 \begin_layout Plain Layout
5561 \begin_layout Plain Layout
5575 \begin_inset space \thinspace{}
5583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5586 \begin_layout Plain Layout
5587 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5588 0 & \textrm{-}\mathrm{i}\\
5589 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5602 \begin_layout Plain Layout
5609 \begin_layout Plain Layout
5623 \begin_inset space \thinspace{}
5631 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5634 \begin_layout Plain Layout
5635 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5636 0 & \textrm{-}\mathrm{i}\\
5637 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5651 \begin_inset space \hfill{}
5657 \begin_layout Standard
5658 \begin_inset VSpace medskip
5662 \begin_inset space \thinspace{}
5666 \begin_inset space \space{}
5675 is inserted, a blue box appears between two vertical lines where the matrix
5679 \begin_layout Standard
5680 \begin_inset VSpace bigskip
5683 As all multiline formulas are matrices, the length
5693 \begin_layout Plain Layout
5701 that is described in
5702 \begin_inset CommandInset ref
5704 reference "sub:Column-Separation"
5708 can also be used to change the column separation of matrices.
5711 \begin_layout Standard
5712 To change the row separation, the command
5722 \begin_layout Plain Layout
5731 It is used as follows:
5734 \begin_layout Standard
5741 arraystretch}{stretch factor}
5745 \begin_layout Plain Layout
5756 \begin_layout Standard
5763 assigns the stretch factor to the predefined command
5771 \begin_inset space \thinspace{}
5775 \begin_inset space \space{}
5778 the row separation, use the factor 2.
5779 This is then used for all following matrices.
5780 To go back to the original separation, assign the factor 1 to
5789 \begin_layout Standard
5790 To set matrices into a text line, the command
5800 \begin_layout Plain Layout
5809 When it is inserted a blue box with two dashed lines appears.
5810 In this box the matrix is inserted.
5813 \begin_layout Standard
5815 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5816 C & D\end{smallmatrix}\right)$
5822 \begin_layout Section
5823 Brackets and Delimiters
5827 \begin_layout Plain Layout
5837 \begin_layout Plain Layout
5846 \begin_layout Subsection
5847 Vertical Brackets and Delimiters
5851 \begin_layout Plain Layout
5860 \begin_layout Standard
5861 \begin_inset space \hfill{}
5865 \begin_inset Tabular
5866 <lyxtabular version="3" rows="9" columns="2">
5868 <column alignment="center" valignment="top" width="0pt">
5869 <column alignment="center" valignment="top" width="0pt">
5871 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5874 \begin_layout Plain Layout
5880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5883 \begin_layout Plain Layout
5891 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5894 \begin_layout Plain Layout
5900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5903 \begin_layout Plain Layout
5904 \begin_inset Formula $($
5914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5917 \begin_layout Plain Layout
5923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5926 \begin_layout Plain Layout
5927 \begin_inset Formula $\{$
5937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5940 \begin_layout Plain Layout
5946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5949 \begin_layout Plain Layout
5950 \begin_inset Formula $[$
5960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5963 \begin_layout Plain Layout
5971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5974 \begin_layout Plain Layout
5975 \begin_inset Formula $\langle$
5985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5988 \begin_layout Plain Layout
5996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5999 \begin_layout Plain Layout
6000 \begin_inset Formula $\lceil$
6010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6013 \begin_layout Plain Layout
6021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6024 \begin_layout Plain Layout
6025 \begin_inset Formula $\lfloor$
6035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6038 \begin_layout Plain Layout
6044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6047 \begin_layout Plain Layout
6048 \begin_inset Formula $/$
6058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6061 \begin_layout Plain Layout
6067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6070 \begin_layout Plain Layout
6071 \begin_inset Formula $|$
6085 \begin_inset space \hfill{}
6089 \begin_inset Tabular
6090 <lyxtabular version="3" rows="9" columns="2">
6092 <column alignment="center" valignment="top" width="0pt">
6093 <column alignment="center" valignment="top" width="0pt">
6095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6098 \begin_layout Plain Layout
6104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6107 \begin_layout Plain Layout
6115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6118 \begin_layout Plain Layout
6124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6127 \begin_layout Plain Layout
6128 \begin_inset Formula $)$
6138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6141 \begin_layout Plain Layout
6147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6150 \begin_layout Plain Layout
6151 \begin_inset Formula $\}$
6161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6164 \begin_layout Plain Layout
6170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6173 \begin_layout Plain Layout
6174 \begin_inset Formula $]$
6184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6187 \begin_layout Plain Layout
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6198 \begin_layout Plain Layout
6199 \begin_inset Formula $\rangle$
6209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6212 \begin_layout Plain Layout
6220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6223 \begin_layout Plain Layout
6224 \begin_inset Formula $\rceil$
6234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6237 \begin_layout Plain Layout
6245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6248 \begin_layout Plain Layout
6249 \begin_inset Formula $\rfloor$
6259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6262 \begin_layout Plain Layout
6272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6275 \begin_layout Plain Layout
6276 \begin_inset Formula $\backslash$
6286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6289 \begin_layout Plain Layout
6297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6300 \begin_layout Plain Layout
6301 \begin_inset Formula $\|$
6315 \begin_inset space \hfill{}
6321 \begin_layout Standard
6324 \begin_inset Note Greyedout
6327 \begin_layout Plain Layout
6332 In TeX-mode the command
6342 \begin_layout Plain Layout
6350 must be used for the backslash, because the command
6358 produces there a line break.
6366 \begin_layout Standard
6367 For all characters listed above the size can be adjusted with the commands
6368 described in the following two subsections.
6369 When using these commands, the characters < and > can directly be used
6370 instead of the commands
6385 \begin_layout Subsubsection
6387 \begin_inset CommandInset label
6389 name "sub:Manual-Bracket-Size"
6397 \begin_layout Plain Layout
6398 Bracket size ! manual
6406 \begin_layout Standard
6407 The bracket size can be specified manually by the LaTeX-commands
6417 \begin_layout Plain Layout
6450 denotes the smallest and
6456 the largest bracket size.
6459 \begin_layout Standard
6460 These commands are used to emphasize levels of brackets:
6463 \begin_layout Standard
6465 \begin_inset Tabular
6466 <lyxtabular version="3" rows="2" columns="2">
6468 <column alignment="center" valignment="top" width="0pt">
6469 <column alignment="center" valignment="top" width="0pt">
6471 <cell alignment="center" valignment="top" usebox="none">
6474 \begin_layout Plain Layout
6475 all brackets in the same size:
6480 <cell alignment="center" valignment="top" usebox="none">
6483 \begin_layout Plain Layout
6484 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6494 <cell alignment="center" valignment="top" usebox="none">
6497 \begin_layout Plain Layout
6503 <cell alignment="center" valignment="top" usebox="none">
6506 \begin_layout Plain Layout
6507 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6521 \begin_inset Note Note
6524 \begin_layout Plain Layout
6531 is only used as spacer.
6539 \begin_layout Standard
6540 For the second formula the command
6550 \begin_layout Plain Layout
6564 \begin_layout Standard
6565 Here is an overview about all bracket sizes:
6568 \begin_layout Standard
6588 \begin_layout Plain Layout
6605 \begin_layout Plain Layout
6618 \begin_layout Plain Layout
6634 \begin_layout Standard
6636 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6642 \begin_layout Standard
6649 -commands there is the variant
6659 \begin_layout Plain Layout
6667 that adds a bit more space between the bracket and its content, and the
6684 \begin_layout Plain Layout
6694 , that don't add additional space.
6699 at the end of the command
6705 is for a left bracket; for a right bracket this will be replaced by an
6711 A left or right bracket can each be an opening or closing bracket.
6714 \begin_layout Standard
6715 In the following table is a comparison of the variants:
6718 \begin_layout Standard
6720 \begin_inset Tabular
6721 <lyxtabular version="3" rows="5" columns="2">
6723 <column alignment="center" valignment="middle" width="0">
6724 <column alignment="center" valignment="middle" width="0">
6726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6729 \begin_layout Plain Layout
6735 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6738 \begin_layout Plain Layout
6740 \begin_inset Note Note
6743 \begin_layout Plain Layout
6750 is only used as spacer.
6762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6765 \begin_layout Plain Layout
6780 \begin_layout Plain Layout
6798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6801 \begin_layout Plain Layout
6802 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6815 \begin_layout Plain Layout
6830 \begin_layout Plain Layout
6848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6851 \begin_layout Plain Layout
6852 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6865 \begin_layout Plain Layout
6880 \begin_layout Plain Layout
6898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6901 \begin_layout Plain Layout
6902 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6915 \begin_layout Plain Layout
6927 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6930 \begin_layout Plain Layout
6931 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6947 \begin_layout Subsubsection
6948 Automatic Bracket Size
6949 \begin_inset CommandInset label
6951 name "sub:Automatic-Bracket-Size"
6959 \begin_layout Plain Layout
6960 Bracket size ! automatic
6968 \begin_layout Standard
6969 Brackets with variable size can be inserted with the commands
6979 \begin_layout Plain Layout
6997 \begin_layout Plain Layout
7005 or via the math toolbar button
7006 \begin_inset Graphics
7007 filename ../images/dialog-show_mathdelimiter.png
7025 the wanted bracket must be inserted.
7026 The bracket size will then automatically be calculated for the output.
7029 \begin_layout Standard
7031 normal bracket: The command
7041 \begin_layout Plain Layout
7051 \begin_inset Formula $\downarrow$
7058 \begin_layout Plain Layout
7070 \begin_inset Formula \[
7078 \begin_layout Standard
7080 multiline bracket: The command
7092 \begin_layout Plain Layout
7102 \begin_inset Formula $\downarrow$
7109 \begin_layout Plain Layout
7123 \begin_inset Formula \[
7124 \ln\left(\frac{A}{C}\right)\]
7131 \begin_layout Standard
7147 \begin_inset space ~
7153 This has the advantage that you can see in LyX immediately the real bracket
7154 size and that the matching right bracket will be created too.
7155 \begin_inset Newline newline
7158 The command for the last example would then be:
7172 \begin_layout Plain Layout
7182 \begin_inset Formula $\downarrow$
7188 \begin_layout Standard
7189 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7190 For example the command
7200 \begin_layout Plain Layout
7210 \begin_inset Formula $\downarrow$
7217 \begin_layout Plain Layout
7233 \begin_inset Formula \[
7234 \left.\frac{A}{B}\right\} \]
7252 will be converted by LyX to brackets in the right size when the document
7253 is reloaded and an omitted bracket will appear as dashed line.
7256 \begin_layout Standard
7257 \begin_inset VSpace bigskip
7260 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7271 \begin_layout Plain Layout
7279 is additionally available for all brackets and limits.
7280 With this command the height of the following character is adapted to the
7281 one of the surrounding brackets, what is e.
7282 \begin_inset space \thinspace{}
7286 \begin_inset space \space{}
7289 needed for physical vectors:
7290 \begin_inset Formula \[
7291 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7295 For physical vectors there is a special LaTeX-package, described in
7296 \begin_inset CommandInset ref
7298 reference "sub:Physical-Vectors"
7305 \begin_layout Subsection
7310 \begin_layout Plain Layout
7311 Brackets ! horizontal
7319 \begin_layout Standard
7321 \begin_inset Tabular
7322 <lyxtabular version="3" rows="4" columns="2">
7324 <column alignment="center" valignment="top" width="0pt">
7325 <column alignment="center" valignment="top" width="0pt">
7327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7330 \begin_layout Plain Layout
7332 \begin_inset Note Note
7335 \begin_layout Plain Layout
7342 is only used as spacer.
7352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7355 \begin_layout Plain Layout
7363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7366 \begin_layout Plain Layout
7370 \begin_layout Plain Layout
7385 \begin_layout Plain Layout
7398 \begin_layout Plain Layout
7411 \begin_layout Plain Layout
7424 \begin_layout Plain Layout
7435 \begin_layout Plain Layout
7448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7451 \begin_layout Plain Layout
7452 \begin_inset Formula $\overbrace{A+B}^{3}$
7462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7465 \begin_layout Plain Layout
7469 \begin_layout Plain Layout
7484 \begin_layout Plain Layout
7497 \begin_layout Plain Layout
7510 \begin_layout Plain Layout
7521 \begin_layout Plain Layout
7534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7537 \begin_layout Plain Layout
7538 \begin_inset Formula $\underbrace{A+B}_{5}$
7548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7551 \begin_layout Plain Layout
7558 \begin_layout Plain Layout
7573 \begin_layout Plain Layout
7586 \begin_layout Plain Layout
7599 \begin_layout Plain Layout
7612 \begin_layout Plain Layout
7625 \begin_layout Plain Layout
7638 \begin_layout Plain Layout
7652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7655 \begin_layout Plain Layout
7656 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7672 \begin_layout Standard
7673 In the last example it doesn't matter if
7685 is inserted at first.
7688 \begin_layout Standard
7689 \begin_inset VSpace bigskip
7692 When brackets are needed that overlap each other, multiline formulas, as
7694 \begin_inset CommandInset ref
7696 reference "sec:Multiline-Formulas"
7701 \begin_inset Formula \begin{eqnarray*}
7702 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7703 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7707 In the first row the formula is inserted together with the first brace.
7708 It is hereby important that the space command
7712 \begin_layout Plain Layout
7713 Space commands are explained in
7714 \begin_inset CommandInset ref
7716 reference "sub:Predefined-Space"
7731 is inserted before the first
7732 \begin_inset Formula $d$
7735 , because the brace that ends behind the
7736 \begin_inset Formula $q$
7739 prevents that the following
7740 \begin_inset Quotes eld
7744 \begin_inset Quotes erd
7747 is surrounded by space.
7751 \begin_layout Plain Layout
7752 because a bracket is not handled as character, see
7753 \begin_inset CommandInset ref
7755 reference "sub:Binary-Operators"
7764 In the second row the second brace is inserted.
7765 As it should begin before the
7766 \begin_inset Formula $b$
7781 \begin_layout Plain Layout
7789 \begin_inset CommandInset ref
7791 reference "sub:Placeholders"
7800 This space is needed because the
7801 \begin_inset Quotes eld
7805 \begin_inset Quotes erd
7808 is also surrounded by space in the formula.
7809 The brace is placed under the command
7818 \begin_layout Standard
7819 It gets more complicated when brackets overlap each other, like in the following
7824 \begin_layout Plain Layout
7836 \begin_inset Formula \begin{eqnarray*}
7837 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7838 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7846 \begin_layout Plain Layout
7857 The first formula row is the same as the second row of the previous example,
7858 with the difference that the brace is above.
7859 The second row contains the formula together with the second brace.
7860 To avoid that there is space between the upper brace in the first row and
7861 the formula, the row spacing need to be reduced.
7862 This is not easily possible due to a bug in LyX
7866 \begin_layout Plain Layout
7867 \begin_inset CommandInset href
7869 name "LyX-bug #1505"
7870 target "http://www.lyx.org/trac/ticket/1505"
7880 As solution for the problem, the global formula row separation
7890 \begin_layout Plain Layout
7898 must be changed to -6
7899 \begin_inset space \thinspace{}
7902 pt before the formula with the command
7917 is set back after the formula to the standard value of 3
7918 \begin_inset space \thinspace{}
7921 pt using the same command.
7922 More about the row separation in formulas is explained in
7923 \begin_inset CommandInset ref
7925 reference "sub:Line-Separation"
7932 \begin_layout Section
7937 \begin_layout Plain Layout
7946 \begin_layout Standard
7947 Arrows can be inserted via the math toolbar button
7948 \begin_inset Graphics
7949 filename ../images/math/leftarrow.png
7954 or the commands listed in the following subsections.
7957 \begin_layout Standard
7958 \begin_inset Newpage newpage
7964 \begin_layout Subsection
7969 \begin_layout Plain Layout
7978 \begin_layout Standard
7979 \begin_inset space \hfill{}
7983 \begin_inset Tabular
7984 <lyxtabular version="3" rows="8" columns="2">
7986 <column alignment="center" valignment="top" width="0pt">
7987 <column alignment="center" valignment="top" width="0pt">
7989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7992 \begin_layout Plain Layout
7998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8001 \begin_layout Plain Layout
8009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8012 \begin_layout Plain Layout
8020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8023 \begin_layout Plain Layout
8024 \begin_inset Formula $\gets$
8034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8037 \begin_layout Plain Layout
8045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8048 \begin_layout Plain Layout
8049 \begin_inset Formula $\Leftarrow$
8059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8062 \begin_layout Plain Layout
8070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8073 \begin_layout Plain Layout
8074 \begin_inset Formula $\longleftarrow$
8084 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8087 \begin_layout Plain Layout
8095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8098 \begin_layout Plain Layout
8099 \begin_inset Formula $\Longleftarrow$
8109 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8112 \begin_layout Plain Layout
8120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8123 \begin_layout Plain Layout
8124 \begin_inset Formula $\leftharpoonup$
8134 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8137 \begin_layout Plain Layout
8145 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8148 \begin_layout Plain Layout
8149 \begin_inset Formula $\leftharpoondown$
8159 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8162 \begin_layout Plain Layout
8170 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8173 \begin_layout Plain Layout
8174 \begin_inset Formula $\hookleftarrow$
8188 \begin_inset space \hfill{}
8192 \begin_inset Tabular
8193 <lyxtabular version="3" rows="8" columns="2">
8195 <column alignment="center" valignment="top" width="0pt">
8196 <column alignment="center" valignment="top" width="0pt">
8198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8201 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8210 \begin_layout Plain Layout
8218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8221 \begin_layout Plain Layout
8229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8232 \begin_layout Plain Layout
8233 \begin_inset Formula $\to$
8243 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8246 \begin_layout Plain Layout
8254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8257 \begin_layout Plain Layout
8258 \begin_inset Formula $\Rightarrow$
8268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8271 \begin_layout Plain Layout
8279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8282 \begin_layout Plain Layout
8283 \begin_inset Formula $\longrightarrow$
8293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8296 \begin_layout Plain Layout
8304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8307 \begin_layout Plain Layout
8308 \begin_inset Formula $\Longrightarrow$
8318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8321 \begin_layout Plain Layout
8329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8332 \begin_layout Plain Layout
8333 \begin_inset Formula $\rightharpoonup$
8343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8346 \begin_layout Plain Layout
8354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8357 \begin_layout Plain Layout
8358 \begin_inset Formula $\rightharpoondown$
8368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8371 \begin_layout Plain Layout
8379 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8382 \begin_layout Plain Layout
8383 \begin_inset Formula $\hookrightarrow$
8397 \begin_inset space \hfill{}
8403 \begin_layout Standard
8404 \begin_inset space \hfill{}
8408 \begin_inset Tabular
8409 <lyxtabular version="3" rows="6" columns="2">
8411 <column alignment="center" valignment="top" width="0pt">
8412 <column alignment="center" valignment="top" width="0pt">
8414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8417 \begin_layout Plain Layout
8423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8426 \begin_layout Plain Layout
8434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8437 \begin_layout Plain Layout
8445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8448 \begin_layout Plain Layout
8449 \begin_inset Formula $\leftrightarrow$
8459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8462 \begin_layout Plain Layout
8470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8473 \begin_layout Plain Layout
8474 \begin_inset Formula $\Leftrightarrow$
8484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8487 \begin_layout Plain Layout
8495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8498 \begin_layout Plain Layout
8499 \begin_inset Formula $\longleftrightarrow$
8509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8512 \begin_layout Plain Layout
8520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8523 \begin_layout Plain Layout
8524 \begin_inset Formula $\Longleftrightarrow$
8534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8537 \begin_layout Plain Layout
8545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8548 \begin_layout Plain Layout
8549 \begin_inset Formula $\rightleftharpoons$
8563 \begin_inset space \hspace{}
8568 \begin_inset space \hfill{}
8572 \begin_inset Tabular
8573 <lyxtabular version="3" rows="5" columns="2">
8575 <column alignment="center" valignment="top" width="0pt">
8576 <column alignment="center" valignment="top" width="0pt">
8578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8581 \begin_layout Plain Layout
8587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8590 \begin_layout Plain Layout
8598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8601 \begin_layout Plain Layout
8609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8612 \begin_layout Plain Layout
8613 \begin_inset Formula $\mapsto$
8623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8626 \begin_layout Plain Layout
8634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8637 \begin_layout Plain Layout
8638 \begin_inset Formula $\longmapsto$
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8662 \begin_layout Plain Layout
8663 \begin_inset Formula $\leadsto$
8673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8676 \begin_layout Plain Layout
8684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8687 \begin_layout Plain Layout
8688 \begin_inset Formula $\dasharrow$
8702 \begin_inset space \hfill{}
8708 \begin_layout Standard
8709 \begin_inset VSpace medskip
8712 Arrows used as accent like e.
8713 \begin_inset space \thinspace{}
8717 \begin_inset space \space{}
8720 vector arrows are listed in
8721 \begin_inset CommandInset ref
8723 reference "sec:Accents"
8730 \begin_layout Standard
8731 \begin_inset VSpace bigskip
8734 Furthermore there are the labeled arrows
8738 \begin_layout Plain Layout
8754 \begin_layout Plain Layout
8772 \begin_layout Plain Layout
8779 \begin_layout Plain Layout
8794 When inserting one of these commands in a formula, an arrow with two blue
8795 boxes appear where the label can be inserted.
8796 The length of the arrow adapts to the label width.
8799 \begin_layout Standard
8801 \begin_inset Tabular
8802 <lyxtabular version="3" rows="3" columns="2">
8804 <column alignment="center" valignment="top" width="0pt">
8805 <column alignment="center" valignment="top" width="0pt">
8807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8810 \begin_layout Plain Layout
8816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8819 \begin_layout Plain Layout
8821 \begin_inset Note Note
8824 \begin_layout Plain Layout
8831 is only used as spacer.
8843 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8846 \begin_layout Plain Layout
8853 \begin_layout Plain Layout
8863 \begin_inset Formula $\downarrow$
8867 \begin_inset Formula $\to$
8875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8878 \begin_layout Plain Layout
8879 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8892 \begin_layout Plain Layout
8899 \begin_layout Plain Layout
8909 \begin_inset Formula $\downarrow$
8913 \begin_inset Formula $\to$
8921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8924 \begin_layout Plain Layout
8925 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8941 \begin_layout Subsection
8942 Vertical and diagonal Arrows
8946 \begin_layout Plain Layout
8956 \begin_layout Plain Layout
8965 \begin_layout Standard
8966 \begin_inset space \hfill{}
8970 \begin_inset Tabular
8971 <lyxtabular version="3" rows="7" columns="2">
8973 <column alignment="center" valignment="top" width="0pt">
8974 <column alignment="center" valignment="top" width="0pt">
8976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8979 \begin_layout Plain Layout
8985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8988 \begin_layout Plain Layout
8996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8999 \begin_layout Plain Layout
9007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9010 \begin_layout Plain Layout
9011 \begin_inset Formula $\uparrow$
9021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9024 \begin_layout Plain Layout
9032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9035 \begin_layout Plain Layout
9036 \begin_inset Formula $\Uparrow$
9046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9049 \begin_layout Plain Layout
9057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9060 \begin_layout Plain Layout
9061 \begin_inset Formula $\updownarrow$
9071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9074 \begin_layout Plain Layout
9082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9085 \begin_layout Plain Layout
9086 \begin_inset Formula $\Updownarrow$
9096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9099 \begin_layout Plain Layout
9107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9110 \begin_layout Plain Layout
9111 \begin_inset Formula $\Downarrow$
9121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9124 \begin_layout Plain Layout
9132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9135 \begin_layout Plain Layout
9136 \begin_inset Formula $\downarrow$
9150 \begin_inset space \hfill{}
9154 \begin_inset Tabular
9155 <lyxtabular version="3" rows="5" columns="2">
9157 <column alignment="center" valignment="top" width="0pt">
9158 <column alignment="center" valignment="top" width="0pt">
9160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9163 \begin_layout Plain Layout
9169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9172 \begin_layout Plain Layout
9180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9183 \begin_layout Plain Layout
9191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9194 \begin_layout Plain Layout
9195 \begin_inset Formula $\nearrow$
9205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9208 \begin_layout Plain Layout
9216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9219 \begin_layout Plain Layout
9220 \begin_inset Formula $\searrow$
9230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9233 \begin_layout Plain Layout
9241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9244 \begin_layout Plain Layout
9245 \begin_inset Formula $\swarrow$
9255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9258 \begin_layout Plain Layout
9266 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9269 \begin_layout Plain Layout
9270 \begin_inset Formula $\nwarrow$
9284 \begin_inset space \hfill{}
9290 \begin_layout Standard
9291 \begin_inset VSpace medskip
9294 Vertical arrows can be used also as delimiter together with the commands
9296 \begin_inset CommandInset ref
9298 reference "sub:Manual-Bracket-Size"
9303 \begin_inset CommandInset ref
9305 reference "sub:Automatic-Bracket-Size"
9312 \begin_layout Standard
9313 \begin_inset Newpage newpage
9319 \begin_layout Section
9321 \begin_inset CommandInset label
9331 \begin_layout Plain Layout
9340 \begin_layout Standard
9341 Accents can be inserted via the math toolbar button
9342 \begin_inset Graphics
9343 filename ../images/math/hat.png
9348 or the commands listed in the following subsections.
9351 \begin_layout Subsection
9352 Accents for one Character
9356 \begin_layout Plain Layout
9369 \begin_layout Plain Layout
9371 \begin_inset CommandInset ref
9373 reference "sub:Accents-in-Text"
9386 \begin_layout Plain Layout
9394 \begin_inset Note Note
9397 \begin_layout Plain Layout
9400 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9403 \begin_layout Plain Layout
9406 texorpdfstring is in section
9407 \begin_inset CommandInset ref
9409 reference "sub:Formulas-in-Section"
9419 \begin_inset CommandInset label
9421 name "sub:Accents-for-one"
9429 \begin_layout Plain Layout
9430 Accents ! for one character
9438 \begin_layout Standard
9439 \begin_inset space \hfill{}
9443 \begin_inset Tabular
9444 <lyxtabular version="3" rows="8" columns="2">
9446 <column alignment="center" valignment="top" width="0pt">
9447 <column alignment="center" valignment="top" width="0pt">
9449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9452 \begin_layout Plain Layout
9458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9461 \begin_layout Plain Layout
9463 \begin_inset Note Note
9466 \begin_layout Plain Layout
9473 is only used as spacer.
9485 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9488 \begin_layout Plain Layout
9495 \begin_layout Plain Layout
9509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9512 \begin_layout Plain Layout
9513 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9526 \begin_layout Plain Layout
9533 \begin_layout Plain Layout
9547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9550 \begin_layout Plain Layout
9551 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9564 \begin_layout Plain Layout
9571 \begin_layout Plain Layout
9585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9588 \begin_layout Plain Layout
9589 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9602 \begin_layout Plain Layout
9610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9613 \begin_layout Plain Layout
9614 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9624 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9634 \begin_layout Plain Layout
9647 \begin_layout Plain Layout
9658 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9661 \begin_layout Plain Layout
9662 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9675 \begin_layout Plain Layout
9682 \begin_layout Plain Layout
9696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9699 \begin_layout Plain Layout
9700 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9710 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9713 \begin_layout Plain Layout
9720 \begin_layout Plain Layout
9734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9737 \begin_layout Plain Layout
9738 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9752 \begin_inset space \hfill{}
9756 \begin_inset Tabular
9757 <lyxtabular version="3" rows="7" columns="2">
9759 <column alignment="center" valignment="top" width="0pt">
9760 <column alignment="center" valignment="top" width="0pt">
9762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9765 \begin_layout Plain Layout
9771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9774 \begin_layout Plain Layout
9782 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9785 \begin_layout Plain Layout
9792 \begin_layout Plain Layout
9806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9809 \begin_layout Plain Layout
9810 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9823 \begin_layout Plain Layout
9830 \begin_layout Plain Layout
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9847 \begin_layout Plain Layout
9848 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9861 \begin_layout Plain Layout
9868 \begin_layout Plain Layout
9882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9885 \begin_layout Plain Layout
9886 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9899 \begin_layout Plain Layout
9906 \begin_layout Plain Layout
9920 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9923 \begin_layout Plain Layout
9924 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9934 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9937 \begin_layout Plain Layout
9944 \begin_layout Plain Layout
9958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9961 \begin_layout Plain Layout
9962 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9975 \begin_layout Plain Layout
9982 \begin_layout Plain Layout
9996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9999 \begin_layout Plain Layout
10000 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10014 \begin_inset space \hfill{}
10020 \begin_layout Standard
10021 \begin_inset VSpace bigskip
10027 \begin_layout Standard
10028 You can directly insert accents like é to formulas.
10029 LyX will transform them to the corresponding accent command.
10034 \begin_layout Plain Layout
10040 it is better to insert a quotation mark before the vowel.
10041 These two characters are then treated by LaTeX as
10045 character when the formula part with the umlaut is marked as German.
10053 \begin_inset Quotes eld
10057 \begin_inset Quotes erd
10060 umlauts are created as demonstrated in the following example:
10063 \begin_layout Standard
10064 \begin_inset VSpace -2mm
10070 \begin_layout Standard
10072 \begin_inset Tabular
10073 <lyxtabular version="3" rows="3" columns="2">
10075 <column alignment="center" valignment="top" width="0">
10076 <column alignment="center" valignment="top" width="0">
10078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10081 \begin_layout Plain Layout
10087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10090 \begin_layout Plain Layout
10092 \begin_inset Note Note
10095 \begin_layout Plain Layout
10103 \begin_inset space \thinspace{}
10106 pt space are only used as spacer.
10118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10121 \begin_layout Plain Layout
10124 \begin_inset Quotes grd
10132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10135 \begin_layout Plain Layout
10136 \begin_inset space \hspace{}
10143 \begin_inset Formula $"i$
10153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10156 \begin_layout Plain Layout
10163 \begin_layout Plain Layout
10177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10180 \begin_layout Plain Layout
10181 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10197 \begin_layout Standard
10198 Another advantage to
10204 is that umlauts can directly be converted to mathematical text because
10205 the accent commands above are
10211 in mathematical text
10214 To convert an accented character to mathematical text, only the character
10215 under the accent may be converted.
10216 This applies also for all other conversions, e.
10217 \begin_inset space \thinspace{}
10221 \begin_inset space \space{}
10227 \begin_layout Standard
10228 In mathematical text, umlauts and other accented characters can directly
10232 \begin_layout Subsection
10233 Accents for Operators
10237 \begin_layout Plain Layout
10238 Accents ! for operators
10246 \begin_layout Standard
10257 \begin_layout Plain Layout
10275 \begin_layout Plain Layout
10283 characters can be placed above or below an operator, respectively, to accent
10295 \begin_layout Plain Layout
10303 characters can be set before and behind an operator.
10304 The command scheme is:
10307 \begin_layout Standard
10323 \begin_layout Standard
10330 must always be before the operator that should be accented.
10331 You can accent with several characters and even with other operators and
10339 for example only characters behind an operator, write nothing between the
10340 first braces but don't omit the braces.
10343 \begin_layout Standard
10344 For example the command
10349 \begin_inset Formula $\to$
10359 \begin_inset Formula $\to$
10368 \begin_layout Plain Layout
10384 \begin_inset Formula \[
10385 \sideset{}{'}\sum_{k=1}^{n}\]
10392 \begin_layout Standard
10401 \begin_layout Plain Layout
10416 \begin_layout Plain Layout
10428 \begin_inset Formula $\uparrow$
10436 \begin_inset Formula \[
10437 \overset{a}{\maltese}\]
10441 As seen in the last example, with
10453 also symbols and characters can be accented; with
10459 this is not possible.
10462 \begin_layout Subsection
10463 Accents for several Characters
10467 \begin_layout Plain Layout
10468 Accents ! for several characters
10476 \begin_layout Standard
10477 \begin_inset space \hfill{}
10481 \begin_inset Tabular
10482 <lyxtabular version="3" rows="5" columns="2">
10484 <column alignment="center" valignment="top" width="0pt">
10485 <column alignment="center" valignment="top" width="0pt">
10487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10490 \begin_layout Plain Layout
10496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10499 \begin_layout Plain Layout
10501 \begin_inset Note Note
10504 \begin_layout Plain Layout
10511 is only used as spacer.
10523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10526 \begin_layout Plain Layout
10533 \begin_layout Plain Layout
10547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10550 \begin_layout Plain Layout
10551 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10561 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10564 \begin_layout Plain Layout
10571 \begin_layout Plain Layout
10585 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10588 \begin_layout Plain Layout
10589 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10599 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10602 \begin_layout Plain Layout
10609 \begin_layout Plain Layout
10623 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10626 \begin_layout Plain Layout
10627 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10637 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10640 \begin_layout Plain Layout
10643 underleftrightarrow
10647 \begin_layout Plain Layout
10661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10664 \begin_layout Plain Layout
10665 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10679 \begin_inset space \hfill{}
10683 \begin_inset Tabular
10684 <lyxtabular version="3" rows="5" columns="2">
10686 <column alignment="center" valignment="top" width="0pt">
10687 <column alignment="center" valignment="top" width="0pt">
10689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10692 \begin_layout Plain Layout
10698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10701 \begin_layout Plain Layout
10709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10712 \begin_layout Plain Layout
10719 \begin_layout Plain Layout
10733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10736 \begin_layout Plain Layout
10737 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10747 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10750 \begin_layout Plain Layout
10757 \begin_layout Plain Layout
10771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10774 \begin_layout Plain Layout
10775 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10785 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10788 \begin_layout Plain Layout
10795 \begin_layout Plain Layout
10809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10812 \begin_layout Plain Layout
10813 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10826 \begin_layout Plain Layout
10833 \begin_layout Plain Layout
10847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10850 \begin_layout Plain Layout
10851 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10865 \begin_inset space \hfill{}
10871 \begin_layout Standard
10872 \begin_inset VSpace medskip
10875 With these commands as many characters as you like can be accented.
10888 will only be set in the output with a length of three characters, as shown
10889 in the following example:
10890 \begin_inset Formula \[
10891 \widetilde{A+B=C-D}\]
10898 \begin_layout Standard
10909 \begin_layout Plain Layout
10927 \begin_layout Plain Layout
10935 described in the previous subsection it is also possible to accent several
10945 \begin_layout Plain Layout
10955 \begin_inset Formula $\downarrow$
10961 \begin_inset Formula \[
10962 \underset{***}{A=B}\]
10969 \begin_layout Section
10971 \begin_inset CommandInset label
10981 \begin_layout Plain Layout
10990 \begin_layout Subsection
10992 \begin_inset CommandInset label
10994 name "sub:Predefined-Space"
11002 \begin_layout Plain Layout
11003 Space ! horizontal ! predefined
11011 \begin_layout Standard
11012 Sometimes it is necessary to insert horizontal space to a formula.
11013 This is done by inserting a protected space (shortcut
11016 arg "space-insert protected"
11021 \begin_inset Quotes eld
11030 \begin_layout Plain Layout
11042 \begin_inset Quotes erd
11045 appears and by pressing
11049 several times one can select one of eight different space sizes.
11050 The spaces can also be inserted using the math toolbar button
11051 \begin_inset Graphics
11052 filename ../images/math/space.png
11057 or special commands.
11058 Independent from the inserted command, one can select the size again by
11066 \begin_layout Standard
11069 \begin_inset VSpace -5mm
11073 \begin_inset Tabular
11074 <lyxtabular version="3" rows="3" columns="7">
11076 <column alignment="center" valignment="middle" width="6.8cm">
11077 <column alignment="center" valignment="top" width="0">
11078 <column alignment="center" valignment="top" width="0">
11079 <column alignment="center" valignment="top" width="0">
11080 <column alignment="center" valignment="top" width="0">
11081 <column alignment="center" valignment="top" width="0">
11082 <column alignment="center" valignment="top" width="0">
11084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11087 \begin_layout Plain Layout
11093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11096 \begin_layout Plain Layout
11104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11107 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11118 \begin_layout Plain Layout
11126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11129 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11140 \begin_layout Plain Layout
11148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11151 \begin_layout Plain Layout
11161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11164 \begin_layout Plain Layout
11169 keystrokes after inserting the protected space
11174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11177 \begin_layout Plain Layout
11183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11186 \begin_layout Plain Layout
11192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11195 \begin_layout Plain Layout
11201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11204 \begin_layout Plain Layout
11210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11213 \begin_layout Plain Layout
11219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11233 \begin_layout Plain Layout
11239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11242 \begin_layout Plain Layout
11243 \begin_inset Formula $A\, B$
11251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11254 \begin_layout Plain Layout
11255 \begin_inset Formula $A\: B$
11263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11266 \begin_layout Plain Layout
11267 \begin_inset Formula $A\; B$
11275 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11278 \begin_layout Plain Layout
11279 \begin_inset Formula $A\quad B$
11287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11290 \begin_layout Plain Layout
11291 \begin_inset Formula $A\qquad B$
11299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11302 \begin_layout Plain Layout
11303 \begin_inset Formula $A\! B$
11319 \begin_layout Standard
11320 The last size seem to produce no space.
11321 It is displayed red in LyX contrary to the other sizes, because it is a
11323 There are two more negative spaces:
11326 \begin_layout Standard
11328 \begin_inset Tabular
11329 <lyxtabular version="3" rows="3" columns="3">
11331 <column alignment="center" valignment="middle" width="6.8cm">
11332 <column alignment="center" valignment="top" width="0pt">
11333 <column alignment="center" valignment="top" width="0pt">
11335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11338 \begin_layout Plain Layout
11344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11347 \begin_layout Plain Layout
11355 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11358 \begin_layout Plain Layout
11368 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11371 \begin_layout Plain Layout
11376 keystrokes after inserting the protected space
11381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11384 \begin_layout Plain Layout
11390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11393 \begin_layout Plain Layout
11401 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11404 \begin_layout Plain Layout
11410 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11413 \begin_layout Plain Layout
11414 \begin_inset Formula $A\negmedspace B$
11422 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11425 \begin_layout Plain Layout
11426 \begin_inset Formula $A\negthickspace B$
11442 \begin_layout Standard
11443 Negative spaces can lead to characters overlapping each other.
11444 Thus they can be used to enforce ligatures, what is e.
11445 \begin_inset space \thinspace{}
11449 \begin_inset space \space{}
11452 useful for summation operators:
11455 \begin_layout Standard
11457 \begin_inset Tabular
11458 <lyxtabular version="3" rows="3" columns="2">
11460 <column alignment="center" valignment="top" width="0">
11461 <column alignment="center" valignment="top" width="0">
11463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11466 \begin_layout Plain Layout
11472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11475 \begin_layout Plain Layout
11477 \begin_inset Note Note
11480 \begin_layout Plain Layout
11487 is only used as spacer.
11499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11502 \begin_layout Plain Layout
11511 \begin_layout Plain Layout
11525 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11528 \begin_layout Plain Layout
11529 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11542 \begin_layout Plain Layout
11553 \begin_layout Plain Layout
11567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11570 \begin_layout Plain Layout
11571 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11587 \begin_layout Standard
11588 Relations like for example equal signs, are always surrounded by space.
11589 To suppress this, the equal sign is placed into a TeX-brace.
11590 The following example demonstrates this:
11593 \begin_layout Standard
11595 \begin_inset Tabular
11596 <lyxtabular version="3" rows="2" columns="2">
11598 <column alignment="center" valignment="top" width="0pt">
11599 <column alignment="center" valignment="top" width="0pt">
11601 <cell alignment="center" valignment="top" usebox="none">
11604 \begin_layout Plain Layout
11610 <cell alignment="center" valignment="top" usebox="none">
11613 \begin_layout Plain Layout
11614 \begin_inset Formula $A=B$
11624 <cell alignment="center" valignment="top" usebox="none">
11627 \begin_layout Plain Layout
11628 \begin_inset Note Note
11631 \begin_layout Plain Layout
11638 is only used as spacer.
11644 \begin_inset Formula $\raisebox{5mm}{}$
11647 equation without space
11652 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11655 \begin_layout Plain Layout
11656 \begin_inset Formula $A{=}B$
11672 \begin_layout Standard
11674 The command for the last formula is:
11679 \begin_inset Formula $\to$
11685 \begin_layout Standard
11686 \begin_inset VSpace bigskip
11689 Spaces are needed for physical units, because the space between the value
11690 and the unit is the smallest one and not a normal space.
11691 For units in text, the smallest space is inserted via the menu
11693 Insert\SpecialChar \menuseparator
11694 Formatting\SpecialChar \menuseparator
11696 \begin_inset space ~
11704 arg "space-insert thin"
11710 \begin_layout Standard
11711 An example to visualize the difference:
11714 \begin_layout Standard
11715 \begin_inset Tabular
11716 <lyxtabular version="3" rows="2" columns="2">
11718 <column alignment="left" valignment="top" width="0">
11719 <column alignment="left" valignment="top" width="0">
11721 <cell alignment="center" valignment="top" usebox="none">
11724 \begin_layout Plain Layout
11726 \begin_inset Formula $\cdot$
11734 <cell alignment="center" valignment="top" usebox="none">
11737 \begin_layout Plain Layout
11738 space between value and unit
11745 <cell alignment="center" valignment="top" usebox="none">
11748 \begin_layout Plain Layout
11750 \begin_inset space \thinspace{}
11754 \begin_inset Formula $\cdot$
11762 <cell alignment="center" valignment="top" usebox="none">
11765 \begin_layout Plain Layout
11766 smallest space between value and unit
11779 \begin_layout Subsection
11784 \begin_layout Plain Layout
11797 \begin_layout Plain Layout
11798 for vertical space in formulas see
11799 \begin_inset CommandInset ref
11801 reference "sub:Line-Separation"
11814 \begin_layout Plain Layout
11822 \begin_inset Note Note
11825 \begin_layout Plain Layout
11828 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11831 \begin_layout Plain Layout
11834 texorpdfstring is in section
11835 \begin_inset CommandInset ref
11837 reference "sub:Formulas-in-Section"
11847 \begin_inset CommandInset label
11849 name "sub:Variable-Space"
11857 \begin_layout Plain Layout
11858 Space ! horizontal ! variable
11866 \begin_layout Standard
11867 Space with a defined length can be inserted with the command
11877 \begin_layout Plain Layout
11887 \begin_inset Quotes eld
11896 \begin_layout Plain Layout
11908 \begin_inset Quotes erd
11912 The length can be specified by left-clicking on the
11913 \begin_inset Quotes eld
11922 \begin_layout Plain Layout
11934 \begin_inset Quotes erd
11938 The length may also be negative.
11939 To insert so many space that the formula uses all available space, the
11950 \begin_layout Plain Layout
11961 \begin_layout Standard
11962 \begin_inset VSpace -1mm
11968 \begin_layout Standard
11970 \begin_inset Tabular
11971 <lyxtabular version="3" rows="4" columns="2">
11973 <column alignment="center" valignment="top" width="0">
11974 <column alignment="center" valignment="top" width="0">
11976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11979 \begin_layout Plain Layout
11987 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11990 \begin_layout Plain Layout
11998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12001 \begin_layout Plain Layout
12008 \begin_layout Plain Layout
12018 \begin_inset Formula $\to$
12024 \begin_inset space \thinspace{}
12032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12035 \begin_layout Plain Layout
12036 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12049 \begin_layout Plain Layout
12056 \begin_layout Plain Layout
12066 \begin_inset Formula $\to$
12072 \begin_inset space \thinspace{}
12080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12083 \begin_layout Plain Layout
12084 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12097 \begin_layout Plain Layout
12104 \begin_layout Plain Layout
12118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12121 \begin_layout Plain Layout
12122 \begin_inset Formula $A=A\hfill B=B$
12138 \begin_layout Standard
12139 In the last example the available space is given by the longest column entry
12141 In an inline formula the space depends on the length of the line in which
12149 Thus, when the line uses the full width, no space will be created.
12156 only has an effect on displayed formulas when the formula style
12161 (Formula styles are explained in
12162 \begin_inset CommandInset ref
12164 reference "sec:Formula-Styles"
12171 \begin_layout Standard
12178 , there are the commands
12190 that fill the space with a pattern, see
12191 \begin_inset CommandInset ref
12193 reference "sub:Ellipses"
12200 \begin_layout Standard
12201 For text, variable space can be inserted via the menu
12203 Insert\SpecialChar \menuseparator
12204 Formatting\SpecialChar \menuseparator
12206 \begin_inset space ~
12214 \begin_layout Standard
12215 This is a line with
12216 \begin_inset space \hspace{}
12221 \begin_inset space \thinspace{}
12227 \begin_layout Standard
12228 This is a line with
12229 \begin_inset space \hfill{}
12235 \begin_layout Subsection
12236 Space besides inline Formulas
12240 \begin_layout Plain Layout
12241 Space ! besides inline formulas
12249 \begin_layout Standard
12250 The space that surrounds inline formulas can be adjusted with the length
12259 \begin_layout Plain Layout
12270 The value of a length is set with the command
12278 \begin_layout Plain Layout
12288 that has the following scheme:
12291 \begin_layout Standard
12296 setlength{length name}{value}
12299 \begin_layout Standard
12307 \begin_inset space \thinspace{}
12313 \begin_layout Standard
12323 \begin_layout Standard
12324 is inserted in TeX-mode.
12326 \begin_inset space \thinspace{}
12329 mm space will now be set around all inline formulas:
12333 \begin_layout Plain Layout
12347 \begin_layout Standard
12348 This is a line with an inline formula
12349 \begin_inset Formula $A=B$
12353 \begin_inset space \thinspace{}
12356 mm surrounding space.
12360 \begin_layout Plain Layout
12374 \begin_layout Standard
12375 To return to the predefined value,
12381 is set to the value 0
12382 \begin_inset space \thinspace{}
12388 \begin_layout Section
12393 \begin_layout Plain Layout
12403 \begin_layout Plain Layout
12408 \begin_layout Plain Layout
12419 \begin_layout Plain Layout
12434 \begin_layout Standard
12435 Boxes for text are described in chapter
12442 \begin_inset space ~
12450 \begin_layout Subsection
12452 \begin_inset CommandInset label
12454 name "sub:Boxes-with-Frame"
12462 \begin_layout Plain Layout
12471 \begin_layout Standard
12472 It is possible to frame formulas or parts of it with the commands
12482 \begin_layout Plain Layout
12500 \begin_layout Plain Layout
12511 \begin_layout Standard
12512 When one of these commands is inserted to a formula, a blue box appears
12513 within a frame to enter formula parts.
12520 an additional formula has to be created by
12524 within this box, because the box content will otherwise be treated as mathemati
12532 is used, a new formula is automatically created inside the frame.
12535 \begin_layout Standard
12542 is not suitable to frame displayed formulas because the formula will always
12543 be set in the size of the text.
12550 is in contrary not suitable to frame inline formulas, because the formula
12551 will always be set in the size of a displayed formula.
12554 \begin_layout Standard
12561 there is the command
12571 \begin_layout Plain Layout
12579 where additionally the frame width and the alignment can be specified.
12586 is used in the following scheme:
12589 \begin_layout Standard
12594 framebox[frame width][position]{box content}
12597 \begin_layout Standard
12598 The position can either be
12615 right aligns the formula in the box.
12616 When no position is given, the formula will be centered.
12617 \begin_inset Newline newline
12620 Is no width given, also no position can be given.
12621 In this case the frame width is adjusted to the box content like for
12630 \begin_layout Standard
12637 is inserted, a box appears containing three blue boxes.
12638 The first two boxes are surrounded by brackets and denote the two optional
12640 The third box is for formula parts like for
12649 \begin_layout Standard
12651 \begin_inset Tabular
12652 <lyxtabular version="3" rows="5" columns="2">
12654 <column alignment="center" valignment="top" width="0">
12655 <column alignment="center" valignment="top" width="0">
12657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12660 \begin_layout Plain Layout
12666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12669 \begin_layout Plain Layout
12671 \begin_inset Note Note
12674 \begin_layout Plain Layout
12681 is only used as spacer.
12693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12696 \begin_layout Plain Layout
12703 \begin_layout Plain Layout
12722 \begin_layout Plain Layout
12736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12739 \begin_layout Plain Layout
12740 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12753 \begin_layout Plain Layout
12760 \begin_layout Plain Layout
12775 \begin_layout Plain Layout
12789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12792 \begin_layout Plain Layout
12793 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12806 \begin_layout Plain Layout
12813 \begin_layout Plain Layout
12827 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12830 \begin_layout Plain Layout
12831 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12844 \begin_layout Plain Layout
12851 \begin_layout Plain Layout
12861 \begin_inset Formula $\to$
12865 \begin_inset Formula $\to$
12878 \begin_layout Plain Layout
12888 \begin_inset Formula $\downarrow$
12896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12899 \begin_layout Plain Layout
12900 \begin_inset Formula $\raisebox{6mm}{}$
12904 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12908 \begin_inset Formula $\raisebox{-4mm}{}$
12924 \begin_layout Standard
12925 The frame thickness can also be adjusted.
12926 To do this the following commands have to be inserted in TeX-mode before
12930 \begin_layout Standard
12940 \begin_inset Quotes eld
12944 \begin_inset Quotes erd
12958 \begin_inset Quotes eld
12962 \begin_inset Quotes erd
12968 \begin_layout Standard
12969 \begin_inset Quotes eld
12973 \begin_inset Quotes erd
12976 specifies the minimal distance between the frame and the first character
12978 An example for this is the following framed formula:
12982 \begin_layout Plain Layout
12994 \begin_inset Formula \[
12999 Before this formula the commands
13002 \begin_layout Standard
13024 \begin_layout Standard
13025 were inserted in TeX-mode.
13026 The given values are used for all following boxes.
13029 \begin_layout Standard
13030 To return to the standard frame size, the command
13033 \begin_layout Standard
13058 \begin_layout Plain Layout
13072 \begin_layout Standard
13073 is inserted in TeX-mode before the next formula.
13076 \begin_layout Subsection
13077 Boxes without Frame
13078 \begin_inset CommandInset label
13080 name "sub:Boxes-without-Frame"
13088 \begin_layout Plain Layout
13089 Boxes ! without frame
13097 \begin_layout Standard
13098 For boxes without a frame there are the following box commands:
13108 \begin_layout Plain Layout
13126 \begin_layout Plain Layout
13144 \begin_layout Plain Layout
13155 \begin_layout Standard
13162 a box can be super- or subscripted.
13163 But in contrary to normal super- and subscripting, the characters in the
13164 box keep their font size.
13171 is used in the following scheme:
13174 \begin_layout Standard
13179 raisebox{height}{box content}
13182 \begin_layout Standard
13183 When the box should contain a formula, an extra formula is needed like for
13194 \begin_inset Note Greyedout
13197 \begin_layout Plain Layout
13208 this extra formula is created by pressing
13212 twice instead of once because LyX doesn't yet support
13226 \begin_layout Standard
13228 \begin_inset Tabular
13229 <lyxtabular version="3" rows="4" columns="2">
13231 <column alignment="center" valignment="top" width="0">
13232 <column alignment="center" valignment="top" width="0">
13234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13237 \begin_layout Plain Layout
13243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13246 \begin_layout Plain Layout
13254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13257 \begin_layout Plain Layout
13261 \begin_inset Formula $\to$
13267 \begin_inset Formula $\to$
13275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13278 \begin_layout Plain Layout
13279 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13289 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13292 \begin_layout Plain Layout
13296 \begin_inset Formula $\to$
13302 \begin_inset Formula $\to$
13310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13313 \begin_layout Plain Layout
13314 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13327 \begin_layout Plain Layout
13331 \begin_inset Formula $\to$
13350 \begin_layout Plain Layout
13364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13367 \begin_layout Plain Layout
13368 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13384 \begin_layout Standard
13409 , with the difference that there is no frame.
13412 \begin_layout Subsection
13414 \begin_inset CommandInset label
13416 name "sub:Colored-Boxes"
13424 \begin_layout Plain Layout
13433 \begin_layout Standard
13434 To be able to use all commands explained in this section, the LaTeX-package
13443 \begin_layout Plain Layout
13448 is part of every LaTeX standard installation.
13457 \begin_layout Plain Layout
13463 has to be loaded in the LaTeX-preamble with the line
13467 \begin_layout Plain Layout
13468 When text is colored somewhere in the document with a predefined color,
13469 LyX loads the LaTeX-package
13474 Thus it is possible that the package is loaded twice, but this doesn't
13481 \begin_inset Note Note
13484 \begin_layout Plain Layout
13485 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13494 \begin_layout Standard
13502 \begin_layout Standard
13503 \begin_inset VSpace medskip
13506 To color boxes, the command
13516 \begin_layout Plain Layout
13524 is used in the following scheme:
13527 \begin_layout Standard
13532 colorbox{color}{box content}
13535 \begin_layout Standard
13536 The box content can also be a box and a
13542 can also be part of another box (see the 2nd and 3rd example).
13543 When the box should contain a formula, an extra formula has to be created,
13544 the same way as for
13554 \begin_layout Plain Layout
13555 This also applies for the command
13569 \begin_layout Standard
13570 One of the following predefined colors can be chosen:
13573 \begin_layout Standard
13607 \begin_layout Standard
13609 \begin_inset Tabular
13610 <lyxtabular version="3" rows="4" columns="2">
13612 <column alignment="center" valignment="top" width="0">
13613 <column alignment="center" valignment="top" width="0">
13615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13618 \begin_layout Plain Layout
13624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13627 \begin_layout Plain Layout
13629 \begin_inset Note Note
13632 \begin_layout Plain Layout
13639 is only used as spacer.
13651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13654 \begin_layout Plain Layout
13658 \begin_inset Formula $\to$
13668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13671 \begin_layout Plain Layout
13672 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13685 \begin_layout Plain Layout
13689 \begin_inset Formula $\to$
13700 \begin_layout Plain Layout
13714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13717 \begin_layout Plain Layout
13718 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13731 \begin_layout Plain Layout
13738 \begin_layout Plain Layout
13750 \begin_inset Formula $\to$
13769 \begin_layout Plain Layout
13783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13786 \begin_layout Plain Layout
13787 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13803 \begin_layout Standard
13810 only colors the box but not the characters in the box.
13811 To color all characters, the whole formula is highlighted and the wanted
13812 color is chosen in the
13815 \begin_inset space ~
13821 The dialog can be called with the toolbar button
13822 \begin_inset Graphics
13823 filename ../images/dialog-show_character.png
13830 Edit\SpecialChar \menuseparator
13832 \begin_inset space ~
13835 Style\SpecialChar \menuseparator
13839 The formula number has then the same color as the formula.
13840 When the formula number should get another color than the formula characters,
13841 the color must be changed within the formula.
13844 \begin_layout Standard
13848 \begin_layout Standard
13851 \begin_inset Formula \begin{equation}
13852 \int A=B\label{eq:red}\end{equation}
13859 \begin_inset Formula \begin{equation}
13860 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13867 \begin_layout Standard
13869 \begin_inset CommandInset ref
13875 is completely colored red.
13876 \begin_inset Newline newline
13880 \begin_inset CommandInset ref
13882 reference "eq:redgreen"
13886 was first completely colored green to set the color for the formula number.
13887 Subsequently the formula characters were colored red.
13890 \begin_layout Standard
13891 \begin_inset VSpace bigskip
13894 To color the frame different than the rest of the box, the command
13904 \begin_layout Plain Layout
13912 is used in the following scheme:
13915 \begin_layout Standard
13920 fcolorbox{frame color}{color}{box content}
13923 \begin_layout Standard
13930 is an extension of the command
13937 The frame width is set, like for
13960 \begin_layout Plain Layout
13972 \begin_inset Formula \[
13973 \fcolorbox{cyan}{magenta}{A=B}\]
13981 \begin_layout Plain Layout
13995 \begin_layout Standard
13996 This formula was created with the command
13997 \begin_inset Newline newline
14005 \begin_inset Formula $\to$
14011 \begin_inset Formula $\to$
14021 \begin_layout Standard
14022 \begin_inset VSpace bigskip
14025 To use other colors than the predefined ones, they have to be defined first.
14028 \begin_layout Standard
14029 One can for example define the color
14030 \begin_inset Quotes eld
14038 \begin_inset Quotes erd
14041 with the LaTeX-preamble line:
14044 \begin_layout Standard
14049 definecolor{darkgreen}{cmyk}{0.5,
14067 \begin_layout Plain Layout
14078 \begin_layout Standard
14083 is the color space that denotes the colors
14100 The four comma separated numbers are the portion factor for the corresponding
14101 colors of the color space.
14102 The factors can be in the range of 0
14103 \begin_inset space \thinspace{}
14107 \begin_inset space \thinspace{}
14115 also the color space
14119 can be used for definitions.
14136 , so that there are in this case three portion factors for the corresponding
14138 Furthermore there is the color space
14142 with one portion factor for the gray value.
14145 \begin_layout Standard
14146 As example a framed box with the new defined color
14150 where the characters have been colored
14155 \begin_inset Formula \begin{equation}
14156 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14163 \begin_layout Standard
14164 Self-defined colors can also be used for text with the help of the command
14175 \begin_layout Plain Layout
14184 \begin_layout Standard
14188 \begin_layout Plain Layout
14192 textcolor{darkgreen}{
14198 \begin_inset Quotes eld
14202 \begin_inset Quotes erd
14209 \begin_layout Plain Layout
14219 \begin_layout Standard
14230 \begin_layout Plain Layout
14238 is used in the scheme
14242 textcolor{color}{characters to color}
14247 \begin_layout Subsection
14249 \begin_inset CommandInset label
14251 name "sub:Paragraph-Boxes"
14259 \begin_layout Plain Layout
14260 Boxes ! as paragraph
14268 \begin_layout Standard
14269 A box that can contain several lines and paragraphs, a so called paragraph
14270 box (parbox), can be created with the menu
14272 Insert\SpecialChar \menuseparator
14275 or the toolbar button
14276 \begin_inset Graphics
14277 filename ../images/box-insert.png
14285 \begin_layout Standard
14286 The following example shows a framed parbox in a line:
14289 \begin_layout Standard
14290 \begin_inset VSpace medskip
14294 \begin_inset Box Boxed
14303 height_special "totalheight"
14306 \begin_layout Plain Layout
14307 This is a paragraph box.
14309 \begin_inset space \thinspace{}
14312 cm long and can also contain formulas:
14313 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14324 \begin_layout Standard
14325 \begin_inset VSpace medskip
14331 \begin_layout Standard
14332 Such a box is created by right-clicking on the gray box inset.
14333 A dialog pops up showing the box properties.
14347 \begin_inset space \thinspace{}
14352 Vertical Box Alignment
14357 \begin_layout Standard
14358 \begin_inset VSpace medskip
14361 In LaTeX a parbox is created with the command
14371 \begin_layout Plain Layout
14379 that has the following scheme:
14382 \begin_layout Standard
14387 parbox[position]{width}{box content}
14390 \begin_layout Standard
14404 for bottom means that the box is aligned within the surrounding text with
14410 for top this is done with the first line.
14411 When no position is given, the box will be vertically centered, see section
14419 \begin_inset space ~
14424 manual for examples.
14427 \begin_layout Standard
14428 \begin_inset VSpace bigskip
14431 To frame formulas completely, including the formula number, the formula
14432 must be set into a parbox.
14433 To do this, the command
14447 is inserted in TeX-mode before the formula.
14456 \begin_layout Plain Layout
14466 is hereby the line width set for the document.
14467 Because the frame is outside the parbox, 2
14468 \begin_inset space \thinspace{}
14471 times the frame separation and the frame thickness must be subtracted from
14473 As this is not automatically done by LyX due to a bug
14477 \begin_layout Plain Layout
14478 \begin_inset CommandInset href
14480 name "LyX-bug #4483"
14481 target "http://www.lyx.org/trac/ticket/4483"
14490 , TeX-mode has to be used.
14491 To be able to multiply and subtract in arguments, the LaTeX-package
14499 \begin_layout Plain Layout
14504 is part of every LaTeX standard installation.
14513 \begin_layout Plain Layout
14519 must be loaded in the LaTeX-preamble with the line
14522 \begin_layout Standard
14530 \begin_layout Standard
14531 Behind the formula both boxes are closed by entering
14536 Here is an example:
14540 \begin_layout Plain Layout
14554 \begin_layout Standard
14558 \begin_layout Plain Layout
14576 \begin_inset Formula \begin{equation}
14577 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14585 \begin_layout Plain Layout
14596 \begin_layout Plain Layout
14610 \begin_layout Standard
14611 \begin_inset VSpace medskip
14614 As a parbox is used as argument of
14620 , there is in this case no difference between
14635 \begin_layout Standard
14636 \begin_inset VSpace bigskip
14639 Paragraph boxes are very useful to comment formulas directly.
14646 is used in combination with the command
14660 \begin_inset CommandInset ref
14662 reference "sub:User-defined-Numbering"
14669 \begin_layout Standard
14670 An example of a formula commented with
14679 \begin_layout Standard
14683 \begin_layout Plain Layout
14696 This is a description.
14697 It is distinctly separated from the formula and multiline.
14701 \begin_layout Plain Layout
14713 \begin_layout Standard
14714 Such a formula must be inserted completely in TeX-mode because LyX does
14715 not yet support the command
14722 The formula is created with the following command sequence:
14725 \begin_layout Standard
14738 is inserted in TeX-mode.
14742 \begin_layout Plain Layout
14743 When the formula style
14755 can also be replaced by
14762 (formula styles see
14763 \begin_inset CommandInset ref
14765 reference "sec:Formula-Styles"
14774 Then the description follows as normal text and finally
14780 is inserted in TeX-mode.
14793 hereby create a displayed formula.
14796 \begin_layout Standard
14803 can be seen in this example that was
14804 \begin_inset Quotes eld
14808 \begin_inset Quotes erd
14811 using the mathematical textmode:
14812 \begin_inset Formula \[
14813 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14820 \begin_layout Section
14825 \begin_layout Plain Layout
14834 \begin_layout Subsection
14836 \begin_inset CommandInset label
14838 name "sub:Big-Operators"
14846 \begin_layout Plain Layout
14856 \begin_layout Plain Layout
14866 \begin_layout Plain Layout
14875 \begin_layout Standard
14876 To be able to use all integral operators listed here, the option
14878 Use esint package automatically
14880 must be set in the document settings under
14883 \begin_inset space ~
14891 \begin_layout Standard
14892 \begin_inset space \hfill{}
14896 \begin_inset Tabular
14897 <lyxtabular version="3" rows="11" columns="2">
14899 <column alignment="center" valignment="top" width="0pt">
14900 <column alignment="center" valignment="top" width="0pt">
14902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14905 \begin_layout Plain Layout
14911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14914 \begin_layout Plain Layout
14922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14925 \begin_layout Plain Layout
14932 \begin_layout Plain Layout
14945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14948 \begin_layout Plain Layout
14949 \begin_inset Formula $\int$
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14962 \begin_layout Plain Layout
14970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14973 \begin_layout Plain Layout
14974 \begin_inset Formula $\oint$
14984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14987 \begin_layout Plain Layout
14995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14998 \begin_layout Plain Layout
14999 \begin_inset Formula $\ointctrclockwise$
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15012 \begin_layout Plain Layout
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15023 \begin_layout Plain Layout
15024 \begin_inset Formula $\ointclockwise$
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15037 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15049 \begin_inset Formula $\sqint$
15059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15075 \begin_inset Formula $\fint$
15085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15088 \begin_layout Plain Layout
15096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15099 \begin_layout Plain Layout
15101 \begin_inset Formula $\landupint$
15111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15114 \begin_layout Plain Layout
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15125 \begin_layout Plain Layout
15127 \begin_inset Formula $\landdownint$
15137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15140 \begin_layout Plain Layout
15148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15151 \begin_layout Plain Layout
15152 \begin_inset Formula $\bigcap$
15162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15165 \begin_layout Plain Layout
15173 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15176 \begin_layout Plain Layout
15177 \begin_inset Formula $\bigcup$
15191 \begin_inset space \hfill{}
15195 \begin_inset Tabular
15196 <lyxtabular version="3" rows="11" columns="2">
15198 <column alignment="center" valignment="top" width="0pt">
15199 <column alignment="center" valignment="top" width="0pt">
15201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15204 \begin_layout Plain Layout
15210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15213 \begin_layout Plain Layout
15221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15224 \begin_layout Plain Layout
15231 \begin_layout Plain Layout
15244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15247 \begin_layout Plain Layout
15248 \begin_inset Formula $\sum$
15258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15261 \begin_layout Plain Layout
15268 \begin_layout Plain Layout
15281 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15284 \begin_layout Plain Layout
15285 \begin_inset Formula $\prod$
15295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15298 \begin_layout Plain Layout
15306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15309 \begin_layout Plain Layout
15310 \begin_inset Formula $\coprod$
15320 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15323 \begin_layout Plain Layout
15331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15334 \begin_layout Plain Layout
15335 \begin_inset Formula $\bigodot$
15345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15348 \begin_layout Plain Layout
15356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15359 \begin_layout Plain Layout
15360 \begin_inset Formula $\bigotimes$
15370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15373 \begin_layout Plain Layout
15381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15384 \begin_layout Plain Layout
15385 \begin_inset Formula $\bigoplus$
15395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15398 \begin_layout Plain Layout
15406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15409 \begin_layout Plain Layout
15410 \begin_inset Formula $\bigwedge$
15420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15423 \begin_layout Plain Layout
15431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15434 \begin_layout Plain Layout
15435 \begin_inset Formula $\bigvee$
15445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15448 \begin_layout Plain Layout
15456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15459 \begin_layout Plain Layout
15460 \begin_inset Formula $\bigsqcup$
15470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15473 \begin_layout Plain Layout
15481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15484 \begin_layout Plain Layout
15485 \begin_inset Formula $\biguplus$
15499 \begin_inset space \hfill{}
15505 \begin_layout Standard
15506 All big operators can also be inserted via the math toolbar button
15507 \begin_inset Graphics
15508 filename ../images/math/intop.png
15516 \begin_layout Standard
15517 The operators are called big because they are bigger than the sometimes
15518 equal looking binary operators.
15519 All big operators can have limits as described in the next subsection.
15522 \begin_layout Standard
15523 For all integral operators there is a second version available, ending on
15541 These operators are different from
15548 \begin_inset space \space{}
15551 in the style the operator limits are displayed, see
15552 \begin_inset CommandInset ref
15554 reference "sub:Operator-Limits"
15562 \begin_layout Subsubsection*
15563 Advice for Integrals
15566 \begin_layout Standard
15571 in an integral is an operator, that therefore has to be set upright.
15572 This is done by highlighting the
15576 and using the keyboard shortcut
15586 \begin_layout Plain Layout
15592 \begin_inset CommandInset ref
15594 reference "sub:Font-Styles"
15604 Finally the smallest space is inserted before the
15608 , as this is usual for operators.
15612 \begin_layout Standard
15614 \begin_inset Formula $\int A(x)dx$
15618 \begin_inset Newline newline
15625 \begin_layout Plain Layout
15635 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15641 \begin_layout Standard
15642 For multiple integrals there are the following commands:
15643 \begin_inset VSpace medskip
15649 \begin_layout Standard
15650 \begin_inset space \hfill{}
15654 \begin_inset Tabular
15655 <lyxtabular version="3" rows="4" columns="2">
15657 <column alignment="center" valignment="top" width="0">
15658 <column alignment="center" valignment="top" width="0">
15660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15663 \begin_layout Plain Layout
15669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15672 \begin_layout Plain Layout
15674 \begin_inset Note Note
15677 \begin_layout Plain Layout
15684 is only used as spacer.
15696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15699 \begin_layout Plain Layout
15707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15710 \begin_layout Plain Layout
15711 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15721 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15724 \begin_layout Plain Layout
15732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15735 \begin_layout Plain Layout
15736 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15749 \begin_layout Plain Layout
15757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15760 \begin_layout Plain Layout
15761 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15775 \begin_inset space \hfill{}
15779 \begin_inset Tabular
15780 <lyxtabular version="3" rows="4" columns="2">
15782 <column alignment="center" valignment="top" width="0">
15783 <column alignment="center" valignment="top" width="0">
15785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15788 \begin_layout Plain Layout
15794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15797 \begin_layout Plain Layout
15805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15808 \begin_layout Plain Layout
15816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15819 \begin_layout Plain Layout
15820 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15833 \begin_layout Plain Layout
15841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15844 \begin_layout Plain Layout
15845 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15858 \begin_layout Plain Layout
15866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15869 \begin_layout Plain Layout
15870 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15884 \begin_inset space \hfill{}
15890 \begin_layout Subsection
15892 \begin_inset CommandInset label
15894 name "sub:Operator-Limits"
15902 \begin_layout Plain Layout
15911 \begin_layout Standard
15912 Limits are created by super- and subscripts:
15915 \begin_layout Standard
15917 \begin_inset Tabular
15918 <lyxtabular version="3" rows="2" columns="2">
15920 <column alignment="center" valignment="top" width="0pt">
15921 <column alignment="center" valignment="top" width="0pt">
15923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15926 \begin_layout Plain Layout
15932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15935 \begin_layout Plain Layout
15937 \begin_inset Note Note
15940 \begin_layout Plain Layout
15947 is only used as spacer.
15959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15962 \begin_layout Plain Layout
15971 \begin_layout Plain Layout
15981 \begin_inset Formula $\to$
15985 \begin_inset Formula $\to$
15993 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15996 \begin_layout Plain Layout
15997 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16013 \begin_layout Standard
16014 Limits of inline formulas are set right beside the operator.
16015 Limits in displayed formulas are set above or below the operator, except
16016 for integral limits.
16019 \begin_layout Standard
16020 To force that the limits are set beside the operator, the cursor is set
16021 directly behind the operator and the limits type is changed with the menu
16024 Edit\SpecialChar \menuseparator
16025 Math\SpecialChar \menuseparator
16044 \begin_layout Standard
16045 The default limits type is this:
16046 \begin_inset Formula \[
16047 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
16051 This is how it looks when the limits type was changed to
16058 \begin_inset Formula \[
16059 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
16063 For integrals, except those ending with
16079 etc., the limits are by default set beside the operator.
16080 But for multiple integrals the limits are often set below the operator.
16081 In the following example the limits type was therefore set to
16085 and so set below the integrals:
16086 \begin_inset Formula \begin{equation}
16087 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
16094 \begin_layout Standard
16095 \begin_inset VSpace medskip
16098 To specify conditions for limits, the commands
16108 \begin_layout Plain Layout
16126 \begin_layout Plain Layout
16135 To create for example this expression
16136 \begin_inset Formula \begin{equation}
16137 \sum_{\begin{subarray}{c}
16139 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16146 \begin_layout Standard
16147 the following has to be done:
16148 \begin_inset Newline newline
16163 \begin_layout Plain Layout
16175 One is now in a blue box under the summation operator and insert there
16184 \begin_layout Plain Layout
16196 The blue box is now within a purple box and now several lines can be written
16198 A new line is created by inserting a line break (
16201 arg "newline-insert newline"
16206 \begin_inset Newline newline
16211 0<k<1000 Ctrl+Return
16212 \begin_inset Newline newline
16217 is typed in, a new box appears below for the new line.
16220 \begin_layout Standard
16221 The alignment of the lines can be changed to left aligned with the
16231 Edit\SpecialChar \menuseparator
16235 To get right alignment,
16243 \begin_layout Plain Layout
16254 is inserted at the beginning of the line.
16257 \begin_layout Standard
16270 with the difference that the lines are always centered.
16273 \begin_layout Standard
16274 \begin_inset VSpace bigskip
16278 \begin_inset CommandInset ref
16280 reference "eq:substack"
16284 there can be too much space beside an operator, because the characters
16285 following the operator are set beside the limits.
16288 \begin_layout Standard
16289 To avoid this, the following macro can be used in the LaTeX-preamble:
16292 \begin_layout Standard
16306 \begin_inset Newline newline
16318 \begin_inset Newline newline
16325 mathclapinternal #1#2{
16329 mathsurround =0pt #1{#2}$}}
16332 \begin_layout Standard
16333 This defines the command
16343 \begin_layout Plain Layout
16351 that sets the width of the limit to 0
16352 \begin_inset space \thinspace{}
16356 The command scheme is
16359 \begin_layout Standard
16367 \begin_layout Standard
16368 where the limit can consist of several conditions.
16371 \begin_layout Standard
16373 \begin_inset CommandInset ref
16375 reference "eq:substack"
16379 , one uses the command
16382 \begin_layout Standard
16395 \begin_layout Plain Layout
16404 0<k<1000 Ctrl+Return
16407 \begin_layout Standard
16408 to create the lower limit.
16409 The summand is now directly behind the summation operator:
16410 \begin_inset Formula \[
16411 \sum_{\mathclap{\substack{0<k<1000\\
16412 \\k\,\in\,\mathbb{N}}
16420 \begin_layout Standard
16421 \begin_inset VSpace bigskip
16424 How to use one limit for several operators is described in
16425 \begin_inset CommandInset ref
16427 reference "sub:Self-defined-Operators"
16434 \begin_layout Subsection
16436 \begin_inset CommandInset label
16438 name "sub:Binary-Operators"
16446 \begin_layout Plain Layout
16455 \begin_layout Standard
16456 Binary operators are surrounded by space when there is a character before
16458 \begin_inset VSpace medskip
16464 \begin_layout Standard
16465 \begin_inset space \hfill{}
16469 \begin_inset Tabular
16470 <lyxtabular version="3" rows="13" columns="2">
16472 <column alignment="center" valignment="top" width="0pt">
16473 <column alignment="center" valignment="top" width="0pt">
16475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16478 \begin_layout Plain Layout
16480 \begin_inset Note Note
16483 \begin_layout Plain Layout
16490 is only used as spacer.
16500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16503 \begin_layout Plain Layout
16511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16514 \begin_layout Plain Layout
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16523 \begin_layout Plain Layout
16524 \begin_inset Formula $+$
16534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16537 \begin_layout Plain Layout
16543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16546 \begin_layout Plain Layout
16547 \begin_inset Formula $-$
16557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16560 \begin_layout Plain Layout
16568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16571 \begin_layout Plain Layout
16572 \begin_inset Formula $\pm$
16582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16585 \begin_layout Plain Layout
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16596 \begin_layout Plain Layout
16597 \begin_inset Formula $\mp$
16607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16610 \begin_layout Plain Layout
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16621 \begin_layout Plain Layout
16622 \begin_inset Formula $\cdot$
16632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16635 \begin_layout Plain Layout
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16646 \begin_layout Plain Layout
16647 \begin_inset Formula $\times$
16657 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16660 \begin_layout Plain Layout
16668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16671 \begin_layout Plain Layout
16672 \begin_inset Formula $\div$
16682 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16685 \begin_layout Plain Layout
16689 \begin_layout Plain Layout
16702 \begin_layout Plain Layout
16714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16717 \begin_layout Plain Layout
16718 \begin_inset Formula $*$
16728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16731 \begin_layout Plain Layout
16739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16742 \begin_layout Plain Layout
16743 \begin_inset Formula $\star$
16753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16756 \begin_layout Plain Layout
16764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16767 \begin_layout Plain Layout
16768 \begin_inset Formula $\circ$
16778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16781 \begin_layout Plain Layout
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16792 \begin_layout Plain Layout
16793 \begin_inset Formula $\diamond$
16803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16806 \begin_layout Plain Layout
16814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16817 \begin_layout Plain Layout
16818 \begin_inset Formula $\bullet$
16832 \begin_inset space \hfill{}
16836 \begin_inset Tabular
16837 <lyxtabular version="3" rows="13" columns="2">
16839 <column alignment="center" valignment="top" width="0pt">
16840 <column alignment="center" valignment="top" width="0pt">
16842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16845 \begin_layout Plain Layout
16851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16854 \begin_layout Plain Layout
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16865 \begin_layout Plain Layout
16873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16876 \begin_layout Plain Layout
16877 \begin_inset Formula $\nabla$
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16890 \begin_layout Plain Layout
16898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16901 \begin_layout Plain Layout
16902 \begin_inset Formula $\bigtriangledown$
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16915 \begin_layout Plain Layout
16923 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16926 \begin_layout Plain Layout
16927 \begin_inset Formula $\bigtriangleup$
16937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16940 \begin_layout Plain Layout
16948 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16951 \begin_layout Plain Layout
16952 \begin_inset Formula $\Box$
16962 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16965 \begin_layout Plain Layout
16973 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16976 \begin_layout Plain Layout
16977 \begin_inset Formula $\cap$
16987 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16990 \begin_layout Plain Layout
16998 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17001 \begin_layout Plain Layout
17002 \begin_inset Formula $\cup$
17012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17015 \begin_layout Plain Layout
17023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17026 \begin_layout Plain Layout
17027 \begin_inset Formula $\dagger$
17037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17040 \begin_layout Plain Layout
17048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17051 \begin_layout Plain Layout
17052 \begin_inset Formula $\ddagger$
17062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17065 \begin_layout Plain Layout
17073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17076 \begin_layout Plain Layout
17077 \begin_inset Formula $\wr$
17087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17090 \begin_layout Plain Layout
17098 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17101 \begin_layout Plain Layout
17102 \begin_inset Formula $\bigcirc$
17112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17115 \begin_layout Plain Layout
17123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17126 \begin_layout Plain Layout
17127 \begin_inset Formula $\wedge$
17137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17140 \begin_layout Plain Layout
17148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17151 \begin_layout Plain Layout
17152 \begin_inset Formula $\vee$
17166 \begin_inset space \hfill{}
17170 \begin_inset Tabular
17171 <lyxtabular version="3" rows="13" columns="2">
17173 <column alignment="center" valignment="top" width="0pt">
17174 <column alignment="center" valignment="top" width="0pt">
17176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17179 \begin_layout Plain Layout
17185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17188 \begin_layout Plain Layout
17196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17199 \begin_layout Plain Layout
17207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17210 \begin_layout Plain Layout
17211 \begin_inset Formula $\oplus$
17221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17224 \begin_layout Plain Layout
17232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17235 \begin_layout Plain Layout
17236 \begin_inset Formula $\ominus$
17246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17249 \begin_layout Plain Layout
17257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17260 \begin_layout Plain Layout
17261 \begin_inset Formula $\otimes$
17271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17274 \begin_layout Plain Layout
17282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17285 \begin_layout Plain Layout
17286 \begin_inset Formula $\oslash$
17296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17299 \begin_layout Plain Layout
17307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17310 \begin_layout Plain Layout
17311 \begin_inset Formula $\odot$
17321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17324 \begin_layout Plain Layout
17332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17335 \begin_layout Plain Layout
17336 \begin_inset Formula $\amalg$
17346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17349 \begin_layout Plain Layout
17357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17360 \begin_layout Plain Layout
17361 \begin_inset Formula $\uplus$
17371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17374 \begin_layout Plain Layout
17382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17385 \begin_layout Plain Layout
17386 \begin_inset Formula $\setminus$
17396 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17399 \begin_layout Plain Layout
17407 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17410 \begin_layout Plain Layout
17411 \begin_inset Formula $\sqcap$
17421 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17424 \begin_layout Plain Layout
17432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17435 \begin_layout Plain Layout
17436 \begin_inset Formula $\sqcup$
17446 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17449 \begin_layout Plain Layout
17457 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17460 \begin_layout Plain Layout
17461 \begin_inset Formula $\triangleleft$
17471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17474 \begin_layout Plain Layout
17482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17485 \begin_layout Plain Layout
17486 \begin_inset Formula $\triangleright$
17500 \begin_inset space \hfill{}
17506 \begin_layout Standard
17507 All binary operators can also be inserted via the math toolbar button
17508 \begin_inset Graphics
17509 filename ../images/math/pm.png
17517 \begin_layout Standard
17518 To typeset the Laplace operator also
17535 \begin_inset Formula $\nabla^{2}$
17538 ) can be used instead of
17547 \begin_layout Standard
17554 Insert\SpecialChar \menuseparator
17566 \begin_layout Subsection
17567 Self-defined Operators
17568 \begin_inset CommandInset label
17570 name "sub:Self-defined-Operators"
17578 \begin_layout Plain Layout
17579 Operators ! self-defined
17587 \begin_layout Standard
17588 With the help of the command
17592 DeclareMathOperator
17598 \begin_layout Plain Layout
17603 DeclareMathOperator
17608 custom operators can be defined in the LaTeX-preamble.
17609 Its command scheme is:
17612 \begin_layout Standard
17617 DeclareMathOperator{new command}{display}
17620 \begin_layout Standard
17621 Display can be characters or symbols that define how the operator looks
17623 To define a big operator a * is set behind the command.
17624 All self-defined big operators can have limits as described in
17625 \begin_inset CommandInset ref
17627 reference "sub:Operator-Limits"
17634 \begin_layout Standard
17635 For example the LaTeX-preamble line
17638 \begin_layout Standard
17643 DeclareMathOperator*{
17650 \begin_layout Standard
17651 defines the command
17657 , that inserts a big operator consisting of the lozenge symbol from
17658 \begin_inset CommandInset ref
17660 reference "sub:Miscellaneous-Symbols"
17665 \begin_inset Formula \[
17666 \Lozenge_{n=1}^{\infty}\]
17670 The command for this formula is:
17681 \begin_inset Formula $\to$
17687 \begin_layout Standard
17688 \begin_inset VSpace bigskip
17691 When self-defined operators are not used several times in the document,
17692 they can also be defined with the commands
17702 \begin_layout Plain Layout
17720 \begin_layout Plain Layout
17728 , which have the following scheme:
17731 \begin_layout Standard
17745 \begin_layout Standard
17752 defines big operators,
17761 \begin_layout Standard
17769 \begin_inset space \thinspace{}
17773 \begin_inset space \space{}
17776 be used to use one limit for several operators:
17779 \begin_layout Standard
17780 \begin_inset Formula \[
17781 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17788 \begin_layout Standard
17789 The command for the formula above is:
17790 \begin_inset Newline newline
17809 \begin_layout Plain Layout
17821 \begin_inset Formula $\to$
17830 \begin_layout Plain Layout
17844 \begin_layout Section
17849 \begin_layout Plain Layout
17858 \begin_layout Subsection
17860 \begin_inset CommandInset label
17862 name "sub:Font-Styles"
17870 \begin_layout Plain Layout
17879 \begin_layout Standard
17880 Latin letters in formulas can be set in one of the following font styles:
17881 \begin_inset VSpace -2mm
17887 \begin_layout Standard
17889 \begin_inset Tabular
17890 <lyxtabular version="3" rows="6" columns="3">
17892 <column alignment="center" valignment="top" width="0">
17893 <column alignment="center" valignment="top" width="0">
17894 <column alignment="center" valignment="top" width="0">
17896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17899 \begin_layout Plain Layout
17905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17908 \begin_layout Plain Layout
17914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17917 \begin_layout Plain Layout
17925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17928 \begin_layout Plain Layout
17937 \begin_layout Plain Layout
17953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17956 \begin_layout Plain Layout
17957 \begin_inset Formula $\mathbb{ABC}$
17965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17968 \begin_layout Plain Layout
17981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17984 \begin_layout Plain Layout
17993 \begin_layout Plain Layout
18009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18012 \begin_layout Plain Layout
18013 \begin_inset Formula $\mathbf{AbC}$
18021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18024 \begin_layout Plain Layout
18037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18040 \begin_layout Plain Layout
18049 \begin_layout Plain Layout
18065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18068 \begin_layout Plain Layout
18069 \begin_inset Formula $\boldsymbol{AbC}$
18077 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18080 \begin_layout Plain Layout
18083 arg "font-boldsymbol"
18093 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18096 \begin_layout Plain Layout
18105 \begin_layout Plain Layout
18121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18124 \begin_layout Plain Layout
18125 \begin_inset Formula $\mathcal{ABC}$
18133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18136 \begin_layout Plain Layout
18149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18152 \begin_layout Plain Layout
18161 \begin_layout Plain Layout
18177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18180 \begin_layout Plain Layout
18181 \begin_inset Formula $\mathfrak{AbC}$
18189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18192 \begin_layout Plain Layout
18206 \begin_layout Standard
18208 \begin_inset Tabular
18209 <lyxtabular version="3" rows="5" columns="3">
18211 <column alignment="center" valignment="top" width="0">
18212 <column alignment="center" valignment="top" width="0">
18213 <column alignment="center" valignment="top" width="0">
18215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18218 \begin_layout Plain Layout
18224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18227 \begin_layout Plain Layout
18233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18236 \begin_layout Plain Layout
18244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18247 \begin_layout Plain Layout
18256 \begin_layout Plain Layout
18272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18275 \begin_layout Plain Layout
18276 \begin_inset Formula $\mathit{AbC}$
18284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18287 \begin_layout Plain Layout
18295 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18298 \begin_layout Plain Layout
18307 \begin_layout Plain Layout
18323 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18326 \begin_layout Plain Layout
18327 \begin_inset Formula $\mathrm{AbC}$
18335 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18338 \begin_layout Plain Layout
18351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18354 \begin_layout Plain Layout
18363 \begin_layout Plain Layout
18379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18382 \begin_layout Plain Layout
18383 \begin_inset Formula $\mathsf{AbC}$
18391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18394 \begin_layout Plain Layout
18407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18410 \begin_layout Plain Layout
18419 \begin_layout Plain Layout
18435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18438 \begin_layout Plain Layout
18439 \begin_inset Formula $\mathtt{AbC}$
18447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18450 \begin_layout Plain Layout
18453 arg "font-typewriter"
18469 \begin_layout Standard
18470 \begin_inset Note Greyedout
18473 \begin_layout Plain Layout
18490 can only be used for big letters.
18498 \begin_layout Standard
18499 Predefined is the style
18508 \begin_layout Standard
18509 The style commands work also for letters in mathematical constructs:
18510 \begin_inset Formula \[
18511 \mathfrak{A=\frac{b}{C}}\]
18518 \begin_layout Standard
18519 Characters in mathematical text don't appear in a math font style but in
18520 the text font style
18527 That their style can't be set correctly via the text style dialog is a
18532 \begin_layout Plain Layout
18533 \begin_inset CommandInset href
18535 name "LyX-bug #4629"
18536 target "http://www.lyx.org/trac/ticket/4629"
18548 \begin_layout Standard
18549 Instead of the style commands the dialog
18551 Edit\SpecialChar \menuseparator
18552 Math\SpecialChar \menuseparator
18555 or the toolbar button
18556 \begin_inset Graphics
18557 filename ../images/math/font.png
18565 \begin_layout Subsection
18567 \begin_inset CommandInset label
18569 name "sub:Bold-Formulas"
18577 \begin_layout Plain Layout
18586 \begin_layout Standard
18587 To make a complete formula bold, the command
18593 from the previous subsection cannot be used, because it doesn't work for
18594 small Greek letters.
18595 Furthermore it prints Latin letters always upright, like in the following
18599 \begin_layout Standard
18600 \begin_inset Formula \[
18601 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18608 \begin_layout Standard
18609 To display the formula correctly, the command
18616 \begin_inset Formula \[
18617 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18621 It is also possible to set the formula in a
18623 boldmath environment
18626 This environment is created by inserting the command
18634 \begin_layout Plain Layout
18645 To end the environment, the command
18653 \begin_layout Plain Layout
18663 is inserted in TeX-mode.
18667 \begin_layout Plain Layout
18677 \begin_inset Formula \[
18678 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18686 \begin_layout Plain Layout
18698 \begin_layout Subsection
18703 \begin_layout Plain Layout
18712 \begin_layout Standard
18713 Formulas can be colored like normal text: Highlight a formula or a formula
18719 Here is a formula in magenta:
18720 \begin_inset Formula \[
18721 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
18728 \begin_layout Standard
18729 You can also define your own colors as described in
18730 \begin_inset CommandInset ref
18732 reference "sub:Colored-Boxes"
18737 They can be used with the TeX code command
18747 \begin_layout Plain Layout
18758 \begin_layout Standard
18763 textcolor{color}{characters or formula}
18766 \begin_layout Standard
18767 The following example was colored completely dark green and partly red:
18770 \begin_layout Standard
18774 \begin_layout Plain Layout
18778 textcolor{darkgreen}{
18784 \begin_inset Formula \[
18785 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
18793 \begin_layout Plain Layout
18803 \begin_layout Standard
18804 Due to a bug in LyX only complete formulas can be colored with self-defined
18809 \begin_layout Plain Layout
18810 \begin_inset CommandInset href
18812 name "LyX-bug #5269"
18813 target "http://www.lyx.org/trac/ticket/5269"
18825 \begin_layout Subsection
18827 \begin_inset CommandInset label
18829 name "sub:Font-Sizes"
18837 \begin_layout Plain Layout
18846 \begin_layout Standard
18847 For characters in formulas there are, analog to characters in text, the
18848 following size commands:
18851 \begin_layout Standard
18895 \begin_inset Newline newline
18917 \begin_layout Standard
18918 The size produced by the commands depends on the document font size, that
18919 corresponds with the command
18926 The other commands produce smaller or larger sizes than
18933 The font size can however not exceed a certain value.
18934 Is for example the document font size 12
18935 \begin_inset space \thinspace{}
18944 switches to the same size as
18954 \begin_layout Standard
18955 A size command is inserted in TeX-mode before the formula and sets the size
18956 for all following formula and text characters.
18957 To switch back to the initial size, the command
18963 is inserted behind the formula in TeX-mode.
18966 \begin_layout Standard
18967 \begin_inset Newpage newpage
18973 \begin_layout Standard
18974 Within a formula the size can be changed using the following size commands:
18977 \begin_layout Standard
18980 \begin_inset Tabular
18981 <lyxtabular version="3" rows="5" columns="2">
18983 <column alignment="center" valignment="top" width="0">
18984 <column alignment="center" valignment="top" width="0">
18986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18989 \begin_layout Plain Layout
18995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18998 \begin_layout Plain Layout
19000 \begin_inset Note Note
19003 \begin_layout Plain Layout
19010 is only used as spacer.
19022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19025 \begin_layout Plain Layout
19032 \begin_layout Plain Layout
19045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19048 \begin_layout Plain Layout
19049 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19062 \begin_layout Plain Layout
19070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19073 \begin_layout Plain Layout
19074 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19087 \begin_layout Plain Layout
19095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19098 \begin_layout Plain Layout
19099 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19112 \begin_layout Plain Layout
19120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19123 \begin_layout Plain Layout
19124 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19140 \begin_layout Standard
19141 After entering these commands, a blue box appears in which the formula parts
19145 \begin_layout Standard
19146 There is a further method to change the font size, that though only works
19147 for symbols or letters in mathematical text.
19148 To use it, one of the above text size commands is inserted in mathematical
19150 All following characters until the end of the mathematical text or until
19151 another size command will have the selected size.
19153 \begin_inset VSpace -2mm
19159 \begin_layout Standard
19163 \begin_layout Plain Layout
19173 \begin_inset Formula \[
19174 A=\frac{B}{c}\cdot\maltese\]
19179 \begin_inset Formula \[
19180 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19188 \begin_layout Plain Layout
19200 \begin_layout Standard
19201 \begin_inset VSpace medskip
19204 Before both formulas the command
19211 The command for the second formula is:
19212 \begin_inset Newline newline
19223 \begin_layout Plain Layout
19238 \begin_layout Plain Layout
19253 \begin_layout Plain Layout
19268 \begin_layout Plain Layout
19278 \begin_inset Formula $\to$
19282 \begin_inset Formula $\to$
19286 \begin_inset Newline newline
19290 \begin_inset space \hspace*{}
19304 \begin_layout Plain Layout
19319 \begin_layout Plain Layout
19334 \begin_layout Plain Layout
19346 \begin_layout Standard
19347 If a symbol cannot be displayed in different sizes, it will always be displayed
19348 in the default size.
19351 \begin_layout Standard
19352 \begin_inset Newpage newpage
19358 \begin_layout Section
19363 \begin_layout Plain Layout
19372 \begin_layout Standard
19373 All Greek letters can also be inserted via the toolbar button
19374 \begin_inset Graphics
19375 filename ../images/math/alpha.png
19383 \begin_layout Subsection
19388 \begin_layout Plain Layout
19389 Greek letters ! small
19397 \begin_layout Standard
19398 \begin_inset space \hfill{}
19402 \begin_inset Tabular
19403 <lyxtabular version="3" rows="11" columns="2">
19405 <column alignment="center" valignment="top" width="0pt">
19406 <column alignment="center" valignment="top" width="0pt">
19408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19420 \begin_layout Plain Layout
19428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19431 \begin_layout Plain Layout
19439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19442 \begin_layout Plain Layout
19443 \begin_inset Formula $\alpha$
19453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19456 \begin_layout Plain Layout
19464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19467 \begin_layout Plain Layout
19468 \begin_inset Formula $\beta$
19478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19481 \begin_layout Plain Layout
19489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19492 \begin_layout Plain Layout
19493 \begin_inset Formula $\gamma$
19503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19506 \begin_layout Plain Layout
19514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19517 \begin_layout Plain Layout
19518 \begin_inset Formula $\delta$
19528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19531 \begin_layout Plain Layout
19539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19542 \begin_layout Plain Layout
19543 \begin_inset Formula $\epsilon$
19553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19556 \begin_layout Plain Layout
19564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19567 \begin_layout Plain Layout
19568 \begin_inset Formula $\varepsilon$
19578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19581 \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 $\zeta$
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 $\eta$
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 $\theta$
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 $\vartheta$
19682 \begin_inset space \hfill{}
19686 \begin_inset Tabular
19687 <lyxtabular version="3" rows="12" 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 $\iota$
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 $\kappa$
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 $\varkappa$
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 $\lambda$
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 $\mu$
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 $\nu$
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 $\xi$
19887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19890 \begin_layout Plain Layout
19896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19899 \begin_layout Plain Layout
19900 \begin_inset Formula $o$
19910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19913 \begin_layout Plain Layout
19921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19924 \begin_layout Plain Layout
19925 \begin_inset Formula $\pi$
19935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19938 \begin_layout Plain Layout
19946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19949 \begin_layout Plain Layout
19950 \begin_inset Formula $\varpi$
19960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19963 \begin_layout Plain Layout
19971 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19974 \begin_layout Plain Layout
19975 \begin_inset Formula $\rho$
19989 \begin_inset space \hfill{}
19993 \begin_inset Tabular
19994 <lyxtabular version="3" rows="11" columns="2">
19996 <column alignment="center" valignment="top" width="0pt">
19997 <column alignment="center" valignment="top" width="0pt">
19999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20002 \begin_layout Plain Layout
20008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20011 \begin_layout Plain Layout
20019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20022 \begin_layout Plain Layout
20030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20033 \begin_layout Plain Layout
20034 \begin_inset Formula $\varrho$
20044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20047 \begin_layout Plain Layout
20055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20058 \begin_layout Plain Layout
20059 \begin_inset Formula $\sigma$
20069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20072 \begin_layout Plain Layout
20080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20083 \begin_layout Plain Layout
20084 \begin_inset Formula $\varsigma$
20094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20097 \begin_layout Plain Layout
20105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20108 \begin_layout Plain Layout
20109 \begin_inset Formula $\tau$
20119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20122 \begin_layout Plain Layout
20130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20133 \begin_layout Plain Layout
20134 \begin_inset Formula $\upsilon$
20144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20147 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20158 \begin_layout Plain Layout
20159 \begin_inset Formula $\phi$
20169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20172 \begin_layout Plain Layout
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20183 \begin_layout Plain Layout
20184 \begin_inset Formula $\varphi$
20194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20197 \begin_layout Plain Layout
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20208 \begin_layout Plain Layout
20209 \begin_inset Formula $\chi$
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 $\psi$
20244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20247 \begin_layout Plain Layout
20255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20258 \begin_layout Plain Layout
20259 \begin_inset Formula $\omega$
20273 \begin_inset space \hfill{}
20279 \begin_layout Standard
20280 \begin_inset VSpace medskip
20286 \begin_layout Standard
20287 How to create upright Greek letters is explained in
20288 \begin_inset CommandInset ref
20290 reference "sub:Upright-small-Greek"
20297 \begin_layout Subsection
20302 \begin_layout Plain Layout
20303 Greek letters ! big
20311 \begin_layout Standard
20312 \begin_inset space \hfill{}
20316 \begin_inset Tabular
20317 <lyxtabular version="3" rows="7" columns="2">
20319 <column alignment="center" valignment="top" width="0pt">
20320 <column alignment="center" valignment="top" width="0pt">
20322 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20325 \begin_layout Plain Layout
20331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20334 \begin_layout Plain Layout
20342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20345 \begin_layout Plain Layout
20353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20356 \begin_layout Plain Layout
20357 \begin_inset Formula $\Gamma$
20367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20370 \begin_layout Plain Layout
20378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20381 \begin_layout Plain Layout
20382 \begin_inset Formula $\Delta$
20392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20395 \begin_layout Plain Layout
20403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20406 \begin_layout Plain Layout
20407 \begin_inset Formula $\Theta$
20417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20420 \begin_layout Plain Layout
20428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20431 \begin_layout Plain Layout
20432 \begin_inset Formula $\Lambda$
20442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20445 \begin_layout Plain Layout
20453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20456 \begin_layout Plain Layout
20457 \begin_inset Formula $\Xi$
20467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20470 \begin_layout Plain Layout
20478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20481 \begin_layout Plain Layout
20482 \begin_inset Formula $\Pi$
20496 \begin_inset space \hfill{}
20500 \begin_inset Tabular
20501 <lyxtabular version="3" rows="6" columns="2">
20503 <column alignment="center" valignment="top" width="0pt">
20504 <column alignment="center" valignment="top" width="0pt">
20506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20518 \begin_layout Plain Layout
20526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20529 \begin_layout Plain Layout
20537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20540 \begin_layout Plain Layout
20541 \begin_inset Formula $\Sigma$
20551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20554 \begin_layout Plain Layout
20562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20565 \begin_layout Plain Layout
20566 \begin_inset Formula $\Upsilon$
20576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20579 \begin_layout Plain Layout
20587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20590 \begin_layout Plain Layout
20591 \begin_inset Formula $\Phi$
20601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20604 \begin_layout Plain Layout
20612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20615 \begin_layout Plain Layout
20616 \begin_inset Formula $\Psi$
20626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20629 \begin_layout Plain Layout
20637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20640 \begin_layout Plain Layout
20641 \begin_inset Formula $\Omega$
20655 \begin_inset space \hfill{}
20661 \begin_layout Standard
20662 \begin_inset VSpace medskip
20665 That the big Greek letters appear upright is caused by a design bug when
20667 To get correct italic big letters, begin every command with
20672 For example the command
20679 \begin_inset Formula $\varGamma$
20685 \begin_layout Subsection
20690 \begin_layout Plain Layout
20691 Greek letters ! bold
20699 \begin_layout Standard
20700 Greek letters cannot be set with different font styles like Latin letters.
20701 They can only be made bold with the command
20711 \begin_layout Plain Layout
20722 \begin_layout Standard
20724 \begin_inset Tabular
20725 <lyxtabular version="3" rows="3" columns="2">
20727 <column alignment="center" valignment="top" width="0">
20728 <column alignment="center" valignment="top" width="0">
20730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20733 \begin_layout Plain Layout
20739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20742 \begin_layout Plain Layout
20750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20753 \begin_layout Plain Layout
20765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20768 \begin_layout Plain Layout
20769 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20782 \begin_layout Plain Layout
20794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20797 \begin_layout Plain Layout
20798 \begin_inset Formula $\theta\boldsymbol{\theta}$
20814 \begin_layout Section
20819 \begin_layout Plain Layout
20832 \begin_layout Plain Layout
20833 A list with all symbols of most of the LaTeX-packages can be found in
20834 \begin_inset CommandInset citation
20849 \begin_layout Plain Layout
20857 \begin_inset Note Note
20860 \begin_layout Plain Layout
20863 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20866 \begin_layout Plain Layout
20869 texorpdfstring is in section
20870 \begin_inset CommandInset ref
20872 reference "sub:Formulas-in-Section"
20885 \begin_layout Plain Layout
20894 \begin_layout Standard
20895 Many of the symbols listed in this section can also be inserted via the
20897 \begin_inset Graphics
20898 filename ../images/math/nabla.png
20904 \begin_inset Graphics
20905 filename ../images/math/digamma.png
20913 \begin_layout Subsection
20914 Mathematical Symbols
20915 \begin_inset CommandInset label
20917 name "sub:Mathematical-Symbols"
20925 \begin_layout Plain Layout
20926 Symbols ! mathematical
20934 \begin_layout Standard
20935 \begin_inset space \hfill{}
20939 \begin_inset Tabular
20940 <lyxtabular version="3" rows="10" columns="2">
20942 <column alignment="center" valignment="top" width="0pt">
20943 <column alignment="center" valignment="top" width="0pt">
20945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20948 \begin_layout Plain Layout
20954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20957 \begin_layout Plain Layout
20965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20968 \begin_layout Plain Layout
20976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20979 \begin_layout Plain Layout
20980 \begin_inset Formula $\neg$
20990 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20993 \begin_layout Plain Layout
21001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21004 \begin_layout Plain Layout
21005 \begin_inset Formula $\Im$
21015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21018 \begin_layout Plain Layout
21026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21029 \begin_layout Plain Layout
21030 \begin_inset Formula $\Re$
21040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21043 \begin_layout Plain Layout
21051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21054 \begin_layout Plain Layout
21055 \begin_inset Formula $\aleph$
21065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21068 \begin_layout Plain Layout
21076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21079 \begin_layout Plain Layout
21080 \begin_inset Formula $\partial$
21090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21093 \begin_layout Plain Layout
21101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21104 \begin_layout Plain Layout
21105 \begin_inset Formula $\infty$
21115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21118 \begin_layout Plain Layout
21126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21129 \begin_layout Plain Layout
21130 \begin_inset Formula $\wp$
21140 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21143 \begin_layout Plain Layout
21151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21154 \begin_layout Plain Layout
21155 \begin_inset Formula $\imath$
21165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21168 \begin_layout Plain Layout
21176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21179 \begin_layout Plain Layout
21180 \begin_inset Formula $\jmath$
21194 \begin_inset space \hfill{}
21198 \begin_inset Tabular
21199 <lyxtabular version="3" rows="10" columns="2">
21201 <column alignment="center" valignment="top" width="0pt">
21202 <column alignment="center" valignment="top" width="0pt">
21204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21207 \begin_layout Plain Layout
21213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21216 \begin_layout Plain Layout
21218 \begin_inset Note Note
21221 \begin_layout Plain Layout
21228 is only used as spacer.
21240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21243 \begin_layout Plain Layout
21251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21254 \begin_layout Plain Layout
21255 \begin_inset Formula $\forall$
21265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21268 \begin_layout Plain Layout
21276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21279 \begin_layout Plain Layout
21280 \begin_inset Formula $\exists$
21290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21293 \begin_layout Plain Layout
21301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21304 \begin_layout Plain Layout
21305 \begin_inset Formula $\nexists$
21315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21318 \begin_layout Plain Layout
21326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21329 \begin_layout Plain Layout
21330 \begin_inset Formula $\emptyset$
21340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21343 \begin_layout Plain Layout
21351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21354 \begin_layout Plain Layout
21355 \begin_inset Formula $\varnothing$
21365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21368 \begin_layout Plain Layout
21376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21379 \begin_layout Plain Layout
21380 \begin_inset Formula $\dag$
21390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21393 \begin_layout Plain Layout
21401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21404 \begin_layout Plain Layout
21405 \begin_inset Formula $\ddag$
21415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21418 \begin_layout Plain Layout
21426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21429 \begin_layout Plain Layout
21433 \begin_layout Plain Layout
21443 \begin_inset Formula $\complement$
21450 \begin_layout Plain Layout
21464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21467 \begin_layout Plain Layout
21475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21478 \begin_layout Plain Layout
21479 \begin_inset Formula $\Bbbk$
21493 \begin_inset space \hfill{}
21497 \begin_inset Tabular
21498 <lyxtabular version="3" rows="10" columns="2">
21500 <column alignment="center" valignment="top" width="0pt">
21501 <column alignment="center" valignment="top" width="0pt">
21503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21506 \begin_layout Plain Layout
21512 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21515 \begin_layout Plain Layout
21523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21526 \begin_layout Plain Layout
21534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21537 \begin_layout Plain Layout
21538 \begin_inset Formula $\prime$
21548 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21551 \begin_layout Plain Layout
21559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21562 \begin_layout Plain Layout
21563 \begin_inset Formula $\backprime$
21573 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21576 \begin_layout Plain Layout
21584 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21587 \begin_layout Plain Layout
21588 \begin_inset Formula $\mho$
21598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21601 \begin_layout Plain Layout
21609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21612 \begin_layout Plain Layout
21613 \begin_inset Formula $\triangle$
21623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21626 \begin_layout Plain Layout
21634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21637 \begin_layout Plain Layout
21638 \begin_inset Formula $\angle$
21648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21651 \begin_layout Plain Layout
21659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21662 \begin_layout Plain Layout
21663 \begin_inset Formula $\measuredangle$
21673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21676 \begin_layout Plain Layout
21684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21687 \begin_layout Plain Layout
21688 \begin_inset Formula $\sphericalangle$
21698 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21701 \begin_layout Plain Layout
21709 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21712 \begin_layout Plain Layout
21713 \begin_inset Formula $\top$
21723 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21726 \begin_layout Plain Layout
21734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21737 \begin_layout Plain Layout
21738 \begin_inset Formula $\bot$
21752 \begin_inset space \hfill{}
21758 \begin_layout Subsection
21759 Miscellaneous Symbols
21760 \begin_inset CommandInset label
21762 name "sub:Miscellaneous-Symbols"
21770 \begin_layout Plain Layout
21771 Symbols ! miscellaneous
21779 \begin_layout Standard
21782 \begin_inset Tabular
21783 <lyxtabular version="3" rows="10" columns="2">
21785 <column alignment="center" valignment="top" width="0pt">
21786 <column alignment="center" valignment="top" width="0pt">
21788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21791 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21811 \begin_layout Plain Layout
21819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21822 \begin_layout Plain Layout
21823 \begin_inset Formula $\flat$
21833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21836 \begin_layout Plain Layout
21844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21847 \begin_layout Plain Layout
21848 \begin_inset Formula $\natural$
21858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21861 \begin_layout Plain Layout
21869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21872 \begin_layout Plain Layout
21873 \begin_inset Formula $\sharp$
21883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21886 \begin_layout Plain Layout
21894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21897 \begin_layout Plain Layout
21898 \begin_inset Formula $\surd$
21908 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21911 \begin_layout Plain Layout
21919 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21922 \begin_layout Plain Layout
21923 \begin_inset Formula $\checkmark$
21933 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21936 \begin_layout Plain Layout
21944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21947 \begin_layout Plain Layout
21948 \begin_inset Formula $\yen$
21958 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21961 \begin_layout Plain Layout
21969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21972 \begin_layout Plain Layout
21973 \begin_inset Formula $\pounds$
21983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21986 \begin_layout Plain Layout
21992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21995 \begin_layout Plain Layout
21996 \begin_inset Formula $\$$
22006 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22009 \begin_layout Plain Layout
22015 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22018 \begin_layout Plain Layout
22019 \begin_inset Formula $§$
22033 \begin_inset Tabular
22034 <lyxtabular version="3" rows="10" columns="2">
22036 <column alignment="center" valignment="top" width="0">
22037 <column alignment="center" valignment="top" width="0">
22039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22042 \begin_layout Plain Layout
22048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22051 \begin_layout Plain Layout
22059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22062 \begin_layout Plain Layout
22070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22073 \begin_layout Plain Layout
22074 \begin_inset Formula $\hbar$
22084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22087 \begin_layout Plain Layout
22095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22098 \begin_layout Plain Layout
22099 \begin_inset Formula $\hslash$
22109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22112 \begin_layout Plain Layout
22120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22123 \begin_layout Plain Layout
22124 \begin_inset Formula $\clubsuit$
22134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22137 \begin_layout Plain Layout
22145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22148 \begin_layout Plain Layout
22149 \begin_inset Formula $\spadesuit$
22159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22162 \begin_layout Plain Layout
22170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22173 \begin_layout Plain Layout
22174 \begin_inset Formula $\bigstar$
22184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22187 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22199 \begin_inset Formula $\blacklozenge$
22209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22212 \begin_layout Plain Layout
22220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22223 \begin_layout Plain Layout
22224 \begin_inset Formula $\blacktriangle$
22234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22237 \begin_layout Plain Layout
22245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22248 \begin_layout Plain Layout
22249 \begin_inset Formula $\blacktriangledown$
22259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22262 \begin_layout Plain Layout
22270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22273 \begin_layout Plain Layout
22274 \begin_inset Formula $\bullet$
22288 \begin_inset Tabular
22289 <lyxtabular version="3" rows="10" columns="2">
22291 <column alignment="center" valignment="top" width="0pt">
22292 <column alignment="center" valignment="top" width="0pt">
22294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22297 \begin_layout Plain Layout
22303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22306 \begin_layout Plain Layout
22314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22317 \begin_layout Plain Layout
22325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22328 \begin_layout Plain Layout
22329 \begin_inset Formula $\diamondsuit$
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\Diamond$
22364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22378 \begin_layout Plain Layout
22379 \begin_inset Formula $\heartsuit$
22389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22392 \begin_layout Plain Layout
22400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22403 \begin_layout Plain Layout
22404 \begin_inset Formula $\P$
22414 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22417 \begin_layout Plain Layout
22425 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22428 \begin_layout Plain Layout
22429 \begin_inset Formula $\copyright$
22439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22442 \begin_layout Plain Layout
22450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22453 \begin_layout Plain Layout
22454 \begin_inset Formula $\circledR$
22464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22467 \begin_layout Plain Layout
22475 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22478 \begin_layout Plain Layout
22479 \begin_inset Formula $\maltese$
22489 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22492 \begin_layout Plain Layout
22500 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22503 \begin_layout Plain Layout
22504 \begin_inset Formula $\diagup$
22514 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22517 \begin_layout Plain Layout
22525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22528 \begin_layout Plain Layout
22529 \begin_inset Formula $\diagdown$
22545 \begin_layout Standard
22546 \begin_inset VSpace medskip
22549 More symbols are listed in
22550 \begin_inset CommandInset ref
22552 reference "sub:Miscellaneous-special-Characters"
22559 \begin_layout Standard
22560 Some symbols can be displayed in different sizes, see
22561 \begin_inset CommandInset ref
22563 reference "sub:Font-Sizes"
22570 \begin_layout Subsection
22575 \begin_layout Plain Layout
22576 Symbols ! Euro-symbol
22585 \begin_layout Plain Layout
22592 \begin_layout Plain Layout
22609 \begin_layout Standard
22610 To use the Euro symbol in formulas, the LaTeX-package
22618 \begin_layout Plain Layout
22624 must be installed and loaded with the LaTeX-preamble line
22627 \begin_layout Standard
22632 usepackage[gennarrow]{eurosym}
22635 \begin_layout Standard
22636 The Euro symbol can now be inserted with the command
22646 \begin_layout Plain Layout
22657 \begin_layout Standard
22658 The Euro symbol can directly be inserted with the € key in mathematical
22659 text, without having
22674 can also be inserted in TeX-mode.
22675 The official currency symbol can then be inserted with the command
22685 \begin_layout Plain Layout
22693 , that is only available in TeX-mode.
22696 \begin_layout Standard
22700 \begin_layout Plain Layout
22710 \begin_inset Note Note
22713 \begin_layout Plain Layout
22714 The following table will only be displayed when the LaTeX-package
22726 \begin_layout Standard
22727 An overview about the different Euro symbols:
22730 \begin_layout Standard
22732 \begin_inset Tabular
22733 <lyxtabular version="3" rows="4" columns="3">
22735 <column alignment="center" valignment="top" width="0pt">
22736 <column alignment="center" valignment="top" width="0pt">
22737 <column alignment="center" valignment="top" width="0pt">
22739 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22742 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22751 \begin_layout Plain Layout
22757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22760 \begin_layout Plain Layout
22768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22771 \begin_layout Plain Layout
22777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22780 \begin_layout Plain Layout
22788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22791 \begin_layout Plain Layout
22792 \begin_inset Formula $\euro$
22802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22805 \begin_layout Plain Layout
22811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22814 \begin_layout Plain Layout
22820 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22823 \begin_layout Plain Layout
22824 \begin_inset Formula $\mbox{€}$
22834 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22837 \begin_layout Plain Layout
22843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22846 \begin_layout Plain Layout
22854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22857 \begin_layout Plain Layout
22861 \begin_layout Plain Layout
22883 \begin_layout Standard
22887 \begin_layout Plain Layout
22897 \begin_inset Note Note
22900 \begin_layout Plain Layout
22901 The following will be displayed when the LaTeX-package
22913 \begin_layout Standard
22914 You need to install the LaTeX-package
22918 to see the rest of this subsection in the output.
22921 \begin_layout Standard
22925 \begin_layout Plain Layout
22937 \begin_layout Section
22939 \begin_inset CommandInset label
22941 name "sec:Relations"
22949 \begin_layout Plain Layout
22959 \begin_layout Plain Layout
22964 \begin_layout Plain Layout
22975 \begin_layout Plain Layout
22990 \begin_layout Standard
22991 All relations can also be inserted via the toolbar button
22992 \begin_inset Graphics
22993 filename ../images/math/leq.png
23001 \begin_layout Standard
23002 \begin_inset space \hfill{}
23006 \begin_inset Tabular
23007 <lyxtabular version="3" rows="17" columns="2">
23009 <column alignment="center" valignment="top" width="0pt">
23010 <column alignment="center" valignment="top" width="0pt">
23012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23015 \begin_layout Plain Layout
23021 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23024 \begin_layout Plain Layout
23032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23035 \begin_layout Plain Layout
23041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23044 \begin_layout Plain Layout
23045 \begin_inset Formula $<$
23055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23058 \begin_layout Plain Layout
23066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23069 \begin_layout Plain Layout
23070 \begin_inset Formula $\le$
23080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23083 \begin_layout Plain Layout
23091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23094 \begin_layout Plain Layout
23095 \begin_inset Formula $\ll$
23105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23108 \begin_layout Plain Layout
23116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23119 \begin_layout Plain Layout
23120 \begin_inset Formula $\prec$
23130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23133 \begin_layout Plain Layout
23141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23144 \begin_layout Plain Layout
23145 \begin_inset Formula $\preceq$
23155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23158 \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 $\subset$
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 $\subseteq$
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 $\sqsubseteq$
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 $\in$
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 $\vdash$
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 $\smile$
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 $\lhd$
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 $\unlhd$
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 $\gtrless$
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 $\mid$
23405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23408 \begin_layout Plain Layout
23416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23419 \begin_layout Plain Layout
23420 \begin_inset Formula $\nmid$
23434 \begin_inset space \hfill{}
23438 \begin_inset Tabular
23439 <lyxtabular version="3" rows="17" columns="2">
23441 <column alignment="center" valignment="top" width="0pt">
23442 <column alignment="center" valignment="top" width="0pt">
23444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23447 \begin_layout Plain Layout
23453 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23467 \begin_layout Plain Layout
23473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23476 \begin_layout Plain Layout
23477 \begin_inset Formula $=$
23487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23490 \begin_layout Plain Layout
23498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23501 \begin_layout Plain Layout
23502 \begin_inset Formula $\not=$
23512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23515 \begin_layout Plain Layout
23523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23526 \begin_layout Plain Layout
23527 \begin_inset Formula $\equiv$
23537 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23540 \begin_layout Plain Layout
23548 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23551 \begin_layout Plain Layout
23552 \begin_inset Formula $\sim$
23562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23565 \begin_layout Plain Layout
23573 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23576 \begin_layout Plain Layout
23577 \begin_inset Formula $\simeq$
23587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23590 \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 $\approx$
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 $\cong$
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 $\bowtie$
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 $\notin$
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 $\perp$
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 $\propto$
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 $\asymp$
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 $\doteq$
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 $\circeq$
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 $\models$
23837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23840 \begin_layout Plain Layout
23848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23851 \begin_layout Plain Layout
23852 \begin_inset Formula $\widehat{=}$
23866 \begin_inset space \hfill{}
23870 \begin_inset Tabular
23871 <lyxtabular version="3" rows="17" columns="2">
23873 <column alignment="center" valignment="top" width="0pt">
23874 <column alignment="center" valignment="top" width="0pt">
23876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23879 \begin_layout Plain Layout
23885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23888 \begin_layout Plain Layout
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23899 \begin_layout Plain Layout
23905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23908 \begin_layout Plain Layout
23909 \begin_inset Formula $>$
23919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23922 \begin_layout Plain Layout
23930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23933 \begin_layout Plain Layout
23934 \begin_inset Formula $\ge$
23944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23947 \begin_layout Plain Layout
23955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23958 \begin_layout Plain Layout
23959 \begin_inset Formula $\gg$
23969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23972 \begin_layout Plain Layout
23980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23983 \begin_layout Plain Layout
23984 \begin_inset Formula $\succ$
23994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23997 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24009 \begin_inset Formula $\succeq$
24019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24022 \begin_layout Plain Layout
24030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24033 \begin_layout Plain Layout
24034 \begin_inset Formula $\supset$
24044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24047 \begin_layout Plain Layout
24055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24058 \begin_layout Plain Layout
24059 \begin_inset Formula $\supseteq$
24069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24072 \begin_layout Plain Layout
24080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24083 \begin_layout Plain Layout
24084 \begin_inset Formula $\sqsupseteq$
24094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24097 \begin_layout Plain Layout
24105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24108 \begin_layout Plain Layout
24109 \begin_inset Formula $\ni$
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24134 \begin_inset Formula $\dashv$
24144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24147 \begin_layout Plain Layout
24155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24158 \begin_layout Plain Layout
24159 \begin_inset Formula $\frown$
24169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24172 \begin_layout Plain Layout
24180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24183 \begin_layout Plain Layout
24184 \begin_inset Formula $\rhd$
24194 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24197 \begin_layout Plain Layout
24205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24208 \begin_layout Plain Layout
24209 \begin_inset Formula $\unrhd$
24219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24222 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24233 \begin_layout Plain Layout
24234 \begin_inset Formula $\lessgtr$
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24247 \begin_layout Plain Layout
24255 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24258 \begin_layout Plain Layout
24259 \begin_inset Formula $\parallel$
24269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24272 \begin_layout Plain Layout
24280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24283 \begin_layout Plain Layout
24284 \begin_inset Formula $\nparallel$
24298 \begin_inset space \hfill{}
24304 \begin_layout Standard
24305 \begin_inset VSpace medskip
24320 are bigger than the equal looking operators
24335 \begin_layout Standard
24336 Relations are, in contrary to symbols, always surrounded by space.
24339 \begin_layout Standard
24340 Relations with labels can be created with the command
24350 \begin_layout Plain Layout
24361 \begin_layout Standard
24363 \begin_inset Tabular
24364 <lyxtabular version="3" rows="2" columns="2">
24366 <column alignment="center" valignment="top" width="0">
24367 <column alignment="center" valignment="top" width="0">
24369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24372 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24381 \begin_layout Plain Layout
24383 \begin_inset Note Note
24386 \begin_layout Plain Layout
24393 is only used as spacer.
24405 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24408 \begin_layout Plain Layout
24415 \begin_layout Plain Layout
24432 \begin_layout Plain Layout
24442 \begin_inset Formula $\downarrow$
24451 \begin_layout Plain Layout
24464 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24498 \begin_layout Section
24502 \begin_layout Subsection
24503 Predefined Functions
24504 \begin_inset CommandInset label
24506 name "sub:Predefined-Functions"
24514 \begin_layout Plain Layout
24515 Functions ! predefined
24523 \begin_layout Standard
24524 In general, variables are set
24528 in mathematical expressions, but not function names, because
24529 \begin_inset Formula $sin$
24532 could be misunderstood as
24533 \begin_inset Formula $s\cdot i\cdot n$
24537 Therefore there are predefined functions, that are additionally a bit separated
24539 They are inserted as commands starting with a backslash before their name.
24542 \begin_layout Standard
24544 \begin_inset Tabular
24545 <lyxtabular version="3" rows="2" columns="4">
24547 <column alignment="center" valignment="top" width="0pt">
24548 <column alignment="center" valignment="top" width="0pt">
24549 <column alignment="center" valignment="top" width="0pt">
24550 <column alignment="center" valignment="top" width="0pt">
24552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24555 \begin_layout Plain Layout
24561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24564 \begin_layout Plain Layout
24570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24573 \begin_layout Plain Layout
24579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24582 \begin_layout Plain Layout
24590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24593 \begin_layout Plain Layout
24599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24602 \begin_layout Plain Layout
24603 \begin_inset Formula $Asin(x)+B$
24611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24614 \begin_layout Plain Layout
24622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24625 \begin_layout Plain Layout
24626 \begin_inset Formula $A\sin(x)+B$
24642 \begin_layout Standard
24643 The following functions are predefined:
24646 \begin_layout Standard
24647 \begin_inset VSpace -2mm
24653 \begin_layout Standard
24655 \begin_inset Tabular
24656 <lyxtabular version="3" rows="9" columns="4">
24658 <column alignment="center" valignment="top" width="0pt">
24659 <column alignment="center" valignment="top" width="0pt">
24660 <column alignment="center" valignment="top" width="0pt">
24661 <column alignment="center" valignment="top" width="0pt">
24663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24666 \begin_layout Plain Layout
24672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24675 \begin_layout Plain Layout
24681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24690 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24693 \begin_layout Plain Layout
24701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24704 \begin_layout Plain Layout
24712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24715 \begin_layout Plain Layout
24723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24726 \begin_layout Plain Layout
24734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24737 \begin_layout Plain Layout
24747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24750 \begin_layout Plain Layout
24758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24761 \begin_layout Plain Layout
24769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24772 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24783 \begin_layout Plain Layout
24793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24796 \begin_layout Plain Layout
24804 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24807 \begin_layout Plain Layout
24815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24818 \begin_layout Plain Layout
24826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24829 \begin_layout Plain Layout
24839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24842 \begin_layout Plain Layout
24850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24853 \begin_layout Plain Layout
24861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24864 \begin_layout Plain Layout
24872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24875 \begin_layout Plain Layout
24885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24888 \begin_layout Plain Layout
24896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24899 \begin_layout Plain Layout
24907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24910 \begin_layout Plain Layout
24918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24921 \begin_layout Plain Layout
24931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24934 \begin_layout Plain Layout
24942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24945 \begin_layout Plain Layout
24953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24956 \begin_layout Plain Layout
24964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24967 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25002 \begin_layout Plain Layout
25010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25013 \begin_layout Plain Layout
25023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25026 \begin_layout Plain Layout
25034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25037 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25048 \begin_layout Plain Layout
25056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25059 \begin_layout Plain Layout
25075 \begin_layout Standard
25076 They can also be inserted with the math toolbar button
25077 \begin_inset Graphics
25078 filename ../images/math/functions.png
25086 \begin_layout Subsection
25087 Self-defined Functions
25091 \begin_layout Plain Layout
25092 Functions ! self-defined
25100 \begin_layout Standard
25101 To use a function that is not predefined, like for example the sign function
25102 sgn(x), there are two possibilities:
25105 \begin_layout Itemize
25106 Define the function by inserting the following line to the LaTeX-preamble
25110 \begin_layout Plain Layout
25115 DeclareMathOperator
25118 \begin_inset CommandInset ref
25120 reference "sub:Self-defined-Operators"
25130 \begin_inset Newline newline
25134 \begin_inset VSpace -3mm
25138 \begin_inset Newline newline
25145 DeclareMathOperator{
25153 \begin_layout Plain Layout
25158 DeclareMathOperator
25164 \begin_inset Newline newline
25168 \begin_inset VSpace -2mm
25172 \begin_inset Newline newline
25175 Now the new defined function can be called with the command
25184 \begin_layout Itemize
25185 Write the the formula as usual, mark the formula name, in our example the
25190 , and change it to mathematical text.
25191 At last a space is inserted between prefactor and function.
25194 \begin_layout Standard
25195 The result is the same with both methods as with a predefined function
25199 \begin_layout Plain Layout
25200 In LyX self-defined functions are displayed red, predefined ones black.
25208 \begin_layout Standard
25210 \begin_inset Tabular
25211 <lyxtabular version="3" rows="3" columns="2">
25213 <column alignment="center" valignment="top" width="0pt">
25214 <column alignment="center" valignment="top" width="0pt">
25216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25219 \begin_layout Plain Layout
25225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25228 \begin_layout Plain Layout
25236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25239 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25250 \begin_layout Plain Layout
25251 \begin_inset Formula $A\sgn(x)+B$
25261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25264 \begin_layout Plain Layout
25268 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25279 \begin_layout Plain Layout
25280 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25296 \begin_layout Standard
25297 The first method is more suitable when the self-defined function should
25298 be used several times.
25301 \begin_layout Subsection
25306 \begin_layout Plain Layout
25315 \begin_layout Standard
25316 For limits there are defined besides
25326 \begin_layout Plain Layout
25346 furthermore the following functions:
25349 \begin_layout Standard
25351 \begin_inset Tabular
25352 <lyxtabular version="3" rows="5" columns="2">
25354 <column alignment="center" valignment="top" width="0">
25355 <column alignment="center" valignment="top" width="0">
25357 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25360 \begin_layout Plain Layout
25366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25369 \begin_layout Plain Layout
25371 \begin_inset Note Note
25374 \begin_layout Plain Layout
25381 is only used as spacer.
25393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25396 \begin_layout Plain Layout
25404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25407 \begin_layout Plain Layout
25408 \begin_inset Formula $\varliminf$
25418 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25421 \begin_layout Plain Layout
25429 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25432 \begin_layout Plain Layout
25433 \begin_inset Formula $\varlimsup$
25443 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25446 \begin_layout Plain Layout
25454 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25457 \begin_layout Plain Layout
25458 \begin_inset Formula $\varprojlim$
25468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25471 \begin_layout Plain Layout
25479 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25482 \begin_layout Plain Layout
25483 \begin_inset Formula $\varinjlim$
25487 \begin_inset Formula $\raisebox{-2.5mm}{}$
25503 \begin_layout Standard
25504 \begin_inset VSpace medskip
25507 The limit is created by inserting a subscript.
25508 It is set right beside the function in an inline formula:
25511 \begin_layout Standard
25513 \begin_inset Tabular
25514 <lyxtabular version="3" rows="2" columns="2">
25516 <column alignment="center" valignment="top" width="0pt">
25517 <column alignment="center" valignment="top" width="0pt">
25519 <cell alignment="center" valignment="top" usebox="none">
25522 \begin_layout Plain Layout
25528 <cell alignment="center" valignment="top" usebox="none">
25531 \begin_layout Plain Layout
25532 \begin_inset space \hspace{}
25537 \begin_inset Note Note
25540 \begin_layout Plain Layout
25547 are used here as spacer.
25559 <cell alignment="center" valignment="top" usebox="none">
25562 \begin_layout Plain Layout
25571 \begin_layout Plain Layout
25584 \begin_layout Plain Layout
25598 <cell alignment="center" valignment="top" usebox="none">
25601 \begin_layout Plain Layout
25602 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25618 \begin_layout Standard
25619 In a displayed formula the limit is set below the formula, as usual:
25620 \begin_inset Formula \[
25628 \begin_layout Subsection
25633 \begin_layout Plain Layout
25634 Functions ! modulo-
25642 \begin_layout Standard
25643 The modulo-function is special, because it exists in four variants.
25646 \begin_layout Standard
25647 The variants in a displayed formula:
25648 \begin_inset Formula \begin{align*}
25649 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25650 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25651 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25652 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25653 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25660 \begin_layout Standard
25661 In an inline formula less space is set before the function names for all
25665 \begin_layout Section
25670 \begin_layout Plain Layout
25679 \begin_layout Subsection
25680 Special Characters in Mathematical Text
25683 \begin_layout Standard
25684 The following commands can only be used in mathematical text or in TeX-mode:
25687 \begin_layout Standard
25688 \begin_inset space \hfill{}
25692 \begin_inset Tabular
25693 <lyxtabular version="3" rows="8" columns="2">
25695 <column alignment="block" valignment="top" width="0">
25696 <column alignment="block" valignment="top" width="0">
25698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25701 \begin_layout Plain Layout
25707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25710 \begin_layout Plain Layout
25718 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25721 \begin_layout Plain Layout
25729 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25732 \begin_layout Plain Layout
25733 \begin_inset Formula $\textrm{œ}$
25743 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25746 \begin_layout Plain Layout
25754 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25757 \begin_layout Plain Layout
25758 \begin_inset Formula $\textrm{Œ}$
25768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25771 \begin_layout Plain Layout
25779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25782 \begin_layout Plain Layout
25783 \begin_inset Formula $\textrm{æ}$
25793 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25796 \begin_layout Plain Layout
25804 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25807 \begin_layout Plain Layout
25808 \begin_inset Formula $\textrm{Æ}$
25818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25821 \begin_layout Plain Layout
25829 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25832 \begin_layout Plain Layout
25833 \begin_inset Formula $\textrm{\aa}$
25843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25846 \begin_layout Plain Layout
25853 \begin_layout Plain Layout
25860 \begin_layout Plain Layout
25881 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25884 \begin_layout Plain Layout
25885 \begin_inset Formula $\textrm{Å}$
25895 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25898 \begin_layout Plain Layout
25906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25909 \begin_layout Plain Layout
25910 \begin_inset Formula $\textrm{ı}$
25924 \begin_inset space \hfill{}
25928 \begin_inset Tabular
25929 <lyxtabular version="3" rows="8" columns="2">
25931 <column alignment="block" valignment="top" width="0">
25932 <column alignment="center" valignment="top" width="0">
25934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25937 \begin_layout Plain Layout
25939 \begin_inset Note Note
25942 \begin_layout Plain Layout
25944 \begin_inset space \thinspace{}
25947 mm is used for separation, because otherwise the output will be ¡ and ¿
25958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25961 \begin_layout Plain Layout
25969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25972 \begin_layout Plain Layout
25980 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25983 \begin_layout Plain Layout
25984 \begin_inset Formula $\textrm{ø}$
25994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25997 \begin_layout Plain Layout
26005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26008 \begin_layout Plain Layout
26009 \begin_inset Formula $\textrm{Ø}$
26019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26022 \begin_layout Plain Layout
26030 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26033 \begin_layout Plain Layout
26034 \begin_inset Formula $\textrm{ł}$
26044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26047 \begin_layout Plain Layout
26055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26058 \begin_layout Plain Layout
26059 \begin_inset Formula $\textrm{Ł}$
26069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26072 \begin_layout Plain Layout
26074 \begin_inset space \hspace{}
26082 \begin_layout Plain Layout
26096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26099 \begin_layout Plain Layout
26100 \begin_inset Formula $\textrm{!`}$
26110 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26113 \begin_layout Plain Layout
26115 \begin_inset space \hspace{}
26123 \begin_layout Plain Layout
26137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26140 \begin_layout Plain Layout
26141 \begin_inset Formula $\textrm{?`}$
26151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26154 \begin_layout Plain Layout
26162 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26165 \begin_layout Plain Layout
26166 \begin_inset Formula $\textrm{ȷ}$
26180 \begin_inset space \hfill{}
26186 \begin_layout Standard
26188 \begin_inset Formula $\textrm{\textrm{Å}}$
26192 \begin_inset Formula $\textrm{\textrm{Ø}}$
26195 can also be inserted via the math toolbar button
26196 \begin_inset Graphics
26197 filename ../images/math/digamma.png
26205 \begin_layout Standard
26206 An exception are the commands
26209 \begin_inset space \hspace{}
26218 \begin_inset space \hspace{}
26224 , because they can be inserted in LyX directly to text.
26227 \begin_layout Subsection
26229 \begin_inset CommandInset label
26231 name "sub:Accents-in-Text"
26239 \begin_layout Plain Layout
26248 \begin_layout Standard
26249 With the following commands all letters can be accented.
26250 The commands must be inserted in TeX-mode.
26253 \begin_layout Standard
26254 \begin_inset space \hfill{}
26258 \begin_inset Tabular
26259 <lyxtabular version="3" rows="8" columns="2">
26261 <column alignment="block" valignment="top" width="0">
26262 <column alignment="block" valignment="top" width="0">
26264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26276 \begin_layout Plain Layout
26284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26287 \begin_layout Plain Layout
26291 \begin_inset Quotes grd
26299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26302 \begin_layout Plain Layout
26306 \begin_layout Plain Layout
26322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26325 \begin_layout Plain Layout
26333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26336 \begin_layout Plain Layout
26340 \begin_layout Plain Layout
26356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26359 \begin_layout Plain Layout
26366 \begin_layout Plain Layout
26380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26383 \begin_layout Plain Layout
26387 \begin_layout Plain Layout
26403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26406 \begin_layout Plain Layout
26414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26417 \begin_layout Plain Layout
26421 \begin_layout Plain Layout
26437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26440 \begin_layout Plain Layout
26447 \begin_layout Plain Layout
26461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26464 \begin_layout Plain Layout
26468 \begin_layout Plain Layout
26484 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26487 \begin_layout Plain Layout
26494 \begin_layout Plain Layout
26508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26511 \begin_layout Plain Layout
26515 \begin_layout Plain Layout
26531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26534 \begin_layout Plain Layout
26541 \begin_layout Plain Layout
26555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26558 \begin_layout Plain Layout
26562 \begin_layout Plain Layout
26582 \begin_inset space \hfill{}
26586 \begin_inset Tabular
26587 <lyxtabular version="3" rows="8" columns="2">
26589 <column alignment="block" valignment="top" width="0">
26590 <column alignment="center" valignment="top" width="0">
26592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26595 \begin_layout Plain Layout
26601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26604 \begin_layout Plain Layout
26612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26615 \begin_layout Plain Layout
26622 \begin_layout Plain Layout
26636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26639 \begin_layout Plain Layout
26643 \begin_layout Plain Layout
26659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26662 \begin_layout Plain Layout
26670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26673 \begin_layout Plain Layout
26677 \begin_layout Plain Layout
26693 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26696 \begin_layout Plain Layout
26703 \begin_layout Plain Layout
26714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26717 \begin_layout Plain Layout
26721 \begin_layout Plain Layout
26737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26740 \begin_layout Plain Layout
26748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26751 \begin_layout Plain Layout
26755 \begin_layout Plain Layout
26771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26774 \begin_layout Plain Layout
26781 \begin_layout Plain Layout
26795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26798 \begin_layout Plain Layout
26802 \begin_layout Plain Layout
26818 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26821 \begin_layout Plain Layout
26828 \begin_layout Plain Layout
26842 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26845 \begin_layout Plain Layout
26849 \begin_layout Plain Layout
26865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26868 \begin_layout Plain Layout
26875 \begin_layout Plain Layout
26889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26892 \begin_layout Plain Layout
26896 \begin_layout Plain Layout
26916 \begin_inset space \hfill{}
26922 \begin_layout Standard
26923 \begin_inset VSpace medskip
26932 also two different characters can be accented.
26941 \begin_layout Plain Layout
26956 \begin_layout Plain Layout
26968 \begin_layout Standard
26981 can in combination with vowels directly be inserted with the keyboard without
26983 The same applies for the tilde
26987 \begin_layout Plain Layout
26988 This only applies for keyboards where the tilde is defined as accent.
26997 in combination with
27012 \begin_layout Standard
27055 and accents that are inserted directly with the keyboard are also available
27056 in mathematical text.
27057 For the other accents there are special math commands to be used in formulas,
27059 \begin_inset CommandInset ref
27061 reference "sub:Accents-for-one"
27068 \begin_layout Standard
27069 \begin_inset VSpace bigskip
27072 Furthermore, with the command
27082 \begin_layout Plain Layout
27090 all numbers and letters can be set into a circle, quasi accented with a
27091 circle, similar to the the copyright symbol.
27094 \begin_layout Standard
27096 \begin_inset Tabular
27097 <lyxtabular version="3" rows="3" columns="2">
27099 <column alignment="center" valignment="top" width="0">
27100 <column alignment="center" valignment="top" width="0">
27102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27105 \begin_layout Plain Layout
27111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27114 \begin_layout Plain Layout
27116 \begin_inset Note Note
27119 \begin_layout Plain Layout
27126 is only used as spacer.
27138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27141 \begin_layout Plain Layout
27149 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27152 \begin_layout Plain Layout
27156 \begin_layout Plain Layout
27172 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27175 \begin_layout Plain Layout
27186 raisebox{-1.5pt}{W}}
27191 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27194 \begin_layout Plain Layout
27195 \begin_inset Formula $\raisebox{4.5mm}{}$
27202 \begin_layout Plain Layout
27220 \begin_inset Formula $\raisebox{-2mm}{}$
27236 \begin_layout Standard
27237 One has to take care that the character fits in the circle.
27248 \begin_layout Plain Layout
27250 \begin_inset CommandInset ref
27252 reference "sub:Font-Sizes"
27261 specifies thereby the size of the circle.
27272 \begin_layout Plain Layout
27274 \begin_inset CommandInset ref
27276 reference "sub:Boxes-without-Frame"
27285 the character can be centered.
27288 \begin_layout Subsection
27293 \begin_layout Plain Layout
27302 \begin_layout Standard
27303 Minuscule numbers are created with the command
27313 \begin_layout Plain Layout
27322 The command can be used in formulas and in TeX-mode.
27323 The command scheme is:
27326 \begin_layout Standard
27331 oldstylenums{number}
27334 \begin_layout Standard
27339 oldstylenums{0123456789
27342 \begin_inset Formula $\oldstylenums{0123456789}$
27348 \begin_layout Subsection
27349 Miscellaneous special Characters
27350 \begin_inset CommandInset label
27352 name "sub:Miscellaneous-special-Characters"
27360 \begin_layout Plain Layout
27361 Special characters ! miscellaneous
27369 \begin_layout Standard
27370 The following characters can only be inserted to formulas by using commands:
27373 \begin_layout Standard
27375 \begin_inset Tabular
27376 <lyxtabular version="3" rows="4" columns="2">
27378 <column alignment="center" valignment="top" width="0">
27379 <column alignment="center" valignment="top" width="0">
27381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27384 \begin_layout Plain Layout
27390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27393 \begin_layout Plain Layout
27401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27404 \begin_layout Plain Layout
27411 \begin_layout Plain Layout
27425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27428 \begin_layout Plain Layout
27429 \begin_inset Formula $\mathcircumflex$
27439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27442 \begin_layout Plain Layout
27450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27453 \begin_layout Plain Layout
27454 \begin_inset Formula $\_$
27464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27467 \begin_layout Plain Layout
27472 \begin_layout Plain Layout
27487 \begin_layout Plain Layout
27500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27503 \begin_layout Plain Layout
27504 \begin_inset Formula $^{\circ}$
27520 \begin_layout Standard
27521 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27522 contains the following line
27526 \begin_layout Plain Layout
27527 More about this is described in
27528 \begin_inset CommandInset ref
27530 reference "sub:Text-Characters-in"
27542 \begin_layout Standard
27547 DeclareInputtext{176}{
27560 \begin_layout Section
27562 \begin_inset CommandInset label
27564 name "sec:Formula-Styles"
27572 \begin_layout Plain Layout
27581 \begin_layout Itemize
27582 There are two different alignment styles:
27586 \begin_layout Description
27587 Centered is the predefined standard
27590 \begin_layout Description
27591 Indented for this the option
27595 must be inserted in the menu
27597 Document\SpecialChar \menuseparator
27603 \begin_inset space ~
27609 \begin_layout Standard
27614 is used, the indentation can be adjusted with the length
27624 \begin_layout Plain Layout
27633 Should the distance be 15
27634 \begin_inset space \thinspace{}
27637 mm, the following command line is inserted in the LaTeX-preamble
27640 \begin_layout Standard
27650 \begin_layout Standard
27651 When no length is specified, the predefined value of 30
27652 \begin_inset space \thinspace{}
27659 \begin_layout Itemize
27660 And two different numbering styles:
27664 \begin_layout Description
27665 Right is the predefined standard
27668 \begin_layout Description
27669 Left for this the option
27673 must be inserted in the menu
27675 Document\SpecialChar \menuseparator
27681 \begin_inset space ~
27688 \begin_layout Standard
27697 can also be used together.
27698 In this case both options are inserted, separated by a comma.
27701 \begin_layout Standard
27702 The chosen styles are used for all displayed formulas of the document.
27703 When both, centered and indented formulas should be created in a document,
27709 The indented formulas are then set in a flalign environment, see
27710 \begin_inset CommandInset ref
27712 reference "sub:Flalign-Environment"
27719 \begin_layout Section
27721 \begin_inset CommandInset label
27723 name "sec:Multiline-Formulas"
27731 \begin_layout Plain Layout
27732 Formula ! multiline
27740 \begin_layout Subsection
27744 \begin_layout Standard
27745 In LyX multiline formulas are created by pressing
27750 arg "newline-insert newline"
27756 This creates either an
27758 eqnarray environment
27760 that is described in
27761 \begin_inset CommandInset ref
27763 reference "sub:Eqnarray-Environment"
27767 or, when the option
27769 Use AMS math package
27771 in the document settings is selected, an
27775 that is described in
27776 \begin_inset CommandInset ref
27778 reference "sub:Standard-align-Environment"
27785 \begin_layout Standard
27786 There are other multiline formula environments that can be created via the
27789 Insert\SpecialChar \menuseparator
27793 These environments are described in the following sections.
27796 \begin_layout Standard
27797 In all multiline formula environments a new line is created by pressing
27801 arg "newline-insert newline"
27805 To add or delete lines, the math toolbar buttons
27806 \begin_inset Graphics
27807 filename ../images/tabular-feature_append-row.png
27813 \begin_inset Graphics
27814 filename ../images/tabular-feature_delete-row.png
27819 , respectively, or the menu
27821 Edit\SpecialChar \menuseparator
27827 \begin_layout Subsubsection
27829 \begin_inset CommandInset label
27831 name "sub:Line-Separation"
27839 \begin_layout Plain Layout
27840 Formula ! multiline ! Line separation
27848 \begin_layout Standard
27849 There is sometimes not enough space in multiline formulas between the lines:
27850 \begin_inset Formula \begin{eqnarray*}
27851 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}\\
27852 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*}
27859 \begin_layout Standard
27860 In LaTeX additional line space is specified as optional argument of the
27862 This is not yet possible in LyX
27866 \begin_layout Plain Layout
27868 \begin_inset CommandInset href
27870 name "LyX-bug #1505"
27871 target "http://www.lyx.org/trac/ticket/1505"
27880 , therefore the whole formula must be inserted in TeX-mode.
27881 To add in our example space, the command
27889 is inserted at the end of the first line.
27894 \begin_layout Plain Layout
27901 \begin_layout Plain Layout
27903 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27906 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27913 \begin_layout Plain Layout
27917 left(B^{2}+x_{0}^{2}
27925 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27930 \begin_layout Plain Layout
27942 \begin_layout Standard
27943 \begin_inset VSpace bigskip
27946 To set the the line separation for all lines in a formula, the length
27956 \begin_layout Plain Layout
27966 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27977 \begin_inset space \thinspace{}
27982 \begin_inset space \thinspace{}
27985 mm additional line separation as in the previous example, the command
27988 \begin_layout Standard
27998 \begin_layout Standard
27999 is inserted in TeX-mode before the formula.
28000 This requires that the LaTeX-package
28008 \begin_layout Plain Layout
28013 is part of every LaTeX standard installation.
28022 \begin_layout Plain Layout
28028 was loaded in LaTeX-preamble with the line
28031 \begin_layout Standard
28039 \begin_layout Standard
28044 \begin_layout Plain Layout
28056 \begin_inset Formula \begin{eqnarray*}
28057 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}\\
28058 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*}
28065 \begin_layout Standard
28069 \begin_layout Plain Layout
28080 To get back to the predefined distance,
28086 is set to the value 3
28087 \begin_inset space \thinspace{}
28093 \begin_layout Subsubsection
28095 \begin_inset CommandInset label
28097 name "sub:Column-Separation"
28105 \begin_layout Plain Layout
28106 Formula ! multiline ! Column separation
28114 \begin_layout Standard
28115 Multiline formulas form a matrix.
28116 A formula in the eqnarray environment is for example a matrix with three
28118 By changing the column separation in this environment, the space beside
28119 the relation sign can be changed.
28122 \begin_layout Standard
28123 The column separation is specified with the length
28133 \begin_layout Plain Layout
28142 \begin_inset Newline newline
28145 column separation = 2
28146 \begin_inset space \thinspace{}
28156 \begin_inset Newline newline
28162 \begin_layout Standard
28172 \begin_layout Standard
28173 inserted in TeX-mode, sets for all following formulas a column separation
28175 \begin_inset space \thinspace{}
28179 To get back to the predefined distance,
28186 \begin_inset space \thinspace{}
28192 \begin_layout Standard
28194 \begin_inset space \thinspace{}
28197 cm column separation:
28201 \begin_layout Plain Layout
28213 \begin_inset Formula \begin{eqnarray*}
28215 C & \ne & A\end{eqnarray*}
28219 A formula with the predefined column separation for matrices of 10
28220 \begin_inset space \thinspace{}
28227 \begin_layout Plain Layout
28239 \begin_inset Formula \begin{eqnarray*}
28241 C & \ne & A\end{eqnarray*}
28248 \begin_layout Subsubsection
28253 \begin_layout Plain Layout
28262 \begin_layout Standard
28263 Long formulas can be typeset using these methods:
28266 \begin_layout Itemize
28267 When one side of the equation is much shorther than the line width, this
28268 one is chosen for the left side and the right side is typeset over two
28270 \begin_inset Formula \begin{eqnarray}
28271 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 \\
28272 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}\end{eqnarray}
28276 The minus sign at the beginning of the second line does normally not appear
28277 as operator because it is the first character of the line.
28278 Thus it would not be surrounded by space and could not be distinguished
28279 from the fraction bar.
28281 \begin_inset space \thinspace{}
28284 pt space was inserted behind the minus sign with the command
28294 \begin_layout Plain Layout
28302 \begin_inset CommandInset ref
28304 reference "sub:Variable-Space"
28317 \begin_layout Plain Layout
28328 \begin_layout Itemize
28329 When both sides of the equation are too long, the command
28339 \begin_layout Plain Layout
28348 It is inserted to the first column of the first line and effects that all
28349 further insertions overwrite the following columns:
28350 \begin_inset Formula \begin{eqnarray}
28351 \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 \\
28352 & & -\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 \\
28353 & & =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}
28357 After the insertion of
28363 , the cursor is in a purple box that is a bit shifted to the left from the
28365 In this the formula is inserted.
28366 \begin_inset Newline newline
28369 The content of the further lines is inserted to the second or another formula
28371 The greater the column number where it was inserted, the larger the indentation.
28372 \begin_inset VSpace medskip
28376 \begin_inset Newline newline
28380 \begin_inset Note Greyedout
28383 \begin_layout Plain Layout
28384 Note the following when using
28393 \begin_layout Itemize
28394 The formula doesn't use the full page width.
28396 \begin_inset space \thinspace{}
28400 \begin_inset space \space{}
28404 \begin_inset Formula $-B^{2}$
28407 is added to the first line in the above example, it would have been outside
28409 To better use the width, negative space can be inserted at the beginning
28413 \begin_layout Itemize
28414 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28419 \begin_layout Plain Layout
28420 \begin_inset CommandInset href
28422 name "LyX-bug #1429"
28423 target "http://www.lyx.org/trac/ticket/1429"
28432 One can only set the cursor at the beginning of the line and move it with
28441 \begin_layout Itemize
28442 Other methods to set long formulas are offered by the environments described
28444 \begin_inset CommandInset ref
28446 reference "sub:Multline-Environment"
28451 \begin_inset CommandInset ref
28453 reference "sub:Multiline-Formula-Parts"
28460 \begin_layout Subsubsection
28462 \begin_inset CommandInset label
28464 name "sub:Multiline-Brackets"
28472 \begin_layout Plain Layout
28473 Brackets ! for multiline expressions
28481 \begin_layout Standard
28482 For brackets spanning multiple lines the following problem occurs:
28483 \begin_inset Formula \begin{eqnarray*}
28484 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28485 & & \left.\cdots+B-D\right]\end{eqnarray*}
28492 \begin_layout Standard
28493 The closing bracket is smaller than the opening bracket because brackets
28494 with variable size may not span multiple lines.
28497 \begin_layout Standard
28498 To set the bracket size for the second line correctly, the first line is
28509 \begin_layout Plain Layout
28517 and the second line with
28525 \begin_layout Plain Layout
28539 \begin_inset CommandInset ref
28541 reference "sub:Automatic-Bracket-Size"
28556 \begin_layout Plain Layout
28582 \begin_layout Plain Layout
28601 \begin_layout Plain Layout
28620 \begin_layout Plain Layout
28632 \begin_inset Formula $\downarrow$
28641 \begin_layout Plain Layout
28649 is inserted, because the multiplication operator with its limits is the
28650 largest symbol in the first line and this should be the size for the bracket
28651 in the second line.
28654 \begin_layout Standard
28655 The result is this:
28656 \begin_inset Formula \begin{eqnarray*}
28657 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28658 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28665 \begin_layout Subsection
28669 \begin_layout Standard
28670 Align environments can be used for every kind of multiline formulas.
28671 They are specially useful to set several formulas side by side.
28674 \begin_layout Standard
28675 Align environments consist of columns.
28676 The odd columns are right aligned, the even ones left aligned.
28677 Every line in an Align environment can be numbered.
28680 \begin_layout Standard
28681 Align environments are created via the menu
28683 Insert\SpecialChar \menuseparator
28689 Edit\SpecialChar \menuseparator
28690 Math\SpecialChar \menuseparator
28691 Change Formula Type
28693 already existing formulas can be converted to Align environments.
28696 \begin_layout Standard
28697 To add or delete columns, the math toolbar buttons
28698 \begin_inset Graphics
28699 filename ../images/tabular-feature_append-column.png
28705 \begin_inset Graphics
28706 filename ../images/tabular-feature_delete-column.png
28711 , respectively, or the menu
28713 Edit\SpecialChar \menuseparator
28719 \begin_layout Subsubsection
28720 Standard align Environment
28721 \begin_inset CommandInset label
28723 name "sub:Standard-align-Environment"
28731 \begin_layout Plain Layout
28732 Formula ! multiline ! align environment
28740 \begin_layout Standard
28741 This Align environment is created by presssing
28744 arg "newline-insert newline"
28747 in a formula or by the menu
28749 Insert\SpecialChar \menuseparator
28750 Math\SpecialChar \menuseparator
28751 AMS align Environment
28756 \begin_layout Standard
28757 An example for two formulas set side by side, that are created with a four
28758 column align environment:
28759 \begin_inset Formula \begin{align*}
28760 A & =\sin(B) & C & =D\\
28761 C & \ne A & B & \ne D\end{align*}
28765 As it can be seen, the formulas in this environment are placed so as if
28774 \begin_layout Plain Layout
28782 \begin_inset CommandInset ref
28784 reference "sub:Variable-Space"
28795 before the first and after every even column.
28796 When the formula style
28802 \begin_layout Plain Layout
28804 \begin_inset CommandInset ref
28806 reference "sec:Formula-Styles"
28817 is used, the formula is set without the
28823 before the first column.
28826 \begin_layout Subsubsection
28827 Alignat Environment
28831 \begin_layout Plain Layout
28832 Formula ! multiline ! alignat environment
28840 \begin_layout Standard
28841 The alignat environment has no predefined column separation.
28842 It can be inserted manually with the spaces that are described
28843 \begin_inset CommandInset ref
28845 reference "sub:Space"
28852 \begin_layout Standard
28853 The above example in the alignat environment where 1
28854 \begin_inset space \thinspace{}
28857 cm space was inserted at the beginning of the second formula:
28858 \begin_inset Formula \begin{alignat*}{2}
28859 A & =\sin(B) & \hspace{1cm}C & =D\\
28860 C & \ne A & B & \ne D\end{alignat*}
28864 Because the column separation can be set separately for every column, this
28865 environment is especially suitable to set three and more formulas side
28869 \begin_layout Subsubsection
28870 Flalign Environment
28871 \begin_inset CommandInset label
28873 name "sub:Flalign-Environment"
28881 \begin_layout Plain Layout
28882 Formula ! multiline ! flalign environment
28890 \begin_layout Standard
28891 In this environment the first two columns are always set as much as possible
28892 to the left and the last two ones to the right.
28894 \begin_inset Formula \begin{flalign*}
28895 A & =1 & B & =2 & C & =3\\
28896 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28903 \begin_layout Standard
28904 By creating a flalign environment with an odd number of columns where an
28905 empty TeX-brace is inserted to the last column, several formulas in a document
28906 can be set to the left, although the formula style
28911 As example the indented formula
28912 \begin_inset CommandInset ref
28914 reference "eq:VolInt"
28919 \begin_inset Formula \begin{flalign}
28920 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28924 The first two columns contain the formula.
28925 To indent it as with the formula style
28930 \begin_inset space \thinspace{}
28933 pt space was inserted at the beginning of the first column.
28936 \begin_layout Subsection
28937 Eqnarray Environment
28938 \begin_inset CommandInset label
28940 name "sub:Eqnarray-Environment"
28948 \begin_layout Plain Layout
28949 Formula ! multiline ! eqnarray environment
28957 \begin_layout Standard
28958 When this environment has been created, three blue boxes appear.
28959 The content of the first box is right aligned, the content of the last
28961 The content of the middle box appears centered and a bit smaller, because
28962 it is designed to insert there only relation characters.
28963 \begin_inset Formula \begin{eqnarray*}
28964 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28966 A & = & A\end{eqnarray*}
28973 \begin_layout Subsection
28978 \begin_layout Plain Layout
28979 Formula ! multiline ! gather environment
28987 \begin_layout Standard
28988 This environment consists of only one centered column.
28989 Every line can be numbered.
28990 \begin_inset Formula \begin{gather}
28992 X=\textrm{-}1\end{gather}
28999 \begin_layout Subsection
29000 Multline Environment
29001 \begin_inset CommandInset label
29003 name "sub:Multline-Environment"
29011 \begin_layout Plain Layout
29012 Formula ! multiline ! multline environment
29020 \begin_layout Standard
29021 The multline environment consists, like the gather environment, of only
29023 But the first line is left aligned, the last one right aligned.
29024 All other lines are centered.
29025 Therefore this environment is suitable for long formulas.
29027 \begin_inset CommandInset ref
29029 reference "eq:lefteqn"
29033 in the multline environment:
29034 \begin_inset Formula \begin{multline}
29035 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}\\
29036 -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}\\
29037 =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}
29044 \begin_layout Standard
29045 In the output only the last (first) line of a multline environment appears
29046 numbered when the document numbering is right (left).
29050 \begin_layout Plain Layout
29051 numbering styles see
29052 \begin_inset CommandInset ref
29054 reference "sec:Formula-Styles"
29066 \begin_layout Standard
29075 \begin_layout Plain Layout
29093 \begin_layout Plain Layout
29103 a centered line can be right or left aligned, respectively.
29104 The commands are used as follows:
29107 \begin_layout Standard
29112 shoveright{line content}
29118 shoveleft{line content}
29121 \begin_layout Standard
29122 \begin_inset VSpace medskip
29133 \begin_layout Plain Layout
29143 specifies the distance of the first line from the left page margin.
29144 Predefined is the length 0
29145 \begin_inset space \thinspace{}
29151 \begin_layout Standard
29152 As example the above formula where the command
29155 \begin_layout Standard
29165 \begin_layout Standard
29166 was inserted in TeX-mode before:
29170 \begin_layout Plain Layout
29182 \begin_inset Formula \begin{multline}
29183 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}\\
29184 \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}}\\
29185 =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}
29193 \begin_layout Plain Layout
29204 The second line was left aligned using
29213 \begin_layout Subsection
29214 Multiline Formula Parts
29215 \begin_inset CommandInset label
29217 name "sub:Multiline-Formula-Parts"
29225 \begin_layout Plain Layout
29226 Formula ! multiline ! formula parts
29234 \begin_layout Standard
29235 To display only parts of a formula with multiple lines, one of the following
29236 environments are used:
29253 They can be inserted via the menu
29255 Insert\SpecialChar \menuseparator
29258 or by using the commands described in this section.
29261 \begin_layout Standard
29262 The first three have the same properties as the corresponding multiline
29263 formula environments, but it is possible to set further formula parts beside
29266 \begin_inset Formula \[
29267 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29268 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29269 \right\} \textrm{Uncertainty relations}\]
29276 \begin_layout Standard
29277 To get this formula, a displayed formula is created where the command
29285 \begin_layout Plain Layout
29296 A purple box appears around the blue formula box where now columns and
29297 lines can be added.
29298 Outside the multiline environment other formula parts can be set, like
29302 \begin_layout Standard
29303 The aligned environment is also suitable for long formulas whose lines are
29304 horizontally aligned.
29305 Using aligned in a displayed formula has the advantage that the formula
29306 number is vertically centered behind the lines.
29308 \begin_inset CommandInset ref
29310 reference "eq:shortlong"
29314 in the aligned environment:
29315 \begin_inset Formula \begin{equation}
29316 \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}|}\\
29317 & -\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}
29325 \begin_layout Standard
29326 To use the environments
29348 \begin_layout Plain Layout
29366 \begin_layout Plain Layout
29384 \begin_layout Plain Layout
29392 are inserted, respectively.
29393 The split environment has the same properties as the aligned environment
29394 but it can only have two columns.
29397 \begin_layout Subsection
29398 Text in multiline Formulas
29399 \begin_inset CommandInset label
29401 name "sub:Text-in-multiline"
29409 \begin_layout Plain Layout
29419 \begin_layout Plain Layout
29420 Formula ! multiline ! text
29428 \begin_layout Standard
29429 In the Align environments, and the multline and gather environment, text
29430 can be inserted that will appear in a separate line and doesn't affect
29431 the column alignment.
29432 To do this, the command
29440 \begin_layout Plain Layout
29450 is used in the following scheme:
29453 \begin_layout Standard
29461 \begin_layout Standard
29462 The text should not be longer than a line because it cannot be hyphenated.
29463 As LyX doesn't yet support
29469 directly, the text is written as mathematical text.
29476 must hereby be at the beginning of a line and appears in the output above
29478 An example where the text was inserted at the beginning of the second line:
29479 \begin_inset Formula \begin{align}
29480 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29481 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29488 \begin_layout Section
29493 \begin_layout Plain Layout
29503 \begin_layout Plain Layout
29504 Formula ! numbering|see
29508 \begin_layout Plain Layout
29519 \begin_layout Plain Layout
29534 \begin_layout Subsection
29538 \begin_layout Standard
29539 Numbered formulas can be created with the menu
29541 Insert\SpecialChar \menuseparator
29542 Math\SpecialChar \menuseparator
29544 \begin_inset space ~
29552 \begin_inset space ~
29558 Existing formulas can be numbered with the menu
29560 Edit\SpecialChar \menuseparator
29561 Math\SpecialChar \menuseparator
29563 \begin_inset space ~
29571 arg "math-number-toggle"
29575 The formula number is displayed in LyX behind the formula as number sign
29577 The number sign is replaced in the output by the formula number.
29580 \begin_layout Standard
29581 When numbering is turned on in multiline formulas, all lines will be numbered.
29582 But the numbering can be controlled with the menu
29584 Edit\SpecialChar \menuseparator
29585 Math\SpecialChar \menuseparator
29587 \begin_inset space ~
29591 \begin_inset space ~
29595 \begin_inset space ~
29603 arg "math-number-line-toggle"
29609 \begin_layout Standard
29610 Except for inline formulas, all formulas can be numbered with two different
29612 \begin_inset CommandInset ref
29614 reference "sec:Formula-Styles"
29621 \begin_layout Subsection
29626 \begin_layout Plain Layout
29627 Cross-references ! to formulas
29635 \begin_layout Standard
29636 All labeled formulas can be cross-referenced.
29637 A label is added by the menu
29639 Insert\SpecialChar \menuseparator
29642 or the toolbar button
29643 \begin_inset Graphics
29644 filename ../images/label-insert.png
29650 The cursor must hereby be inside a displayed formula.
29651 A dialog pops up displaying the prefix
29656 The label is inserted there behind the prefix.
29657 The predefined prefix means
29658 \begin_inset Quotes eld
29662 \begin_inset Quotes erd
29665 and makes it easier to find labels in large documents because it marks
29666 it as formula label to divide it from e.
29667 \begin_inset space \thinspace{}
29671 \begin_inset space \space{}
29675 To change a label, the menu
29677 Insert\SpecialChar \menuseparator
29683 \begin_layout Standard
29684 The name of the label is displayed in LyX within two parentheses behind
29686 A formula with a label is always numbered.
29689 \begin_layout Standard
29690 Cross-references are inserted via the menu
29692 Insert\SpecialChar \menuseparator
29695 or with the toolbar button
29696 \begin_inset Graphics
29697 filename ../images/dialog-show-new-inset_ref.png
29703 A formula cross-reference appears in the output as formula number.
29704 When in the cross-reference dialog window the format
29708 is chosen, the cross-reference appears in the output as formula number
29710 \begin_inset Newline newline
29713 By right-clicking on a cross-reference in LyX, one jumps to the formula
29714 that is referenced.
29717 \begin_layout Standard
29718 Here are as examples cross-references to formulas of the following subsections:
29719 \begin_inset Note Note
29722 \begin_layout Plain Layout
29723 Note the different cross-reference types.
29731 \begin_layout Standard
29733 \begin_inset CommandInset ref
29740 \begin_inset CommandInset ref
29748 \begin_inset CommandInset ref
29754 ) big Latin letters are used for the numbering in contrary to (
29755 \begin_inset CommandInset ref
29764 \begin_layout Standard
29765 \begin_inset VSpace medskip
29768 When the argument of
29776 \begin_layout Plain Layout
29784 \begin_inset CommandInset ref
29786 reference "sub:User-defined-Numbering"
29797 contains a box like in
29798 \begin_inset CommandInset ref
29800 reference "sub:Paragraph-Boxes"
29804 , the formula cannot be referenced.
29807 \begin_layout Subsection
29812 \begin_layout Plain Layout
29813 Formula numbering ! subnumbering
29821 \begin_layout Standard
29822 With the help of the commands
29826 begin{subequations}
29834 formulas can be subnumbered.
29835 Both commands are inserted in TeX-mode.
29838 \begin_layout Standard
29840 \begin_inset Formula \begin{equation}
29841 A=C-B\label{eq:a}\end{equation}
29849 \begin_layout Plain Layout
29853 addtocounter{equation}{-1}
29862 \begin_layout Plain Layout
29866 begin{subequations}
29872 \begin_inset VSpace -5mm
29876 \begin_inset Formula \begin{equation}
29877 B=C-A\label{eq:b}\end{equation}
29882 \begin_inset Formula \begin{equation}
29883 C=A+B\label{eq:c}\end{equation}
29890 \begin_layout Standard
29894 \begin_layout Plain Layout
29906 \begin_layout Standard
29907 To create the example, the following is done:
29910 \begin_layout Enumerate
29911 first formula is inserted
29914 \begin_layout Enumerate
29919 addtocounter{equation}{-1}
29921 begin{subequations}
29925 \begin_layout Plain Layout
29934 \begin_inset Newline newline
29939 is inserted after the first formula
29942 \begin_layout Enumerate
29943 second formula is inserted
29946 \begin_layout Enumerate
29947 third formula is inserted
29950 \begin_layout Enumerate
29957 is inserted after the third formula
29960 \begin_layout Standard
29961 Every formula between the commands
29973 is subnumbered as a, b,
29974 \begin_inset Newline linebreak
29977 c, \SpecialChar \ldots{}
29978 For multiline formulas every line will be subnumbered.
29979 All subnumbered formulas are treated as
29984 But as every numbered formula increases the counter
29988 by one, the command
29994 is needed to decrease it.
29995 Otherwise the formulas
29996 \begin_inset CommandInset ref
30003 \begin_inset CommandInset ref
30010 \begin_inset CommandInset ref
30016 would be numbered as
30017 \begin_inset CommandInset ref
30024 \begin_inset CommandInset ref
30031 \begin_inset CommandInset ref
30040 \begin_layout Standard
30041 By inserting the commands in TeX-mode, a space is created between the first
30044 \begin_inset space \thinspace{}
30047 mm vertical space is inserted after the command
30051 begin{subequations}
30054 When the formula style
30060 \begin_layout Plain Layout
30062 \begin_inset CommandInset ref
30064 reference "sec:Formula-Styles"
30076 \begin_inset space \thinspace{}
30079 mm space is inserted instead.
30082 \begin_layout Standard
30083 Here is an example for a multiline formula where the numbering was turned
30084 off for the second line:
30088 \begin_layout Plain Layout
30092 begin{subequations}
30098 \begin_inset Formula \begin{eqnarray}
30099 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30100 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30101 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
30109 \begin_layout Plain Layout
30121 \begin_layout Subsection
30122 User-defined Numbering
30123 \begin_inset CommandInset label
30125 name "sub:User-defined-Numbering"
30133 \begin_layout Plain Layout
30134 Formula numbering ! user-defined
30142 \begin_layout Standard
30146 \begin_layout Plain Layout
30147 Formula numbering ! self-defined delimiters
30152 With the standard numbering parentheses are set around the formula number.
30153 To replace the parentheses for example by vertical bars, the following
30154 line is added to the LaTeX-preamble:
30157 \begin_layout Standard
30169 \begin_inset Note Note
30172 \begin_layout Plain Layout
30173 This macro is already declared in the LaTeX-preamble for testing.
30174 To activate it, remove the percent sign at the beginning.
30182 \begin_layout Standard
30183 To use other characters, the vertical bars besides the
30187 are replaced by one ore more characters.
30188 To get only the formula number the vertical bars are omitted.
30191 \begin_layout Standard
30192 \begin_inset VSpace bigskip
30195 When there should be an expression of your choice instead of the consecutive
30196 formula number in parentheses behind the formula, the command
30206 \begin_layout Plain Layout
30215 \begin_inset Formula \begin{equation}
30216 A+B=C\tag{something}\label{eq:tag}\end{equation}
30220 In this example the command
30228 \begin_layout Plain Layout
30239 was inserted to the formula.
30242 \begin_layout Standard
30251 \begin_layout Plain Layout
30262 is inserted instead, the star prevents the parentheses around the expression:
30263 \begin_inset Formula \[
30264 A+B=C\tag*{something}\]
30271 \begin_layout Standard
30272 \begin_inset VSpace bigskip
30275 To restart the formula numbering with new document parts or sections, the
30276 following command is used:
30279 \begin_layout Standard
30284 @addtoreset{equation}{part}
30290 \begin_layout Plain Layout
30295 \begin_layout Plain Layout
30306 \begin_layout Plain Layout
30319 \begin_layout Plain Layout
30330 \begin_layout Plain Layout
30343 \begin_inset Newline newline
30347 \begin_inset Newline newline
30354 @addtoreset{equation}{section}
30357 \begin_layout Standard
30358 To be able to use these commands in TeX-mode, the
30359 \begin_inset Quotes eld
30363 \begin_inset Quotes erd
30366 character has to be made
30367 \begin_inset Quotes eld
30371 \begin_inset Quotes erd
30374 for LaTeX using the command
30388 So the command sequence in TeX-mode is:
30391 \begin_layout Standard
30397 \begin_inset Newline newline
30402 @addtoreset{equation}{section}
30403 \begin_inset Newline newline
30411 \begin_layout Standard
30412 In the LaTeX-preamble
30424 can be omitted as they are automatically internally inserted by LyX.
30427 \begin_layout Standard
30442 \begin_layout Plain Layout
30447 is part of the LaTeX-package
30455 \begin_layout Plain Layout
30456 Packages ! carlisle
30461 that is part of every LaTeX standard installation.
30470 \begin_layout Plain Layout
30471 Packages ! remreset
30476 has to be loaded in the LaTeX-preamble with the line
30479 \begin_layout Standard
30484 usepackage{remreset}
30487 \begin_layout Standard
30498 \begin_layout Plain Layout
30503 \begin_layout Plain Layout
30514 \begin_layout Plain Layout
30527 \begin_layout Plain Layout
30538 \begin_layout Plain Layout
30550 can be used with the same scheme as
30559 \begin_layout Standard
30560 \begin_inset VSpace bigskip
30563 Sometimes formulas should be numbered in the following form:
30566 \begin_layout Standard
30569 (section number.formula number)
30572 \begin_layout Standard
30573 The formula number should start with every section with
30574 \begin_inset Quotes eld
30578 \begin_inset Quotes erd
30584 \begin_layout Standard
30585 For this case there is the command
30595 \begin_layout Plain Layout
30603 , which is used with the following scheme:
30606 \begin_layout Standard
30611 numberwithin{counter}{sectioning}
30614 \begin_layout Standard
30615 Counter denotes what kind of numbering is affected, sectioning denotes what
30616 number is before the dot.
30619 \begin_layout Standard
30620 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30623 \begin_layout Standard
30628 numberwithin{equation}{section}
30631 \begin_layout Standard
30632 This is the result:
30636 \begin_layout Plain Layout
30640 numberwithin{equation}{section}
30646 \begin_inset Formula \begin{equation}
30647 A+B=C\end{equation}
30654 \begin_layout Standard
30656 \begin_inset space \thinspace{}
30660 \begin_inset space \space{}
30663 tables so that the number of the part is the sectioning,
30664 \begin_inset Newline newline
30671 numberwithin{table}{part}
30676 \begin_layout Standard
30677 To go back to the standard numbering or to prevent this kind of numbering
30678 when it is defined by the document class, the following command is inserted
30679 as TeX-Code or to the LaTeX-preamble:
30682 \begin_layout Standard
30695 \begin_layout Plain Layout
30709 \begin_layout Plain Layout
30725 \begin_inset Newline newline
30733 \begin_inset Newline newline
30745 \begin_layout Standard
30752 uses internally the command
30758 , described above, that also needs to be reverted.
30762 \begin_layout Plain Layout
30769 \begin_layout Plain Layout
30773 @removefromreset{equation}{section}
30776 \begin_layout Plain Layout
30788 \begin_layout Subsection
30789 Numbering with Roman Numbers and Letters
30793 \begin_layout Plain Layout
30794 Formula numbering ! with letters
30803 \begin_layout Plain Layout
30804 Formula numbering ! with Roman numbers
30812 \begin_layout Standard
30813 Formulas can also be numbered with Roman numbers and Latin letters.
30814 To number for example with small Roman numbers, the command
30817 \begin_layout Standard
30829 \begin_layout Standard
30830 is inserted before the formula in TeX-mode.
30841 \begin_layout Plain Layout
30849 redefines the predefined command
30865 \begin_layout Plain Layout
30872 has the same scheme like the command
30878 that is described in
30879 \begin_inset CommandInset ref
30881 reference "sub:The-Command-newcommand"
30894 is the formula counter.
30901 is used as prefix for a counter, the value of the counter is output as
30903 When a formula is numbered, LaTeX sets internally the command
30909 behind the formula.
30918 \begin_layout Plain Layout
30928 outputs the counter as small Roman number.
30931 \begin_layout Standard
30932 All formulas behind the command
30942 are now numbered Roman.
30943 To switch to numbering with big Roman numbers, the command is inserted
30960 \begin_layout Plain Layout
30972 \begin_inset Quotes eld
30976 \begin_inset Quotes erd
30979 with small Latin letters there is the command
30989 \begin_layout Plain Layout
30997 , for big ones there is the command
31007 \begin_layout Plain Layout
31020 \begin_layout Standard
31021 \begin_inset Note Greyedout
31024 \begin_layout Plain Layout
31029 Only maximal 26 formulas can be numbered with Latin letters in one document.
31037 \begin_layout Standard
31041 \begin_layout Plain Layout
31057 \begin_layout Standard
31058 \begin_inset Formula \begin{equation}
31059 A=\textrm{small roman}\end{equation}
31067 \begin_layout Plain Layout
31081 \begin_inset Formula \begin{equation}
31082 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
31090 \begin_layout Plain Layout
31104 \begin_inset Formula \begin{equation}
31105 C=\textrm{small Latin}\end{equation}
31113 \begin_layout Plain Layout
31127 \begin_inset Formula \begin{equation}
31128 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
31135 \begin_layout Standard
31136 To switch back to the default numbering, insert the command:
31139 \begin_layout Standard
31152 \begin_layout Plain Layout
31163 \begin_layout Standard
31167 \begin_layout Plain Layout
31181 \begin_inset Formula \begin{equation}
31182 E=\textrm{Arabic}\end{equation}
31189 \begin_layout Standard
31190 \begin_inset VSpace medskip
31193 As you see, formulas are numbered serially independent from the numbering
31195 When then numbering should start with
31196 \begin_inset Quotes eld
31200 \begin_inset Quotes erd
31203 when the style is changed, new equation counters have to be defined.
31204 A description about this can be found in the file
31205 \begin_inset CommandInset href
31207 name "Formula-numbering.lyx"
31208 target "run:Formula-numbering.lyx"
31215 \begin_layout Section
31216 Chemical Symbols and Equations
31217 \begin_inset CommandInset label
31219 name "sub:Chemical-Symbols-and"
31227 \begin_layout Plain Layout
31228 Chemical characters ! Symbols
31237 \begin_layout Plain Layout
31247 \begin_layout Plain Layout
31256 \begin_layout Standard
31257 An example text from chemistry:
31260 \begin_layout Quote
31262 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31265 -ion reacts with two
31266 \begin_inset Formula $\mathrm{Na^{+}}$
31269 -ions to sodium sulfate
31270 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31274 The chemical equation for this is:
31275 \begin_inset Formula \begin{equation}
31276 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31283 \begin_layout Standard
31284 This chemical equation can directly be created as formula.
31285 To avoid that the symbols appear italic, everything is highlighted and
31286 changed by the shortcut
31292 to the upright font style.
31296 \begin_layout Plain Layout
31302 \begin_inset CommandInset ref
31304 reference "sub:Font-Styles"
31316 \begin_layout Standard
31317 A more convenient way to typeset chemical formulas is to use the command
31328 \begin_layout Plain Layout
31336 that is available when the LaTeX-package
31344 \begin_layout Plain Layout
31357 to a formula a new blue box appears where chemical formulas can be inserted
31358 in an intuitive way.
31361 \begin_layout Standard
31363 \begin_inset Tabular
31364 <lyxtabular version="3" rows="9" columns="2">
31366 <column alignment="center" valignment="top" width="0">
31367 <column alignment="center" valignment="top" width="0">
31369 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31372 \begin_layout Plain Layout
31378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31381 \begin_layout Plain Layout
31383 \begin_inset Note Note
31386 \begin_layout Plain Layout
31393 is only used as spacer.
31405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31408 \begin_layout Plain Layout
31415 \begin_layout Plain Layout
31429 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31432 \begin_layout Plain Layout
31433 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31443 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31446 \begin_layout Plain Layout
31453 \begin_layout Plain Layout
31467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31470 \begin_layout Plain Layout
31471 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31484 \begin_layout Plain Layout
31491 \begin_layout Plain Layout
31505 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31508 \begin_layout Plain Layout
31509 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31519 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31522 \begin_layout Plain Layout
31529 \begin_layout Plain Layout
31543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31546 \begin_layout Plain Layout
31547 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31560 \begin_layout Plain Layout
31567 \begin_layout Plain Layout
31582 \begin_layout Plain Layout
31597 \begin_layout Plain Layout
31611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31614 \begin_layout Plain Layout
31615 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31625 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31628 \begin_layout Plain Layout
31635 \begin_layout Plain Layout
31645 \begin_inset Formula $\downarrow$
31649 \begin_inset Formula $\to$
31657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31660 \begin_layout Plain Layout
31661 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31674 \begin_layout Plain Layout
31681 \begin_layout Plain Layout
31694 \begin_layout Plain Layout
31707 \begin_layout Plain Layout
31720 \begin_layout Plain Layout
31733 \begin_layout Plain Layout
31747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31750 \begin_layout Plain Layout
31751 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31764 \begin_layout Plain Layout
31771 \begin_layout Plain Layout
31784 \begin_layout Plain Layout
31797 \begin_layout Plain Layout
31810 \begin_layout Plain Layout
31827 \begin_layout Plain Layout
31841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31844 \begin_layout Plain Layout
31845 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31861 \begin_layout Standard
31862 \begin_inset Note Greyedout
31865 \begin_layout Plain Layout
31870 Inserting a formula to a
31876 box will lead to LaTeX errors.
31877 In this case TeX code has to be used like for
31891 \begin_layout Plain Layout
31912 \begin_layout Standard
31919 the command for equation
31920 \begin_inset space ~
31924 \begin_inset CommandInset ref
31926 reference "eq:chem-reaction"
31931 \begin_inset Newline newline
31942 \begin_layout Plain Layout
31955 \begin_layout Plain Layout
31968 \begin_layout Plain Layout
31981 \begin_layout Plain Layout
31994 \begin_layout Plain Layout
32007 \begin_layout Plain Layout
32019 \begin_layout Standard
32020 To create multiline chemical equations first a multiline formula is created
32022 \begin_inset CommandInset ref
32024 reference "sec:Multiline-Formulas"
32029 Afterwards the command
32035 is used in every small blue box of the formula.
32037 \begin_inset CommandInset ref
32039 reference "eq:TEOS-reaction-1"
32044 \begin_inset CommandInset ref
32046 reference "eq:TEOS-reaction-2"
32050 are an example of a multi-stage chemical reaction where every equation
32051 has its own number.
32052 \begin_inset Formula \begin{eqnarray}
32053 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32054 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
32061 \begin_layout Standard
32072 package provides the command
32082 \begin_layout Plain Layout
32090 that has to be used for special cases.
32091 For more information about
32097 and more examples have a look at the documentation of
32102 \begin_inset CommandInset citation
32111 \begin_layout Standard
32112 \begin_inset Newpage newpage
32118 \begin_layout Section
32122 \begin_layout Standard
32123 LyX supports two types of commutative diagrams:
32131 that are explained in the following.
32134 \begin_layout Subsection
32139 \begin_layout Plain Layout
32148 \begin_layout Standard
32149 Diagrams of this type visualize relations by vertical and horizontal lines
32151 \begin_inset Formula \[
32152 \begin{CD}A@>>>B@>>>C\\
32154 F@<<<E@<<<D\end{CD}\]
32161 \begin_layout Standard
32162 To get them, the command
32170 \begin_layout Plain Layout
32180 is inserted to a formula.
32181 A blue box appears with two dashed lines where further commands can be
32186 arg "newline-insert newline"
32189 a new line is created.
32190 Horizontal relations are inserted in odd, vertical in even formula lines.
32193 \begin_layout Standard
32194 To create the relations there are the following commands:
32197 \begin_layout Itemize
32202 creates a left arrow,
32213 \begin_layout Itemize
32218 creates an up arrow,
32226 a vertical equal sign
32229 \begin_layout Itemize
32235 is a placeholder for non-existent relations
32238 \begin_layout Standard
32239 All arrows can be labeled as follows:
32242 \begin_layout Itemize
32243 Is text inserted between the first and second < or >, resp., it is placed
32245 When it is inserted between the second and third one, it appears under
32249 \begin_layout Itemize
32250 When text for vertical arrows is inserted between the first and second A
32251 or V, resp., it is placed left beside the arrow.
32252 When it is inserted between the second and third one, it appears right
32254 If the text contains an A or V, these letters must be set into a TeX-brace.
32257 \begin_layout Standard
32258 As example a diagram with all possible relations:
32261 \begin_layout Standard
32262 \begin_inset Formula \[
32263 \begin{CD}A@>j>>B@>>k>C@=F\\
32265 D@<<j<E@>k>>F@=C\end{CD}\]
32272 \begin_layout Standard
32273 The command for this is:
32274 \begin_inset Newline newline
32285 \begin_layout Plain Layout
32294 A@>j>>B@>>k>C@=F Ctrl+Return
32295 \begin_inset Newline newline
32302 \begin_layout Plain Layout
32317 \begin_layout Plain Layout
32330 \begin_layout Plain Layout
32342 \begin_inset Formula $\to$
32348 \begin_inset Newline newline
32355 \begin_layout Plain Layout
32370 \begin_layout Plain Layout
32383 \begin_layout Plain Layout
32393 \begin_layout Subsection
32398 \begin_layout Plain Layout
32399 Diagrams ! xymatrix
32407 \begin_layout Standard
32408 To be able to use xymatrices, the LaTeX-package
32413 A xymatrix is created by inserting the command
32420 Then you are able to add new matrix columns and rows like for normal matrices,
32422 \begin_inset CommandInset ref
32424 reference "sec:Matrices"
32431 \begin_layout Standard
32432 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32434 All possibilities to create commutative diagrams and decorations are explained
32439 that you find in the menu
32441 Help\SpecialChar \menuseparator
32443 \begin_inset space ~
32446 Manuals\SpecialChar \menuseparator
32448 \begin_inset space ~
32456 \begin_layout Section
32457 User-defined Commands
32461 \begin_layout Plain Layout
32462 User-defined commands
32470 \begin_layout Standard
32471 \begin_inset Note Greyedout
32474 \begin_layout Plain Layout
32479 The names of user-defined commands and macros may only consist of Latin
32488 \begin_layout Subsection
32492 \begin_inset CommandInset label
32494 name "sub:The-Command-newcommand"
32502 \begin_layout Plain Layout
32503 User-defined commands !
32514 \begin_layout Plain Layout
32525 \begin_layout Standard
32526 Many LaTeX-commands are too long to be used frequently.
32527 But it is possible to define with the command
32533 new shorter commands.
32536 \begin_layout Standard
32537 The command scheme of
32546 \begin_layout Standard
32551 newcommand{new command name}[number of arguments][optional
32556 \begin_inset Newline newline
32563 \begin_layout Plain Layout
32578 \begin_layout Plain Layout
32585 {command definition}
32588 \begin_layout Standard
32589 \begin_inset Note Greyedout
32592 \begin_layout Plain Layout
32597 Assure that the name of the new command is not already used in your document
32598 or by LaTeX-packages that you use.
32599 When you for example define the command
32611 , you get an error message because
32617 is already defined as command for
32618 \begin_inset Quotes eld
32622 \begin_inset Formula $\le$
32626 \begin_inset Quotes erd
32637 \begin_layout Standard
32638 The number of arguments is an integer in the range 0
32639 \begin_inset space \thinspace{}
32643 \begin_inset space \thinspace{}
32646 9 and specifies how many arguments the new command should have.
32647 With the optional value a value for an optional argument can be predefined.
32648 When this is done, the
32656 rgument of the new command is automatically an optional one.
32659 \begin_layout Standard
32660 Here are some examples:
32663 \begin_layout Itemize
32664 To define the command
32676 , the LaTeX-preamble line is:
32677 \begin_inset VSpace medskip
32681 \begin_inset Newline newline
32695 \begin_layout Itemize
32696 To define the command
32708 , the argument (that should be underlined) must be taken into account.
32709 For this the preamble line is:
32710 \begin_inset VSpace medskip
32714 \begin_inset Newline newline
32728 \begin_inset VSpace medskip
32732 \begin_inset Newline newline
32739 acts as argument placeholder, the
32743 behind it denotes that it is the placeholder for the first argument.
32746 \begin_layout Itemize
32754 \begin_inset space \thinspace{}
32758 \begin_inset space \space{}
32768 \begin_inset VSpace medskip
32772 \begin_inset Newline newline
32783 framebox#1#2{$#3$}}
32786 \begin_inset VSpace medskip
32790 \begin_inset Newline newline
32793 The two Dollar signs creates the extra formula needed for
32800 \begin_inset CommandInset ref
32802 reference "sub:Boxes-with-Frame"
32809 \begin_layout Itemize
32810 To create a new command for
32816 where the color for the box needn't to be specified, the argument for the
32817 color is defined optional:
32818 \begin_inset VSpace medskip
32822 \begin_inset Newline newline
32833 fcolorbox{#2}{#1}{$#3$}}
32836 \begin_inset VSpace medskip
32840 \begin_inset Newline newline
32843 When the color is not specified when using
32849 , the predefined color
32856 \begin_layout Standard
32857 A test of the new defined commands:
32860 \begin_layout Standard
32862 \begin_inset Tabular
32863 <lyxtabular version="3" rows="6" columns="2">
32865 <column alignment="center" valignment="top" width="0">
32866 <column alignment="center" valignment="top" width="0">
32868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32871 \begin_layout Plain Layout
32877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32880 \begin_layout Plain Layout
32882 \begin_inset Note Note
32885 \begin_layout Plain Layout
32892 is only used as spacer.
32904 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32907 \begin_layout Plain Layout
32914 \begin_layout Plain Layout
32928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32931 \begin_layout Plain Layout
32932 \begin_inset Formula $A\gr B$
32942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32945 \begin_layout Plain Layout
32953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32956 \begin_layout Plain Layout
32957 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32970 \begin_layout Plain Layout
32974 \begin_inset Formula $\to$
32980 \begin_inset Formula $\to$
32991 \begin_layout Plain Layout
33005 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33008 \begin_layout Plain Layout
33009 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33019 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33022 \begin_layout Plain Layout
33026 \begin_inset Formula $\to$
33037 \begin_layout Plain Layout
33051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33054 \begin_layout Plain Layout
33055 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33068 \begin_layout Plain Layout
33074 \begin_inset Formula $\to$
33085 \begin_layout Plain Layout
33099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33102 \begin_layout Plain Layout
33103 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33119 \begin_layout Subsection
33124 \begin_layout Plain Layout
33125 User-defined commands! Math macros
33134 \begin_layout Plain Layout
33143 \begin_layout Standard
33144 User-defined commands are especially convenient for complex expressions.
33145 When you are for example dealing in a document with quadratic equations,
33146 the same solution type occurs several times.
33147 The general form of a quadratic equation is
33148 \begin_inset Formula \[
33149 0=\lambda^{2}+p\lambda+q\]
33153 The general form of the solution is
33154 \begin_inset Formula \[
33155 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33162 \begin_layout Standard
33163 To define a command for the solution formula where only the three parameters
33165 \begin_inset Formula $\lambda$
33169 \begin_inset Formula $p$
33173 \begin_inset Formula $q$
33176 need to be specified and the index of
33177 \begin_inset Formula $\lambda$
33180 can be given optionally, the LaTeX-preamble line is
33181 \begin_inset Newline newline
33197 \begin_inset Newline newline
33204 \begin_layout Plain Layout
33219 \begin_layout Plain Layout
33230 frac{#3^{2}}{4}-#4}}
33233 \begin_layout Standard
33234 To create with this the solution formula, the command
33235 \begin_inset Newline newline
33245 \begin_inset Formula $\to$
33251 \begin_inset Formula $\to$
33258 is inserted to a formula
33263 \begin_layout Standard
33264 The definition of the new command is unintuitive because one has to know
33265 the schemes of all used LaTeX commands, e.
33266 \begin_inset space \thinspace{}
33270 \begin_inset space \space{}
33273 that a fraction is inserted in LaTeX as
33277 frac{numerator}{denominator}
33280 Furthermore one can easily forget a brace in the definition and cannot
33281 see in LyX what the new command is doing.
33282 To avoid these problems LyX offers the possibility to use math macros instead
33292 \begin_layout Standard
33293 A math macro is created by using the menu
33295 Insert\SpecialChar \menuseparator
33296 Math\SpecialChar \menuseparator
33299 or the toolbar button
33300 \begin_inset Graphics
33301 filename ../images/math-macro_newmacroname_newcommand.png
33307 The math macro toolbar appears together with the following box where the
33309 \begin_inset Newline newline
33313 \begin_inset space \hspace*{\fill}
33317 \begin_inset Graphics
33318 filename clipart/macrobox.png
33323 \begin_inset space \hspace*{\fill}
33327 \begin_inset Newline newline
33331 \begin_inset FormulaMacro
33332 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33337 newmacroname is the default name of the macro that should be changed to
33338 something sensible.
33339 The wanted formula is inserted in the first blue box.
33340 An argument placeholder is inserted with the command
33347 \begin_inset space \thinspace{}
33351 \begin_inset space \space{}
33360 or by using the macro toolbar button
33361 \begin_inset Graphics
33362 filename ../images/math-macro-add-param.png
33368 Argument placeholders are displayed red.
33369 Maximum 9 arguments are possible.
33370 Optional arguments are created with the toolbar button
33371 \begin_inset Graphics
33372 filename ../images/math-macro-add-optional-param.png
33378 The first non-optional argument can be transformed to an optional one with
33380 \begin_inset Graphics
33381 filename ../images/math-macro-make-optional.png
33387 In the second blue box the appearance of the macro in LyX can be defined.
33388 Normally you want to see it as it is defined, so the box is kept empty.
33389 But when you have created a macro that needs lot of space on the screen,
33390 you can insert in the box for example
33391 \begin_inset Newline newline
33421 \begin_inset Newline newline
33426 For the macro only the arguments with the macro name in front of them will
33427 then be displayed in LyX, leading to a better overview.
33428 The formula appears in the output as defined in the first box.
33429 \begin_inset Newline newline
33432 The appearance of macros in formulas can furthermore be changed for single
33433 macros by setting the cursor in the macro and using the menu
33435 View\SpecialChar \menuseparator
33437 \begin_inset space ~
33441 \begin_inset space ~
33449 \begin_layout Standard
33450 To use a macro, the macro name is inserted as command to a formula, in our
33458 Our macro looks in LyX like this:
33459 \begin_inset Newline newline
33463 \begin_inset space \hspace*{\fill}
33467 \begin_inset Graphics
33468 filename clipart/macrouse.png
33473 \begin_inset space \hspace*{\fill}
33477 \begin_inset Newline newline
33480 Here is our macro example with the arguments
33481 \begin_inset Formula $x$
33485 \begin_inset Formula $\ln(x)$
33489 \begin_inset Formula $B$
33495 \begin_layout Standard
33496 \begin_inset Formula \[
33504 \begin_layout Standard
33505 LyX offers in the menu
33507 Tools\SpecialChar \menuseparator
33508 Preferences\SpecialChar \menuseparator
33509 Editing\SpecialChar \menuseparator
33512 different styles to edit macros.
33513 To find the style that suits you the most, choose a style and set the cursor
33514 in a macro formula to see the difference.
33517 \begin_layout Standard
33518 A math macro is transformed internally to a
33524 command when exporting the document.
33531 command is not placed in the LaTeX-preamble, therefore macros can only
33532 be used in formulas that are in the document below the macro definition
33536 \begin_layout Standard
33537 Math macros can also be directly be created from a
33544 When writing for example the command
33547 \begin_inset Newline newline
33556 xleftarrow[#2]{#1}}
33557 \begin_inset Newline newline
33562 in LyX as normal text, highlighting it completely and using then the shortcut
33567 , the command will be transformed to a math macro.
33568 Using this method you need to be careful that the
33574 command is typed correctly, otherwise you get a faulty macro leading to
33578 \begin_layout Standard
33579 Math macros currently yet have the problem that further formulas in macro
33580 definitions are handled wrongly.
33581 Therefore the example
33588 \begin_inset CommandInset ref
33590 reference "sub:The-Command-newcommand"
33594 cannot be created as macro.
33597 \begin_layout Standard
33598 When the cursor is in a macro definition box, you will see the macro toolbar
33602 \begin_layout Standard
33603 \begin_inset VSpace defskip
33609 \begin_layout Standard
33610 \begin_inset Graphics
33611 filename clipart/MacroToolbar.png
33619 \begin_layout Plain Layout
33628 \begin_layout Standard
33629 \begin_inset VSpace defskip
33635 \begin_layout Standard
33636 The macro toolbar contains from left to right the following buttons:
33639 \begin_layout Standard
33640 \begin_inset VSpace defskip
33646 \begin_layout Standard
33647 \begin_inset Tabular
33648 <lyxtabular version="3" rows="9" columns="2">
33649 <features islongtable="true">
33650 <column alignment="left" valignment="top" width="0">
33651 <column alignment="left" valignment="top" width="85col%">
33652 <row interlinespace="2.5mm">
33653 <cell alignment="center" valignment="top" usebox="none">
33656 \begin_layout Plain Layout
33657 \begin_inset Graphics
33658 filename ../images/math-macro-remove-param.png
33659 BoundingBox 0bp 5bp 20bp 25bp
33660 rotateOrigin center
33669 <cell alignment="center" valignment="top" usebox="none">
33672 \begin_layout Plain Layout
33675 Edit\SpecialChar \menuseparator
33676 Math\SpecialChar \menuseparator
33678 \begin_inset space ~
33681 Definition\SpecialChar \menuseparator
33682 Remove Last Argument
33688 <row interlinespace="2.5mm">
33689 <cell alignment="center" valignment="top" usebox="none">
33692 \begin_layout Plain Layout
33693 \begin_inset Graphics
33694 filename ../images/math-macro-add-param.png
33695 BoundingBox 0bp 5bp 20bp 25bp
33696 rotateOrigin center
33705 <cell alignment="center" valignment="top" usebox="none">
33708 \begin_layout Plain Layout
33711 Edit\SpecialChar \menuseparator
33712 Math\SpecialChar \menuseparator
33714 \begin_inset space ~
33717 Definition\SpecialChar \menuseparator
33724 <row interlinespace="2.5mm">
33725 <cell alignment="center" valignment="top" usebox="none">
33728 \begin_layout Plain Layout
33729 \begin_inset Graphics
33730 filename ../images/math-macro-make-optional.png
33731 BoundingBox 0bp 5bp 20bp 25bp
33732 rotateOrigin center
33741 <cell alignment="center" valignment="top" usebox="none">
33744 \begin_layout Plain Layout
33747 Edit\SpecialChar \menuseparator
33748 Math\SpecialChar \menuseparator
33750 \begin_inset space ~
33753 Definition\SpecialChar \menuseparator
33754 Make First Non-Optional into
33755 \begin_inset Newline newline
33762 \begin_layout Plain Layout
33771 Edit\SpecialChar \menuseparator
33772 Math\SpecialChar \menuseparator
33774 \begin_inset space ~
33777 Definition\SpecialChar \menuseparator
33782 \begin_layout Plain Layout
33795 <row interlinespace="2.5mm">
33796 <cell alignment="center" valignment="top" usebox="none">
33799 \begin_layout Plain Layout
33800 \begin_inset Graphics
33801 filename ../images/math-macro-make-nonoptional.png
33802 BoundingBox 0bp 5bp 20bp 25bp
33803 rotateOrigin center
33812 <cell alignment="center" valignment="top" usebox="none">
33815 \begin_layout Plain Layout
33818 Edit\SpecialChar \menuseparator
33819 Math\SpecialChar \menuseparator
33821 \begin_inset space ~
33824 Definition\SpecialChar \menuseparator
33825 Make Last Optional into
33826 \begin_inset Newline newline
33833 \begin_layout Plain Layout
33842 Edit\SpecialChar \menuseparator
33843 Math\SpecialChar \menuseparator
33845 \begin_inset space ~
33848 Definition\SpecialChar \menuseparator
33853 \begin_layout Plain Layout
33860 Non-Optional Argument
33866 <row interlinespace="2.5mm">
33867 <cell alignment="center" valignment="top" usebox="none">
33870 \begin_layout Plain Layout
33871 \begin_inset Graphics
33872 filename ../images/math-macro-remove-optional-param.png
33873 BoundingBox 0bp 5bp 20bp 25bp
33874 rotateOrigin center
33883 <cell alignment="center" valignment="top" usebox="none">
33886 \begin_layout Plain Layout
33889 Edit\SpecialChar \menuseparator
33890 Math\SpecialChar \menuseparator
33892 \begin_inset space ~
33895 Definition\SpecialChar \menuseparator
33896 Remove Optional Argument
33902 <row interlinespace="2.5mm">
33903 <cell alignment="center" valignment="top" usebox="none">
33906 \begin_layout Plain Layout
33907 \begin_inset Graphics
33908 filename ../images/math-macro-add-optional-param.png
33909 BoundingBox 0bp 5bp 20bp 25bp
33910 rotateOrigin center
33919 <cell alignment="center" valignment="top" usebox="none">
33922 \begin_layout Plain Layout
33925 Edit\SpecialChar \menuseparator
33926 Math\SpecialChar \menuseparator
33928 \begin_inset space ~
33931 Definition\SpecialChar \menuseparator
33932 Insert Optional Argument
33938 <row interlinespace="2.5mm">
33939 <cell alignment="center" valignment="top" usebox="none">
33942 \begin_layout Plain Layout
33943 \begin_inset Graphics
33944 filename ../images/math-macro-remove-greedy-param.png
33945 BoundingBox 0bp 5bp 20bp 25bp
33946 rotateOrigin center
33955 <cell alignment="center" valignment="top" usebox="none">
33958 \begin_layout Plain Layout
33961 Edit\SpecialChar \menuseparator
33962 Math\SpecialChar \menuseparator
33964 \begin_inset space ~
33967 Definition\SpecialChar \menuseparator
33968 Remove Last Argument
33969 \begin_inset Newline newline
33976 \begin_layout Plain Layout
33985 Edit\SpecialChar \menuseparator
33986 Math\SpecialChar \menuseparator
33988 \begin_inset space ~
33991 Definition\SpecialChar \menuseparator
33996 \begin_layout Plain Layout
34003 Spitting Out To The Right
34009 <row interlinespace="2.5mm">
34010 <cell alignment="center" valignment="top" usebox="none">
34013 \begin_layout Plain Layout
34014 \begin_inset Graphics
34015 filename ../images/math-macro-append-greedy-param.png
34016 BoundingBox 0bp 5bp 20bp 25bp
34017 rotateOrigin center
34026 <cell alignment="center" valignment="top" usebox="none">
34029 \begin_layout Plain Layout
34032 Edit\SpecialChar \menuseparator
34033 Math\SpecialChar \menuseparator
34035 \begin_inset space ~
34038 Definition\SpecialChar \menuseparator
34040 \begin_inset Newline newline
34047 \begin_layout Plain Layout
34056 Edit\SpecialChar \menuseparator
34057 Math\SpecialChar \menuseparator
34059 \begin_inset space ~
34062 Definition\SpecialChar \menuseparator
34067 \begin_layout Plain Layout
34074 Eating From The Right
34080 <row interlinespace="2.5mm">
34081 <cell alignment="center" valignment="top" usebox="none">
34084 \begin_layout Plain Layout
34085 \begin_inset Graphics
34086 filename ../images/math-macro-add-greedy-optional-param.png
34087 BoundingBox 0bp 5bp 20bp 25bp
34088 rotateOrigin center
34097 <cell alignment="center" valignment="top" usebox="none">
34100 \begin_layout Plain Layout
34103 Edit\SpecialChar \menuseparator
34104 Math\SpecialChar \menuseparator
34106 \begin_inset space ~
34109 Definition\SpecialChar \menuseparator
34110 Append Optional Argument
34111 \begin_inset Newline newline
34118 \begin_layout Plain Layout
34127 Edit\SpecialChar \menuseparator
34128 Math\SpecialChar \menuseparator
34130 \begin_inset space ~
34133 Definition\SpecialChar \menuseparator
34138 \begin_layout Plain Layout
34145 Eating From The Right
34158 \begin_layout Standard
34159 \begin_inset Newpage newpage
34165 \begin_layout Section
34170 \begin_layout Plain Layout
34179 \begin_layout Subsection
34184 \begin_layout Plain Layout
34193 \begin_layout Standard
34194 Negative numbers often look ugly in formulas because the minus sign before
34195 the number is set with the same length as the minus operator sign.
34196 When writing the negative number in normal text, the minus sign appears
34200 \begin_layout Standard
34201 Thus, the problem disappears when converting the minus sign to mathematical
34205 \begin_layout Standard
34206 An example to visualize the problem:
34209 \begin_layout Standard
34211 \begin_inset Tabular
34212 <lyxtabular version="3" rows="3" columns="2">
34214 <column alignment="right" valignment="top" width="0">
34215 <column alignment="left" valignment="top" width="0">
34217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34220 \begin_layout Plain Layout
34226 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34229 \begin_layout Plain Layout
34237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34240 \begin_layout Plain Layout
34246 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34249 \begin_layout Plain Layout
34250 \begin_inset Formula $x=-2$
34260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34263 \begin_layout Plain Layout
34269 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34272 \begin_layout Plain Layout
34273 \begin_inset Formula $x=\textrm{-}2$
34289 \begin_layout Subsection
34290 Comma as decimal Separator
34294 \begin_layout Plain Layout
34303 \begin_layout Standard
34304 In LaTeX a comma inside a formula is used, according to the English convention,
34305 as number group separator.
34306 So there will be space added behind all commas in formulas.
34309 \begin_layout Standard
34310 To avoid this, the comma is highlighted and changed to mathematical text
34320 \begin_layout Standard
34321 To use all formula commas in the document as decimal separator, the file
34330 \begin_layout Plain Layout
34335 is part of the LaTeX-package
34343 \begin_layout Plain Layout
34348 \begin_layout Plain Layout
34371 \begin_layout Plain Layout
34377 is loaded with the LaTeX-preamble line
34380 \begin_layout Standard
34388 \begin_layout Subsection
34390 \begin_inset CommandInset label
34392 name "sub:Physical-Vectors"
34400 \begin_layout Plain Layout
34409 \begin_layout Standard
34410 Predefined vectors are offered by the LaTeX-package
34418 \begin_layout Plain Layout
34423 should be part of every LaTeX standard installation.
34432 \begin_layout Plain Layout
34438 that is loaded with the LaTeX-preamble line
34441 \begin_layout Standard
34449 \begin_layout Standard
34453 \begin_layout Plain Layout
34463 \begin_inset Note Note
34466 \begin_layout Plain Layout
34467 The following table will only be displayed when the LaTeX-package
34476 The following commands are defined:
34479 \begin_layout Standard
34481 \begin_inset Tabular
34482 <lyxtabular version="3" rows="4" columns="2">
34484 <column alignment="center" valignment="top" width="0">
34485 <column alignment="center" valignment="top" width="0">
34487 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34490 \begin_layout Plain Layout
34496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34499 \begin_layout Plain Layout
34507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34510 \begin_layout Plain Layout
34520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34523 \begin_layout Plain Layout
34524 \begin_inset Formula $\Bra{\psi}$
34534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34537 \begin_layout Plain Layout
34547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34550 \begin_layout Plain Layout
34551 \begin_inset Formula $\Ket{\psi}$
34561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34564 \begin_layout Plain Layout
34576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34579 \begin_layout Plain Layout
34580 \begin_inset Formula $\Braket{\psi|\phi}$
34596 \begin_layout Standard
34603 assures that all vertical bars are set in the size of the surrounding brackets:
34604 \begin_inset Formula \[
34605 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34613 \begin_layout Plain Layout
34623 \begin_inset Note Note
34626 \begin_layout Plain Layout
34627 The following will be displayed when the LaTeX-package
34639 \begin_layout Standard
34640 You need to install the LaTeX-package
34644 to see the rest of this subsection in the output.
34647 \begin_layout Standard
34651 \begin_layout Plain Layout
34663 \begin_layout Standard
34670 can also be achieved using the command
34676 , that is described in
34677 \begin_inset CommandInset ref
34679 reference "sub:Automatic-Bracket-Size"
34686 \begin_layout Subsection
34687 Self-defined Fractions
34688 \begin_inset CommandInset label
34690 name "sub:Self-defined-Fractions"
34698 \begin_layout Plain Layout
34699 Fractions ! self-defined
34707 \begin_layout Standard
34708 To define custom commands for fractions, the command
34718 \begin_layout Plain Layout
34726 is used in the following scheme:
34729 \begin_layout Standard
34742 bracket}{fraction bar thickness}{style}
34743 \begin_inset Newline newline
34750 \begin_layout Plain Layout
34765 \begin_layout Plain Layout
34772 {numerator}{denominator}
34775 \begin_layout Standard
34776 The style is a number in the range of 0
34777 \begin_inset space \thinspace{}
34781 \begin_inset space \thinspace{}
34787 \begin_layout Standard
34789 \begin_inset Tabular
34790 <lyxtabular version="3" rows="5" columns="2">
34792 <column alignment="center" valignment="top" width="0">
34793 <column alignment="center" valignment="top" width="0">
34795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34798 \begin_layout Plain Layout
34804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34807 \begin_layout Plain Layout
34815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34818 \begin_layout Plain Layout
34824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34827 \begin_layout Plain Layout
34828 display style formula
34835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34838 \begin_layout Plain Layout
34844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34847 \begin_layout Plain Layout
34855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34858 \begin_layout Plain Layout
34864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34867 \begin_layout Plain Layout
34875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34878 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34887 \begin_layout Plain Layout
34901 \begin_layout Standard
34902 When no style is given, the size is adjusted to the surrounding environment
34903 like for the command
34912 \begin_layout Standard
34913 When no fraction bar thickness is given, the predefined value of 0.4
34914 \begin_inset space \thinspace{}
34920 \begin_layout Standard
34921 \begin_inset VSpace medskip
34924 For example, the commands
34937 \begin_inset CommandInset ref
34939 reference "sub:Fractions"
34943 are defined with the commands
34946 \begin_layout Standard
34955 genfrac{}{}{}{0}{#1}{#2}}
34958 \begin_layout Standard
34962 \begin_layout Standard
34971 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34974 \begin_layout Standard
34975 \begin_inset VSpace medskip
34978 To define a fraction where the fraction bar thickness can be given as optional
34979 argument, the following line is inserted to the LaTeX-preamble:
34982 \begin_layout Standard
34991 genfrac{}{}{#1}{}{#2}{#3}}
34994 \begin_layout Standard
34996 \begin_inset Formula \begin{align*}
34997 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34998 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
35002 As one can see, the distance of the numerator and the denominator to the
35003 fraction bar is round about three times the bar thickness.
35006 \begin_layout Subsection
35011 \begin_layout Plain Layout
35020 \begin_layout Standard
35021 To cancel formulas or formula parts, the LaTeX-package
35029 \begin_layout Plain Layout
35034 is part of every LaTeX standard installation.
35043 \begin_layout Plain Layout
35049 has to be loaded with the LaTeX-preamble line
35052 \begin_layout Standard
35057 usepackage[samesize]{cancel}
35060 \begin_layout Standard
35061 There are four ways to cancel formulas:
35064 \begin_layout Standard
35066 \begin_inset Tabular
35067 <lyxtabular version="3" rows="5" columns="2">
35069 <column alignment="center" valignment="top" width="0">
35070 <column alignment="center" valignment="top" width="0">
35072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35075 \begin_layout Plain Layout
35081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35084 \begin_layout Plain Layout
35086 \begin_inset Note Note
35089 \begin_layout Plain Layout
35096 are used here as spacer.
35108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35111 \begin_layout Plain Layout
35120 \begin_layout Plain Layout
35134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35137 \begin_layout Plain Layout
35138 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35151 \begin_layout Plain Layout
35160 \begin_layout Plain Layout
35174 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35177 \begin_layout Plain Layout
35178 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35191 \begin_layout Plain Layout
35200 \begin_layout Plain Layout
35214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35217 \begin_layout Plain Layout
35218 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35231 \begin_layout Plain Layout
35235 \begin_inset Formula $\to$
35246 \begin_layout Plain Layout
35260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35263 \begin_layout Plain Layout
35264 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35280 \begin_layout Standard
35287 is especially suitable to visualize the reduction of fractions within formulas:
35288 \begin_inset Formula \[
35289 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35296 \begin_layout Subsection
35297 Formulas in Section Headings
35298 \begin_inset CommandInset label
35300 name "sub:Formulas-in-Section"
35308 \begin_layout Plain Layout
35309 Formula ! in section headings
35317 \begin_layout Standard
35318 When formulas are used in section headings, the following has to be taken
35322 \begin_layout Standard
35323 \begin_inset Note Greyedout
35326 \begin_layout Plain Layout
35335 \begin_layout Plain Layout
35336 Packages ! hyperref
35341 support is enabled in the document settings dialog under
35344 \begin_inset space ~
35349 , PDF-bookmarks are created for every section heading in the table of contents.
35350 If a section heading contains formulas, they are incorrectly displayed
35351 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35360 \begin_layout Standard
35361 Both problems can be solved by inserting at the end of the section heading
35362 a short title with the menu
35364 Insert\SpecialChar \menuseparator
35366 \begin_inset space ~
35372 Short titles are used as alternative for multiline section headings to
35373 keep the table of contents clearly arranged.
35374 Only the short title appears in the table of contents and therefore also
35375 in the PDF-bookmark.
35378 \begin_layout Standard
35379 When formulas should be used in the table of contents but
35383 is used, one can use the following command in TeX-mode:
35386 \begin_layout Standard
35391 texorpdfstring{part}{alternative}
35395 \begin_layout Plain Layout
35406 \begin_layout Standard
35407 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35408 This can be characters, formulas, footnotes, but also cross-references.
35409 The alternative is used instead of the part for the bookmark.
35412 \begin_layout Standard
35413 Here are two example headings:
35414 \begin_inset VSpace -3mm
35421 \begin_layout Plain Layout
35433 \begin_layout Subsubsection
35434 Heading without formula in table of contents
35435 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35439 \begin_inset OptArg
35442 \begin_layout Plain Layout
35443 Heading without formula in table of contents
35451 \begin_layout Subsubsection
35452 Heading with formula in table of contents
35456 \begin_layout Plain Layout
35466 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35473 \begin_layout Plain Layout
35483 \begin_layout Standard
35487 \begin_layout Plain Layout
35496 In the first heading a short title was used, in the second one
35505 \begin_layout Standard
35506 To get the same formatting as for the other headings, the complete heading
35515 \begin_layout Plain Layout
35517 \begin_inset CommandInset ref
35519 reference "sub:Bold-Formulas"
35531 \begin_layout Subsection
35532 Formulas in multi-column Text
35536 \begin_layout Plain Layout
35537 Formula ! in multi-column text
35545 \begin_layout Standard
35546 Formulas in multi-column text are often too wide to fit into a column and
35547 thus need to be set over the whole page width.
35548 This is done by using the LaTeX-package
35556 \begin_layout Plain Layout
35561 is part of every LaTeX standard installation.
35570 \begin_layout Plain Layout
35571 Packages ! multicol
35576 , that is loaded with the LaTeX-preamble line
35579 \begin_layout Standard
35584 usepackage{multicol}
35587 \begin_layout Standard
35588 \begin_inset Note Greyedout
35591 \begin_layout Plain Layout
35592 Note herby that the setting
35595 \begin_inset space ~
35602 Document\SpecialChar \menuseparator
35608 \begin_inset space ~
35628 \begin_layout Standard
35629 Before the multi-column text the command
35632 \begin_layout Standard
35637 begin{multicols}{column number}
35640 \begin_layout Standard
35641 is written in TeX-mode.
35642 The column number is a number in the range of 2
35643 \begin_inset space \thinspace{}
35647 \begin_inset space \thinspace{}
35651 Before the formula the multi-column text is ended by inserting the command
35654 \begin_layout Standard
35662 \begin_layout Standard
35666 \begin_layout Standard
35667 Due to the command some space is automatically added before the formula.
35669 \begin_inset space \thinspace{}
35672 mm vertical space is inserted before the formula.
35673 When the formula style
35679 \begin_layout Plain Layout
35681 \begin_inset CommandInset ref
35683 reference "sec:Formula-Styles"
35695 \begin_inset space \thinspace{}
35698 mm space is inserted instead.
35701 \begin_layout Standard
35702 As example a multi-column text with a displayed formula:
35705 \begin_layout Standard
35711 \begin_layout Plain Layout
35715 begin{multicols}{2}
35720 Das Spektrum wird fouriertransformiert.
35721 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35722 , Lösungsmittel) zu trennen.
35723 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35724 nun das Aussehen des Ausgangssignals.
35725 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35726 über alle Phasen integrieren muss.
35728 \begin_inset Formula $S$
35731 unser normiertes Ausgangssignal und
35732 \begin_inset Formula $P$
35735 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35739 \begin_layout Plain Layout
35749 \begin_inset VSpace -6mm
35753 \begin_inset Formula \begin{equation}
35754 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35762 \begin_layout Plain Layout
35766 begin{multicols}{2}
35772 \begin_inset Formula $S_{0}$
35775 das Signal ohne Gradient ist und die Normierungsbedingung
35776 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35780 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35782 \begin_inset Formula $\nicefrac{\pi}{2}$
35786 \begin_inset space \thinspace{}
35789 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35790 das Signal zusätzlich abschwächt.
35791 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35793 \begin_inset Formula $T_{2}$
35799 \begin_layout Standard
35805 \begin_layout Plain Layout
35817 \begin_layout Subsection
35818 Formulas with Description of Variables
35822 \begin_layout Plain Layout
35823 Formula ! with description of variables
35831 \begin_layout Standard
35832 To describe variables within a formula, like in formula
35833 \begin_inset CommandInset ref
35835 reference "eq:within"
35844 \begin_inset Formula $n$
35848 \begin_inset space ~
35851 matrix is used with left aligned columns for the
35852 \begin_inset Formula $n$
35859 \begin_layout Plain Layout
35861 \begin_inset CommandInset ref
35863 reference "sec:Matrices"
35872 To set the description in a smaller size, before the matrix e.
35873 \begin_inset space \thinspace{}
35877 \begin_inset space \space{}
35890 \begin_layout Plain Layout
35892 \begin_inset CommandInset ref
35894 reference "sub:Font-Sizes"
35906 \begin_layout Standard
35907 When the formula style
35913 \begin_layout Plain Layout
35915 \begin_inset CommandInset ref
35917 reference "sec:Formula-Styles"
35938 \begin_layout Plain Layout
35945 only works in formulas with the style
35950 \begin_inset CommandInset ref
35952 reference "sub:Variable-Space"
35961 is inserted before and after the matrix to have the same separation of
35962 the matrix from the equation and the side margin.
35965 \begin_layout Standard
35966 When the formula style
35970 is used, the method described in
35971 \begin_inset CommandInset ref
35973 reference "sub:Flalign-Environment"
35977 is used to indent formulas.
35979 \begin_inset CommandInset ref
35981 reference "eq:within"
35985 consists of five columns whereas in the first two columns contain the equation,
35986 the third the matrix and the last one an empty TeX-brace.
35987 \begin_inset Formula \begin{flalign}
35988 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35989 \rho & \textrm{density}\\
35990 V & \textrm{volume}\\
35991 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35998 \begin_layout Subsection
35999 Upright small Greek Letters
36000 \begin_inset CommandInset label
36002 name "sub:Upright-small-Greek"
36010 \begin_layout Plain Layout
36011 Greek letters ! upright
36019 \begin_layout Standard
36020 Most of the math fonts only provide italic small Greek letters.
36021 But for symbols of elementary particles like pions and neutrinos, upright
36022 Greek letters are needed.
36031 \begin_layout Plain Layout
36036 is part of the LaTeX-package
36044 \begin_layout Plain Layout
36049 \begin_layout Plain Layout
36072 \begin_layout Plain Layout
36078 that is loaded with the LaTeX-preamble line
36081 \begin_layout Standard
36086 usepackage{upgreek}
36089 \begin_layout Standard
36095 \begin_layout Plain Layout
36105 \begin_inset Note Note
36108 \begin_layout Plain Layout
36109 The following table will only be displayed when the LaTeX-package
36118 They are created when the command for a small Greek letters is started
36124 For example the command
36131 \begin_inset Formula $\uptau$
36137 \begin_layout Standard
36138 With these commands reactions of elementary particles can be typeset:
36139 \begin_inset Formula \[
36140 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
36147 \begin_layout Standard
36148 The upright letters are more bold and wider than the italic ones.
36149 They should therefore not be used for units like
36150 \begin_inset Quotes eld
36154 \begin_inset Quotes erd
36160 \begin_layout Standard
36164 \begin_layout Plain Layout
36174 \begin_inset Note Note
36177 \begin_layout Plain Layout
36178 The following will be displayed when the LaTeX-package
36190 \begin_layout Standard
36191 You need to install the LaTeX-package
36195 to see the rest of this subsection in the output.
36198 \begin_layout Standard
36202 \begin_layout Plain Layout
36214 \begin_layout Subsection
36215 Text Characters in Formulas
36216 \begin_inset CommandInset label
36218 name "sub:Text-Characters-in"
36226 \begin_layout Plain Layout
36235 \begin_layout Standard
36236 In some cases you might want to insert text characters directly into formulas.
36237 When for example the centered dot · is often used in formulas like
36238 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36241 , one would have to insert the command
36251 \begin_layout Plain Layout
36253 \begin_inset CommandInset ref
36255 reference "sub:Binary-Operators"
36264 all the time, because this character is defined in all encodings as text
36266 But the encoding can be changed by this LaTeX-preamble line:
36269 \begin_layout Standard
36274 Declare Inputtext{183}{
36284 f\SpecialChar \textcompwordmark{}
36288 \begin_layout Standard
36289 The character encoding (menu
36291 Document\SpecialChar \menuseparator
36292 Settings\SpecialChar \menuseparator
36295 ) specifies what character appears when a keyboard key is pressed.
36296 When the key for the character '·' is pressed, internally the command
36303 But this command is not available in a formula so that you would get LaTeX-erro
36305 With the changed encoding the right command is chosen automatically, depending
36306 on if the character was inserted into a formula or not.
36309 \begin_layout Standard
36310 The encoding of several characters is saved in definition files.
36311 Fore example the encoding
36315 is defined in the file
36319 that is in the installation folder of LaTeX.
36320 Encodings should only be changed via the LaTeX-preamble and not in the
36322 Otherwise own documents could not be edited by other LyX users working
36323 on other computers.
36326 \begin_layout Standard
36327 \begin_inset VSpace medskip
36330 Besides the centered dot, in this document the degree sign ° is defined
36331 with the following LaTeX-preamble line so that it can directly be inserted
36335 \begin_layout Standard
36340 DeclareInputtext{176}{
36350 f\SpecialChar \textcompwordmark{}
36354 \begin_layout Standard
36355 \begin_inset Newpage newpage
36361 \begin_layout Section
36367 \begin_layout Plain Layout
36376 \begin_layout Standard
36377 This section is a summary of the most important typographic rules, listed
36382 \begin_layout Plain Layout
36383 This collection was partly taken from the German semi-official dictionary
36385 \begin_inset Quotes eld
36389 \begin_inset Quotes erd
36393 \begin_inset CommandInset citation
36399 that lists some of the ISO rules.
36400 More rules are listed in
36401 \begin_inset CommandInset citation
36415 \begin_layout Itemize
36424 \begin_layout Plain Layout
36425 done with font styles, see
36426 \begin_inset CommandInset ref
36428 reference "sub:Font-Styles"
36437 , no matter if they appear in italic text: 30
36438 \begin_inset space \thinspace{}
36442 \begin_inset Newline newline
36445 Between the value and the unit is the smallest space, see
36446 \begin_inset CommandInset ref
36448 reference "sub:Predefined-Space"
36453 \begin_inset Newline newline
36456 This convention is automatically fulfilled when the command
36463 When it is entered to a formula, two boxes appear.
36464 In the first one the value is inserted, in the second one the unit, and
36466 \begin_inset Formula $\unit[30]{km/h}$
36470 \begin_inset space \thinspace{}
36480 is not a real LaTeX command but the command
36486 , therefore you cannot use it in TeX code.
36489 \begin_layout Itemize
36490 Percent and perthousand signs are set like physical units:
36491 \begin_inset Newline newline
36495 \begin_inset space \thinspace{}
36501 \begin_layout Itemize
36502 The degree sign follows directly on the value: 15°, but not when it is used
36504 \begin_inset space \thinspace{}
36510 \begin_layout Itemize
36511 In numbers with more than four digits the smallest space is inserted before
36512 every third digit to group them:
36522 \begin_inset space \thinspace{}
36526 \begin_inset space \thinspace{}
36532 \begin_layout Itemize
36533 For dimensions like 120×90×40
36534 \begin_inset space \thinspace{}
36537 cm the multiplication sign
36538 \begin_inset Quotes eld
36542 \begin_inset Quotes erd
36546 It is available either via the command
36554 Insert\SpecialChar \menuseparator
36555 Special Character\SpecialChar \menuseparator
36561 \begin_layout Itemize
36562 Functions with names consisting of several letters are set upright to avoid
36564 \begin_inset CommandInset ref
36566 reference "sub:Predefined-Functions"
36573 \begin_layout Itemize
36574 Indices consisting of several letters, are set upright:
36575 \begin_inset Formula $E_{\mathrm{kin}}$
36579 \begin_inset Newline newline
36582 Components of matrices are set italic:
36583 \begin_inset Formula $\hat{H}_{kl}$
36589 \begin_layout Itemize
36590 The differentiation/integration operator 'd', the Euler's number 'e' and
36591 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36595 \begin_layout Itemize
36596 The character that denotes a
36600 transformation is inserted either by the command
36608 \begin_layout Plain Layout
36625 \begin_layout Plain Layout
36635 Insert\SpecialChar \menuseparator
36636 Special Character\SpecialChar \menuseparator
36637 Symbols\SpecialChar \menuseparator
36639 \begin_inset space ~
36645 \begin_inset Formula $\mathscr{F}$
36649 \begin_inset Newline newline
36652 To be able to use the command
36658 , the LaTeX package
36666 \begin_layout Plain Layout
36667 Packages ! mathrsfs
36672 needs to be loaded with the LaTeX-preamble line
36676 usepackage{mathrsfs}
36681 \begin_layout Standard
36682 \begin_inset Newpage newpage
36688 \begin_layout Section
36693 \begin_layout Plain Layout
36702 \begin_layout Standard
36703 Some characters and symbols can be created with several commands.
36704 Here is a list of the synonym commands:
36707 \begin_layout Standard
36708 \begin_inset VSpace bigskip
36712 \begin_inset space \hfill{}
36716 \begin_inset Tabular
36717 <lyxtabular version="3" rows="12" columns="2">
36719 <column alignment="center" valignment="top" width="0pt">
36720 <column alignment="center" valignment="top" width="0pt">
36722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36725 \begin_layout Plain Layout
36731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36734 \begin_layout Plain Layout
36736 \begin_inset Note Note
36739 \begin_layout Plain Layout
36746 is only used as spacer.
36758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36761 \begin_layout Plain Layout
36769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36772 \begin_layout Plain Layout
36776 \begin_layout Plain Layout
36789 \begin_layout Plain Layout
36803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36806 \begin_layout Plain Layout
36814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36817 \begin_layout Plain Layout
36827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36830 \begin_layout Plain Layout
36838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36841 \begin_layout Plain Layout
36851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36854 \begin_layout Plain Layout
36862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36865 \begin_layout Plain Layout
36873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36876 \begin_layout Plain Layout
36884 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36887 \begin_layout Plain Layout
36895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36898 \begin_layout Plain Layout
36906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36909 \begin_layout Plain Layout
36919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36922 \begin_layout Plain Layout
36930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36933 \begin_layout Plain Layout
36943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36946 \begin_layout Plain Layout
36954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36957 \begin_layout Plain Layout
36967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36970 \begin_layout Plain Layout
36978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36981 \begin_layout Plain Layout
36991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36994 \begin_layout Plain Layout
37002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37005 \begin_layout Plain Layout
37013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37016 \begin_layout Plain Layout
37024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37027 \begin_layout Plain Layout
37039 \begin_inset space \hfill{}
37043 \begin_inset Tabular
37044 <lyxtabular version="3" rows="12" columns="2">
37046 <column alignment="center" valignment="top" width="0pt">
37047 <column alignment="center" valignment="top" width="0pt">
37049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37052 \begin_layout Plain Layout
37058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37061 \begin_layout Plain Layout
37069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37072 \begin_layout Plain Layout
37080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37083 \begin_layout Plain Layout
37095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37098 \begin_layout Plain Layout
37106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37109 \begin_layout Plain Layout
37119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37122 \begin_layout Plain Layout
37130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37133 \begin_layout Plain Layout
37143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37146 \begin_layout Plain Layout
37154 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37157 \begin_layout Plain Layout
37165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37168 \begin_layout Plain Layout
37176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37179 \begin_layout Plain Layout
37187 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37190 \begin_layout Plain Layout
37198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37201 \begin_layout Plain Layout
37211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37214 \begin_layout Plain Layout
37222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37225 \begin_layout Plain Layout
37235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37238 \begin_layout Plain Layout
37246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37249 \begin_layout Plain Layout
37259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37262 \begin_layout Plain Layout
37270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37273 \begin_layout Plain Layout
37283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37286 \begin_layout Plain Layout
37294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37297 \begin_layout Plain Layout
37307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37310 \begin_layout Plain Layout
37318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37321 \begin_layout Plain Layout
37335 \begin_inset space \hfill{}
37341 \begin_layout Standard
37342 \begin_inset Newpage newpage
37348 \begin_layout Bibliography
37349 \begin_inset CommandInset bibitem
37350 LatexCommand bibitem
37362 The LaTeX Companion
37365 Addison Wesley, 2004
37368 \begin_layout Bibliography
37369 \begin_inset CommandInset bibitem
37370 LatexCommand bibitem
37376 \begin_inset CommandInset href
37379 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
37383 of LaTeX's math abilities
37386 \begin_layout Bibliography
37387 \begin_inset CommandInset bibitem
37388 LatexCommand bibitem
37394 \begin_inset CommandInset href
37397 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
37405 \begin_layout Plain Layout
37417 \begin_layout Bibliography
37418 \begin_inset CommandInset bibitem
37419 LatexCommand bibitem
37425 \begin_inset CommandInset href
37428 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
37432 of all symbols available with LaTeX-packages
37435 \begin_layout Bibliography
37436 \begin_inset CommandInset bibitem
37437 LatexCommand bibitem
37443 \begin_inset CommandInset href
37445 name "Documentation"
37446 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
37450 of the LaTeX-package
37458 \begin_layout Plain Layout
37459 Packages ! hyperref
37467 \begin_layout Bibliography
37468 \begin_inset CommandInset bibitem
37469 LatexCommand bibitem
37475 \begin_inset CommandInset href
37477 name "Documentation"
37478 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
37482 of the LaTeX-package
37490 \begin_layout Plain Layout
37499 \begin_layout Bibliography
37500 \begin_inset CommandInset bibitem
37501 LatexCommand bibitem
37507 \begin_inset CommandInset href
37510 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
37521 \begin_inset CommandInset ref
37523 reference "sub:Operator-Limits"
37531 \begin_layout Plain Layout
37542 \begin_layout Bibliography
37543 \begin_inset CommandInset bibitem
37544 LatexCommand bibitem
37555 Auflage, Duden 2001
37558 \begin_layout Bibliography
37559 \begin_inset CommandInset bibitem
37560 LatexCommand bibitem
37566 \begin_inset CommandInset href
37569 target "http://physics.nist.gov/Document/checklist.pdf"
37573 for reviewing manuscripts
37576 \begin_layout Standard
37577 \begin_inset CommandInset index_print
37578 LatexCommand printindex