1 #LyX 1.6.5 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.
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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
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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
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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,
549 \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
829 \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 Within a formula the size can only be changed for symbols or letters in
18969 To do this, the size command is inserted in mathematical text.
18970 All following characters until the end of the mathematical text or until
18971 another size command will have the selected size.
18973 \begin_inset VSpace -2mm
18979 \begin_layout Standard
18983 \begin_layout Plain Layout
18993 \begin_inset Formula \[
18994 A=\frac{B}{c}\cdot\maltese\]
18999 \begin_inset Formula \[
19000 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
19008 \begin_layout Plain Layout
19020 \begin_layout Standard
19021 \begin_inset VSpace medskip
19024 Before both formulas the command
19031 The command for the second formula is:
19032 \begin_inset Newline newline
19043 \begin_layout Plain Layout
19058 \begin_layout Plain Layout
19073 \begin_layout Plain Layout
19088 \begin_layout Plain Layout
19098 \begin_inset Formula $\to$
19102 \begin_inset Formula $\to$
19106 \begin_inset Newline newline
19110 \begin_inset space \hspace*{}
19124 \begin_layout Plain Layout
19139 \begin_layout Plain Layout
19154 \begin_layout Plain Layout
19166 \begin_layout Standard
19167 If a symbol cannot be displayed in different sizes, it will always be displayed
19168 in the default size.
19171 \begin_layout Section
19176 \begin_layout Plain Layout
19185 \begin_layout Standard
19186 All Greek letters can also be inserted via the toolbar button
19187 \begin_inset Graphics
19188 filename ../images/math/alpha.png
19196 \begin_layout Subsection
19201 \begin_layout Plain Layout
19202 Greek letters ! small
19210 \begin_layout Standard
19211 \begin_inset space \hfill{}
19215 \begin_inset Tabular
19216 <lyxtabular version="3" rows="11" columns="2">
19218 <column alignment="center" valignment="top" width="0pt">
19219 <column alignment="center" valignment="top" width="0pt">
19221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19224 \begin_layout Plain Layout
19230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19233 \begin_layout Plain Layout
19241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19244 \begin_layout Plain Layout
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19255 \begin_layout Plain Layout
19256 \begin_inset Formula $\alpha$
19266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19269 \begin_layout Plain Layout
19277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19280 \begin_layout Plain Layout
19281 \begin_inset Formula $\beta$
19291 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19294 \begin_layout Plain Layout
19302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19305 \begin_layout Plain Layout
19306 \begin_inset Formula $\gamma$
19316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19319 \begin_layout Plain Layout
19327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19330 \begin_layout Plain Layout
19331 \begin_inset Formula $\delta$
19341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19344 \begin_layout Plain Layout
19352 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19355 \begin_layout Plain Layout
19356 \begin_inset Formula $\epsilon$
19366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19369 \begin_layout Plain Layout
19377 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19380 \begin_layout Plain Layout
19381 \begin_inset Formula $\varepsilon$
19391 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19394 \begin_layout Plain Layout
19402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19405 \begin_layout Plain Layout
19406 \begin_inset Formula $\zeta$
19416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19419 \begin_layout Plain Layout
19427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19430 \begin_layout Plain Layout
19431 \begin_inset Formula $\eta$
19441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19444 \begin_layout Plain Layout
19452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19455 \begin_layout Plain Layout
19456 \begin_inset Formula $\theta$
19466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19469 \begin_layout Plain Layout
19477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19480 \begin_layout Plain Layout
19481 \begin_inset Formula $\vartheta$
19495 \begin_inset space \hfill{}
19499 \begin_inset Tabular
19500 <lyxtabular version="3" rows="12" columns="2">
19502 <column alignment="center" valignment="top" width="0pt">
19503 <column alignment="center" valignment="top" width="0pt">
19505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19508 \begin_layout Plain Layout
19514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19517 \begin_layout Plain Layout
19525 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19528 \begin_layout Plain Layout
19536 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19539 \begin_layout Plain Layout
19540 \begin_inset Formula $\iota$
19550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19553 \begin_layout Plain Layout
19561 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19564 \begin_layout Plain Layout
19565 \begin_inset Formula $\kappa$
19575 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19578 \begin_layout Plain Layout
19586 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19589 \begin_layout Plain Layout
19590 \begin_inset Formula $\varkappa$
19600 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19603 \begin_layout Plain Layout
19611 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19614 \begin_layout Plain Layout
19615 \begin_inset Formula $\lambda$
19625 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19628 \begin_layout Plain Layout
19636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19639 \begin_layout Plain Layout
19640 \begin_inset Formula $\mu$
19650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19653 \begin_layout Plain Layout
19661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19664 \begin_layout Plain Layout
19665 \begin_inset Formula $\nu$
19675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19678 \begin_layout Plain Layout
19686 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19689 \begin_layout Plain Layout
19690 \begin_inset Formula $\xi$
19700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19703 \begin_layout Plain Layout
19709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19712 \begin_layout Plain Layout
19713 \begin_inset Formula $o$
19723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19726 \begin_layout Plain Layout
19734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19737 \begin_layout Plain Layout
19738 \begin_inset Formula $\pi$
19748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19751 \begin_layout Plain Layout
19759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19762 \begin_layout Plain Layout
19763 \begin_inset Formula $\varpi$
19773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19776 \begin_layout Plain Layout
19784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19787 \begin_layout Plain Layout
19788 \begin_inset Formula $\rho$
19802 \begin_inset space \hfill{}
19806 \begin_inset Tabular
19807 <lyxtabular version="3" rows="11" columns="2">
19809 <column alignment="center" valignment="top" width="0pt">
19810 <column alignment="center" valignment="top" width="0pt">
19812 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19815 \begin_layout Plain Layout
19821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19824 \begin_layout Plain Layout
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19847 \begin_inset Formula $\varrho$
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19871 \begin_layout Plain Layout
19872 \begin_inset Formula $\sigma$
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19885 \begin_layout Plain Layout
19893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19896 \begin_layout Plain Layout
19897 \begin_inset Formula $\varsigma$
19907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19910 \begin_layout Plain Layout
19918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19921 \begin_layout Plain Layout
19922 \begin_inset Formula $\tau$
19932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19935 \begin_layout Plain Layout
19943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19946 \begin_layout Plain Layout
19947 \begin_inset Formula $\upsilon$
19957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19960 \begin_layout Plain Layout
19968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19971 \begin_layout Plain Layout
19972 \begin_inset Formula $\phi$
19982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19985 \begin_layout Plain Layout
19993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19996 \begin_layout Plain Layout
19997 \begin_inset Formula $\varphi$
20007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20010 \begin_layout Plain Layout
20018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20021 \begin_layout Plain Layout
20022 \begin_inset Formula $\chi$
20032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20035 \begin_layout Plain Layout
20043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20046 \begin_layout Plain Layout
20047 \begin_inset Formula $\psi$
20057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20060 \begin_layout Plain Layout
20068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20071 \begin_layout Plain Layout
20072 \begin_inset Formula $\omega$
20086 \begin_inset space \hfill{}
20092 \begin_layout Standard
20093 \begin_inset VSpace medskip
20099 \begin_layout Standard
20100 How to create upright Greek letters is explained in
20101 \begin_inset CommandInset ref
20103 reference "sub:Upright-small-Greek"
20110 \begin_layout Subsection
20115 \begin_layout Plain Layout
20116 Greek letters ! big
20124 \begin_layout Standard
20125 \begin_inset space \hfill{}
20129 \begin_inset Tabular
20130 <lyxtabular version="3" rows="7" columns="2">
20132 <column alignment="center" valignment="top" width="0pt">
20133 <column alignment="center" valignment="top" width="0pt">
20135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20138 \begin_layout Plain Layout
20144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20147 \begin_layout Plain Layout
20155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20158 \begin_layout Plain Layout
20166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20169 \begin_layout Plain Layout
20170 \begin_inset Formula $\Gamma$
20180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20183 \begin_layout Plain Layout
20191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20194 \begin_layout Plain Layout
20195 \begin_inset Formula $\Delta$
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20208 \begin_layout Plain Layout
20216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20219 \begin_layout Plain Layout
20220 \begin_inset Formula $\Theta$
20230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20233 \begin_layout Plain Layout
20241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20244 \begin_layout Plain Layout
20245 \begin_inset Formula $\Lambda$
20255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20258 \begin_layout Plain Layout
20266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20269 \begin_layout Plain Layout
20270 \begin_inset Formula $\Xi$
20280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20283 \begin_layout Plain Layout
20291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20294 \begin_layout Plain Layout
20295 \begin_inset Formula $\Pi$
20309 \begin_inset space \hfill{}
20313 \begin_inset Tabular
20314 <lyxtabular version="3" rows="6" columns="2">
20316 <column alignment="center" valignment="top" width="0pt">
20317 <column alignment="center" valignment="top" width="0pt">
20319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20322 \begin_layout Plain Layout
20328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20331 \begin_layout Plain Layout
20339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20342 \begin_layout Plain Layout
20350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20353 \begin_layout Plain Layout
20354 \begin_inset Formula $\Sigma$
20364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20367 \begin_layout Plain Layout
20375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20378 \begin_layout Plain Layout
20379 \begin_inset Formula $\Upsilon$
20389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20392 \begin_layout Plain Layout
20400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20403 \begin_layout Plain Layout
20404 \begin_inset Formula $\Phi$
20414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20417 \begin_layout Plain Layout
20425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20428 \begin_layout Plain Layout
20429 \begin_inset Formula $\Psi$
20439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20442 \begin_layout Plain Layout
20450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20453 \begin_layout Plain Layout
20454 \begin_inset Formula $\Omega$
20468 \begin_inset space \hfill{}
20474 \begin_layout Standard
20475 \begin_inset VSpace medskip
20478 That the big Greek letters appear upright is caused by a design bug when
20480 To get correct italic big letters, begin every command with
20485 For example the command
20492 \begin_inset Formula $\varGamma$
20498 \begin_layout Subsection
20503 \begin_layout Plain Layout
20504 Greek letters ! bold
20512 \begin_layout Standard
20513 Greek letters cannot be set with different font styles like Latin letters.
20514 They can only be made bold with the command
20524 \begin_layout Plain Layout
20535 \begin_layout Standard
20537 \begin_inset Tabular
20538 <lyxtabular version="3" rows="3" columns="2">
20540 <column alignment="center" valignment="top" width="0">
20541 <column alignment="center" valignment="top" width="0">
20543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20546 \begin_layout Plain Layout
20552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20555 \begin_layout Plain Layout
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20581 \begin_layout Plain Layout
20582 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20595 \begin_layout Plain Layout
20607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20610 \begin_layout Plain Layout
20611 \begin_inset Formula $\theta\boldsymbol{\theta}$
20627 \begin_layout Section
20632 \begin_layout Plain Layout
20645 \begin_layout Plain Layout
20646 A list with all symbols of most of the LaTeX-packages can be found in
20647 \begin_inset CommandInset citation
20662 \begin_layout Plain Layout
20670 \begin_inset Note Note
20673 \begin_layout Plain Layout
20676 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20679 \begin_layout Plain Layout
20682 texorpdfstring is in section
20683 \begin_inset CommandInset ref
20685 reference "sub:Formulas-in-Section"
20698 \begin_layout Plain Layout
20707 \begin_layout Standard
20708 Many of the symbols listed in this section can also be inserted via the
20710 \begin_inset Graphics
20711 filename ../images/math/nabla.png
20717 \begin_inset Graphics
20718 filename ../images/math/digamma.png
20726 \begin_layout Subsection
20727 Mathematical Symbols
20728 \begin_inset CommandInset label
20730 name "sub:Mathematical-Symbols"
20738 \begin_layout Plain Layout
20739 Symbols ! mathematical
20747 \begin_layout Standard
20748 \begin_inset space \hfill{}
20752 \begin_inset Tabular
20753 <lyxtabular version="3" rows="10" columns="2">
20755 <column alignment="center" valignment="top" width="0pt">
20756 <column alignment="center" valignment="top" width="0pt">
20758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20761 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20770 \begin_layout Plain Layout
20778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20781 \begin_layout Plain Layout
20789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20792 \begin_layout Plain Layout
20793 \begin_inset Formula $\neg$
20803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20806 \begin_layout Plain Layout
20814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20817 \begin_layout Plain Layout
20818 \begin_inset Formula $\Im$
20828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20831 \begin_layout Plain Layout
20839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20842 \begin_layout Plain Layout
20843 \begin_inset Formula $\Re$
20853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20856 \begin_layout Plain Layout
20864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20867 \begin_layout Plain Layout
20868 \begin_inset Formula $\aleph$
20878 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20881 \begin_layout Plain Layout
20889 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20892 \begin_layout Plain Layout
20893 \begin_inset Formula $\partial$
20903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20906 \begin_layout Plain Layout
20914 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20917 \begin_layout Plain Layout
20918 \begin_inset Formula $\infty$
20928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20931 \begin_layout Plain Layout
20939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20942 \begin_layout Plain Layout
20943 \begin_inset Formula $\wp$
20953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20956 \begin_layout Plain Layout
20964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20967 \begin_layout Plain Layout
20968 \begin_inset Formula $\imath$
20978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20981 \begin_layout Plain Layout
20989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20992 \begin_layout Plain Layout
20993 \begin_inset Formula $\jmath$
21007 \begin_inset space \hfill{}
21011 \begin_inset Tabular
21012 <lyxtabular version="3" rows="10" columns="2">
21014 <column alignment="center" valignment="top" width="0pt">
21015 <column alignment="center" valignment="top" width="0pt">
21017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21020 \begin_layout Plain Layout
21026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21029 \begin_layout Plain Layout
21031 \begin_inset Note Note
21034 \begin_layout Plain Layout
21041 is only used as spacer.
21053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21056 \begin_layout Plain Layout
21064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21067 \begin_layout Plain Layout
21068 \begin_inset Formula $\forall$
21078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21081 \begin_layout Plain Layout
21089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21092 \begin_layout Plain Layout
21093 \begin_inset Formula $\exists$
21103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21106 \begin_layout Plain Layout
21114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21117 \begin_layout Plain Layout
21118 \begin_inset Formula $\nexists$
21128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21131 \begin_layout Plain Layout
21139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21142 \begin_layout Plain Layout
21143 \begin_inset Formula $\emptyset$
21153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21156 \begin_layout Plain Layout
21164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21167 \begin_layout Plain Layout
21168 \begin_inset Formula $\varnothing$
21178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21181 \begin_layout Plain Layout
21189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21192 \begin_layout Plain Layout
21193 \begin_inset Formula $\dag$
21203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21206 \begin_layout Plain Layout
21214 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21217 \begin_layout Plain Layout
21218 \begin_inset Formula $\ddag$
21228 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21231 \begin_layout Plain Layout
21239 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21242 \begin_layout Plain Layout
21246 \begin_layout Plain Layout
21256 \begin_inset Formula $\complement$
21263 \begin_layout Plain Layout
21277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21280 \begin_layout Plain Layout
21288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21291 \begin_layout Plain Layout
21292 \begin_inset Formula $\Bbbk$
21306 \begin_inset space \hfill{}
21310 \begin_inset Tabular
21311 <lyxtabular version="3" rows="10" columns="2">
21313 <column alignment="center" valignment="top" width="0pt">
21314 <column alignment="center" valignment="top" width="0pt">
21316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21319 \begin_layout Plain Layout
21325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21328 \begin_layout Plain Layout
21336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21339 \begin_layout Plain Layout
21347 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21350 \begin_layout Plain Layout
21351 \begin_inset Formula $\prime$
21361 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21364 \begin_layout Plain Layout
21372 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21375 \begin_layout Plain Layout
21376 \begin_inset Formula $\backprime$
21386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21389 \begin_layout Plain Layout
21397 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21400 \begin_layout Plain Layout
21401 \begin_inset Formula $\mho$
21411 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21414 \begin_layout Plain Layout
21422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21425 \begin_layout Plain Layout
21426 \begin_inset Formula $\triangle$
21436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21439 \begin_layout Plain Layout
21447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21450 \begin_layout Plain Layout
21451 \begin_inset Formula $\angle$
21461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21464 \begin_layout Plain Layout
21472 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21475 \begin_layout Plain Layout
21476 \begin_inset Formula $\measuredangle$
21486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21500 \begin_layout Plain Layout
21501 \begin_inset Formula $\sphericalangle$
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21525 \begin_layout Plain Layout
21526 \begin_inset Formula $\top$
21536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21539 \begin_layout Plain Layout
21547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21550 \begin_layout Plain Layout
21551 \begin_inset Formula $\bot$
21565 \begin_inset space \hfill{}
21571 \begin_layout Subsection
21572 Miscellaneous Symbols
21573 \begin_inset CommandInset label
21575 name "sub:Miscellaneous-Symbols"
21583 \begin_layout Plain Layout
21584 Symbols ! miscellaneous
21592 \begin_layout Standard
21595 \begin_inset Tabular
21596 <lyxtabular version="3" rows="10" columns="2">
21598 <column alignment="center" valignment="top" width="0pt">
21599 <column alignment="center" valignment="top" width="0pt">
21601 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21604 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21613 \begin_layout Plain Layout
21621 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21624 \begin_layout Plain Layout
21632 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21635 \begin_layout Plain Layout
21636 \begin_inset Formula $\flat$
21646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21649 \begin_layout Plain Layout
21657 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21660 \begin_layout Plain Layout
21661 \begin_inset Formula $\natural$
21671 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21674 \begin_layout Plain Layout
21682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21685 \begin_layout Plain Layout
21686 \begin_inset Formula $\sharp$
21696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21699 \begin_layout Plain Layout
21707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21710 \begin_layout Plain Layout
21711 \begin_inset Formula $\surd$
21721 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21724 \begin_layout Plain Layout
21732 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21735 \begin_layout Plain Layout
21736 \begin_inset Formula $\checkmark$
21746 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21749 \begin_layout Plain Layout
21757 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21760 \begin_layout Plain Layout
21761 \begin_inset Formula $\yen$
21771 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21774 \begin_layout Plain Layout
21782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21785 \begin_layout Plain Layout
21786 \begin_inset Formula $\pounds$
21796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21799 \begin_layout Plain Layout
21805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21808 \begin_layout Plain Layout
21809 \begin_inset Formula $\$$
21819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21822 \begin_layout Plain Layout
21828 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21831 \begin_layout Plain Layout
21832 \begin_inset Formula $§$
21846 \begin_inset Tabular
21847 <lyxtabular version="3" rows="10" columns="2">
21849 <column alignment="center" valignment="top" width="0">
21850 <column alignment="center" valignment="top" width="0">
21852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21855 \begin_layout Plain Layout
21861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21875 \begin_layout Plain Layout
21883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21886 \begin_layout Plain Layout
21887 \begin_inset Formula $\hbar$
21897 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21900 \begin_layout Plain Layout
21908 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21911 \begin_layout Plain Layout
21912 \begin_inset Formula $\hslash$
21922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21925 \begin_layout Plain Layout
21933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21936 \begin_layout Plain Layout
21937 \begin_inset Formula $\clubsuit$
21947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21950 \begin_layout Plain Layout
21958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21961 \begin_layout Plain Layout
21962 \begin_inset Formula $\spadesuit$
21972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21975 \begin_layout Plain Layout
21983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21986 \begin_layout Plain Layout
21987 \begin_inset Formula $\bigstar$
21997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22000 \begin_layout Plain Layout
22008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22011 \begin_layout Plain Layout
22012 \begin_inset Formula $\blacklozenge$
22022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22025 \begin_layout Plain Layout
22033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22036 \begin_layout Plain Layout
22037 \begin_inset Formula $\blacktriangle$
22047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22050 \begin_layout Plain Layout
22058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22061 \begin_layout Plain Layout
22062 \begin_inset Formula $\blacktriangledown$
22072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22075 \begin_layout Plain Layout
22083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22086 \begin_layout Plain Layout
22087 \begin_inset Formula $\bullet$
22101 \begin_inset Tabular
22102 <lyxtabular version="3" rows="10" columns="2">
22104 <column alignment="center" valignment="top" width="0pt">
22105 <column alignment="center" valignment="top" width="0pt">
22107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22110 \begin_layout Plain Layout
22116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22119 \begin_layout Plain Layout
22127 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22130 \begin_layout Plain Layout
22138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22141 \begin_layout Plain Layout
22142 \begin_inset Formula $\diamondsuit$
22152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22155 \begin_layout Plain Layout
22163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22166 \begin_layout Plain Layout
22167 \begin_inset Formula $\Diamond$
22177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22180 \begin_layout Plain Layout
22188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22191 \begin_layout Plain Layout
22192 \begin_inset Formula $\heartsuit$
22202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22205 \begin_layout Plain Layout
22213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22216 \begin_layout Plain Layout
22217 \begin_inset Formula $\P$
22227 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22230 \begin_layout Plain Layout
22238 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22241 \begin_layout Plain Layout
22242 \begin_inset Formula $\copyright$
22252 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22255 \begin_layout Plain Layout
22263 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22266 \begin_layout Plain Layout
22267 \begin_inset Formula $\circledR$
22277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22280 \begin_layout Plain Layout
22288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22291 \begin_layout Plain Layout
22292 \begin_inset Formula $\maltese$
22302 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22305 \begin_layout Plain Layout
22313 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22316 \begin_layout Plain Layout
22317 \begin_inset Formula $\diagup$
22327 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22330 \begin_layout Plain Layout
22338 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22341 \begin_layout Plain Layout
22342 \begin_inset Formula $\diagdown$
22358 \begin_layout Standard
22359 \begin_inset VSpace medskip
22362 More symbols are listed in
22363 \begin_inset CommandInset ref
22365 reference "sub:Miscellaneous-special-Characters"
22372 \begin_layout Standard
22373 Some symbols can be displayed in different sizes, see
22374 \begin_inset CommandInset ref
22376 reference "sub:Font-Sizes"
22383 \begin_layout Subsection
22388 \begin_layout Plain Layout
22389 Symbols ! Euro-symbol
22398 \begin_layout Plain Layout
22405 \begin_layout Plain Layout
22422 \begin_layout Standard
22423 To use the Euro symbol in formulas, the LaTeX-package
22431 \begin_layout Plain Layout
22437 must be installed and loaded with the LaTeX-preamble line
22440 \begin_layout Standard
22445 usepackage[gennarrow]{eurosym}
22448 \begin_layout Standard
22449 The Euro symbol can now be inserted with the command
22459 \begin_layout Plain Layout
22470 \begin_layout Standard
22471 The Euro symbol can directly be inserted with the € key in mathematical
22472 text, without having
22487 can also be inserted in TeX-mode.
22488 The official currency symbol can then be inserted with the command
22498 \begin_layout Plain Layout
22506 , that is only available in TeX-mode.
22509 \begin_layout Standard
22513 \begin_layout Plain Layout
22523 \begin_inset Note Note
22526 \begin_layout Plain Layout
22527 The following table will only be displayed when the LaTeX-package
22539 \begin_layout Standard
22540 An overview about the different Euro symbols:
22543 \begin_layout Standard
22545 \begin_inset Tabular
22546 <lyxtabular version="3" rows="4" columns="3">
22548 <column alignment="center" valignment="top" width="0pt">
22549 <column alignment="center" valignment="top" width="0pt">
22550 <column alignment="center" valignment="top" width="0pt">
22552 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22555 \begin_layout Plain Layout
22561 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22564 \begin_layout Plain Layout
22570 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22573 \begin_layout Plain Layout
22581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22584 \begin_layout Plain Layout
22590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22593 \begin_layout Plain Layout
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22604 \begin_layout Plain Layout
22605 \begin_inset Formula $\euro$
22615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22618 \begin_layout Plain Layout
22624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22627 \begin_layout Plain Layout
22633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22636 \begin_layout Plain Layout
22637 \begin_inset Formula $\mbox{€}$
22647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22650 \begin_layout Plain Layout
22656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22659 \begin_layout Plain Layout
22667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22670 \begin_layout Plain Layout
22674 \begin_layout Plain Layout
22696 \begin_layout Standard
22700 \begin_layout Plain Layout
22710 \begin_inset Note Note
22713 \begin_layout Plain Layout
22714 The following will be displayed when the LaTeX-package
22726 \begin_layout Standard
22727 You need to install the LaTeX-package
22731 to see the rest of this subsection in the output.
22734 \begin_layout Standard
22738 \begin_layout Plain Layout
22750 \begin_layout Standard
22751 \begin_inset Newpage newpage
22757 \begin_layout Section
22759 \begin_inset CommandInset label
22761 name "sec:Relations"
22769 \begin_layout Plain Layout
22779 \begin_layout Plain Layout
22784 \begin_layout Plain Layout
22795 \begin_layout Plain Layout
22810 \begin_layout Standard
22811 All relations can also be inserted via the toolbar button
22812 \begin_inset Graphics
22813 filename ../images/math/leq.png
22821 \begin_layout Standard
22822 \begin_inset space \hfill{}
22826 \begin_inset Tabular
22827 <lyxtabular version="3" rows="17" columns="2">
22829 <column alignment="center" valignment="top" width="0pt">
22830 <column alignment="center" valignment="top" width="0pt">
22832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22835 \begin_layout Plain Layout
22841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22844 \begin_layout Plain Layout
22852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22855 \begin_layout Plain Layout
22861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22864 \begin_layout Plain Layout
22865 \begin_inset Formula $<$
22875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22878 \begin_layout Plain Layout
22886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22889 \begin_layout Plain Layout
22890 \begin_inset Formula $\le$
22900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22903 \begin_layout Plain Layout
22911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22914 \begin_layout Plain Layout
22915 \begin_inset Formula $\ll$
22925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22928 \begin_layout Plain Layout
22936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22939 \begin_layout Plain Layout
22940 \begin_inset Formula $\prec$
22950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22953 \begin_layout Plain Layout
22961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22964 \begin_layout Plain Layout
22965 \begin_inset Formula $\preceq$
22975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22978 \begin_layout Plain Layout
22986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22989 \begin_layout Plain Layout
22990 \begin_inset Formula $\subset$
23000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23003 \begin_layout Plain Layout
23011 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23014 \begin_layout Plain Layout
23015 \begin_inset Formula $\subseteq$
23025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23028 \begin_layout Plain Layout
23036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23039 \begin_layout Plain Layout
23040 \begin_inset Formula $\sqsubseteq$
23050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23053 \begin_layout Plain Layout
23061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23064 \begin_layout Plain Layout
23065 \begin_inset Formula $\in$
23075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23078 \begin_layout Plain Layout
23086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23089 \begin_layout Plain Layout
23090 \begin_inset Formula $\vdash$
23100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23103 \begin_layout Plain Layout
23111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23114 \begin_layout Plain Layout
23115 \begin_inset Formula $\smile$
23125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23128 \begin_layout Plain Layout
23136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23139 \begin_layout Plain Layout
23140 \begin_inset Formula $\lhd$
23150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23153 \begin_layout Plain Layout
23161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23164 \begin_layout Plain Layout
23165 \begin_inset Formula $\unlhd$
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23178 \begin_layout Plain Layout
23186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23189 \begin_layout Plain Layout
23190 \begin_inset Formula $\gtrless$
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Plain Layout
23211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23214 \begin_layout Plain Layout
23215 \begin_inset Formula $\mid$
23225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23228 \begin_layout Plain Layout
23236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23239 \begin_layout Plain Layout
23240 \begin_inset Formula $\nmid$
23254 \begin_inset space \hfill{}
23258 \begin_inset Tabular
23259 <lyxtabular version="3" rows="17" columns="2">
23261 <column alignment="center" valignment="top" width="0pt">
23262 <column alignment="center" valignment="top" width="0pt">
23264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23267 \begin_layout Plain Layout
23273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23276 \begin_layout Plain Layout
23284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23287 \begin_layout Plain Layout
23293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23296 \begin_layout Plain Layout
23297 \begin_inset Formula $=$
23307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23310 \begin_layout Plain Layout
23318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23321 \begin_layout Plain Layout
23322 \begin_inset Formula $\not=$
23332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23335 \begin_layout Plain Layout
23343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23346 \begin_layout Plain Layout
23347 \begin_inset Formula $\equiv$
23357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23360 \begin_layout Plain Layout
23368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23371 \begin_layout Plain Layout
23372 \begin_inset Formula $\sim$
23382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23385 \begin_layout Plain Layout
23393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23396 \begin_layout Plain Layout
23397 \begin_inset Formula $\simeq$
23407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23410 \begin_layout Plain Layout
23418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23421 \begin_layout Plain Layout
23422 \begin_inset Formula $\approx$
23432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23435 \begin_layout Plain Layout
23443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23446 \begin_layout Plain Layout
23447 \begin_inset Formula $\cong$
23457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23460 \begin_layout Plain Layout
23468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23471 \begin_layout Plain Layout
23472 \begin_inset Formula $\bowtie$
23482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23485 \begin_layout Plain Layout
23493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23496 \begin_layout Plain Layout
23497 \begin_inset Formula $\notin$
23507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23510 \begin_layout Plain Layout
23518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23521 \begin_layout Plain Layout
23522 \begin_inset Formula $\perp$
23532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23535 \begin_layout Plain Layout
23543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23546 \begin_layout Plain Layout
23547 \begin_inset Formula $\propto$
23557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23560 \begin_layout Plain Layout
23568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23571 \begin_layout Plain Layout
23572 \begin_inset Formula $\asymp$
23582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23585 \begin_layout Plain Layout
23593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23596 \begin_layout Plain Layout
23597 \begin_inset Formula $\doteq$
23607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23610 \begin_layout Plain Layout
23618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23621 \begin_layout Plain Layout
23622 \begin_inset Formula $\circeq$
23632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23635 \begin_layout Plain Layout
23643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23646 \begin_layout Plain Layout
23647 \begin_inset Formula $\models$
23657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23660 \begin_layout Plain Layout
23668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23671 \begin_layout Plain Layout
23672 \begin_inset Formula $\widehat{=}$
23686 \begin_inset space \hfill{}
23690 \begin_inset Tabular
23691 <lyxtabular version="3" rows="17" columns="2">
23693 <column alignment="center" valignment="top" width="0pt">
23694 <column alignment="center" valignment="top" width="0pt">
23696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23699 \begin_layout Plain Layout
23705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23708 \begin_layout Plain Layout
23716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23719 \begin_layout Plain Layout
23725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23728 \begin_layout Plain Layout
23729 \begin_inset Formula $>$
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23742 \begin_layout Plain Layout
23750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23753 \begin_layout Plain Layout
23754 \begin_inset Formula $\ge$
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23767 \begin_layout Plain Layout
23775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23778 \begin_layout Plain Layout
23779 \begin_inset Formula $\gg$
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23792 \begin_layout Plain Layout
23800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23803 \begin_layout Plain Layout
23804 \begin_inset Formula $\succ$
23814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23817 \begin_layout Plain Layout
23825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23828 \begin_layout Plain Layout
23829 \begin_inset Formula $\succeq$
23839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23842 \begin_layout Plain Layout
23850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23853 \begin_layout Plain Layout
23854 \begin_inset Formula $\supset$
23864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23867 \begin_layout Plain Layout
23875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23878 \begin_layout Plain Layout
23879 \begin_inset Formula $\supseteq$
23889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23892 \begin_layout Plain Layout
23900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23903 \begin_layout Plain Layout
23904 \begin_inset Formula $\sqsupseteq$
23914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23917 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23929 \begin_inset Formula $\ni$
23939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23953 \begin_layout Plain Layout
23954 \begin_inset Formula $\dashv$
23964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23967 \begin_layout Plain Layout
23975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23978 \begin_layout Plain Layout
23979 \begin_inset Formula $\frown$
23989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23992 \begin_layout Plain Layout
24000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24003 \begin_layout Plain Layout
24004 \begin_inset Formula $\rhd$
24014 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24025 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24028 \begin_layout Plain Layout
24029 \begin_inset Formula $\unrhd$
24039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24042 \begin_layout Plain Layout
24050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24053 \begin_layout Plain Layout
24054 \begin_inset Formula $\lessgtr$
24064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24067 \begin_layout Plain Layout
24075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24078 \begin_layout Plain Layout
24079 \begin_inset Formula $\parallel$
24089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24092 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24103 \begin_layout Plain Layout
24104 \begin_inset Formula $\nparallel$
24118 \begin_inset space \hfill{}
24124 \begin_layout Standard
24125 \begin_inset VSpace medskip
24140 are bigger than the equal looking operators
24155 \begin_layout Standard
24156 Relations are, in contrary to symbols, always surrounded by space.
24159 \begin_layout Standard
24160 Relations with labels can be created with the command
24170 \begin_layout Plain Layout
24181 \begin_layout Standard
24183 \begin_inset Tabular
24184 <lyxtabular version="3" rows="2" columns="2">
24186 <column alignment="center" valignment="top" width="0">
24187 <column alignment="center" valignment="top" width="0">
24189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24201 \begin_layout Plain Layout
24203 \begin_inset Note Note
24206 \begin_layout Plain Layout
24213 is only used as spacer.
24225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24228 \begin_layout Plain Layout
24235 \begin_layout Plain Layout
24252 \begin_layout Plain Layout
24262 \begin_inset Formula $\downarrow$
24271 \begin_layout Plain Layout
24284 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24301 \begin_layout Plain Layout
24302 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24318 \begin_layout Section
24322 \begin_layout Subsection
24323 Predefined Functions
24324 \begin_inset CommandInset label
24326 name "sub:Predefined-Functions"
24334 \begin_layout Plain Layout
24335 Functions ! predefined
24343 \begin_layout Standard
24344 In general, variables are set
24348 in mathematical expressions, but not function names, because
24349 \begin_inset Formula $sin$
24352 could be misunderstood as
24353 \begin_inset Formula $s\cdot i\cdot n$
24357 Therefore there are predefined functions, that are additionally a bit separated
24359 They are inserted as commands starting with a backslash before their name.
24362 \begin_layout Standard
24364 \begin_inset Tabular
24365 <lyxtabular version="3" rows="2" columns="4">
24367 <column alignment="center" valignment="top" width="0pt">
24368 <column alignment="center" valignment="top" width="0pt">
24369 <column alignment="center" valignment="top" width="0pt">
24370 <column alignment="center" valignment="top" width="0pt">
24372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24375 \begin_layout Plain Layout
24381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24384 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24402 \begin_layout Plain Layout
24410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24413 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24422 \begin_layout Plain Layout
24423 \begin_inset Formula $Asin(x)+B$
24431 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24434 \begin_layout Plain Layout
24442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24445 \begin_layout Plain Layout
24446 \begin_inset Formula $A\sin(x)+B$
24462 \begin_layout Standard
24463 The following functions are predefined:
24466 \begin_layout Standard
24467 \begin_inset VSpace -2mm
24473 \begin_layout Standard
24475 \begin_inset Tabular
24476 <lyxtabular version="3" rows="9" columns="4">
24478 <column alignment="center" valignment="top" width="0pt">
24479 <column alignment="center" valignment="top" width="0pt">
24480 <column alignment="center" valignment="top" width="0pt">
24481 <column alignment="center" valignment="top" width="0pt">
24483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24486 \begin_layout Plain Layout
24492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24504 \begin_layout Plain Layout
24510 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24513 \begin_layout Plain Layout
24521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24524 \begin_layout Plain Layout
24532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24535 \begin_layout Plain Layout
24543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24546 \begin_layout Plain Layout
24554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24557 \begin_layout Plain Layout
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24581 \begin_layout Plain Layout
24589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24592 \begin_layout Plain Layout
24600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24603 \begin_layout Plain Layout
24613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24616 \begin_layout Plain Layout
24624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24627 \begin_layout Plain Layout
24635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24638 \begin_layout Plain Layout
24646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24649 \begin_layout Plain Layout
24659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24662 \begin_layout Plain Layout
24670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24673 \begin_layout Plain Layout
24681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24684 \begin_layout Plain Layout
24692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24695 \begin_layout Plain Layout
24705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24708 \begin_layout Plain Layout
24716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24719 \begin_layout Plain Layout
24727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24730 \begin_layout Plain Layout
24738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24741 \begin_layout Plain Layout
24751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24754 \begin_layout Plain Layout
24762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24765 \begin_layout Plain Layout
24773 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24776 \begin_layout Plain Layout
24784 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24787 \begin_layout Plain Layout
24797 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24800 \begin_layout Plain Layout
24808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24811 \begin_layout Plain Layout
24819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24833 \begin_layout Plain Layout
24843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24846 \begin_layout Plain Layout
24854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24857 \begin_layout Plain Layout
24865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24868 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24895 \begin_layout Standard
24896 They can also be inserted with the math toolbar button
24897 \begin_inset Graphics
24898 filename ../images/math/functions.png
24906 \begin_layout Subsection
24907 Self-defined Functions
24911 \begin_layout Plain Layout
24912 Functions ! self-defined
24920 \begin_layout Standard
24921 To use a function that is not predefined, like for example the sign function
24922 sgn(x), there are two possibilities:
24925 \begin_layout Itemize
24926 Define the function by inserting the following line to the LaTeX-preamble
24930 \begin_layout Plain Layout
24935 DeclareMathOperator
24938 \begin_inset CommandInset ref
24940 reference "sub:Self-defined-Operators"
24950 \begin_inset Newline newline
24954 \begin_inset VSpace -3mm
24958 \begin_inset Newline newline
24965 DeclareMathOperator{
24973 \begin_layout Plain Layout
24978 DeclareMathOperator
24984 \begin_inset Newline newline
24988 \begin_inset VSpace -2mm
24992 \begin_inset Newline newline
24995 Now the new defined function can be called with the command
25004 \begin_layout Itemize
25005 Write the the formula as usual, mark the formula name, in our example the
25010 , and change it to mathematical text.
25011 At last a space is inserted between prefactor and function.
25014 \begin_layout Standard
25015 The result is the same with both methods as with a predefined function
25019 \begin_layout Plain Layout
25020 In LyX self-defined functions are displayed red, predefined ones black.
25028 \begin_layout Standard
25030 \begin_inset Tabular
25031 <lyxtabular version="3" rows="3" columns="2">
25033 <column alignment="center" valignment="top" width="0pt">
25034 <column alignment="center" valignment="top" width="0pt">
25036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25039 \begin_layout Plain Layout
25045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25048 \begin_layout Plain Layout
25056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25059 \begin_layout Plain Layout
25067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25070 \begin_layout Plain Layout
25071 \begin_inset Formula $A\sgn(x)+B$
25081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25084 \begin_layout Plain Layout
25088 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25099 \begin_layout Plain Layout
25100 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25116 \begin_layout Standard
25117 The first method is more suitable when the self-defined function should
25118 be used several times.
25121 \begin_layout Subsection
25126 \begin_layout Plain Layout
25135 \begin_layout Standard
25136 For limits there are defined besides
25146 \begin_layout Plain Layout
25166 furthermore the following functions:
25169 \begin_layout Standard
25171 \begin_inset Tabular
25172 <lyxtabular version="3" rows="5" columns="2">
25174 <column alignment="center" valignment="top" width="0">
25175 <column alignment="center" valignment="top" width="0">
25177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25180 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25189 \begin_layout Plain Layout
25191 \begin_inset Note Note
25194 \begin_layout Plain Layout
25201 is only used as spacer.
25213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25216 \begin_layout Plain Layout
25224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25227 \begin_layout Plain Layout
25228 \begin_inset Formula $\varliminf$
25238 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25241 \begin_layout Plain Layout
25249 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25252 \begin_layout Plain Layout
25253 \begin_inset Formula $\varlimsup$
25263 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25266 \begin_layout Plain Layout
25274 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25277 \begin_layout Plain Layout
25278 \begin_inset Formula $\varprojlim$
25288 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25291 \begin_layout Plain Layout
25299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25302 \begin_layout Plain Layout
25303 \begin_inset Formula $\varinjlim$
25307 \begin_inset Formula $\raisebox{-2.5mm}{}$
25323 \begin_layout Standard
25324 \begin_inset VSpace medskip
25327 The limit is created by inserting a subscript.
25328 It is set right beside the function in an inline formula:
25331 \begin_layout Standard
25333 \begin_inset Tabular
25334 <lyxtabular version="3" rows="2" columns="2">
25336 <column alignment="center" valignment="top" width="0pt">
25337 <column alignment="center" valignment="top" width="0pt">
25339 <cell alignment="center" valignment="top" usebox="none">
25342 \begin_layout Plain Layout
25348 <cell alignment="center" valignment="top" usebox="none">
25351 \begin_layout Plain Layout
25352 \begin_inset space \hspace{}
25357 \begin_inset Note Note
25360 \begin_layout Plain Layout
25367 are used here as spacer.
25379 <cell alignment="center" valignment="top" usebox="none">
25382 \begin_layout Plain Layout
25391 \begin_layout Plain Layout
25404 \begin_layout Plain Layout
25418 <cell alignment="center" valignment="top" usebox="none">
25421 \begin_layout Plain Layout
25422 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25438 \begin_layout Standard
25439 In a displayed formula the limit is set below the formula, as usual:
25440 \begin_inset Formula \[
25448 \begin_layout Subsection
25453 \begin_layout Plain Layout
25454 Functions ! modulo-
25462 \begin_layout Standard
25463 The modulo-function is special, because it exists in four variants.
25466 \begin_layout Standard
25467 The variants in a displayed formula:
25468 \begin_inset Formula \begin{align*}
25469 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25470 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25471 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25472 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25473 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25480 \begin_layout Standard
25481 In an inline formula less space is set before the function names for all
25485 \begin_layout Standard
25486 \begin_inset Newpage newpage
25492 \begin_layout Section
25497 \begin_layout Plain Layout
25506 \begin_layout Subsection
25507 Special Characters in Mathematical Text
25510 \begin_layout Standard
25511 The following commands can only be used in mathematical text or in TeX-mode:
25514 \begin_layout Standard
25515 \begin_inset space \hfill{}
25519 \begin_inset Tabular
25520 <lyxtabular version="3" rows="8" columns="2">
25522 <column alignment="block" valignment="top" width="0">
25523 <column alignment="block" valignment="top" width="0">
25525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25528 \begin_layout Plain Layout
25534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25537 \begin_layout Plain Layout
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25548 \begin_layout Plain Layout
25556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25559 \begin_layout Plain Layout
25560 \begin_inset Formula $\textrm{œ}$
25570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25573 \begin_layout Plain Layout
25581 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25584 \begin_layout Plain Layout
25585 \begin_inset Formula $\textrm{Œ}$
25595 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25598 \begin_layout Plain Layout
25606 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25609 \begin_layout Plain Layout
25610 \begin_inset Formula $\textrm{æ}$
25620 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25623 \begin_layout Plain Layout
25631 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25634 \begin_layout Plain Layout
25635 \begin_inset Formula $\textrm{Æ}$
25645 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25648 \begin_layout Plain Layout
25656 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25659 \begin_layout Plain Layout
25660 \begin_inset Formula $\textrm{\aa}$
25670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25673 \begin_layout Plain Layout
25680 \begin_layout Plain Layout
25687 \begin_layout Plain Layout
25708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25711 \begin_layout Plain Layout
25712 \begin_inset Formula $\textrm{Å}$
25722 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25725 \begin_layout Plain Layout
25733 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25736 \begin_layout Plain Layout
25737 \begin_inset Formula $\textrm{ı}$
25751 \begin_inset space \hfill{}
25755 \begin_inset Tabular
25756 <lyxtabular version="3" rows="8" columns="2">
25758 <column alignment="block" valignment="top" width="0">
25759 <column alignment="center" valignment="top" width="0">
25761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25764 \begin_layout Plain Layout
25766 \begin_inset Note Note
25769 \begin_layout Plain Layout
25771 \begin_inset space \thinspace{}
25774 mm is used for separation, because otherwise the output will be ¡ and ¿
25785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25788 \begin_layout Plain Layout
25796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25799 \begin_layout Plain Layout
25807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25810 \begin_layout Plain Layout
25811 \begin_inset Formula $\textrm{ø}$
25821 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25824 \begin_layout Plain Layout
25832 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25835 \begin_layout Plain Layout
25836 \begin_inset Formula $\textrm{Ø}$
25846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25849 \begin_layout Plain Layout
25857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25860 \begin_layout Plain Layout
25861 \begin_inset Formula $\textrm{ł}$
25871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25874 \begin_layout Plain Layout
25882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25885 \begin_layout Plain Layout
25886 \begin_inset Formula $\textrm{Ł}$
25896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25899 \begin_layout Plain Layout
25901 \begin_inset space \hspace{}
25909 \begin_layout Plain Layout
25923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25926 \begin_layout Plain Layout
25927 \begin_inset Formula $\textrm{!`}$
25937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25940 \begin_layout Plain Layout
25942 \begin_inset space \hspace{}
25950 \begin_layout Plain Layout
25964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25967 \begin_layout Plain Layout
25968 \begin_inset Formula $\textrm{?`}$
25978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25981 \begin_layout Plain Layout
25989 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25992 \begin_layout Plain Layout
25993 \begin_inset Formula $\textrm{ȷ}$
26007 \begin_inset space \hfill{}
26013 \begin_layout Standard
26015 \begin_inset Formula $\textrm{\textrm{Å}}$
26019 \begin_inset Formula $\textrm{\textrm{Ø}}$
26022 can also be inserted via the math toolbar button
26023 \begin_inset Graphics
26024 filename ../images/math/digamma.png
26032 \begin_layout Standard
26033 An exception are the commands
26036 \begin_inset space \hspace{}
26045 \begin_inset space \hspace{}
26051 , because they can be inserted in LyX directly to text.
26054 \begin_layout Subsection
26056 \begin_inset CommandInset label
26058 name "sub:Accents-in-Text"
26066 \begin_layout Plain Layout
26075 \begin_layout Standard
26076 With the following commands all letters can be accented.
26077 The commands must be inserted in TeX-mode.
26080 \begin_layout Standard
26081 \begin_inset space \hfill{}
26085 \begin_inset Tabular
26086 <lyxtabular version="3" rows="8" columns="2">
26088 <column alignment="block" valignment="top" width="0">
26089 <column alignment="block" valignment="top" width="0">
26091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26094 \begin_layout Plain Layout
26100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26103 \begin_layout Plain Layout
26111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26114 \begin_layout Plain Layout
26118 \begin_inset Quotes grd
26126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26129 \begin_layout Plain Layout
26133 \begin_layout Plain Layout
26149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26152 \begin_layout Plain Layout
26160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26163 \begin_layout Plain Layout
26167 \begin_layout Plain Layout
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26186 \begin_layout Plain Layout
26193 \begin_layout Plain Layout
26207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26210 \begin_layout Plain Layout
26214 \begin_layout Plain Layout
26230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26233 \begin_layout Plain Layout
26241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26244 \begin_layout Plain Layout
26248 \begin_layout Plain Layout
26264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26267 \begin_layout Plain Layout
26274 \begin_layout Plain Layout
26288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26291 \begin_layout Plain Layout
26295 \begin_layout Plain Layout
26311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26314 \begin_layout Plain Layout
26321 \begin_layout Plain Layout
26335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26338 \begin_layout Plain Layout
26342 \begin_layout Plain Layout
26358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26361 \begin_layout Plain Layout
26368 \begin_layout Plain Layout
26382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26385 \begin_layout Plain Layout
26389 \begin_layout Plain Layout
26409 \begin_inset space \hfill{}
26413 \begin_inset Tabular
26414 <lyxtabular version="3" rows="8" columns="2">
26416 <column alignment="block" valignment="top" width="0">
26417 <column alignment="center" valignment="top" width="0">
26419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26422 \begin_layout Plain Layout
26428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26431 \begin_layout Plain Layout
26439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26442 \begin_layout Plain Layout
26449 \begin_layout Plain Layout
26463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26466 \begin_layout Plain Layout
26470 \begin_layout Plain Layout
26486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26489 \begin_layout Plain Layout
26497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26500 \begin_layout Plain Layout
26504 \begin_layout Plain Layout
26520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26523 \begin_layout Plain Layout
26530 \begin_layout Plain Layout
26541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26544 \begin_layout Plain Layout
26548 \begin_layout Plain Layout
26564 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26567 \begin_layout Plain Layout
26575 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26578 \begin_layout Plain Layout
26582 \begin_layout Plain Layout
26598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26601 \begin_layout Plain Layout
26608 \begin_layout Plain Layout
26622 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26625 \begin_layout Plain Layout
26629 \begin_layout Plain Layout
26645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26648 \begin_layout Plain Layout
26655 \begin_layout Plain Layout
26669 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26672 \begin_layout Plain Layout
26676 \begin_layout Plain Layout
26692 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26695 \begin_layout Plain Layout
26702 \begin_layout Plain Layout
26716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26719 \begin_layout Plain Layout
26723 \begin_layout Plain Layout
26743 \begin_inset space \hfill{}
26749 \begin_layout Standard
26750 \begin_inset VSpace medskip
26759 also two different characters can be accented.
26768 \begin_layout Plain Layout
26783 \begin_layout Plain Layout
26795 \begin_layout Standard
26808 can in combination with vowels directly be inserted with the keyboard without
26810 The same applies for the tilde
26814 \begin_layout Plain Layout
26815 This only applies for keyboards where the tilde is defined as accent.
26824 in combination with
26839 \begin_layout Standard
26882 , and accents inserted directly with the keyboard are also available in
26884 For the other accents there are special math commands to be used in formulas,
26886 \begin_inset CommandInset ref
26888 reference "sub:Accents-for-one"
26895 \begin_layout Standard
26896 \begin_inset VSpace bigskip
26899 Furthermore, with the command
26909 \begin_layout Plain Layout
26917 all numbers and letters can be set into a circle, quasi accented with a
26918 circle, similar to the the copyright symbol.
26921 \begin_layout Standard
26923 \begin_inset Tabular
26924 <lyxtabular version="3" rows="3" columns="2">
26926 <column alignment="center" valignment="top" width="0">
26927 <column alignment="center" valignment="top" width="0">
26929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26932 \begin_layout Plain Layout
26938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26941 \begin_layout Plain Layout
26943 \begin_inset Note Note
26946 \begin_layout Plain Layout
26953 is only used as spacer.
26965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26968 \begin_layout Plain Layout
26976 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26979 \begin_layout Plain Layout
26983 \begin_layout Plain Layout
26999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27002 \begin_layout Plain Layout
27013 raisebox{-1.5pt}{W}}
27018 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27021 \begin_layout Plain Layout
27022 \begin_inset Formula $\raisebox{4.5mm}{}$
27029 \begin_layout Plain Layout
27047 \begin_inset Formula $\raisebox{-2mm}{}$
27063 \begin_layout Standard
27064 One has to take care that the character fits in the circle.
27075 \begin_layout Plain Layout
27077 \begin_inset CommandInset ref
27079 reference "sub:Font-Sizes"
27088 specifies thereby the size of the circle.
27099 \begin_layout Plain Layout
27101 \begin_inset CommandInset ref
27103 reference "sub:Boxes-without-Frame"
27112 the character can be centered.
27115 \begin_layout Subsection
27120 \begin_layout Plain Layout
27129 \begin_layout Standard
27130 Minuscule numbers are created with the command
27140 \begin_layout Plain Layout
27149 The command can be used in formulas and in TeX-mode.
27150 The command scheme is:
27153 \begin_layout Standard
27158 oldstylenums{number}
27161 \begin_layout Standard
27166 oldstylenums{0123456789
27169 \begin_inset Formula $\oldstylenums{0123456789}$
27175 \begin_layout Subsection
27176 Miscellaneous special Characters
27177 \begin_inset CommandInset label
27179 name "sub:Miscellaneous-special-Characters"
27187 \begin_layout Plain Layout
27188 Special characters ! miscellaneous
27196 \begin_layout Standard
27197 The following characters can only be inserted to formulas by using commands:
27200 \begin_layout Standard
27202 \begin_inset Tabular
27203 <lyxtabular version="3" rows="4" columns="2">
27205 <column alignment="center" valignment="top" width="0">
27206 <column alignment="center" valignment="top" width="0">
27208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27211 \begin_layout Plain Layout
27217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27220 \begin_layout Plain Layout
27228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27231 \begin_layout Plain Layout
27238 \begin_layout Plain Layout
27252 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27255 \begin_layout Plain Layout
27256 \begin_inset Formula $\mathcircumflex$
27266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27269 \begin_layout Plain Layout
27277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27280 \begin_layout Plain Layout
27281 \begin_inset Formula $\_$
27291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27294 \begin_layout Plain Layout
27299 \begin_layout Plain Layout
27314 \begin_layout Plain Layout
27327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27330 \begin_layout Plain Layout
27331 \begin_inset Formula $^{\circ}$
27347 \begin_layout Standard
27348 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27349 contains the following line
27353 \begin_layout Plain Layout
27354 More about this is described in
27355 \begin_inset CommandInset ref
27357 reference "sub:Text-Characters-in"
27369 \begin_layout Standard
27374 DeclareInputtext{176}{
27387 \begin_layout Standard
27388 \begin_inset Newpage newpage
27394 \begin_layout Section
27396 \begin_inset CommandInset label
27398 name "sec:Formula-Styles"
27406 \begin_layout Plain Layout
27415 \begin_layout Itemize
27416 There are two different alignment styles:
27420 \begin_layout Description
27421 Centered is the predefined standard
27424 \begin_layout Description
27425 Indented for this the option
27429 must be inserted in the menu
27431 Document\SpecialChar \menuseparator
27437 \begin_inset space ~
27443 \begin_layout Standard
27448 is used, the indentation can be adjusted with the length
27458 \begin_layout Plain Layout
27467 Should the distance be 15
27468 \begin_inset space \thinspace{}
27471 mm, the following command line is inserted in the LaTeX-preamble
27474 \begin_layout Standard
27484 \begin_layout Standard
27485 When no length is specified, the predefined value of 30
27486 \begin_inset space \thinspace{}
27493 \begin_layout Itemize
27494 And two different numbering styles:
27498 \begin_layout Description
27499 Right is the predefined standard
27502 \begin_layout Description
27503 Left for this the option
27507 must be inserted in the menu
27509 Document\SpecialChar \menuseparator
27515 \begin_inset space ~
27522 \begin_layout Standard
27531 can also be used together.
27532 In this case both options are inserted, separated by a comma.
27535 \begin_layout Standard
27536 The chosen styles are used for all displayed formulas of the document.
27537 When both, centered and indented formulas should be created in a document,
27543 The indented formulas are then set in a flalign environment, see
27544 \begin_inset CommandInset ref
27546 reference "sub:Flalign-Environment"
27553 \begin_layout Section
27555 \begin_inset CommandInset label
27557 name "sec:Multiline-Formulas"
27565 \begin_layout Plain Layout
27566 Formula ! multiline
27574 \begin_layout Subsection
27578 \begin_layout Standard
27579 In LyX multiline formulas are created by pressing
27584 arg "newline-insert newline"
27590 This creates either an
27592 eqnarray environment
27594 that is described in
27595 \begin_inset CommandInset ref
27597 reference "sub:Eqnarray-Environment"
27601 or, when the option
27603 Use AMS math package
27605 in the document settings is selected, an
27609 that is described in
27610 \begin_inset CommandInset ref
27612 reference "sub:Standard-align-Environment"
27619 \begin_layout Standard
27620 There are other multiline formula environments that can be created via the
27623 Insert\SpecialChar \menuseparator
27627 These environments are described in the following sections.
27630 \begin_layout Standard
27631 In all multiline formula environments a new line is created by pressing
27635 arg "newline-insert newline"
27639 To add or delete lines, the math toolbar buttons
27640 \begin_inset Graphics
27641 filename ../images/tabular-feature_append-row.png
27647 \begin_inset Graphics
27648 filename ../images/tabular-feature_delete-row.png
27653 , respectively, or the menu
27655 Edit\SpecialChar \menuseparator
27661 \begin_layout Subsubsection
27663 \begin_inset CommandInset label
27665 name "sub:Line-Separation"
27673 \begin_layout Plain Layout
27674 Formula ! multiline ! Line separation
27682 \begin_layout Standard
27683 There is sometimes not enough space in multiline formulas between the lines:
27684 \begin_inset Formula \begin{eqnarray*}
27685 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}\\
27686 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*}
27693 \begin_layout Standard
27694 In LaTeX additional line space is specified as optional argument of the
27696 This is not yet possible in LyX
27700 \begin_layout Plain Layout
27702 \begin_inset CommandInset href
27704 name "LyX-bug #1505"
27705 target "http://www.lyx.org/trac/ticket/1505"
27714 , therefore the whole formula must be inserted in TeX-mode.
27715 To add in our example space, the command
27723 is inserted at the end of the first line.
27728 \begin_layout Plain Layout
27735 \begin_layout Plain Layout
27737 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27740 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27747 \begin_layout Plain Layout
27751 left(B^{2}+x_{0}^{2}
27759 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27764 \begin_layout Plain Layout
27776 \begin_layout Standard
27777 \begin_inset VSpace bigskip
27780 To set the the line separation for all lines in a formula, the length
27790 \begin_layout Plain Layout
27800 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27811 \begin_inset space \thinspace{}
27816 \begin_inset space \thinspace{}
27819 mm additional line separation as in the previous example, the command
27822 \begin_layout Standard
27832 \begin_layout Standard
27833 is inserted in TeX-mode before the formula.
27834 This requires that the LaTeX-package
27842 \begin_layout Plain Layout
27847 is part of every LaTeX standard installation.
27856 \begin_layout Plain Layout
27862 was loaded in LaTeX-preamble with the line
27865 \begin_layout Standard
27873 \begin_layout Standard
27878 \begin_layout Plain Layout
27890 \begin_inset Formula \begin{eqnarray*}
27891 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}\\
27892 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*}
27899 \begin_layout Standard
27903 \begin_layout Plain Layout
27914 To get back to the predefined distance,
27920 is set to the value 3
27921 \begin_inset space \thinspace{}
27927 \begin_layout Subsubsection
27929 \begin_inset CommandInset label
27931 name "sub:Column-Separation"
27939 \begin_layout Plain Layout
27940 Formula ! multiline ! Column separation
27948 \begin_layout Standard
27949 Multiline formulas form a matrix.
27950 A formula in the eqnarray environment is for example a matrix with three
27952 By changing the column separation in this environment, the space beside
27953 the relation sign can be changed.
27956 \begin_layout Standard
27957 The column separation is specified with the length
27967 \begin_layout Plain Layout
27976 \begin_inset Newline newline
27979 column separation = 2
27980 \begin_inset space \thinspace{}
27990 \begin_inset Newline newline
27996 \begin_layout Standard
28006 \begin_layout Standard
28007 inserted in TeX-mode, sets for all following formulas a column separation
28009 \begin_inset space \thinspace{}
28013 To get back to the predefined distance,
28020 \begin_inset space \thinspace{}
28026 \begin_layout Standard
28028 \begin_inset space \thinspace{}
28031 cm column separation:
28035 \begin_layout Plain Layout
28047 \begin_inset Formula \begin{eqnarray*}
28049 C & \ne & A\end{eqnarray*}
28053 A formula with the predefined column separation for matrices of 10
28054 \begin_inset space \thinspace{}
28061 \begin_layout Plain Layout
28073 \begin_inset Formula \begin{eqnarray*}
28075 C & \ne & A\end{eqnarray*}
28082 \begin_layout Subsubsection
28087 \begin_layout Plain Layout
28096 \begin_layout Standard
28097 Long formulas can be typeset using these methods:
28100 \begin_layout Itemize
28101 When one side of the equation is much shorther than the line width, this
28102 one is chosen for the left side and the right side is typeset over two
28104 \begin_inset Formula \begin{eqnarray}
28105 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 \\
28106 & & -\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}
28110 The minus sign at the beginning of the second line does normally not appear
28111 as operator because it is the first character of the line.
28112 Thus it would not be surrounded by space and could not be distinguished
28113 from the fraction bar.
28115 \begin_inset space \thinspace{}
28118 pt space was inserted behind the minus sign with the command
28128 \begin_layout Plain Layout
28136 \begin_inset CommandInset ref
28138 reference "sub:Variable-Space"
28151 \begin_layout Plain Layout
28162 \begin_layout Itemize
28163 When both sides of the equation are too long, the command
28173 \begin_layout Plain Layout
28182 It is inserted to the first column of the first line and effects that all
28183 further insertions overwrite the following columns:
28184 \begin_inset Formula \begin{eqnarray}
28185 \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 \\
28186 & & -\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 \\
28187 & & =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}
28191 After the insertion of
28197 , the cursor is in a purple box that is a bit shifted to the left from the
28199 In this the formula is inserted.
28200 \begin_inset Newline newline
28203 The content of the further lines is inserted to the second or another formula
28205 The greater the column number where it was inserted, the larger the indentation.
28206 \begin_inset VSpace medskip
28210 \begin_inset Newline newline
28214 \begin_inset Note Greyedout
28217 \begin_layout Plain Layout
28218 Note the following when using
28227 \begin_layout Itemize
28228 The formula doesn't use the full page width.
28230 \begin_inset space \thinspace{}
28234 \begin_inset space \space{}
28238 \begin_inset Formula $-B^{2}$
28241 is added to the first line in the above example, it would have been outside
28243 To better use the width, negative space can be inserted at the beginning
28247 \begin_layout Itemize
28248 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28253 \begin_layout Plain Layout
28254 \begin_inset CommandInset href
28256 name "LyX-bug #1429"
28257 target "http://www.lyx.org/trac/ticket/1429"
28266 One can only set the cursor at the beginning of the line and move it with
28275 \begin_layout Itemize
28276 Other methods to set long formulas are offered by the environments described
28278 \begin_inset CommandInset ref
28280 reference "sub:Multline-Environment"
28285 \begin_inset CommandInset ref
28287 reference "sub:Multiline-Formula-Parts"
28294 \begin_layout Subsubsection
28296 \begin_inset CommandInset label
28298 name "sub:Multiline-Brackets"
28306 \begin_layout Plain Layout
28307 Brackets ! for multiline expressions
28315 \begin_layout Standard
28316 For brackets spanning multiple lines the following problem occurs:
28317 \begin_inset Formula \begin{eqnarray*}
28318 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28319 & & \left.\cdots+B-D\right]\end{eqnarray*}
28326 \begin_layout Standard
28327 The closing bracket is smaller than the opening bracket because brackets
28328 with variable size may not span multiple lines.
28331 \begin_layout Standard
28332 To set the bracket size for the second line correctly, the first line is
28343 \begin_layout Plain Layout
28351 and the second line with
28359 \begin_layout Plain Layout
28373 \begin_inset CommandInset ref
28375 reference "sub:Automatic-Bracket-Size"
28390 \begin_layout Plain Layout
28416 \begin_layout Plain Layout
28435 \begin_layout Plain Layout
28454 \begin_layout Plain Layout
28466 \begin_inset Formula $\downarrow$
28475 \begin_layout Plain Layout
28483 is inserted, because the multiplication operator with its limits is the
28484 largest symbol in the first line and this should be the size for the bracket
28485 in the second line.
28488 \begin_layout Standard
28489 The result is this:
28490 \begin_inset Formula \begin{eqnarray*}
28491 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28492 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28499 \begin_layout Subsection
28503 \begin_layout Standard
28504 Align environments can be used for every kind of multiline formulas.
28505 They are specially useful to set several formulas side by side.
28508 \begin_layout Standard
28509 Align environments consist of columns.
28510 The odd columns are right aligned, the even ones left aligned.
28511 Every line in an Align environment can be numbered.
28514 \begin_layout Standard
28515 Align environments are created via the menu
28517 Insert\SpecialChar \menuseparator
28523 Edit\SpecialChar \menuseparator
28524 Math\SpecialChar \menuseparator
28525 Change Formula Type
28527 already existing formulas can be converted to Align environments.
28530 \begin_layout Standard
28531 To add or delete columns, the math toolbar buttons
28532 \begin_inset Graphics
28533 filename ../images/tabular-feature_append-column.png
28539 \begin_inset Graphics
28540 filename ../images/tabular-feature_delete-column.png
28545 , respectively, or the menu
28547 Edit\SpecialChar \menuseparator
28553 \begin_layout Subsubsection
28554 Standard align Environment
28555 \begin_inset CommandInset label
28557 name "sub:Standard-align-Environment"
28565 \begin_layout Plain Layout
28566 Formula ! multiline ! align environment
28574 \begin_layout Standard
28575 This Align environment is created by presssing
28578 arg "newline-insert newline"
28581 in a formula or by the menu
28583 Insert\SpecialChar \menuseparator
28584 Math\SpecialChar \menuseparator
28585 AMS align Environment
28590 \begin_layout Standard
28591 An example for two formulas set side by side, that are created with a four
28592 column align environment:
28593 \begin_inset Formula \begin{align*}
28594 A & =\sin(B) & C & =D\\
28595 C & \ne A & B & \ne D\end{align*}
28599 As it can be seen, the formulas in this environment are placed so as if
28608 \begin_layout Plain Layout
28616 \begin_inset CommandInset ref
28618 reference "sub:Variable-Space"
28629 before the first and after every even column.
28630 When the formula style
28636 \begin_layout Plain Layout
28638 \begin_inset CommandInset ref
28640 reference "sec:Formula-Styles"
28651 is used, the formula is set without the
28657 before the first column.
28660 \begin_layout Subsubsection
28661 Alignat Environment
28665 \begin_layout Plain Layout
28666 Formula ! multiline ! alignat environment
28674 \begin_layout Standard
28675 The alignat environment has no predefined column separation.
28676 It can be inserted manually with the spaces that are described
28677 \begin_inset CommandInset ref
28679 reference "sub:Space"
28686 \begin_layout Standard
28687 The above example in the alignat environment where 1
28688 \begin_inset space \thinspace{}
28691 cm space was inserted at the beginning of the second formula:
28692 \begin_inset Formula \begin{alignat*}{2}
28693 A & =\sin(B) & \hspace{1cm}C & =D\\
28694 C & \ne A & B & \ne D\end{alignat*}
28698 Because the column separation can be set separately for every column, this
28699 environment is especially suitable to set three and more formulas side
28703 \begin_layout Subsubsection
28704 Flalign Environment
28705 \begin_inset CommandInset label
28707 name "sub:Flalign-Environment"
28715 \begin_layout Plain Layout
28716 Formula ! multiline ! flalign environment
28724 \begin_layout Standard
28725 In this environment the first two columns are always set as much as possible
28726 to the left and the last two ones to the right.
28728 \begin_inset Formula \begin{flalign*}
28729 A & =1 & B & =2 & C & =3\\
28730 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28737 \begin_layout Standard
28738 By creating a flalign environment with an odd number of columns where an
28739 empty TeX-brace is inserted to the last column, several formulas in a document
28740 can be set to the left, although the formula style
28745 As example the indented formula
28746 \begin_inset CommandInset ref
28748 reference "eq:VolInt"
28753 \begin_inset Formula \begin{flalign}
28754 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28758 The first two columns contain the formula.
28759 To indent it as with the formula style
28764 \begin_inset space \thinspace{}
28767 pt space was inserted at the beginning of the first column.
28770 \begin_layout Subsection
28771 Eqnarray Environment
28772 \begin_inset CommandInset label
28774 name "sub:Eqnarray-Environment"
28782 \begin_layout Plain Layout
28783 Formula ! multiline ! eqnarray environment
28791 \begin_layout Standard
28792 When this environment has been created, three blue boxes appear.
28793 The content of the first box is right aligned, the content of the last
28795 The content of the middle box appears centered and a bit smaller, because
28796 it is designed to insert there only relation characters.
28797 \begin_inset Formula \begin{eqnarray*}
28798 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28800 A & = & A\end{eqnarray*}
28807 \begin_layout Subsection
28812 \begin_layout Plain Layout
28813 Formula ! multiline ! gather environment
28821 \begin_layout Standard
28822 This environment consists of only one centered column.
28823 Every line can be numbered.
28824 \begin_inset Formula \begin{gather}
28826 X=\textrm{-}1\end{gather}
28833 \begin_layout Subsection
28834 Multline Environment
28835 \begin_inset CommandInset label
28837 name "sub:Multline-Environment"
28845 \begin_layout Plain Layout
28846 Formula ! multiline ! multline environment
28854 \begin_layout Standard
28855 The multline environment consists, like the gather environment, of only
28857 But the first line is left aligned, the last one right aligned.
28858 All other lines are centered.
28859 Therefore this environment is suitable for long formulas.
28861 \begin_inset CommandInset ref
28863 reference "eq:lefteqn"
28867 in the multline environment:
28868 \begin_inset Formula \begin{multline}
28869 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}\\
28870 -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}\\
28871 =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}
28878 \begin_layout Standard
28879 In the output only the last (first) line of a multline environment appears
28880 numbered when the document numbering is right (left).
28884 \begin_layout Plain Layout
28885 numbering styles see
28886 \begin_inset CommandInset ref
28888 reference "sec:Formula-Styles"
28900 \begin_layout Standard
28909 \begin_layout Plain Layout
28927 \begin_layout Plain Layout
28937 a centered line can be right or left aligned, respectively.
28938 The commands are used as follows:
28941 \begin_layout Standard
28946 shoveright{line content}
28952 shoveleft{line content}
28955 \begin_layout Standard
28956 \begin_inset VSpace medskip
28967 \begin_layout Plain Layout
28977 specifies the distance of the first line from the left page margin.
28978 Predefined is the length 0
28979 \begin_inset space \thinspace{}
28985 \begin_layout Standard
28986 As example the above formula where the command
28989 \begin_layout Standard
28999 \begin_layout Standard
29000 was inserted in TeX-mode before:
29004 \begin_layout Plain Layout
29016 \begin_inset Formula \begin{multline}
29017 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}\\
29018 \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}}\\
29019 =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}
29027 \begin_layout Plain Layout
29038 The second line was left aligned using
29047 \begin_layout Subsection
29048 Multiline Formula Parts
29049 \begin_inset CommandInset label
29051 name "sub:Multiline-Formula-Parts"
29059 \begin_layout Plain Layout
29060 Formula ! multiline ! formula parts
29068 \begin_layout Standard
29069 To display only parts of a formula with multiple lines, one of the following
29070 environments are used:
29087 They can be inserted via the menu
29089 Insert\SpecialChar \menuseparator
29092 or by using the commands described in this section.
29095 \begin_layout Standard
29096 The first three have the same properties as the corresponding multiline
29097 formula environments, but it is possible to set further formula parts beside
29100 \begin_inset Formula \[
29101 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29102 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
29103 \right\} \textrm{Uncertainty relations}\]
29110 \begin_layout Standard
29111 To get this formula, a displayed formula is created where the command
29119 \begin_layout Plain Layout
29130 A purple box appears around the blue formula box where now columns and
29131 lines can be added.
29132 Outside the multiline environment other formula parts can be set, like
29136 \begin_layout Standard
29137 The aligned environment is also suitable for long formulas whose lines are
29138 horizontally aligned.
29139 Using aligned in a displayed formula has the advantage that the formula
29140 number is vertically centered behind the lines.
29142 \begin_inset CommandInset ref
29144 reference "eq:shortlong"
29148 in the aligned environment:
29149 \begin_inset Formula \begin{equation}
29150 \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}|}\\
29151 & -\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}
29159 \begin_layout Standard
29160 To use the environments
29182 \begin_layout Plain Layout
29200 \begin_layout Plain Layout
29218 \begin_layout Plain Layout
29226 are inserted, respectively.
29227 The split environment has the same properties as the aligned environment
29228 but it can only have two columns.
29231 \begin_layout Subsection
29232 Text in multiline Formulas
29233 \begin_inset CommandInset label
29235 name "sub:Text-in-multiline"
29243 \begin_layout Plain Layout
29253 \begin_layout Plain Layout
29254 Formula ! multiline ! text
29262 \begin_layout Standard
29263 In the Align environments, and the multline and gather environment, text
29264 can be inserted that will appear in a separate line and doesn't affect
29265 the column alignment.
29266 To do this, the command
29274 \begin_layout Plain Layout
29284 is used in the following scheme:
29287 \begin_layout Standard
29295 \begin_layout Standard
29296 The text should not be longer than a line because it cannot be hyphenated.
29297 As LyX doesn't yet support
29303 directly, the text is written as mathematical text.
29310 must hereby be at the beginning of a line and appears in the output above
29312 An example where the text was inserted at the beginning of the second line:
29313 \begin_inset Formula \begin{align}
29314 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29315 \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}
29322 \begin_layout Section
29327 \begin_layout Plain Layout
29337 \begin_layout Plain Layout
29338 Formula ! numbering|see
29342 \begin_layout Plain Layout
29353 \begin_layout Plain Layout
29368 \begin_layout Subsection
29372 \begin_layout Standard
29373 Numbered formulas can be created with the menu
29375 Insert\SpecialChar \menuseparator
29376 Math\SpecialChar \menuseparator
29378 \begin_inset space ~
29386 \begin_inset space ~
29392 Existing formulas can be numbered with the menu
29394 Edit\SpecialChar \menuseparator
29395 Math\SpecialChar \menuseparator
29397 \begin_inset space ~
29405 arg "math-number-toggle"
29409 The formula number is displayed in LyX behind the formula as number sign
29411 The number sign is replaced in the output by the formula number.
29414 \begin_layout Standard
29415 When numbering is turned on in multiline formulas, all lines will be numbered.
29416 But the numbering can be controlled with the menu
29418 Edit\SpecialChar \menuseparator
29419 Math\SpecialChar \menuseparator
29421 \begin_inset space ~
29425 \begin_inset space ~
29429 \begin_inset space ~
29437 arg "math-number-line-toggle"
29443 \begin_layout Standard
29444 Except for inline formulas, all formulas can be numbered with two different
29446 \begin_inset CommandInset ref
29448 reference "sec:Formula-Styles"
29455 \begin_layout Subsection
29460 \begin_layout Plain Layout
29461 Cross-references ! to formulas
29469 \begin_layout Standard
29470 All labeled formulas can be cross-referenced.
29471 A label is added by the menu
29473 Insert\SpecialChar \menuseparator
29476 or the toolbar button
29477 \begin_inset Graphics
29478 filename ../images/label-insert.png
29484 The cursor must hereby be inside a displayed formula.
29485 A dialog pops up displaying the prefix
29490 The label is inserted there behind the prefix.
29491 The predefined prefix means
29492 \begin_inset Quotes eld
29496 \begin_inset Quotes erd
29499 and makes it easier to find labels in large documents because it marks
29500 it as formula label to divide it from e.
29501 \begin_inset space \thinspace{}
29505 \begin_inset space \space{}
29509 To change a label, the menu
29511 Insert\SpecialChar \menuseparator
29517 \begin_layout Standard
29518 The name of the label is displayed in LyX within two parentheses behind
29520 A formula with a label is always numbered.
29523 \begin_layout Standard
29524 Cross-references are inserted via the menu
29526 Insert\SpecialChar \menuseparator
29529 or with the toolbar button
29530 \begin_inset Graphics
29531 filename ../images/dialog-show-new-inset_ref.png
29537 A formula cross-reference appears in the output as formula number.
29538 When in the cross-reference dialog window the format
29542 is chosen, the cross-reference appears in the output as formula number
29544 \begin_inset Newline newline
29547 By right-clicking on a cross-reference in LyX, one jumps to the formula
29548 that is referenced.
29551 \begin_layout Standard
29552 Here are as examples cross-references to formulas of the following subsections:
29553 \begin_inset Note Note
29556 \begin_layout Plain Layout
29557 Note the different cross-reference types.
29565 \begin_layout Standard
29567 \begin_inset CommandInset ref
29574 \begin_inset CommandInset ref
29582 \begin_inset CommandInset ref
29588 ) big Latin letters are used for the numbering in contrary to (
29589 \begin_inset CommandInset ref
29598 \begin_layout Standard
29599 \begin_inset VSpace medskip
29602 When the argument of
29610 \begin_layout Plain Layout
29618 \begin_inset CommandInset ref
29620 reference "sub:User-defined-Numbering"
29631 contains a box like in
29632 \begin_inset CommandInset ref
29634 reference "sub:Paragraph-Boxes"
29638 , the formula cannot be referenced.
29641 \begin_layout Subsection
29646 \begin_layout Plain Layout
29647 Formula numbering ! subnumbering
29655 \begin_layout Standard
29656 With the help of the commands
29660 begin{subequations}
29668 formulas can be subnumbered.
29669 Both commands are inserted in TeX-mode.
29672 \begin_layout Standard
29674 \begin_inset Formula \begin{equation}
29675 A=C-B\label{eq:a}\end{equation}
29683 \begin_layout Plain Layout
29687 addtocounter{equation}{-1}
29696 \begin_layout Plain Layout
29700 begin{subequations}
29706 \begin_inset VSpace -5mm
29710 \begin_inset Formula \begin{equation}
29711 B=C-A\label{eq:b}\end{equation}
29716 \begin_inset Formula \begin{equation}
29717 C=A+B\label{eq:c}\end{equation}
29724 \begin_layout Standard
29728 \begin_layout Plain Layout
29740 \begin_layout Standard
29741 To create the example, the following is done:
29744 \begin_layout Enumerate
29745 first formula is inserted
29748 \begin_layout Enumerate
29753 addtocounter{equation}{-1}
29755 begin{subequations}
29759 \begin_layout Plain Layout
29768 \begin_inset Newline newline
29773 is inserted after the first formula
29776 \begin_layout Enumerate
29777 second formula is inserted
29780 \begin_layout Enumerate
29781 third formula is inserted
29784 \begin_layout Enumerate
29791 is inserted after the third formula
29794 \begin_layout Standard
29795 Every formula between the commands
29807 is subnumbered as a, b,
29808 \begin_inset Newline linebreak
29811 c, \SpecialChar \ldots{}
29812 For multiline formulas every line will be subnumbered.
29813 All subnumbered formulas are treated as
29818 But as every numbered formula increases the counter
29822 by one, the command
29828 is needed to decrease it.
29829 Otherwise the formulas
29830 \begin_inset CommandInset ref
29837 \begin_inset CommandInset ref
29844 \begin_inset CommandInset ref
29850 would be numbered as
29851 \begin_inset CommandInset ref
29858 \begin_inset CommandInset ref
29865 \begin_inset CommandInset ref
29874 \begin_layout Standard
29875 By inserting the commands in TeX-mode, a space is created between the first
29878 \begin_inset space \thinspace{}
29881 mm vertical space is inserted after the command
29885 begin{subequations}
29888 When the formula style
29894 \begin_layout Plain Layout
29896 \begin_inset CommandInset ref
29898 reference "sec:Formula-Styles"
29910 \begin_inset space \thinspace{}
29913 mm space is inserted instead.
29916 \begin_layout Standard
29917 Here is an example for a multiline formula where the numbering was turned
29918 off for the second line:
29922 \begin_layout Plain Layout
29926 begin{subequations}
29932 \begin_inset Formula \begin{eqnarray}
29933 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29934 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29935 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29943 \begin_layout Plain Layout
29955 \begin_layout Subsection
29956 User-defined Numbering
29957 \begin_inset CommandInset label
29959 name "sub:User-defined-Numbering"
29967 \begin_layout Plain Layout
29968 Formula numbering ! user-defined
29976 \begin_layout Standard
29980 \begin_layout Plain Layout
29981 Formula numbering ! self-defined delimiters
29986 With the standard numbering parentheses are set around the formula number.
29987 To replace the parentheses for example by vertical bars, the following
29988 line is added to the LaTeX-preamble:
29991 \begin_layout Standard
30003 \begin_inset Note Note
30006 \begin_layout Plain Layout
30007 This macro is already declared in the LaTeX-preamble for testing.
30008 To activate it, remove the percent sign at the beginning.
30016 \begin_layout Standard
30017 To use other characters, the vertical bars besides the
30021 are replaced by one ore more characters.
30022 To get only the formula number the vertical bars are omitted.
30025 \begin_layout Standard
30026 \begin_inset VSpace bigskip
30029 When there should be an expression of your choice instead of the consecutive
30030 formula number in parentheses behind the formula, the command
30040 \begin_layout Plain Layout
30049 \begin_inset Formula \begin{equation}
30050 A+B=C\tag{something}\label{eq:tag}\end{equation}
30054 In this example the command
30062 \begin_layout Plain Layout
30073 was inserted to the formula.
30076 \begin_layout Standard
30085 \begin_layout Plain Layout
30096 is inserted instead, the star prevents the parentheses around the expression:
30097 \begin_inset Formula \[
30098 A+B=C\tag*{something}\]
30105 \begin_layout Standard
30106 \begin_inset VSpace bigskip
30109 To restart the formula numbering with new document parts or sections, the
30110 following command is used:
30113 \begin_layout Standard
30118 @addtoreset{equation}{part}
30124 \begin_layout Plain Layout
30129 \begin_layout Plain Layout
30140 \begin_layout Plain Layout
30153 \begin_layout Plain Layout
30164 \begin_layout Plain Layout
30177 \begin_inset Newline newline
30181 \begin_inset Newline newline
30188 @addtoreset{equation}{section}
30191 \begin_layout Standard
30192 To be able to use these commands in TeX-mode, the
30193 \begin_inset Quotes eld
30197 \begin_inset Quotes erd
30200 character has to be made
30201 \begin_inset Quotes eld
30205 \begin_inset Quotes erd
30208 for LaTeX using the command
30222 So the command sequence in TeX-mode is:
30225 \begin_layout Standard
30231 \begin_inset Newline newline
30236 @addtoreset{equation}{section}
30237 \begin_inset Newline newline
30245 \begin_layout Standard
30246 In the LaTeX-preamble
30258 can be omitted as they are automatically internally inserted by LyX.
30261 \begin_layout Standard
30276 \begin_layout Plain Layout
30281 is part of the LaTeX-package
30289 \begin_layout Plain Layout
30290 Packages ! carlisle
30295 that is part of every LaTeX standard installation.
30304 \begin_layout Plain Layout
30305 Packages ! remreset
30310 has to be loaded in the LaTeX-preamble with the line
30313 \begin_layout Standard
30318 usepackage{remreset}
30321 \begin_layout Standard
30332 \begin_layout Plain Layout
30337 \begin_layout Plain Layout
30348 \begin_layout Plain Layout
30361 \begin_layout Plain Layout
30372 \begin_layout Plain Layout
30384 can be used with the same scheme as
30393 \begin_layout Standard
30394 \begin_inset VSpace bigskip
30397 Sometimes formulas should be numbered in the following form:
30400 \begin_layout Standard
30403 (section number.formula number)
30406 \begin_layout Standard
30407 The formula number should start with every section with
30408 \begin_inset Quotes eld
30412 \begin_inset Quotes erd
30418 \begin_layout Standard
30419 For this case there is the command
30429 \begin_layout Plain Layout
30437 , which is used with the following scheme:
30440 \begin_layout Standard
30445 numberwithin{counter}{sectioning}
30448 \begin_layout Standard
30449 Counter denotes what kind of numbering is affected, sectioning denotes what
30450 number is before the dot.
30453 \begin_layout Standard
30454 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30457 \begin_layout Standard
30462 numberwithin{equation}{section}
30465 \begin_layout Standard
30466 This is the result:
30470 \begin_layout Plain Layout
30474 numberwithin{equation}{section}
30480 \begin_inset Formula \begin{equation}
30481 A+B=C\end{equation}
30488 \begin_layout Standard
30490 \begin_inset space \thinspace{}
30494 \begin_inset space \space{}
30497 tables so that the number of the part is the sectioning,
30498 \begin_inset Newline newline
30505 numberwithin{table}{part}
30510 \begin_layout Standard
30511 To go back to the standard numbering or to prevent this kind of numbering
30512 when it is defined by the document class, the following command is inserted
30513 as TeX-Code or to the LaTeX-preamble:
30516 \begin_layout Standard
30529 \begin_layout Plain Layout
30543 \begin_layout Plain Layout
30559 \begin_inset Newline newline
30567 \begin_inset Newline newline
30579 \begin_layout Standard
30586 uses internally the command
30592 , described above, that also needs to be reverted.
30596 \begin_layout Plain Layout
30603 \begin_layout Plain Layout
30607 @removefromreset{equation}{section}
30610 \begin_layout Plain Layout
30622 \begin_layout Subsection
30623 Numbering with Roman Numbers and Letters
30627 \begin_layout Plain Layout
30628 Formula numbering ! with letters
30637 \begin_layout Plain Layout
30638 Formula numbering ! with Roman numbers
30646 \begin_layout Standard
30647 Formulas can also be numbered with Roman numbers and Latin letters.
30648 To number for example with small Roman numbers, the command
30651 \begin_layout Standard
30663 \begin_layout Standard
30664 is inserted before the formula in TeX-mode.
30675 \begin_layout Plain Layout
30683 redefines the predefined command
30699 \begin_layout Plain Layout
30706 has the same scheme like the command
30712 that is described in
30713 \begin_inset CommandInset ref
30715 reference "sub:The-Command-newcommand"
30728 is the formula counter.
30735 is used as prefix for a counter, the value of the counter is output as
30737 When a formula is numbered, LaTeX sets internally the command
30743 behind the formula.
30752 \begin_layout Plain Layout
30762 outputs the counter as small Roman number.
30765 \begin_layout Standard
30766 All formulas behind the command
30776 are now numbered Roman.
30777 To switch to numbering with big Roman numbers, the command is inserted
30794 \begin_layout Plain Layout
30806 \begin_inset Quotes eld
30810 \begin_inset Quotes erd
30813 with small Latin letters there is the command
30823 \begin_layout Plain Layout
30831 , for big ones there is the command
30841 \begin_layout Plain Layout
30854 \begin_layout Standard
30855 \begin_inset Note Greyedout
30858 \begin_layout Plain Layout
30863 Only maximal 26 formulas can be numbered with Latin letters in one document.
30871 \begin_layout Standard
30872 \begin_inset Newpage pagebreak
30878 \begin_layout Standard
30882 \begin_layout Plain Layout
30898 \begin_layout Standard
30899 \begin_inset Formula \begin{equation}
30900 A=\textrm{small roman}\end{equation}
30908 \begin_layout Plain Layout
30922 \begin_inset Formula \begin{equation}
30923 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30931 \begin_layout Plain Layout
30945 \begin_inset Formula \begin{equation}
30946 C=\textrm{small Latin}\end{equation}
30954 \begin_layout Plain Layout
30968 \begin_inset Formula \begin{equation}
30969 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30976 \begin_layout Standard
30977 To switch back to the default numbering, insert the command:
30980 \begin_layout Standard
30993 \begin_layout Plain Layout
31004 \begin_layout Standard
31008 \begin_layout Plain Layout
31022 \begin_inset Formula \begin{equation}
31023 E=\textrm{Arabic}\end{equation}
31030 \begin_layout Standard
31031 \begin_inset VSpace medskip
31034 As you see, formulas are numbered serially independent from the numbering
31036 When then numbering should start with
31037 \begin_inset Quotes eld
31041 \begin_inset Quotes erd
31044 when the style is changed, new equation counters have to be defined.
31045 A description about this can be found in the file
31046 \begin_inset CommandInset href
31048 name "Formula-numbering.lyx"
31049 target "run:Formula-numbering.lyx"
31056 \begin_layout Section
31057 Chemical Symbols and Equations
31058 \begin_inset CommandInset label
31060 name "sub:Chemical-Symbols-and"
31068 \begin_layout Plain Layout
31069 Chemical characters ! Symbols
31078 \begin_layout Plain Layout
31088 \begin_layout Plain Layout
31097 \begin_layout Standard
31098 An example text from chemistry:
31101 \begin_layout Quote
31103 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31106 -ion reacts with two
31107 \begin_inset Formula $\mathrm{Na^{+}}$
31110 -ions to sodium sulfate
31111 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31115 The chemical equation for this is:
31116 \begin_inset Formula \begin{equation}
31117 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
31124 \begin_layout Standard
31125 This chemical equation can directly be created as formula.
31126 To avoid that the symbols appear italic, everything is highlighted and
31127 changed by the shortcut
31133 to the upright font style.
31137 \begin_layout Plain Layout
31143 \begin_inset CommandInset ref
31145 reference "sub:Font-Styles"
31157 \begin_layout Standard
31158 A more convenient way to typeset chemical formulas is to use the command
31169 \begin_layout Plain Layout
31177 that is available when the LaTeX-package
31185 \begin_layout Plain Layout
31198 to a formula a new blue box appears where chemical formulas can be inserted
31199 in an intuitive way.
31202 \begin_layout Standard
31204 \begin_inset Tabular
31205 <lyxtabular version="3" rows="9" columns="2">
31207 <column alignment="center" valignment="top" width="0">
31208 <column alignment="center" valignment="top" width="0">
31210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31213 \begin_layout Plain Layout
31219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31222 \begin_layout Plain Layout
31224 \begin_inset Note Note
31227 \begin_layout Plain Layout
31234 is only used as spacer.
31246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31249 \begin_layout Plain Layout
31256 \begin_layout Plain Layout
31270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31273 \begin_layout Plain Layout
31274 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31287 \begin_layout Plain Layout
31294 \begin_layout Plain Layout
31308 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31311 \begin_layout Plain Layout
31312 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31325 \begin_layout Plain Layout
31332 \begin_layout Plain Layout
31346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31349 \begin_layout Plain Layout
31350 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
31360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31363 \begin_layout Plain Layout
31370 \begin_layout Plain Layout
31384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31387 \begin_layout Plain Layout
31388 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
31398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31401 \begin_layout Plain Layout
31408 \begin_layout Plain Layout
31423 \begin_layout Plain Layout
31438 \begin_layout Plain Layout
31452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31455 \begin_layout Plain Layout
31456 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
31466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31469 \begin_layout Plain Layout
31476 \begin_layout Plain Layout
31486 \begin_inset Formula $\downarrow$
31490 \begin_inset Formula $\to$
31498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31501 \begin_layout Plain Layout
31502 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
31512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31515 \begin_layout Plain Layout
31522 \begin_layout Plain Layout
31535 \begin_layout Plain Layout
31548 \begin_layout Plain Layout
31561 \begin_layout Plain Layout
31574 \begin_layout Plain Layout
31588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31591 \begin_layout Plain Layout
31592 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
31602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31605 \begin_layout Plain Layout
31612 \begin_layout Plain Layout
31625 \begin_layout Plain Layout
31638 \begin_layout Plain Layout
31651 \begin_layout Plain Layout
31668 \begin_layout Plain Layout
31682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31685 \begin_layout Plain Layout
31686 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
31702 \begin_layout Standard
31703 \begin_inset Note Greyedout
31706 \begin_layout Plain Layout
31711 Inserting a formula to a
31717 box will lead to LaTeX errors.
31718 In this case TeX code has to be used like for
31732 \begin_layout Plain Layout
31753 \begin_layout Standard
31760 the command for equation
31761 \begin_inset space ~
31765 \begin_inset CommandInset ref
31767 reference "eq:chem-reaction"
31772 \begin_inset Newline newline
31783 \begin_layout Plain Layout
31796 \begin_layout Plain Layout
31809 \begin_layout Plain Layout
31822 \begin_layout Plain Layout
31835 \begin_layout Plain Layout
31848 \begin_layout Plain Layout
31860 \begin_layout Standard
31861 To create multiline chemical equations first a multiline formula is created
31863 \begin_inset CommandInset ref
31865 reference "sec:Multiline-Formulas"
31870 Afterwards the command
31876 is used in every small blue box of the formula.
31878 \begin_inset CommandInset ref
31880 reference "eq:TEOS-reaction-1"
31885 \begin_inset CommandInset ref
31887 reference "eq:TEOS-reaction-2"
31891 are an example of a multi-stage chemical reaction where every equation
31892 has its own number.
31893 \begin_inset Formula \begin{eqnarray}
31894 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
31895 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}\end{eqnarray}
31902 \begin_layout Standard
31913 package provides the command
31923 \begin_layout Plain Layout
31931 that has to be used for special cases.
31932 For more information about
31938 and more examples have a look at the documentation of
31943 \begin_inset CommandInset citation
31952 \begin_layout Section
31956 \begin_layout Standard
31957 LyX supports two types of commutative diagrams:
31965 that are explained in the following.
31968 \begin_layout Subsection
31973 \begin_layout Plain Layout
31982 \begin_layout Standard
31983 Diagrams of this type visualize relations by vertical and horizontal lines
31985 \begin_inset Formula \[
31986 \begin{CD}A@>>>B@>>>C\\
31988 F@<<<E@<<<D\end{CD}\]
31995 \begin_layout Standard
31996 To get them, the command
32004 \begin_layout Plain Layout
32014 is inserted to a formula.
32015 A blue box appears with two dashed lines where further commands can be
32020 arg "newline-insert newline"
32023 a new line is created.
32024 Horizontal relations are inserted in odd, vertical in even formula lines.
32027 \begin_layout Standard
32028 To create the relations there are the following commands:
32031 \begin_layout Itemize
32036 creates a left arrow,
32047 \begin_layout Itemize
32052 creates an up arrow,
32060 a vertical equal sign
32063 \begin_layout Itemize
32069 is a placeholder for non-existent relations
32072 \begin_layout Standard
32073 All arrows can be labeled as follows:
32076 \begin_layout Itemize
32077 Is text inserted between the first and second < or >, resp., it is placed
32079 When it is inserted between the second and third one, it appears under
32083 \begin_layout Itemize
32084 When text for vertical arrows is inserted between the first and second A
32085 or V, resp., it is placed left beside the arrow.
32086 When it is inserted between the second and third one, it appears right
32088 If the text contains an A or V, these letters must be set into a TeX-brace.
32091 \begin_layout Standard
32092 As example a diagram with all possible relations:
32095 \begin_layout Standard
32096 \begin_inset Formula \[
32097 \begin{CD}A@>j>>B@>>k>C@=F\\
32099 D@<<j<E@>k>>F@=C\end{CD}\]
32106 \begin_layout Standard
32107 The command for this is:
32108 \begin_inset Newline newline
32119 \begin_layout Plain Layout
32128 A@>j>>B@>>k>C@=F Ctrl+Return
32129 \begin_inset Newline newline
32136 \begin_layout Plain Layout
32151 \begin_layout Plain Layout
32164 \begin_layout Plain Layout
32176 \begin_inset Formula $\to$
32182 \begin_inset Newline newline
32189 \begin_layout Plain Layout
32204 \begin_layout Plain Layout
32217 \begin_layout Plain Layout
32227 \begin_layout Subsection
32232 \begin_layout Plain Layout
32233 Diagrams ! xymatrix
32241 \begin_layout Standard
32242 To be able to use xymatrices, the LaTeX-package
32247 A xymatrix is created by inserting the command
32254 Then you are able to add new matrix columns and rows like for normal matrices,
32256 \begin_inset CommandInset ref
32258 reference "sec:Matrices"
32265 \begin_layout Standard
32266 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32268 All possibilities to create commutative diagrams and decorations are explained
32273 that you find in the menu
32275 Help\SpecialChar \menuseparator
32277 \begin_inset space ~
32280 Manuals\SpecialChar \menuseparator
32282 \begin_inset space ~
32290 \begin_layout Standard
32291 \begin_inset Newpage newpage
32297 \begin_layout Section
32298 User-defined Commands
32302 \begin_layout Plain Layout
32303 User-defined commands
32311 \begin_layout Standard
32312 \begin_inset Note Greyedout
32315 \begin_layout Plain Layout
32320 The names of user-defined commands and macros may only consist of Latin
32329 \begin_layout Subsection
32333 \begin_inset CommandInset label
32335 name "sub:The-Command-newcommand"
32343 \begin_layout Plain Layout
32344 User-defined commands !
32355 \begin_layout Plain Layout
32366 \begin_layout Standard
32367 Many LaTeX-commands are too long to be used frequently.
32368 But it is possible to define with the command
32374 new shorter commands.
32377 \begin_layout Standard
32378 The command scheme of
32387 \begin_layout Standard
32392 newcommand{new command name}[number of arguments][optional
32397 \begin_inset Newline newline
32404 \begin_layout Plain Layout
32419 \begin_layout Plain Layout
32426 {command definition}
32429 \begin_layout Standard
32430 \begin_inset Note Greyedout
32433 \begin_layout Plain Layout
32438 Assure that the name of the new command is not already used in your document
32439 or by LaTeX-packages that you use.
32440 When you for example define the command
32452 , you get an error message because
32458 is already defined as command for
32459 \begin_inset Quotes eld
32463 \begin_inset Formula $\le$
32467 \begin_inset Quotes erd
32478 \begin_layout Standard
32479 The number of arguments is an integer in the range 0
32480 \begin_inset space \thinspace{}
32484 \begin_inset space \thinspace{}
32487 9 and specifies how many arguments the new command should have.
32488 With the optional value a value for an optional argument can be predefined.
32489 When this is done, the
32497 rgument of the new command is automatically an optional one.
32500 \begin_layout Standard
32501 Here are some examples:
32504 \begin_layout Itemize
32505 To define the command
32517 , the LaTeX-preamble line is:
32518 \begin_inset VSpace medskip
32522 \begin_inset Newline newline
32536 \begin_layout Itemize
32537 To define the command
32549 , the argument (that should be underlined) must be taken into account.
32550 For this the preamble line is:
32551 \begin_inset VSpace medskip
32555 \begin_inset Newline newline
32569 \begin_inset VSpace medskip
32573 \begin_inset Newline newline
32580 acts as argument placeholder, the
32584 behind it denotes that it is the placeholder for the first argument.
32587 \begin_layout Itemize
32595 \begin_inset space \thinspace{}
32599 \begin_inset space \space{}
32609 \begin_inset VSpace medskip
32613 \begin_inset Newline newline
32624 framebox#1#2{$#3$}}
32627 \begin_inset VSpace medskip
32631 \begin_inset Newline newline
32634 The two Dollar signs creates the extra formula needed for
32641 \begin_inset CommandInset ref
32643 reference "sub:Boxes-with-Frame"
32650 \begin_layout Itemize
32651 To create a new command for
32657 where the color for the box needn't to be specified, the argument for the
32658 color is defined optional:
32659 \begin_inset VSpace medskip
32663 \begin_inset Newline newline
32674 fcolorbox{#2}{#1}{$#3$}}
32677 \begin_inset VSpace medskip
32681 \begin_inset Newline newline
32684 When the color is not specified when using
32690 , the predefined color
32697 \begin_layout Standard
32698 A test of the new defined commands:
32701 \begin_layout Standard
32703 \begin_inset Tabular
32704 <lyxtabular version="3" rows="6" columns="2">
32706 <column alignment="center" valignment="top" width="0">
32707 <column alignment="center" valignment="top" width="0">
32709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32712 \begin_layout Plain Layout
32718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32721 \begin_layout Plain Layout
32723 \begin_inset Note Note
32726 \begin_layout Plain Layout
32733 is only used as spacer.
32745 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32748 \begin_layout Plain Layout
32755 \begin_layout Plain Layout
32769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32772 \begin_layout Plain Layout
32773 \begin_inset Formula $A\gr B$
32783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32786 \begin_layout Plain Layout
32794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32797 \begin_layout Plain Layout
32798 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
32808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32811 \begin_layout Plain Layout
32815 \begin_inset Formula $\to$
32821 \begin_inset Formula $\to$
32832 \begin_layout Plain Layout
32846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32849 \begin_layout Plain Layout
32850 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
32860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32863 \begin_layout Plain Layout
32867 \begin_inset Formula $\to$
32878 \begin_layout Plain Layout
32892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32895 \begin_layout Plain Layout
32896 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
32906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32909 \begin_layout Plain Layout
32915 \begin_inset Formula $\to$
32926 \begin_layout Plain Layout
32940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32943 \begin_layout Plain Layout
32944 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
32960 \begin_layout Subsection
32965 \begin_layout Plain Layout
32966 User-defined commands! Math macros
32975 \begin_layout Plain Layout
32984 \begin_layout Standard
32985 User-defined commands are especially convenient for complex expressions.
32986 When you are for example dealing in a document with quadratic equations,
32987 the same solution type occurs several times.
32988 The general form of a quadratic equation is
32989 \begin_inset Formula \[
32990 0=\lambda^{2}+p\lambda+q\]
32994 The general form of the solution is
32995 \begin_inset Formula \[
32996 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
33003 \begin_layout Standard
33004 To define a command for the solution formula where only the three parameters
33006 \begin_inset Formula $\lambda$
33010 \begin_inset Formula $p$
33014 \begin_inset Formula $q$
33017 need to be specified and the index of
33018 \begin_inset Formula $\lambda$
33021 can be given optionally, the LaTeX-preamble line is
33022 \begin_inset Newline newline
33038 \begin_inset Newline newline
33045 \begin_layout Plain Layout
33060 \begin_layout Plain Layout
33071 frac{#3^{2}}{4}-#4}}
33074 \begin_layout Standard
33075 To create with this the solution formula, the command
33076 \begin_inset Newline newline
33086 \begin_inset Formula $\to$
33092 \begin_inset Formula $\to$
33099 is inserted to a formula
33104 \begin_layout Standard
33105 The definition of the new command is unintuitive because one has to know
33106 the schemes of all used LaTeX commands, e.
33107 \begin_inset space \thinspace{}
33111 \begin_inset space \space{}
33114 that a fraction is inserted in LaTeX as
33118 frac{numerator}{denominator}
33121 Furthermore one can easily forget a brace in the definition and cannot
33122 see in LyX what the new command is doing.
33123 To avoid these problems LyX offers the possibility to use math macros instead
33133 \begin_layout Standard
33134 A math macro is created by using the menu
33136 Insert\SpecialChar \menuseparator
33137 Math\SpecialChar \menuseparator
33140 or the toolbar button
33141 \begin_inset Graphics
33142 filename ../images/math-macro_newmacroname_newcommand.png
33148 The math macro toolbar appears together with the following box where the
33150 \begin_inset Newline newline
33154 \begin_inset space \hspace*{\fill}
33158 \begin_inset Graphics
33159 filename clipart/macrobox.png
33164 \begin_inset space \hspace*{\fill}
33168 \begin_inset Newline newline
33172 \begin_inset FormulaMacro
33173 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33178 newmacroname is the default name of the macro that should be changed to
33179 something sensible.
33180 The wanted formula is inserted in the first blue box.
33181 An argument placeholder is inserted with the command
33188 \begin_inset space \thinspace{}
33192 \begin_inset space \space{}
33201 or by using the macro toolbar button
33202 \begin_inset Graphics
33203 filename ../images/math-macro-add-param.png
33209 Argument placeholders are displayed red.
33210 Maximum 9 arguments are possible.
33211 Optional arguments are created with the toolbar button
33212 \begin_inset Graphics
33213 filename ../images/math-macro-add-optional-param.png
33219 The first non-optional argument can be transformed to an optional one with
33221 \begin_inset Graphics
33222 filename ../images/math-macro-make-optional.png
33228 In the second blue box the appearance of the macro in LyX can be defined.
33229 Normally you want to see it as it is defined, so the box is kept empty.
33230 But when you have created a macro that needs lot of space on the screen,
33231 you can insert in the box for example
33232 \begin_inset Newline newline
33262 \begin_inset Newline newline
33267 For the macro only the arguments with the macro name in front of them will
33268 then be displayed in LyX, leading to a better overview.
33269 The formula appears in the output as defined in the first box.
33270 \begin_inset Newline newline
33273 The appearance of macros in formulas can furthermore be changed for single
33274 macros by setting the cursor in the macro and using the menu
33276 View\SpecialChar \menuseparator
33278 \begin_inset space ~
33282 \begin_inset space ~
33290 \begin_layout Standard
33291 To use a macro, the macro name is inserted as command to a formula, in our
33299 Our macro looks in LyX like this:
33300 \begin_inset Newline newline
33304 \begin_inset space \hspace*{\fill}
33308 \begin_inset Graphics
33309 filename clipart/macrouse.png
33314 \begin_inset space \hspace*{\fill}
33318 \begin_inset Newline newline
33321 Here is our macro example with the arguments
33322 \begin_inset Formula $x$
33326 \begin_inset Formula $\ln(x)$
33330 \begin_inset Formula $B$
33336 \begin_layout Standard
33337 \begin_inset Formula \[
33345 \begin_layout Standard
33346 LyX offers in the menu
33348 Tools\SpecialChar \menuseparator
33349 Preferences\SpecialChar \menuseparator
33350 Editing\SpecialChar \menuseparator
33353 different styles to edit macros.
33354 To find the style that suits you the most, choose a style and set the cursor
33355 in a macro formula to see the difference.
33358 \begin_layout Standard
33359 A math macro is transformed internally to a
33365 command when exporting the document.
33372 command is not placed in the LaTeX-preamble, therefore macros can only
33373 be used in formulas that are in the document below the macro definition
33377 \begin_layout Standard
33378 Math macros can also be directly be created from a
33385 When writing for example the command
33388 \begin_inset Newline newline
33397 xleftarrow[#2]{#1}}
33398 \begin_inset Newline newline
33403 in LyX as normal text, highlighting it completely and using then the shortcut
33408 , the command will be transformed to a math macro.
33409 Using this method you need to be careful that the
33415 command is typed correctly, otherwise you get a faulty macro leading to
33419 \begin_layout Standard
33420 Math macros currently yet have the problem that further formulas in macro
33421 definitions are handled wrongly.
33422 Therefore the example
33429 \begin_inset CommandInset ref
33431 reference "sub:The-Command-newcommand"
33435 cannot be created as macro.
33438 \begin_layout Standard
33439 When the cursor is in a macro definition box, you will see the macro toolbar
33443 \begin_layout Standard
33444 \begin_inset VSpace defskip
33450 \begin_layout Standard
33451 \begin_inset Graphics
33452 filename clipart/MacroToolbar.png
33460 \begin_layout Plain Layout
33469 \begin_layout Standard
33470 \begin_inset VSpace defskip
33476 \begin_layout Standard
33477 The macro toolbar contains from left to right the following buttons:
33480 \begin_layout Standard
33481 \begin_inset VSpace defskip
33487 \begin_layout Standard
33488 \begin_inset Tabular
33489 <lyxtabular version="3" rows="9" columns="2">
33490 <features islongtable="true">
33491 <column alignment="left" valignment="top" width="0">
33492 <column alignment="left" valignment="top" width="85col%">
33493 <row interlinespace="2.5mm">
33494 <cell alignment="center" valignment="top" usebox="none">
33497 \begin_layout Plain Layout
33498 \begin_inset Graphics
33499 filename ../images/math-macro-remove-param.png
33500 BoundingBox 0bp 5bp 20bp 25bp
33501 rotateOrigin center
33510 <cell alignment="center" valignment="top" usebox="none">
33513 \begin_layout Plain Layout
33516 Edit\SpecialChar \menuseparator
33517 Math\SpecialChar \menuseparator
33519 \begin_inset space ~
33522 Definition\SpecialChar \menuseparator
33523 Remove Last Argument
33529 <row interlinespace="2.5mm">
33530 <cell alignment="center" valignment="top" usebox="none">
33533 \begin_layout Plain Layout
33534 \begin_inset Graphics
33535 filename ../images/math-macro-add-param.png
33536 BoundingBox 0bp 5bp 20bp 25bp
33537 rotateOrigin center
33546 <cell alignment="center" valignment="top" usebox="none">
33549 \begin_layout Plain Layout
33552 Edit\SpecialChar \menuseparator
33553 Math\SpecialChar \menuseparator
33555 \begin_inset space ~
33558 Definition\SpecialChar \menuseparator
33565 <row interlinespace="2.5mm">
33566 <cell alignment="center" valignment="top" usebox="none">
33569 \begin_layout Plain Layout
33570 \begin_inset Graphics
33571 filename ../images/math-macro-make-optional.png
33572 BoundingBox 0bp 5bp 20bp 25bp
33573 rotateOrigin center
33582 <cell alignment="center" valignment="top" usebox="none">
33585 \begin_layout Plain Layout
33588 Edit\SpecialChar \menuseparator
33589 Math\SpecialChar \menuseparator
33591 \begin_inset space ~
33594 Definition\SpecialChar \menuseparator
33595 Make First Non-Optional into
33596 \begin_inset Newline newline
33603 \begin_layout Plain Layout
33612 Edit\SpecialChar \menuseparator
33613 Math\SpecialChar \menuseparator
33615 \begin_inset space ~
33618 Definition\SpecialChar \menuseparator
33623 \begin_layout Plain Layout
33636 <row interlinespace="2.5mm">
33637 <cell alignment="center" valignment="top" usebox="none">
33640 \begin_layout Plain Layout
33641 \begin_inset Graphics
33642 filename ../images/math-macro-make-nonoptional.png
33643 BoundingBox 0bp 5bp 20bp 25bp
33644 rotateOrigin center
33653 <cell alignment="center" valignment="top" usebox="none">
33656 \begin_layout Plain Layout
33659 Edit\SpecialChar \menuseparator
33660 Math\SpecialChar \menuseparator
33662 \begin_inset space ~
33665 Definition\SpecialChar \menuseparator
33666 Make Last Optional into
33667 \begin_inset Newline newline
33674 \begin_layout Plain Layout
33683 Edit\SpecialChar \menuseparator
33684 Math\SpecialChar \menuseparator
33686 \begin_inset space ~
33689 Definition\SpecialChar \menuseparator
33694 \begin_layout Plain Layout
33701 Non-Optional Argument
33707 <row interlinespace="2.5mm">
33708 <cell alignment="center" valignment="top" usebox="none">
33711 \begin_layout Plain Layout
33712 \begin_inset Graphics
33713 filename ../images/math-macro-remove-optional-param.png
33714 BoundingBox 0bp 5bp 20bp 25bp
33715 rotateOrigin center
33724 <cell alignment="center" valignment="top" usebox="none">
33727 \begin_layout Plain Layout
33730 Edit\SpecialChar \menuseparator
33731 Math\SpecialChar \menuseparator
33733 \begin_inset space ~
33736 Definition\SpecialChar \menuseparator
33737 Remove Optional Argument
33743 <row interlinespace="2.5mm">
33744 <cell alignment="center" valignment="top" usebox="none">
33747 \begin_layout Plain Layout
33748 \begin_inset Graphics
33749 filename ../images/math-macro-add-optional-param.png
33750 BoundingBox 0bp 5bp 20bp 25bp
33751 rotateOrigin center
33760 <cell alignment="center" valignment="top" usebox="none">
33763 \begin_layout Plain Layout
33766 Edit\SpecialChar \menuseparator
33767 Math\SpecialChar \menuseparator
33769 \begin_inset space ~
33772 Definition\SpecialChar \menuseparator
33773 Insert Optional Argument
33779 <row interlinespace="2.5mm">
33780 <cell alignment="center" valignment="top" usebox="none">
33783 \begin_layout Plain Layout
33784 \begin_inset Graphics
33785 filename ../images/math-macro-remove-greedy-param.png
33786 BoundingBox 0bp 5bp 20bp 25bp
33787 rotateOrigin center
33796 <cell alignment="center" valignment="top" usebox="none">
33799 \begin_layout Plain Layout
33802 Edit\SpecialChar \menuseparator
33803 Math\SpecialChar \menuseparator
33805 \begin_inset space ~
33808 Definition\SpecialChar \menuseparator
33809 Remove Last Argument
33810 \begin_inset Newline newline
33817 \begin_layout Plain Layout
33826 Edit\SpecialChar \menuseparator
33827 Math\SpecialChar \menuseparator
33829 \begin_inset space ~
33832 Definition\SpecialChar \menuseparator
33837 \begin_layout Plain Layout
33844 Spitting Out To The Right
33850 <row interlinespace="2.5mm">
33851 <cell alignment="center" valignment="top" usebox="none">
33854 \begin_layout Plain Layout
33855 \begin_inset Graphics
33856 filename ../images/math-macro-append-greedy-param.png
33857 BoundingBox 0bp 5bp 20bp 25bp
33858 rotateOrigin center
33867 <cell alignment="center" valignment="top" usebox="none">
33870 \begin_layout Plain Layout
33873 Edit\SpecialChar \menuseparator
33874 Math\SpecialChar \menuseparator
33876 \begin_inset space ~
33879 Definition\SpecialChar \menuseparator
33881 \begin_inset Newline newline
33888 \begin_layout Plain Layout
33897 Edit\SpecialChar \menuseparator
33898 Math\SpecialChar \menuseparator
33900 \begin_inset space ~
33903 Definition\SpecialChar \menuseparator
33908 \begin_layout Plain Layout
33915 Eating From The Right
33921 <row interlinespace="2.5mm">
33922 <cell alignment="center" valignment="top" usebox="none">
33925 \begin_layout Plain Layout
33926 \begin_inset Graphics
33927 filename ../images/math-macro-add-greedy-optional-param.png
33928 BoundingBox 0bp 5bp 20bp 25bp
33929 rotateOrigin center
33938 <cell alignment="center" valignment="top" usebox="none">
33941 \begin_layout Plain Layout
33944 Edit\SpecialChar \menuseparator
33945 Math\SpecialChar \menuseparator
33947 \begin_inset space ~
33950 Definition\SpecialChar \menuseparator
33951 Append Optional Argument
33952 \begin_inset Newline newline
33959 \begin_layout Plain Layout
33968 Edit\SpecialChar \menuseparator
33969 Math\SpecialChar \menuseparator
33971 \begin_inset space ~
33974 Definition\SpecialChar \menuseparator
33979 \begin_layout Plain Layout
33986 Eating From The Right
33999 \begin_layout Standard
34000 \begin_inset Newpage newpage
34006 \begin_layout Section
34011 \begin_layout Plain Layout
34020 \begin_layout Subsection
34025 \begin_layout Plain Layout
34034 \begin_layout Standard
34035 Negative numbers often look ugly in formulas because the minus sign before
34036 the number is set with the same length as the minus operator sign.
34037 When writing the negative number in normal text, the minus sign appears
34041 \begin_layout Standard
34042 Thus, the problem disappears when converting the minus sign to mathematical
34046 \begin_layout Standard
34047 An example to visualize the problem:
34050 \begin_layout Standard
34052 \begin_inset Tabular
34053 <lyxtabular version="3" rows="3" columns="2">
34055 <column alignment="right" valignment="top" width="0">
34056 <column alignment="left" valignment="top" width="0">
34058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34061 \begin_layout Plain Layout
34067 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34070 \begin_layout Plain Layout
34078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34081 \begin_layout Plain Layout
34087 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34090 \begin_layout Plain Layout
34091 \begin_inset Formula $x=-2$
34101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34104 \begin_layout Plain Layout
34110 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34113 \begin_layout Plain Layout
34114 \begin_inset Formula $x=\textrm{-}2$
34130 \begin_layout Subsection
34131 Comma as decimal Separator
34135 \begin_layout Plain Layout
34144 \begin_layout Standard
34145 In LaTeX a comma inside a formula is used, according to the English convention,
34146 as number group separator.
34147 So there will be space added behind all commas in formulas.
34150 \begin_layout Standard
34151 To avoid this, the comma is highlighted and changed to mathematical text
34161 \begin_layout Standard
34162 To use all formula commas in the document as decimal separator, the file
34171 \begin_layout Plain Layout
34176 is part of the LaTeX-package
34184 \begin_layout Plain Layout
34189 \begin_layout Plain Layout
34212 \begin_layout Plain Layout
34218 is loaded with the LaTeX-preamble line
34221 \begin_layout Standard
34229 \begin_layout Subsection
34231 \begin_inset CommandInset label
34233 name "sub:Physical-Vectors"
34241 \begin_layout Plain Layout
34250 \begin_layout Standard
34251 Predefined vectors are offered by the LaTeX-package
34259 \begin_layout Plain Layout
34264 should be part of every LaTeX standard installation.
34273 \begin_layout Plain Layout
34279 that is loaded with the LaTeX-preamble line
34282 \begin_layout Standard
34290 \begin_layout Standard
34294 \begin_layout Plain Layout
34304 \begin_inset Note Note
34307 \begin_layout Plain Layout
34308 The following table will only be displayed when the LaTeX-package
34317 The following commands are defined:
34320 \begin_layout Standard
34322 \begin_inset Tabular
34323 <lyxtabular version="3" rows="4" columns="2">
34325 <column alignment="center" valignment="top" width="0">
34326 <column alignment="center" valignment="top" width="0">
34328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34331 \begin_layout Plain Layout
34337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34340 \begin_layout Plain Layout
34348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34351 \begin_layout Plain Layout
34361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34364 \begin_layout Plain Layout
34365 \begin_inset Formula $\Bra{\psi}$
34375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34378 \begin_layout Plain Layout
34388 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34391 \begin_layout Plain Layout
34392 \begin_inset Formula $\Ket{\psi}$
34402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34405 \begin_layout Plain Layout
34417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34420 \begin_layout Plain Layout
34421 \begin_inset Formula $\Braket{\psi|\phi}$
34437 \begin_layout Standard
34444 assures that all vertical bars are set in the size of the surrounding brackets:
34445 \begin_inset Formula \[
34446 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
34454 \begin_layout Plain Layout
34464 \begin_inset Note Note
34467 \begin_layout Plain Layout
34468 The following will be displayed when the LaTeX-package
34480 \begin_layout Standard
34481 You need to install the LaTeX-package
34485 to see the rest of this subsection in the output.
34488 \begin_layout Standard
34492 \begin_layout Plain Layout
34504 \begin_layout Standard
34511 can also be achieved using the command
34517 , that is described in
34518 \begin_inset CommandInset ref
34520 reference "sub:Automatic-Bracket-Size"
34527 \begin_layout Subsection
34528 Self-defined Fractions
34529 \begin_inset CommandInset label
34531 name "sub:Self-defined-Fractions"
34539 \begin_layout Plain Layout
34540 Fractions ! self-defined
34548 \begin_layout Standard
34549 To define custom commands for fractions, the command
34559 \begin_layout Plain Layout
34567 is used in the following scheme:
34570 \begin_layout Standard
34583 bracket}{fraction bar thickness}{style}
34584 \begin_inset Newline newline
34591 \begin_layout Plain Layout
34606 \begin_layout Plain Layout
34613 {numerator}{denominator}
34616 \begin_layout Standard
34617 The style is a number in the range of 0
34618 \begin_inset space \thinspace{}
34622 \begin_inset space \thinspace{}
34628 \begin_layout Standard
34630 \begin_inset Tabular
34631 <lyxtabular version="3" rows="5" columns="2">
34633 <column alignment="center" valignment="top" width="0">
34634 <column alignment="center" valignment="top" width="0">
34636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34639 \begin_layout Plain Layout
34645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34648 \begin_layout Plain Layout
34656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34659 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34668 \begin_layout Plain Layout
34669 display style formula
34676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34679 \begin_layout Plain Layout
34685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34688 \begin_layout Plain Layout
34696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34699 \begin_layout Plain Layout
34705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34708 \begin_layout Plain Layout
34716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34719 \begin_layout Plain Layout
34725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34728 \begin_layout Plain Layout
34742 \begin_layout Standard
34743 When no style is given, the size is adjusted to the surrounding environment
34744 like for the command
34753 \begin_layout Standard
34754 When no fraction bar thickness is given, the predefined value of 0.4
34755 \begin_inset space \thinspace{}
34761 \begin_layout Standard
34762 \begin_inset VSpace medskip
34765 For example, the commands
34778 \begin_inset CommandInset ref
34780 reference "sub:Fractions"
34784 are defined with the commands
34787 \begin_layout Standard
34796 genfrac{}{}{}{0}{#1}{#2}}
34799 \begin_layout Standard
34803 \begin_layout Standard
34812 genfrac{(}{)}{0pt}{1}{#1}{#2}}
34815 \begin_layout Standard
34816 \begin_inset VSpace medskip
34819 To define a fraction where the fraction bar thickness can be given as optional
34820 argument, the following line is inserted to the LaTeX-preamble:
34823 \begin_layout Standard
34832 genfrac{}{}{#1}{}{#2}{#3}}
34835 \begin_layout Standard
34837 \begin_inset Formula \begin{align*}
34838 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
34839 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
34843 As one can see, the distance of the numerator and the denominator to the
34844 fraction bar is round about three times the bar thickness.
34847 \begin_layout Subsection
34852 \begin_layout Plain Layout
34861 \begin_layout Standard
34862 To cancel formulas or formula parts, the LaTeX-package
34870 \begin_layout Plain Layout
34875 is part of every LaTeX standard installation.
34884 \begin_layout Plain Layout
34890 has to be loaded with the LaTeX-preamble line
34893 \begin_layout Standard
34898 usepackage[samesize]{cancel}
34901 \begin_layout Standard
34902 There are four ways to cancel formulas:
34905 \begin_layout Standard
34907 \begin_inset Tabular
34908 <lyxtabular version="3" rows="5" columns="2">
34910 <column alignment="center" valignment="top" width="0">
34911 <column alignment="center" valignment="top" width="0">
34913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34916 \begin_layout Plain Layout
34922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34925 \begin_layout Plain Layout
34927 \begin_inset Note Note
34930 \begin_layout Plain Layout
34937 are used here as spacer.
34949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34952 \begin_layout Plain Layout
34961 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34978 \begin_layout Plain Layout
34979 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
34989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34992 \begin_layout Plain Layout
35001 \begin_layout Plain Layout
35015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35018 \begin_layout Plain Layout
35019 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35032 \begin_layout Plain Layout
35041 \begin_layout Plain Layout
35055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35058 \begin_layout Plain Layout
35059 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35072 \begin_layout Plain Layout
35076 \begin_inset Formula $\to$
35087 \begin_layout Plain Layout
35101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35104 \begin_layout Plain Layout
35105 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35121 \begin_layout Standard
35128 is especially suitable to visualize the reduction of fractions within formulas:
35129 \begin_inset Formula \[
35130 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
35137 \begin_layout Subsection
35138 Formulas in Section Headings
35139 \begin_inset CommandInset label
35141 name "sub:Formulas-in-Section"
35149 \begin_layout Plain Layout
35150 Formula ! in section headings
35158 \begin_layout Standard
35159 When formulas are used in section headings, the following has to be taken
35163 \begin_layout Standard
35164 \begin_inset Note Greyedout
35167 \begin_layout Plain Layout
35176 \begin_layout Plain Layout
35177 Packages ! hyperref
35182 support is enabled in the document settings dialog under
35185 \begin_inset space ~
35190 , PDF-bookmarks are created for every section heading in the table of contents.
35191 If a section heading contains formulas, they are incorrectly displayed
35192 in the bookmark text, because formulas in bookmarks infringe the PDF convention
35201 \begin_layout Standard
35202 Both problems can be solved by inserting at the end of the section heading
35203 a short title with the menu
35205 Insert\SpecialChar \menuseparator
35207 \begin_inset space ~
35213 Short titles are used as alternative for multiline section headings to
35214 keep the table of contents clearly arranged.
35215 Only the short title appears in the table of contents and therefore also
35216 in the PDF-bookmark.
35219 \begin_layout Standard
35220 When formulas should be used in the table of contents but
35224 is used, one can use the following command in TeX-mode:
35227 \begin_layout Standard
35232 texorpdfstring{part}{alternative}
35236 \begin_layout Plain Layout
35247 \begin_layout Standard
35248 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
35249 This can be characters, formulas, footnotes, but also cross-references.
35250 The alternative is used instead of the part for the bookmark.
35253 \begin_layout Standard
35254 Here are two example headings:
35255 \begin_inset VSpace -3mm
35262 \begin_layout Plain Layout
35274 \begin_layout Subsubsection
35275 Heading without formula in table of contents
35276 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35280 \begin_inset OptArg
35283 \begin_layout Plain Layout
35284 Heading without formula in table of contents
35292 \begin_layout Subsubsection
35293 Heading with formula in table of contents
35297 \begin_layout Plain Layout
35307 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
35314 \begin_layout Plain Layout
35324 \begin_layout Standard
35328 \begin_layout Plain Layout
35337 In the first heading a short title was used, in the second one
35346 \begin_layout Standard
35347 To get the same formatting as for the other headings, the complete heading
35356 \begin_layout Plain Layout
35358 \begin_inset CommandInset ref
35360 reference "sub:Bold-Formulas"
35372 \begin_layout Subsection
35373 Formulas in multi-column Text
35377 \begin_layout Plain Layout
35378 Formula ! in multi-column text
35386 \begin_layout Standard
35387 Formulas in multi-column text are often too wide to fit into a column and
35388 thus need to be set over the whole page width.
35389 This is done by using the LaTeX-package
35397 \begin_layout Plain Layout
35402 is part of every LaTeX standard installation.
35411 \begin_layout Plain Layout
35412 Packages ! multicol
35417 , that is loaded with the LaTeX-preamble line
35420 \begin_layout Standard
35425 usepackage{multicol}
35428 \begin_layout Standard
35429 \begin_inset Note Greyedout
35432 \begin_layout Plain Layout
35433 Note herby that the setting
35436 \begin_inset space ~
35443 Document\SpecialChar \menuseparator
35449 \begin_inset space ~
35469 \begin_layout Standard
35470 Before the multi-column text the command
35473 \begin_layout Standard
35478 begin{multicols}{column number}
35481 \begin_layout Standard
35482 is written in TeX-mode.
35483 The column number is a number in the range of 2
35484 \begin_inset space \thinspace{}
35488 \begin_inset space \thinspace{}
35492 Before the formula the multi-column text is ended by inserting the command
35495 \begin_layout Standard
35503 \begin_layout Standard
35507 \begin_layout Standard
35508 Due to the command some space is automatically added before the formula.
35510 \begin_inset space \thinspace{}
35513 mm vertical space is inserted before the formula.
35514 When the formula style
35520 \begin_layout Plain Layout
35522 \begin_inset CommandInset ref
35524 reference "sec:Formula-Styles"
35536 \begin_inset space \thinspace{}
35539 mm space is inserted instead.
35542 \begin_layout Standard
35543 As example a multi-column text with a displayed formula:
35546 \begin_layout Standard
35552 \begin_layout Plain Layout
35556 begin{multicols}{2}
35561 Das Spektrum wird fouriertransformiert.
35562 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
35563 , Lösungsmittel) zu trennen.
35564 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
35565 nun das Aussehen des Ausgangssignals.
35566 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
35567 über alle Phasen integrieren muss.
35569 \begin_inset Formula $S$
35572 unser normiertes Ausgangssignal und
35573 \begin_inset Formula $P$
35576 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
35580 \begin_layout Plain Layout
35590 \begin_inset VSpace -6mm
35594 \begin_inset Formula \begin{equation}
35595 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
35603 \begin_layout Plain Layout
35607 begin{multicols}{2}
35613 \begin_inset Formula $S_{0}$
35616 das Signal ohne Gradient ist und die Normierungsbedingung
35617 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
35621 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
35623 \begin_inset Formula $\nicefrac{\pi}{2}$
35627 \begin_inset space \thinspace{}
35630 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
35631 das Signal zusätzlich abschwächt.
35632 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
35634 \begin_inset Formula $T_{2}$
35640 \begin_layout Standard
35646 \begin_layout Plain Layout
35658 \begin_layout Subsection
35659 Formulas with Description of Variables
35663 \begin_layout Plain Layout
35664 Formula ! with description of variables
35672 \begin_layout Standard
35673 To describe variables within a formula, like in formula
35674 \begin_inset CommandInset ref
35676 reference "eq:within"
35685 \begin_inset Formula $n$
35689 \begin_inset space ~
35692 matrix is used with left aligned columns for the
35693 \begin_inset Formula $n$
35700 \begin_layout Plain Layout
35702 \begin_inset CommandInset ref
35704 reference "sec:Matrices"
35713 To set the description in a smaller size, before the matrix e.
35714 \begin_inset space \thinspace{}
35718 \begin_inset space \space{}
35731 \begin_layout Plain Layout
35733 \begin_inset CommandInset ref
35735 reference "sub:Font-Sizes"
35747 \begin_layout Standard
35748 When the formula style
35754 \begin_layout Plain Layout
35756 \begin_inset CommandInset ref
35758 reference "sec:Formula-Styles"
35779 \begin_layout Plain Layout
35786 only works in formulas with the style
35791 \begin_inset CommandInset ref
35793 reference "sub:Variable-Space"
35802 is inserted before and after the matrix to have the same separation of
35803 the matrix from the equation and the side margin.
35806 \begin_layout Standard
35807 When the formula style
35811 is used, the method described in
35812 \begin_inset CommandInset ref
35814 reference "sub:Flalign-Environment"
35818 is used to indent formulas.
35820 \begin_inset CommandInset ref
35822 reference "eq:within"
35826 consists of five columns whereas in the first two columns contain the equation,
35827 the third the matrix, and the last one an empty TeX-brace.
35828 \begin_inset Formula \begin{flalign}
35829 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
35830 \rho & \textrm{density}\\
35831 V & \textrm{volume}\\
35832 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
35839 \begin_layout Subsection
35840 Upright small Greek Letters
35841 \begin_inset CommandInset label
35843 name "sub:Upright-small-Greek"
35851 \begin_layout Plain Layout
35852 Greek letters ! upright
35860 \begin_layout Standard
35861 Most of the math fonts only provide italic small Greek letters.
35862 But for symbols of elementary particles like pions and neutrinos, upright
35863 Greek letters are needed.
35872 \begin_layout Plain Layout
35877 is part of the LaTeX-package
35885 \begin_layout Plain Layout
35890 \begin_layout Plain Layout
35913 \begin_layout Plain Layout
35919 that is loaded with the LaTeX-preamble line
35922 \begin_layout Standard
35927 usepackage{upgreek}
35930 \begin_layout Standard
35936 \begin_layout Plain Layout
35946 \begin_inset Note Note
35949 \begin_layout Plain Layout
35950 The following table will only be displayed when the LaTeX-package
35959 They are created when the command for a small Greek letters is started
35965 For example the command
35972 \begin_inset Formula $\uptau$
35978 \begin_layout Standard
35979 With these commands reactions of elementary particles can be typeset:
35980 \begin_inset Formula \[
35981 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
35988 \begin_layout Standard
35989 The upright letters are more bold and wider than the italic ones.
35990 They should therefore not be used for units like
35991 \begin_inset Quotes eld
35995 \begin_inset Quotes erd
36001 \begin_layout Standard
36005 \begin_layout Plain Layout
36015 \begin_inset Note Note
36018 \begin_layout Plain Layout
36019 The following will be displayed when the LaTeX-package
36031 \begin_layout Standard
36032 You need to install the LaTeX-package
36036 to see the rest of this subsection in the output.
36039 \begin_layout Standard
36043 \begin_layout Plain Layout
36055 \begin_layout Subsection
36056 Text Characters in Formulas
36057 \begin_inset CommandInset label
36059 name "sub:Text-Characters-in"
36067 \begin_layout Plain Layout
36076 \begin_layout Standard
36077 In some cases you might want to insert text characters directly into formulas.
36078 When for example the centered dot · is often used in formulas like
36079 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
36082 , one would have to insert the command
36092 \begin_layout Plain Layout
36094 \begin_inset CommandInset ref
36096 reference "sub:Binary-Operators"
36105 all the time, because this character is defined in all encodings as text
36107 But the encoding can be changed by this LaTeX-preamble line:
36110 \begin_layout Standard
36115 Declare Inputtext{183}{
36125 f\SpecialChar \textcompwordmark{}
36129 \begin_layout Standard
36130 The character encoding (menu
36132 Document\SpecialChar \menuseparator
36133 Settings\SpecialChar \menuseparator
36136 ) specifies what character appears when a keyboard key is pressed.
36137 When the key for the character '·' is pressed, internally the command
36144 But this command is not available in a formula so that you would get LaTeX-erro
36146 With the changed encoding the right command is chosen automatically, depending
36147 on if the character was inserted into a formula or not.
36150 \begin_layout Standard
36151 The encoding of several characters is saved in definition files.
36152 Fore example the encoding
36156 is defined in the file
36160 that is in the installation folder of LaTeX.
36161 Encodings should only be changed via the LaTeX-preamble and not in the
36163 Otherwise own documents could not be edited by other LyX users working
36164 on other computers.
36167 \begin_layout Standard
36168 \begin_inset VSpace medskip
36171 Besides the centered dot, in this document the degree sign ° is defined
36172 with the following LaTeX-preamble line so that it can directly be inserted
36176 \begin_layout Standard
36181 DeclareInputtext{176}{
36191 f\SpecialChar \textcompwordmark{}
36195 \begin_layout Standard
36196 \begin_inset Newpage newpage
36202 \begin_layout Section
36208 \begin_layout Plain Layout
36217 \begin_layout Standard
36218 This section is a summary of the most important typographic rules, listed
36223 \begin_layout Plain Layout
36224 This collection was partly taken from the German semi-official dictionary
36226 \begin_inset Quotes eld
36230 \begin_inset Quotes erd
36234 \begin_inset CommandInset citation
36240 that lists some of the ISO rules.
36248 \begin_layout Itemize
36257 \begin_layout Plain Layout
36258 done with font styles, see
36259 \begin_inset CommandInset ref
36261 reference "sub:Font-Styles"
36271 \begin_inset space \thinspace{}
36275 \begin_inset Newline newline
36278 Between the value and the unit is the smallest space, see
36279 \begin_inset CommandInset ref
36281 reference "sub:Predefined-Space"
36286 \begin_inset Newline newline
36289 This convention is automatically fulfilled when the command
36296 When it is entered to a formula, two boxes appear.
36297 In the first one the value is inserted, in the second one the unit, and
36299 \begin_inset Formula $\unit[30]{km/h}$
36303 \begin_inset space \thinspace{}
36313 is not a real LaTeX command but the command
36319 , therefore you cannot use it in TeX code.
36322 \begin_layout Itemize
36323 Percent and perthousand signs are set like physical units:
36324 \begin_inset Newline newline
36328 \begin_inset space \thinspace{}
36334 \begin_layout Itemize
36335 The degree sign follows directly on the value: 15°, but not when it is used
36337 \begin_inset space \thinspace{}
36343 \begin_layout Itemize
36344 In numbers with more than four digits the smallest space is inserted before
36345 every third digit to group them:
36355 \begin_inset space \thinspace{}
36359 \begin_inset space \thinspace{}
36365 \begin_layout Itemize
36366 For dimensions like 120×90×40
36367 \begin_inset space \thinspace{}
36370 cm the multiplication sign
36371 \begin_inset Quotes eld
36375 \begin_inset Quotes erd
36379 It is available either via the command
36387 Insert\SpecialChar \menuseparator
36388 Special Character\SpecialChar \menuseparator
36394 \begin_layout Itemize
36395 Functions with names consisting of several letters are set upright to avoid
36397 \begin_inset CommandInset ref
36399 reference "sub:Predefined-Functions"
36406 \begin_layout Itemize
36407 Indices consisting of several letters, are set upright:
36408 \begin_inset Formula $E_{\mathrm{kin}}$
36412 \begin_inset Newline newline
36415 Components of matrices are set italic:
36416 \begin_inset Formula $\hat{H}_{kl}$
36422 \begin_layout Itemize
36423 The differentiation/integration operator 'd', the Euler's number 'e', and
36424 the imaginary unit 'i' should be set upright, to avoid mixing them up with
36428 \begin_layout Itemize
36429 The character that denotes a
36433 transformation is inserted either by the command
36441 \begin_layout Plain Layout
36458 \begin_layout Plain Layout
36468 Insert\SpecialChar \menuseparator
36469 Special Character\SpecialChar \menuseparator
36470 Symbols\SpecialChar \menuseparator
36472 \begin_inset space ~
36478 \begin_inset Formula $\mathscr{F}$
36482 \begin_inset Newline newline
36485 To be able to use the command
36491 , the LaTeX package
36499 \begin_layout Plain Layout
36500 Packages ! mathrsfs
36505 needs to be loaded with the LaTeX-preamble line
36509 usepackage{mathrsfs}
36514 \begin_layout Standard
36515 \begin_inset Newpage newpage
36521 \begin_layout Section
36526 \begin_layout Plain Layout
36535 \begin_layout Standard
36536 Some characters and symbols can be created with several commands.
36537 Here is a list of the synonym commands:
36540 \begin_layout Standard
36541 \begin_inset VSpace bigskip
36545 \begin_inset space \hfill{}
36549 \begin_inset Tabular
36550 <lyxtabular version="3" rows="12" columns="2">
36552 <column alignment="center" valignment="top" width="0pt">
36553 <column alignment="center" valignment="top" width="0pt">
36555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
36558 \begin_layout Plain Layout
36564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
36567 \begin_layout Plain Layout
36569 \begin_inset Note Note
36572 \begin_layout Plain Layout
36579 is only used as spacer.
36591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36594 \begin_layout Plain Layout
36602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36605 \begin_layout Plain Layout
36609 \begin_layout Plain Layout
36622 \begin_layout Plain Layout
36636 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
36639 \begin_layout Plain Layout
36647 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
36650 \begin_layout Plain Layout
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