1 #LyX 1.6.0rc2 created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
42 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 \settowidth{\abc}{\space}
46 \renewcommand{\equationautorefname}{\hspace{-\abc}}
47 \renewcommand{\sectionautorefname}{sec.\negthinspace}
48 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
49 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{\contentsname}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
68 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
70 % provides caption formatting
71 \setkomafont{captionlabel}{\bfseries}
74 \usepackage[samesize]{cancel}
76 % enables calculation of values,
79 % for multiple table row and column cells
86 % center multirows (e.g. in sec. 13.3)
87 \renewcommand{\multirowsetup}{\centering}
89 % define a color, used in sec.9.3
90 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
92 % declare operators (see sec. 10.4 and sec. 15.2)
93 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
94 \DeclareMathOperator{\sgn}{sgn}
96 \newcommand{\spce}{\textvisiblespace}
98 % example definitions for sec. 20.1
99 \newcommand{\gr}{\Longrightarrow}
100 \newcommand{\us}[1]{\underline{#1}}
101 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
102 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
103 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
105 % example macro from sec. 19.4
106 %\def\tagform@#1{\maketag@@@{|#1|}}
108 % macro from sec. 10.2
109 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
110 \def\mathclap {\mathpalette \mathclapinternal}
111 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
113 % redefine the greyed out note
114 \renewenvironment{lyxgreyedout}
115 {\textcolor{blue}\bgroup}{\egroup}
117 % ------------------------------------
118 % used to check for needed LaTeX packages
121 % check for package eurosym
122 % used for the Euro symbol
124 \IfFileExists{eurosym.sty}
125 {\usepackage[gennarrow]{eurosym}
126 \setboolean{eurosym}{true}}
127 {\setboolean{eurosym}{false}}
129 % needed in sec. 22.4
130 % check for package braket
132 \IfFileExists{braket.sty}
134 \setboolean{braket}{true}}
135 {\setboolean{braket}{false}}
137 % needed in sec. 22.10
138 % check for package upgreek
140 \IfFileExists{upgreek.sty}
141 {\usepackage{upgreek}
142 \setboolean{upgreek}{true}}
143 {\setboolean{upgreek}{false}}
145 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
150 \font_typewriter default
151 \font_default_family default
161 \pdf_title "LyX's Math Manual"
162 \pdf_author "LyX Team, Uwe Stöhr"
163 \pdf_subject "LyX-documentation about math"
164 \pdf_keywords "LyX, Mathed"
166 \pdf_bookmarksnumbered true
167 \pdf_bookmarksopen true
168 \pdf_bookmarksopenlevel 1
169 \pdf_breaklinks false
173 \pdf_pagebackref false
174 \pdf_pdfusetitle false
175 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
182 \paperorientation portrait
185 \paragraph_separation skip
187 \quotes_language english
190 \paperpagestyle plain
194 \tracking_changes false
195 \output_changes false
202 LyX's detailed Math manual
210 \begin_layout Plain Layout
212 If you have comments or error corrections, please send them to the LyX Documenta
216 \begin_inset CommandInset href
218 name "lyx-docs@lists.lyx.org"
219 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
230 \begin_inset Note Note
233 \begin_layout Plain Layout
240 \begin_inset Newline newline
244 \begin_inset Newline newline
252 \begin_layout Standard
253 \begin_inset CommandInset toc
254 LatexCommand tableofcontents
261 \begin_layout Standard
262 \begin_inset Note Note
265 \begin_layout Plain Layout
266 To export this document to PDF, PS, or DVI the LaTeX-packages
279 If they are not installed you can export the document anyway but the sections
280 where the packages are required won't appear in the output.
283 \begin_layout Plain Layout
284 The latest PDF-version of this document can be found here:
285 \begin_inset Newline newline
290 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
298 \begin_layout Standard
299 \begin_inset Newpage newpage
305 \begin_layout Section
307 \begin_inset CommandInset label
309 name "sec:Introduction"
316 \begin_layout Standard
317 This document explains LyX's math features and is furthermore a collection
318 of LaTeX-commands used for mathematical characters and constructs.
319 The explanations are designed for the usage of commands.
320 It is therefore required that you have read the section
331 \begin_layout Standard
332 Most of the characters and many constructs explained in this manual are
333 also accessible via the menu
337 \SpecialChar \menuseparator
353 But everybody who has to write lots of formulas will notice that it is
354 much faster to use commands instead of the math toolbar.
355 Therefore this manual is focused on commands but also mentions the correspondin
356 g toolbar buttons when available.
359 \begin_layout Standard
360 If not specially mentioned the commands are only available within formulas.
361 To be able to use all commands explained in this document, the option
365 must be used in the document settings (menu
367 Document\SpecialChar \menuseparator
368 Settings\SpecialChar \menuseparator
379 \begin_layout Plain Layout
382 Use AMS math package automatically
388 \begin_layout Plain Layout
397 -math when math constructs are found that are supported by LyX.
405 \begin_layout Standard
406 This document doesn't list all
410 \begin_layout Plain Layout
423 \begin_layout Plain Layout
428 \begin_layout Plain Layout
437 -math commands is in the file
440 \begin_inset CommandInset href
443 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
449 , which is part of every LaTeX standard installation.
454 for lucidity reasons.
457 \begin_layout Section
459 \begin_inset CommandInset label
461 name "sec:General-Instructions"
468 \begin_layout Standard
469 To create an inline formula
473 \begin_layout Plain Layout
479 that is embedded into a text line, press
483 or the toolbar button
484 \begin_inset Graphics
485 filename ../images/math-mode.png
491 \begin_inset Newline newline
494 To create a display style formula
498 \begin_layout Plain Layout
499 Formula ! display style
504 that will appear bigger and in an own paragraph, press
511 \begin_layout Standard
512 To change a display style formula to an inline formula, set the cursor into
513 the formula and press
519 Edit\SpecialChar \menuseparator
520 Math\SpecialChar \menuseparator
524 The same way is used to change an inline formula to a display style formula.
527 \begin_layout Standard
528 To display parts of an inline formula in the size of a display style formula,
537 \begin_layout Plain Layout
548 Then a new blue box appears in which the desired formula part is inserted.
551 \begin_layout Standard
552 Only inline formulas are allowed inside tables.
555 \begin_layout Standard
560 can be turned on in the menu
562 View\SpecialChar \menuseparator
566 When you click there on
567 \begin_inset Quotes eld
571 \begin_inset Quotes erd
574 the toolbar will be shown permanently at the bottom; this state is visualized
579 menu with a checkmark.
580 When you click in this state again on
581 \begin_inset Quotes eld
585 \begin_inset Quotes erd
596 is only shown when the cursor is within a formula; this state is visualized
597 by the renaming of the menu entry from
598 \begin_inset Quotes eld
602 \begin_inset Quotes erd
606 \begin_inset Quotes eld
614 \begin_inset Quotes erd
620 \begin_layout Standard
625 \begin_layout Plain Layout
631 is invoked by pressing the toolbar button
632 \begin_inset Graphics
633 filename ../images/ert-insert.png
640 Insert\SpecialChar \menuseparator
645 \begin_layout Plain Layout
659 \begin_inset Note Note
662 \begin_layout Plain Layout
663 In LyX there are three
664 \begin_inset Quotes eld
668 \begin_inset Quotes erd
671 that appear in the output with sub- and superscript letters: TeX, LaTeX,
675 \begin_layout Plain Layout
676 To avoid that these names are recognized as proper names, a TeX-brace pair
685 \begin_layout Standard
686 To change the LaTeX-preamble
690 \begin_layout Plain Layout
698 Document\SpecialChar \menuseparator
699 Settings\SpecialChar \menuseparator
704 \begin_layout Plain Layout
720 \begin_layout Standard
721 To edit matrices, case differentiations, and multiline formulas subsequently,
724 Edit\SpecialChar \menuseparator
729 Edit\SpecialChar \menuseparator
731 \begin_inset space \thinspace{}
735 \begin_inset space \thinspace{}
745 When lines and columns are swapped via the menu, the column or line where
746 the cursor is in is exchanged with the column to the right or the line
748 Is the cursor in the last column or row, the exchange is done with the
749 column to the left or the line above.
752 \begin_layout Standard
753 To write text in formulas
757 \begin_layout Plain Layout
758 For multiline formulas the command
765 \begin_inset CommandInset ref
767 reference "sub:Text-in-multiline"
784 \begin_layout Plain Layout
794 \begin_layout Plain Layout
801 This mode is invoked with the the shortcut
809 or by the insertion of the command
817 \begin_layout Plain Layout
828 The text appears black in LyX and can therefore be distinguished from the
829 other formula parts that appear blue.
830 In the output mathematical text is set upright, in contrary to other formula
834 \begin_layout Subsection*
838 \begin_layout Standard
839 Most of the LaTeX-commands for math constructs have the following scheme:
842 \begin_layout Standard
858 \begin_layout Standard
859 A command starts always with a backslash
860 \begin_inset Quotes gld
870 \begin_inset Quotes grd
874 To omit optional arguments, also omit the associated brackets.
875 The braces around the required arguments are named in this document as
880 \begin_layout Plain Layout
887 If you add in a formula a left brace to a command name, LyX creates automatical
889 In all other cases TeX-braces are created in formulas with the command
897 TeX-braces appear red in LyX, in contrary to normal braces that appear
899 In TeX-mode no command is needed to get TeX-braces.
900 TeX-braces don't appear in the output.
903 \begin_layout Standard
904 When commands without arguments, like commands for symbols are entered in
905 TeX-mode, a space character must
909 be behind the command to end it.
910 This space doesn't appear in the output.
911 When the space should appear in the output, the space must be followed
912 by a protected space in normal text.
915 \begin_layout Standard
916 A protected space is inserted with
923 \begin_layout Subsection*
924 \begin_inset Newpage newpage
930 \begin_layout Itemize
935 \begin_layout Plain Layout
936 This visible space character can be created with the command
946 \begin_layout Plain Layout
954 , inserted in TeX-mode.
963 \begin_layout Plain Layout
976 denotes a space character to be input.
979 \begin_layout Itemize
981 \begin_inset Formula $\to$
984 denotes the usage of the corresponding arrow key on the keyboard.
987 \begin_layout Subsection*
991 \begin_layout Standard
993 \begin_inset Float table
999 \begin_layout Plain Layout
1001 \begin_inset Caption
1003 \begin_layout Plain Layout
1004 \begin_inset CommandInset label
1006 name "tab:Available-units"
1018 \begin_layout Plain Layout
1020 \begin_inset Tabular
1021 <lyxtabular version="3" rows="13" columns="2">
1023 <column alignment="center" valignment="top" width="0">
1024 <column alignment="center" valignment="top" width="0">
1026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1029 \begin_layout Plain Layout
1035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1038 \begin_layout Plain Layout
1046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1049 \begin_layout Plain Layout
1055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1058 \begin_layout Plain Layout
1066 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1069 \begin_layout Plain Layout
1075 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1078 \begin_layout Plain Layout
1086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1089 \begin_layout Plain Layout
1095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1098 \begin_layout Plain Layout
1100 \begin_inset space \thinspace{}
1104 \begin_inset space \thinspace{}
1114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1117 \begin_layout Plain Layout
1123 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1126 \begin_layout Plain Layout
1128 \begin_inset space \thinspace{}
1132 \begin_inset space \thinspace{}
1142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1145 \begin_layout Plain Layout
1151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1154 \begin_layout Plain Layout
1156 \begin_inset space \thinspace{}
1160 \begin_inset space \thinspace{}
1170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1173 \begin_layout Plain Layout
1179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1182 \begin_layout Plain Layout
1184 \begin_inset space \thinspace{}
1188 \begin_inset space \thinspace{}
1198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1201 \begin_layout Plain Layout
1207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1210 \begin_layout Plain Layout
1212 \begin_inset space \thinspace{}
1216 \begin_inset space \thinspace{}
1226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1229 \begin_layout Plain Layout
1235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1238 \begin_layout Plain Layout
1240 \begin_inset space \thinspace{}
1244 \begin_inset Formula $\approx$
1248 \begin_inset space \thinspace{}
1258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1261 \begin_layout Plain Layout
1267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1270 \begin_layout Plain Layout
1272 \begin_inset space \thinspace{}
1276 \begin_inset space \thinspace{}
1286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1289 \begin_layout Plain Layout
1295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1298 \begin_layout Plain Layout
1302 \begin_inset Quotes eld
1308 \begin_inset Quotes erd
1318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1321 \begin_layout Plain Layout
1327 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1330 \begin_layout Plain Layout
1332 \begin_inset Quotes eld
1340 \begin_inset Quotes erd
1350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1353 \begin_layout Plain Layout
1359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1362 \begin_layout Plain Layout
1364 \begin_inset space \thinspace{}
1368 \begin_inset Formula $\nicefrac{1}{18}$
1372 \begin_inset space \thinspace{}
1393 \begin_layout Standard
1394 \begin_inset Newpage newpage
1400 \begin_layout Section
1404 \begin_layout Subsection
1409 \begin_layout Plain Layout
1419 \begin_layout Plain Layout
1429 \begin_layout Plain Layout
1434 \begin_layout Plain Layout
1445 \begin_layout Plain Layout
1461 \begin_layout Plain Layout
1466 \begin_layout Plain Layout
1477 \begin_layout Plain Layout
1492 \begin_layout Standard
1493 Indices are created with an underscore
1494 \begin_inset Quotes eld
1498 \begin_inset Quotes erd
1501 or via the math toolbar button
1502 \begin_inset Graphics
1503 filename ../images/math-subscript.png
1508 , exponents with a caret
1509 \begin_inset Quotes eld
1513 \begin_inset Quotes erd
1516 or via the math toolbar button
1517 \begin_inset Graphics
1518 filename ../images/math-superscript.png
1526 \begin_layout Standard
1528 \begin_inset Tabular
1529 <lyxtabular version="3" rows="4" columns="2">
1531 <column alignment="center" valignment="top" width="0pt">
1532 <column alignment="center" valignment="top" width="0pt">
1534 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1537 \begin_layout Plain Layout
1543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1546 \begin_layout Plain Layout
1548 \begin_inset Note Note
1551 \begin_layout Plain Layout
1558 is only used as spacer.
1570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1573 \begin_layout Plain Layout
1579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1582 \begin_layout Plain Layout
1583 \begin_inset Formula $B_{V}$
1593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1596 \begin_layout Plain Layout
1602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1605 \begin_layout Plain Layout
1606 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1619 \begin_layout Plain Layout
1624 \begin_layout Plain Layout
1638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1641 \begin_layout Plain Layout
1642 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1658 \begin_layout Standard
1659 As the caret is in some languages an accent, vowels will be accentuated
1660 in this case and not set as exponents
1664 \begin_layout Plain Layout
1665 Depending on the used keyboard settings this can also happen for other character
1672 To get in this case exponents, press
1676 after the caret as in the last example.
1679 \begin_layout Subsection
1681 \begin_inset CommandInset label
1683 name "sub:Fractions"
1691 \begin_layout Plain Layout
1700 \begin_layout Standard
1701 Fractions are generated with the command
1711 \begin_layout Plain Layout
1719 or via the math toolbar button
1720 \begin_inset Graphics
1721 filename ../images/math/frac.png
1727 The font size is adjusted automatically, depending on whether the fraction
1728 is in an inline or display style formula.
1729 With the math toolbar button
1730 \begin_inset Graphics
1731 filename ../images/math/frac-square.png
1736 you can select different fraction types.
1739 \begin_layout Standard
1748 \begin_layout Plain Layout
1758 a fraction can be created that has in any case the size of a display style
1768 \begin_layout Plain Layout
1778 the fraction appears always with the size of an inline formula.
1782 \begin_layout Standard
1783 A line with the fraction
1784 \begin_inset Formula $\frac{1}{2}$
1787 that was created with the command
1796 \begin_layout Standard
1797 A line with the fraction
1798 \begin_inset Formula $\dfrac{1}{2}$
1801 that was created with the command
1810 \begin_layout Standard
1812 \begin_inset Tabular
1813 <lyxtabular version="3" rows="4" columns="2">
1815 <column alignment="center" valignment="top" width="0pt">
1816 <column alignment="center" valignment="top" width="0pt">
1818 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1821 \begin_layout Plain Layout
1827 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1830 \begin_layout Plain Layout
1832 \begin_inset Note Note
1835 \begin_layout Plain Layout
1842 is only used as spacer.
1854 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1857 \begin_layout Plain Layout
1864 \begin_layout Plain Layout
1874 \begin_inset Formula $\downarrow$
1882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1885 \begin_layout Plain Layout
1886 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1899 \begin_layout Plain Layout
1906 \begin_layout Plain Layout
1916 \begin_inset Formula $\downarrow$
1924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1927 \begin_layout Plain Layout
1928 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1941 \begin_layout Plain Layout
1948 \begin_layout Plain Layout
1961 \begin_layout Plain Layout
1976 \begin_layout Plain Layout
1986 \begin_inset Formula $\downarrow$
1990 \begin_inset Formula $\downarrow\downarrow$
1998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2001 \begin_layout Plain Layout
2002 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2018 \begin_layout Standard
2019 \begin_inset VSpace bigskip
2023 \begin_inset Newpage newpage
2026 For nested fractions the command
2036 \begin_layout Plain Layout
2046 \begin_inset VSpace -3mm
2052 \begin_layout Standard
2053 \begin_inset Formula \begin{align*}
2054 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2055 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2062 \begin_layout Standard
2063 The command for the example above is:
2066 \begin_layout Standard
2072 \begin_inset Formula $\to$
2082 \begin_inset Formula $\to$
2088 \begin_inset Formula $\to\to$
2096 \begin_layout Standard
2097 \begin_inset VSpace medskip
2103 \begin_layout Standard
2110 sets the fraction always in the size of a displayed formula, also when
2111 it is part of another fraction.
2118 has the following command scheme:
2121 \begin_layout Standard
2126 cfrac[numerator position]{numerator}{denominator}
2129 \begin_layout Standard
2130 The numerator position can be
2143 l or r aligns the numerator to the left or right, resp.
2144 \begin_inset space ~
2147 with the fraction stroke.
2152 or no position is given, the numerator appears centered.
2153 These fractions demonstrate the different alignments:
2154 \begin_inset Newline newline
2160 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2164 \begin_inset Formula $\cfrac{A}{B+C}$
2168 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2174 \begin_layout Standard
2175 \begin_inset VSpace medskip
2178 It is often advantageous to combine
2191 \begin_inset Formula \[
2192 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2199 \begin_layout Standard
2200 For inline fractions with a sloped fraction stroke you can use the command
2211 \begin_layout Plain Layout
2220 \begin_inset Formula $\nicefrac{5}{31}$
2233 \begin_layout Plain Layout
2242 \begin_inset Formula $\unitfrac{5}{31}$
2245 There is furthermore the command
2251 that offers to write a fraction in combination with a number:
2252 \begin_inset Formula $\unitfrac[2]{1}{3}$
2256 \begin_inset Newline newline
2265 is not a real LaTeX command but the command
2266 \begin_inset Newline newline
2273 unitfrac[number]{numerator}{denominator}
2275 , therefore you cannot use it in TeX code.
2278 \begin_layout Standard
2279 How to define own fractions where the fraction stroke can be changed, is
2281 \begin_inset CommandInset ref
2283 reference "sub:Self-defined-Fractions"
2290 \begin_layout Subsection
2295 \begin_layout Plain Layout
2304 \begin_layout Standard
2305 Square roots are created with
2315 \begin_layout Plain Layout
2323 or the math toolbar button
2324 \begin_inset Graphics
2325 filename ../images/math/sqrt.png
2330 , all other roots with the command
2340 \begin_layout Plain Layout
2348 or with the math toolbar button
2349 \begin_inset Graphics
2350 filename ../images/math/root.png
2358 \begin_layout Standard
2360 \begin_inset Tabular
2361 <lyxtabular version="3" rows="3" columns="2">
2363 <column alignment="center" valignment="top" width="0pt">
2364 <column alignment="center" valignment="top" width="0pt">
2366 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2369 \begin_layout Plain Layout
2375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2378 \begin_layout Plain Layout
2380 \begin_inset Note Note
2383 \begin_layout Plain Layout
2390 is only used as spacer.
2402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2405 \begin_layout Plain Layout
2412 \begin_layout Plain Layout
2426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2429 \begin_layout Plain Layout
2430 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2440 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2443 \begin_layout Plain Layout
2450 \begin_layout Plain Layout
2460 \begin_inset Formula $\downarrow$
2468 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2471 \begin_layout Plain Layout
2472 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2488 \begin_layout Standard
2489 A square root can also be created with
2495 when the root index field is left empty.
2498 \begin_layout Standard
2499 With certain indices the distance to the root is too small, like in this
2501 \begin_inset Formula $\sqrt[\beta]{B}$
2505 \begin_inset Newline newline
2509 \begin_inset Formula $\beta$
2513 To avoid this, the commands
2523 \begin_layout Plain Layout
2541 \begin_layout Plain Layout
2549 are used with the following scheme:
2552 \begin_layout Standard
2566 \begin_layout Standard
2567 Distance is the number of Big Points (unit bp;
2568 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2571 ), that the index should be moved to the left or top, resp..
2572 The commands are written to the index.
2573 This way the command
2574 \begin_inset Newline newline
2584 \begin_inset Formula $\to$
2590 \begin_inset Formula $\to$
2599 \begin_layout Plain Layout
2609 \begin_inset Formula $\to$
2613 \begin_inset Newline newline
2618 produces a correct typeset formula:
2619 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2625 \begin_layout Subsection
2626 Binomial Coefficients
2630 \begin_layout Plain Layout
2631 Binomial coefficients
2639 \begin_layout Standard
2640 Binomial coefficients are inserted with the command
2650 \begin_layout Plain Layout
2658 or with the submenu of the math toolbar button
2659 \begin_inset Graphics
2660 filename ../images/math/frac-square.png
2666 Analog to fractions (
2686 \begin_layout Plain Layout
2706 \begin_layout Plain Layout
2715 For other brackets around binomial coeficients there are the commands
2725 \begin_layout Plain Layout
2743 \begin_layout Plain Layout
2754 \begin_layout Standard
2756 \begin_inset Tabular
2757 <lyxtabular version="3" rows="6" columns="2">
2759 <column alignment="center" valignment="top" width="0pt">
2760 <column alignment="center" valignment="top" width="0pt">
2762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2765 \begin_layout Plain Layout
2771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2774 \begin_layout Plain Layout
2776 \begin_inset Note Note
2779 \begin_layout Plain Layout
2786 is only used as spacer.
2798 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2801 \begin_layout Plain Layout
2808 \begin_layout Plain Layout
2818 \begin_inset Formula $\downarrow$
2826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2829 \begin_layout Plain Layout
2830 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2843 \begin_layout Plain Layout
2850 \begin_layout Plain Layout
2860 \begin_inset Formula $\downarrow$
2868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2871 \begin_layout Plain Layout
2872 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2885 \begin_layout Plain Layout
2892 \begin_layout Plain Layout
2902 \begin_inset Formula $\downarrow$
2910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2913 \begin_layout Plain Layout
2914 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2927 \begin_layout Plain Layout
2934 \begin_layout Plain Layout
2944 \begin_inset Formula $\downarrow$
2952 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2955 \begin_layout Plain Layout
2956 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2969 \begin_layout Plain Layout
2976 \begin_layout Plain Layout
2986 \begin_inset Formula $\downarrow$
2994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2997 \begin_layout Plain Layout
2998 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3014 \begin_layout Subsection
3015 Case Differentiations
3019 \begin_layout Plain Layout
3020 Case differentiations
3028 \begin_layout Standard
3030 \begin_inset Tabular
3031 <lyxtabular version="3" rows="3" columns="2">
3033 <column alignment="center" valignment="top" width="0pt">
3034 <column alignment="center" valignment="top" width="0pt">
3036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3039 \begin_layout Plain Layout
3045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3048 \begin_layout Plain Layout
3056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3059 \begin_layout Plain Layout
3066 \begin_layout Plain Layout
3076 \begin_inset Formula $\to$
3083 \begin_layout Plain Layout
3096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3099 \begin_layout Plain Layout
3100 \begin_inset Formula $\begin{cases}
3111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3114 \begin_layout Plain Layout
3121 \begin_layout Plain Layout
3135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3138 \begin_layout Plain Layout
3139 \begin_inset Formula $\begin{cases}
3140 A & \textrm{for }x>0\\
3141 B & \textrm{for }x=0\end{cases}$
3157 \begin_layout Standard
3164 or the usage of the math toolbar button
3165 \begin_inset Graphics
3166 filename ../images/math/cases.png
3171 you can create new lines with the shortcut
3175 or the table toolbar button
3176 \begin_inset Graphics
3177 filename ../images/tabular-feature_append-row.png
3185 \begin_layout Standard
3192 is also available via the menu
3194 Insert\SpecialChar \menuseparator
3195 Math\SpecialChar \menuseparator
3201 \begin_layout Subsection
3206 \begin_layout Plain Layout
3215 \begin_layout Standard
3226 \begin_layout Plain Layout
3234 every character can be displayed canceled.
3235 The characters are quasi accentuated by a slash.
3238 \begin_layout Standard
3240 \begin_inset Tabular
3241 <lyxtabular version="3" rows="4" columns="2">
3243 <column alignment="center" valignment="top" width="0pt">
3244 <column alignment="center" valignment="top" width="0pt">
3246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3249 \begin_layout Plain Layout
3255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3258 \begin_layout Plain Layout
3266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3269 \begin_layout Plain Layout
3277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3280 \begin_layout Plain Layout
3281 \begin_inset Formula $\not=$
3291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3294 \begin_layout Plain Layout
3304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3307 \begin_layout Plain Layout
3308 \begin_inset Formula $\not\le$
3318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3321 \begin_layout Plain Layout
3331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3334 \begin_layout Plain Layout
3335 \begin_inset Formula $\not\parallel$
3351 \begin_layout Standard
3352 The last example shows, that not all negations look good.
3353 Therefore there are for some negations special commands (see
3354 \begin_inset CommandInset ref
3356 reference "sub:Mathematical-Symbols"
3361 \begin_inset CommandInset ref
3363 reference "sec:Relations"
3370 \begin_layout Subsection
3372 \begin_inset CommandInset label
3374 name "sub:Placeholders"
3382 \begin_layout Plain Layout
3392 \begin_layout Plain Layout
3393 Chemical characters ! Isotopes
3402 \begin_layout Plain Layout
3407 \begin_layout Plain Layout
3418 \begin_layout Plain Layout
3433 \begin_layout Standard
3435 \begin_inset space \thinspace{}
3439 \begin_inset space ~
3446 \begin_layout Plain Layout
3447 More about chemical symbols is written in
3448 \begin_inset CommandInset ref
3450 reference "sub:Chemical-Symbols-and"
3459 the following problem occurs:
3462 \begin_layout Standard
3464 \begin_inset Tabular
3465 <lyxtabular version="3" rows="2" columns="2">
3467 <column alignment="center" valignment="top" width="0pt">
3468 <column alignment="center" valignment="top" width="0pt">
3470 <cell alignment="center" valignment="top" usebox="none">
3473 \begin_layout Plain Layout
3474 Indices created with sub- and superscripts:
3479 <cell alignment="center" valignment="top" usebox="none">
3482 \begin_layout Plain Layout
3483 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3493 <cell alignment="center" valignment="top" usebox="none">
3496 \begin_layout Plain Layout
3502 <cell alignment="center" valignment="top" usebox="none">
3505 \begin_layout Plain Layout
3506 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3520 \begin_inset Note Note
3523 \begin_layout Plain Layout
3530 is only used as spacer.
3538 \begin_layout Standard
3539 The shorter index is by default placed below or above the first character
3540 of the longer index.
3541 To avoid this there is the command
3551 \begin_layout Plain Layout
3559 or the math toolbar button
3560 \begin_inset space \thinspace{}
3567 \begin_layout Plain Layout
3568 can be found in the submenu of the toolbar button
3569 \begin_inset Graphics
3570 filename ../images/math/space.png
3581 \begin_inset Graphics
3582 filename ../images/math/phantom.png
3587 that creates one or more phantom characters.
3594 a small blue box appears that is superposed with two red arrows.
3595 The arrows indicate that the complete width and height of the box content
3596 will be created as placeholder.
3597 Phantom characters are accordingly placeholders with the size of the characters.
3600 \begin_layout Standard
3602 \begin_inset Tabular
3603 <lyxtabular version="3" rows="4" columns="2">
3605 <column alignment="center" valignment="top" width="0">
3606 <column alignment="center" valignment="top" width="0">
3608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3611 \begin_layout Plain Layout
3617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3620 \begin_layout Plain Layout
3622 \begin_inset Note Note
3625 \begin_layout Plain Layout
3632 is only used as spacer.
3644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3647 \begin_layout Plain Layout
3652 \begin_layout Plain Layout
3667 \begin_layout Plain Layout
3677 \begin_inset Formula $\to$
3684 \begin_layout Plain Layout
3698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3701 \begin_layout Plain Layout
3702 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3715 \begin_layout Plain Layout
3720 \begin_layout Plain Layout
3735 \begin_layout Plain Layout
3745 \begin_inset Formula $\to$
3752 \begin_layout Plain Layout
3766 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3769 \begin_layout Plain Layout
3770 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3780 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3783 \begin_layout Plain Layout
3790 \begin_layout Plain Layout
3805 \begin_layout Plain Layout
3815 \begin_inset Formula $\to$
3822 \begin_layout Plain Layout
3836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3839 \begin_layout Plain Layout
3840 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3856 \begin_layout Standard
3857 Furthermore there are the commands
3867 \begin_layout Plain Layout
3876 \begin_inset space ~
3880 \begin_inset Graphics
3881 filename ../images/math/vphantom.png
3896 \begin_layout Plain Layout
3905 \begin_inset space ~
3909 \begin_inset Graphics
3910 filename ../images/math/hphantom.png
3922 creates only space for the maximal height of the characters in the box
3923 but not for its width.
3930 creates only space for the width of the box content.
3931 Therefore the boxes of both commands have only one red arrow.
3934 \begin_layout Standard
3945 \begin_layout Plain Layout
3960 space for the height of the integral sign,
3964 \begin_layout Plain Layout
3971 creates an integral sign, see
3972 \begin_inset CommandInset ref
3974 reference "sub:Big-Operators"
3983 because this is the larger character.
3984 An example application is in
3985 \begin_inset CommandInset ref
3987 reference "sub:Multiline-Brackets"
3994 \begin_layout Subsection
3999 \begin_layout Plain Layout
4009 \begin_layout Plain Layout
4010 Formula ! underlined
4018 \begin_layout Standard
4020 \begin_inset Tabular
4021 <lyxtabular version="3" rows="4" columns="2">
4023 <column alignment="center" valignment="top" width="0pt">
4024 <column alignment="center" valignment="top" width="0pt">
4026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4029 \begin_layout Plain Layout
4035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4038 \begin_layout Plain Layout
4040 \begin_inset Note Note
4043 \begin_layout Plain Layout
4050 is only used as spacer.
4062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4065 \begin_layout Plain Layout
4072 \begin_layout Plain Layout
4085 \begin_layout Plain Layout
4098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4101 \begin_layout Plain Layout
4102 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4112 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4115 \begin_layout Plain Layout
4122 \begin_layout Plain Layout
4135 \begin_layout Plain Layout
4148 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4151 \begin_layout Plain Layout
4152 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4165 \begin_layout Plain Layout
4172 \begin_layout Plain Layout
4187 \begin_layout Plain Layout
4201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4204 \begin_layout Plain Layout
4205 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4221 \begin_layout Standard
4222 In the last example it doesn't matter if first
4237 \begin_layout Standard
4238 To double underline e.
4239 \begin_inset space \thinspace{}
4252 \begin_layout Standard
4253 It is possible to place up to 6 lines above or below characters.
4256 \begin_layout Standard
4257 \begin_inset VSpace bigskip
4260 Custom lines can be created using the command
4270 \begin_layout Plain Layout
4278 which has the following scheme:
4281 \begin_layout Standard
4286 rule[vertical offset]{length}{thickness}
4289 \begin_layout Standard
4290 The optional vertical offset shifts the line upwards (or downwards, when
4291 the value is negative).
4293 \begin_inset CommandInset ref
4295 reference "tab:Available-units"
4299 can be used for the values.
4300 Here are two example lines created with the commands
4301 \begin_inset Newline newline
4308 rule[-2ex]{3cm}{2pt}
4319 \begin_layout Standard
4321 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4327 \begin_layout Standard
4334 can also be used for text when it is inserted in TeX-mode.
4337 \begin_layout Subsection
4339 \begin_inset CommandInset label
4349 \begin_layout Plain Layout
4358 \begin_layout Standard
4359 There are different types of ellipses available.
4363 \begin_layout Plain Layout
4364 In the math toolbar in the submenu of the button
4365 \begin_inset Graphics
4366 filename ../images/math/ldots.png
4376 For listings dots at the baseline are used (
4386 \begin_layout Plain Layout
4394 ), while for operations dots are needed that are on the same height as the
4405 \begin_layout Plain Layout
4414 When using the command
4424 \begin_layout Plain Layout
4432 , LaTeX decides on the basis of the next character what type is used.
4435 \begin_layout Standard
4437 \begin_inset Tabular
4438 <lyxtabular version="3" rows="8" columns="2">
4440 <column alignment="center" valignment="top" width="0pt">
4441 <column alignment="center" valignment="top" width="0pt">
4443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4446 \begin_layout Plain Layout
4452 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4455 \begin_layout Plain Layout
4463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4466 \begin_layout Plain Layout
4471 \begin_layout Plain Layout
4486 \begin_layout Plain Layout
4500 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4503 \begin_layout Plain Layout
4504 \begin_inset Formula $A_{1},\dots,A_{n}$
4514 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4517 \begin_layout Plain Layout
4522 \begin_layout Plain Layout
4537 \begin_layout Plain Layout
4551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4554 \begin_layout Plain Layout
4555 \begin_inset Formula $A_{1}+\dots+A_{n}$
4565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4568 \begin_layout Plain Layout
4573 \begin_layout Plain Layout
4588 \begin_layout Plain Layout
4602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4605 \begin_layout Plain Layout
4606 \begin_inset Formula $A_{1},\ldots,A_{n}$
4616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4619 \begin_layout Plain Layout
4624 \begin_layout Plain Layout
4639 \begin_layout Plain Layout
4653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4656 \begin_layout Plain Layout
4657 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4670 \begin_layout Plain Layout
4678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4681 \begin_layout Plain Layout
4682 \begin_inset Formula $\vdots$
4692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4695 \begin_layout Plain Layout
4703 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4706 \begin_layout Plain Layout
4707 \begin_inset Formula $\ddots$
4717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4720 \begin_layout Plain Layout
4722 \begin_inset space \thinspace{}
4725 matrix with the different dots
4730 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4733 \begin_layout Plain Layout
4734 \begin_inset Formula $\begin{array}{ccc}
4735 A_{11} & \cdots & A_{1m}\\
4736 \vdots & \ddots & \vdots\\
4737 A_{n1} & \cdots & A_{nm}\end{array}$
4753 \begin_layout Standard
4754 The ellipses available in menu
4756 Insert\SpecialChar \menuseparator
4758 \begin_inset space ~
4772 \begin_layout Standard
4773 \begin_inset VSpace medskip
4776 Specially for matrices there are ellipses that span over several columns.
4777 They are created with the command
4787 \begin_layout Plain Layout
4795 , that has the following scheme:
4798 \begin_layout Standard
4803 hdotsfor[distance]{number of columns}
4806 \begin_layout Standard
4807 The number of columns specifies how many columns should be spanned.
4808 Distance is a factor for the distance between the dots.
4811 \begin_layout Standard
4812 In the following matrix the command
4818 was inserted in the first box of the second line, to get an ellipsis with
4819 a dot distance twice as long as with the command
4826 \begin_inset Formula \[
4827 \left(\begin{array}{cccc}
4830 q & w & e & r\end{array}\right)\]
4834 Note that the matrix fields that should be spanned must be empty, otherwise
4835 you get LaTeX-errors.
4838 \begin_layout Standard
4839 \begin_inset VSpace bigskip
4842 Furthermore you can fill with the command
4852 \begin_layout Plain Layout
4860 the rest of a line with dots.
4861 The effect of these commands is the same like with
4868 \begin_inset CommandInset ref
4870 reference "sub:Variable-Space"
4877 \begin_layout Standard
4878 For example the command
4886 \begin_layout Plain Layout
4900 \begin_layout Standard
4901 \begin_inset Formula $A\dotfill B$
4907 \begin_layout Standard
4914 there is for a line the command
4924 \begin_layout Plain Layout
4935 \begin_layout Standard
4936 \begin_inset Formula $A\hrulefill B$
4942 \begin_layout Standard
4943 To use the commands for text, they have to be inserted in TeX-mode.
4946 \begin_layout Section
4948 \begin_inset CommandInset label
4958 \begin_layout Plain Layout
4967 \begin_layout Standard
4968 Matrices can be inserted via the math toolbar button
4969 \begin_inset Graphics
4970 filename ../images/dialog-show_mathmatrix.png
4977 Insert\SpecialChar \menuseparator
4978 Math\SpecialChar \menuseparator
4982 You will be asked for the number of matrix columns and rows, and the alignment.
4983 The vertical alignment is hereby only of importance for matrices in inline
4987 \begin_layout Standard
4988 The first matrix is top
4989 \begin_inset Formula $\begin{array}[t]{cccc}
4992 C & F & I & L\end{array}$
4996 \begin_inset Formula $\begin{array}{cccc}
4999 C & F & I & L\end{array}$
5002 , and the third bottom
5003 \begin_inset Formula $\begin{array}[b]{cccc}
5006 C & F & I & L\end{array}$
5012 \begin_layout Standard
5013 The horizontal alignment specifies how the column entries should be aligned.
5014 It is set by entering a letter for every column.
5019 denotes left aligned,
5028 To create for example a 4
5033 \begin_inset space ~
5036 matrix where the first column is left aligned, the second and third are
5037 centered, and the last one is right aligned, one enters for the horizontal
5043 Normally are in a matrix all columns centered, therefore the default is
5044 for every column is a
5051 \begin_layout Standard
5052 Horizontal alignment:
5055 \begin_layout Standard
5061 \begin_inset Formula $\begin{array}{lll}
5064 C & F & 10000\end{array}$
5072 \begin_inset Formula $\begin{array}{ccc}
5075 C & F & 10000\end{array}$
5083 \begin_inset Formula $\begin{array}{rrr}
5086 C & F & 10000\end{array}$
5092 \begin_layout Standard
5093 To add or delete rows and columns subsequently, the math toolbar buttons
5095 \begin_inset Graphics
5096 filename ../images/tabular-feature_append-row.png
5102 \begin_inset Graphics
5103 filename ../images/tabular-feature_delete-row.png
5109 \begin_inset space \thinspace{}
5114 Edit\SpecialChar \menuseparator
5118 New rows can also be created with
5125 \begin_layout Standard
5126 \begin_inset VSpace bigskip
5129 Parentheses around a matrix can can either be created with the commands
5140 \begin_layout Plain Layout
5158 \begin_layout Plain Layout
5169 \begin_inset space ~
5175 \begin_inset CommandInset ref
5177 reference "sub:Automatic-Bracket-Size"
5181 , or by using the following commands:
5182 \begin_inset VSpace medskip
5188 \begin_layout Standard
5189 \begin_inset space \hfill{}
5193 \begin_inset Tabular
5194 <lyxtabular version="3" rows="4" columns="2">
5196 <column alignment="center" valignment="top" width="0">
5197 <column alignment="center" valignment="top" width="0">
5199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5202 \begin_layout Plain Layout
5208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5211 \begin_layout Plain Layout
5213 \begin_inset Note Note
5216 \begin_layout Plain Layout
5223 is only used as spacer.
5235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5238 \begin_layout Plain Layout
5245 \begin_layout Plain Layout
5259 \begin_inset space \thinspace{}
5267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5270 \begin_layout Plain Layout
5271 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5272 0 & \textrm{-}\mathrm{i}\\
5273 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5286 \begin_layout Plain Layout
5293 \begin_layout Plain Layout
5307 \begin_inset space \thinspace{}
5315 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5318 \begin_layout Plain Layout
5319 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5320 0 & \textrm{-}\mathrm{i}\\
5321 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5334 \begin_layout Plain Layout
5341 \begin_layout Plain Layout
5355 \begin_inset space \thinspace{}
5363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5366 \begin_layout Plain Layout
5367 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5368 0 & \textrm{-}\mathrm{i}\\
5369 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5383 \begin_inset space \hfill{}
5387 \begin_inset Tabular
5388 <lyxtabular version="3" rows="4" columns="2">
5390 <column alignment="center" valignment="top" width="0">
5391 <column alignment="center" valignment="top" width="0">
5393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5396 \begin_layout Plain Layout
5402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5405 \begin_layout Plain Layout
5413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5416 \begin_layout Plain Layout
5423 \begin_layout Plain Layout
5437 \begin_inset space \thinspace{}
5445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5448 \begin_layout Plain Layout
5449 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5450 0 & \textrm{-}\mathrm{i}\\
5451 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5461 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5464 \begin_layout Plain Layout
5471 \begin_layout Plain Layout
5485 \begin_inset space \thinspace{}
5493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5496 \begin_layout Plain Layout
5497 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5498 0 & \textrm{-}\mathrm{i}\\
5499 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5512 \begin_layout Plain Layout
5519 \begin_layout Plain Layout
5533 \begin_inset space \thinspace{}
5541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5544 \begin_layout Plain Layout
5545 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5546 0 & \textrm{-}\mathrm{i}\\
5547 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5561 \begin_inset space \hfill{}
5567 \begin_layout Standard
5568 \begin_inset VSpace medskip
5572 \begin_inset space \thinspace{}
5576 \begin_inset space ~
5585 is inserted, a blue box appears between two vertical lines where the matrix
5589 \begin_layout Standard
5590 \begin_inset VSpace bigskip
5593 As all multiline formulas are matrices, the length
5603 \begin_layout Plain Layout
5611 that is described in
5612 \begin_inset CommandInset ref
5614 reference "sub:Column-Separation"
5618 can also be used to change the column separation of matrices.
5621 \begin_layout Standard
5622 To change the row separation, the command
5632 \begin_layout Plain Layout
5641 It is used as follows:
5644 \begin_layout Standard
5651 arraystretch}{stretch factor}
5655 \begin_layout Plain Layout
5666 \begin_layout Standard
5673 assigns the stretch factor to the predefined command
5681 \begin_inset space \thinspace{}
5685 \begin_inset space ~
5688 the row separation, use the factor 2.
5689 This is then used for all following matrices.
5690 To go back to the original separation, assign the factor 1 to
5699 \begin_layout Standard
5700 To set matrices into a text line, the command
5710 \begin_layout Plain Layout
5719 When it is inserted a blue box with two dashed lines appears.
5720 In this box the matrix is inserted.
5723 \begin_layout Standard
5725 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5726 C & D\end{smallmatrix}\right)$
5732 \begin_layout Section
5733 Brackets and Delimiters
5737 \begin_layout Plain Layout
5747 \begin_layout Plain Layout
5756 \begin_layout Subsection
5757 Vertical Brackets and Delimiters
5761 \begin_layout Plain Layout
5770 \begin_layout Standard
5771 \begin_inset space \hfill{}
5775 \begin_inset Tabular
5776 <lyxtabular version="3" rows="9" columns="2">
5778 <column alignment="center" valignment="top" width="0pt">
5779 <column alignment="center" valignment="top" width="0pt">
5781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5784 \begin_layout Plain Layout
5790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5793 \begin_layout Plain Layout
5801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5804 \begin_layout Plain Layout
5810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5813 \begin_layout Plain Layout
5814 \begin_inset Formula $($
5824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5827 \begin_layout Plain Layout
5833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5836 \begin_layout Plain Layout
5837 \begin_inset Formula $\{$
5847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5850 \begin_layout Plain Layout
5856 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5859 \begin_layout Plain Layout
5860 \begin_inset Formula $[$
5870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5873 \begin_layout Plain Layout
5881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5884 \begin_layout Plain Layout
5885 \begin_inset Formula $\langle$
5895 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5898 \begin_layout Plain Layout
5906 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5909 \begin_layout Plain Layout
5910 \begin_inset Formula $\lceil$
5920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5923 \begin_layout Plain Layout
5931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5934 \begin_layout Plain Layout
5935 \begin_inset Formula $\lfloor$
5945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5948 \begin_layout Plain Layout
5954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5957 \begin_layout Plain Layout
5958 \begin_inset Formula $/$
5968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5971 \begin_layout Plain Layout
5977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5980 \begin_layout Plain Layout
5981 \begin_inset Formula $|$
5995 \begin_inset space \hfill{}
5999 \begin_inset Tabular
6000 <lyxtabular version="3" rows="9" columns="2">
6002 <column alignment="center" valignment="top" width="0pt">
6003 <column alignment="center" valignment="top" width="0pt">
6005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6008 \begin_layout Plain Layout
6014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6017 \begin_layout Plain Layout
6025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6028 \begin_layout Plain Layout
6034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6037 \begin_layout Plain Layout
6038 \begin_inset Formula $)$
6048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6051 \begin_layout Plain Layout
6057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6060 \begin_layout Plain Layout
6061 \begin_inset Formula $\}$
6071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6074 \begin_layout Plain Layout
6080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6083 \begin_layout Plain Layout
6084 \begin_inset Formula $]$
6094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6097 \begin_layout Plain Layout
6105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6108 \begin_layout Plain Layout
6109 \begin_inset Formula $\rangle$
6119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6122 \begin_layout Plain Layout
6130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6133 \begin_layout Plain Layout
6134 \begin_inset Formula $\rceil$
6144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6147 \begin_layout Plain Layout
6155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6158 \begin_layout Plain Layout
6159 \begin_inset Formula $\rfloor$
6169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6172 \begin_layout Plain Layout
6182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6185 \begin_layout Plain Layout
6186 \begin_inset Formula $\backslash$
6196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6199 \begin_layout Plain Layout
6207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6210 \begin_layout Plain Layout
6211 \begin_inset Formula $\|$
6225 \begin_inset space \hfill{}
6231 \begin_layout Standard
6234 \begin_inset Note Greyedout
6237 \begin_layout Plain Layout
6242 In TeX-mode the command
6252 \begin_layout Plain Layout
6260 must be used for the backslash, because the command
6268 produces there a line break.
6276 \begin_layout Standard
6277 For all characters listed above the size can be adjusted with the commands
6278 described in the following two subsections.
6279 When using these commands, the characters < and > can directly be used
6280 instead of the commands
6295 \begin_layout Subsubsection
6297 \begin_inset CommandInset label
6299 name "sub:Manual-Bracket-Size"
6307 \begin_layout Plain Layout
6308 Bracket size ! manual
6316 \begin_layout Standard
6317 The bracket size can be specified manually by the LaTeX-commands
6327 \begin_layout Plain Layout
6360 denotes the smallest and
6366 the largest bracket size.
6369 \begin_layout Standard
6370 These commands are used to emphasize levels of brackets:
6373 \begin_layout Standard
6375 \begin_inset Tabular
6376 <lyxtabular version="3" rows="2" columns="2">
6378 <column alignment="center" valignment="top" width="0pt">
6379 <column alignment="center" valignment="top" width="0pt">
6381 <cell alignment="center" valignment="top" usebox="none">
6384 \begin_layout Plain Layout
6385 all brackets in the same size:
6390 <cell alignment="center" valignment="top" usebox="none">
6393 \begin_layout Plain Layout
6394 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6404 <cell alignment="center" valignment="top" usebox="none">
6407 \begin_layout Plain Layout
6413 <cell alignment="center" valignment="top" usebox="none">
6416 \begin_layout Plain Layout
6417 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6431 \begin_inset Note Note
6434 \begin_layout Plain Layout
6441 is only used as spacer.
6449 \begin_layout Standard
6450 For the second formula the command
6460 \begin_layout Plain Layout
6474 \begin_layout Standard
6475 Here is an overview about all bracket sizes:
6478 \begin_layout Standard
6498 \begin_layout Plain Layout
6515 \begin_layout Plain Layout
6528 \begin_layout Plain Layout
6544 \begin_layout Standard
6546 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6552 \begin_layout Standard
6559 -commands there is the variant
6569 \begin_layout Plain Layout
6577 that adds a bit more space between the bracket and its content, and the
6594 \begin_layout Plain Layout
6604 , that don't add additional space.
6609 at the end of the command
6615 is for a left bracket; for a right bracket this will be replaced by an
6621 A left or right bracket can each be an opening or closing bracket.
6624 \begin_layout Standard
6625 In the following table is a comparison of the variants:
6628 \begin_layout Standard
6630 \begin_inset Tabular
6631 <lyxtabular version="3" rows="5" columns="2">
6633 <column alignment="center" valignment="middle" width="0">
6634 <column alignment="center" valignment="middle" width="0">
6636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6639 \begin_layout Plain Layout
6645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6648 \begin_layout Plain Layout
6650 \begin_inset Note Note
6653 \begin_layout Plain Layout
6660 is only used as spacer.
6672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6675 \begin_layout Plain Layout
6690 \begin_layout Plain Layout
6708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6711 \begin_layout Plain Layout
6712 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6725 \begin_layout Plain Layout
6740 \begin_layout Plain Layout
6758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6761 \begin_layout Plain Layout
6762 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6775 \begin_layout Plain Layout
6790 \begin_layout Plain Layout
6808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6811 \begin_layout Plain Layout
6812 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6825 \begin_layout Plain Layout
6837 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6840 \begin_layout Plain Layout
6841 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6857 \begin_layout Subsubsection
6858 Automatic Bracket Size
6859 \begin_inset CommandInset label
6861 name "sub:Automatic-Bracket-Size"
6869 \begin_layout Plain Layout
6870 Bracket size ! automatic
6878 \begin_layout Standard
6879 Brackets with variable size can be inserted with the commands
6889 \begin_layout Plain Layout
6907 \begin_layout Plain Layout
6915 or via the math toolbar button
6916 \begin_inset Graphics
6917 filename ../images/dialog-show_mathdelimiter.png
6935 the wanted bracket must be inserted.
6936 The bracket size will then automatically be calculated for the output.
6939 \begin_layout Standard
6941 normal bracket: The command
6951 \begin_layout Plain Layout
6961 \begin_inset Formula $\downarrow$
6968 \begin_layout Plain Layout
6980 \begin_inset Formula \[
6988 \begin_layout Standard
6990 multiline bracket: The command
7002 \begin_layout Plain Layout
7012 \begin_inset Formula $\downarrow$
7019 \begin_layout Plain Layout
7033 \begin_inset Formula \[
7034 \ln\left(\frac{A}{C}\right)\]
7041 \begin_layout Standard
7057 \begin_inset space ~
7063 This has the advantage that you can see in LyX immediately the real bracket
7064 size and that the matching right bracket will be created too.
7065 \begin_inset Newline newline
7068 The command for the last example would then be:
7082 \begin_layout Plain Layout
7092 \begin_inset Formula $\downarrow$
7098 \begin_layout Standard
7099 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7100 For example the command
7110 \begin_layout Plain Layout
7120 \begin_inset Formula $\downarrow$
7127 \begin_layout Plain Layout
7143 \begin_inset Formula \[
7144 \left.\frac{A}{B}\right\} \]
7162 will be converted by LyX to brackets in the right size when the document
7163 is reloaded and an omitted bracket will appear as dashed line.
7166 \begin_layout Standard
7167 \begin_inset VSpace bigskip
7170 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7181 \begin_layout Plain Layout
7189 is additionally available for all brackets and limits.
7190 With this command the height of the following character is adapted to the
7191 one of the surrounding brackets, what is e.
7192 \begin_inset space \thinspace{}
7196 \begin_inset space ~
7199 needed for physical vectors:
7200 \begin_inset Formula \[
7201 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7205 For physical vectors there is a special LaTeX-package, described in
7206 \begin_inset CommandInset ref
7208 reference "sub:Physical-Vectors"
7215 \begin_layout Subsection
7220 \begin_layout Plain Layout
7221 Brackets ! horizontal
7229 \begin_layout Standard
7231 \begin_inset Tabular
7232 <lyxtabular version="3" rows="4" columns="2">
7234 <column alignment="center" valignment="top" width="0pt">
7235 <column alignment="center" valignment="top" width="0pt">
7237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7240 \begin_layout Plain Layout
7242 \begin_inset Note Note
7245 \begin_layout Plain Layout
7252 is only used as spacer.
7262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7265 \begin_layout Plain Layout
7273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7276 \begin_layout Plain Layout
7280 \begin_layout Plain Layout
7295 \begin_layout Plain Layout
7308 \begin_layout Plain Layout
7321 \begin_layout Plain Layout
7334 \begin_layout Plain Layout
7345 \begin_layout Plain Layout
7358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7361 \begin_layout Plain Layout
7362 \begin_inset Formula $\overbrace{A+B}^{3}$
7372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7375 \begin_layout Plain Layout
7379 \begin_layout Plain Layout
7394 \begin_layout Plain Layout
7407 \begin_layout Plain Layout
7420 \begin_layout Plain Layout
7431 \begin_layout Plain Layout
7444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7447 \begin_layout Plain Layout
7448 \begin_inset Formula $\underbrace{A+B}_{5}$
7458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7461 \begin_layout Plain Layout
7468 \begin_layout Plain Layout
7483 \begin_layout Plain Layout
7496 \begin_layout Plain Layout
7509 \begin_layout Plain Layout
7522 \begin_layout Plain Layout
7535 \begin_layout Plain Layout
7548 \begin_layout Plain Layout
7562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7565 \begin_layout Plain Layout
7566 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7582 \begin_layout Standard
7583 In the last example it doesn't matter if
7595 is inserted at first.
7598 \begin_layout Standard
7599 \begin_inset VSpace bigskip
7602 When brackets are needed that overlap each other, multiline formulas, as
7604 \begin_inset CommandInset ref
7606 reference "sec:Multiline-Formulas"
7611 \begin_inset Formula \begin{eqnarray*}
7612 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7613 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7617 In the first row the formula is inserted together with the first brace.
7618 It is hereby important that the space command
7622 \begin_layout Plain Layout
7623 Space commands are explained in
7624 \begin_inset CommandInset ref
7626 reference "sub:Predefined-Space"
7641 is inserted before the first
7642 \begin_inset Formula $d$
7645 , because the brace that ends behind the
7646 \begin_inset Formula $q$
7649 prevents that the following
7650 \begin_inset Quotes eld
7654 \begin_inset Quotes erd
7657 is surrounded by space.
7661 \begin_layout Plain Layout
7662 because a bracket is not handled as character, see
7663 \begin_inset CommandInset ref
7665 reference "sub:Binary-Operators"
7674 In the second row the second brace is inserted.
7675 As it should begin before the
7676 \begin_inset Formula $b$
7691 \begin_layout Plain Layout
7699 \begin_inset CommandInset ref
7701 reference "sub:Placeholders"
7710 This space is needed because the
7711 \begin_inset Quotes eld
7715 \begin_inset Quotes erd
7718 is also surrounded by space in the formula.
7719 The brace is placed under the command
7728 \begin_layout Standard
7729 It gets more complicated when brackets overlap each other, like in the following
7734 \begin_layout Plain Layout
7746 \begin_inset Formula \begin{eqnarray*}
7747 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7748 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7756 \begin_layout Plain Layout
7767 The first formula row is the same as the second row of the previous example,
7768 with the difference that the brace is above.
7769 The second row contains the formula together with the second brace.
7770 To avoid that there is space between the upper brace in the first row and
7771 the formula, the row spacing need to be reduced.
7772 This is not easily possible due to a bug in LyX
7776 \begin_layout Plain Layout
7777 \begin_inset CommandInset href
7779 name "LyX-bug #1505"
7780 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7790 As solution for the problem, the global formula row separation
7800 \begin_layout Plain Layout
7808 must be changed to -6
7809 \begin_inset space \thinspace{}
7812 pt before the formula with the command
7827 is set back after the formula to the standard value of 3
7828 \begin_inset space \thinspace{}
7831 pt using the same command.
7832 More about the row separation in formulas is explained in
7833 \begin_inset CommandInset ref
7835 reference "sub:Line-Separation"
7842 \begin_layout Section
7847 \begin_layout Plain Layout
7856 \begin_layout Standard
7857 Arrows can be inserted via the math toolbar button
7858 \begin_inset Graphics
7859 filename ../images/math/leftarrow.png
7864 or the commands listed in the following subsections.
7867 \begin_layout Standard
7868 \begin_inset Newpage newpage
7874 \begin_layout Subsection
7879 \begin_layout Plain Layout
7888 \begin_layout Standard
7889 \begin_inset space \hfill{}
7893 \begin_inset Tabular
7894 <lyxtabular version="3" rows="8" columns="2">
7896 <column alignment="center" valignment="top" width="0pt">
7897 <column alignment="center" valignment="top" width="0pt">
7899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7902 \begin_layout Plain Layout
7908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7911 \begin_layout Plain Layout
7919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7922 \begin_layout Plain Layout
7930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7933 \begin_layout Plain Layout
7934 \begin_inset Formula $\gets$
7944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7947 \begin_layout Plain Layout
7955 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7958 \begin_layout Plain Layout
7959 \begin_inset Formula $\Leftarrow$
7969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7972 \begin_layout Plain Layout
7980 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7983 \begin_layout Plain Layout
7984 \begin_inset Formula $\longleftarrow$
7994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7997 \begin_layout Plain Layout
8005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8008 \begin_layout Plain Layout
8009 \begin_inset Formula $\Longleftarrow$
8019 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8022 \begin_layout Plain Layout
8030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8033 \begin_layout Plain Layout
8034 \begin_inset Formula $\leftharpoonup$
8044 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8047 \begin_layout Plain Layout
8055 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8058 \begin_layout Plain Layout
8059 \begin_inset Formula $\leftharpoondown$
8069 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8072 \begin_layout Plain Layout
8080 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8083 \begin_layout Plain Layout
8084 \begin_inset Formula $\hookleftarrow$
8098 \begin_inset space \hfill{}
8102 \begin_inset Tabular
8103 <lyxtabular version="3" rows="8" columns="2">
8105 <column alignment="center" valignment="top" width="0pt">
8106 <column alignment="center" valignment="top" width="0pt">
8108 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8111 \begin_layout Plain Layout
8117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8120 \begin_layout Plain Layout
8128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8131 \begin_layout Plain Layout
8139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8142 \begin_layout Plain Layout
8143 \begin_inset Formula $\to$
8153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8156 \begin_layout Plain Layout
8164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8167 \begin_layout Plain Layout
8168 \begin_inset Formula $\Rightarrow$
8178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8181 \begin_layout Plain Layout
8189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8192 \begin_layout Plain Layout
8193 \begin_inset Formula $\longrightarrow$
8203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8206 \begin_layout Plain Layout
8214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8217 \begin_layout Plain Layout
8218 \begin_inset Formula $\Longrightarrow$
8228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8231 \begin_layout Plain Layout
8239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8242 \begin_layout Plain Layout
8243 \begin_inset Formula $\rightharpoonup$
8253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8256 \begin_layout Plain Layout
8264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8267 \begin_layout Plain Layout
8268 \begin_inset Formula $\rightharpoondown$
8278 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8281 \begin_layout Plain Layout
8289 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8292 \begin_layout Plain Layout
8293 \begin_inset Formula $\hookrightarrow$
8307 \begin_inset space \hfill{}
8313 \begin_layout Standard
8314 \begin_inset space \hfill{}
8318 \begin_inset Tabular
8319 <lyxtabular version="3" rows="6" columns="2">
8321 <column alignment="center" valignment="top" width="0pt">
8322 <column alignment="center" valignment="top" width="0pt">
8324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8333 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8336 \begin_layout Plain Layout
8344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8347 \begin_layout Plain Layout
8355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8358 \begin_layout Plain Layout
8359 \begin_inset Formula $\leftrightarrow$
8369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8372 \begin_layout Plain Layout
8380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8383 \begin_layout Plain Layout
8384 \begin_inset Formula $\Leftrightarrow$
8394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8397 \begin_layout Plain Layout
8405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8408 \begin_layout Plain Layout
8409 \begin_inset Formula $\longleftrightarrow$
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8422 \begin_layout Plain Layout
8430 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8433 \begin_layout Plain Layout
8434 \begin_inset Formula $\Longleftrightarrow$
8444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8447 \begin_layout Plain Layout
8455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8458 \begin_layout Plain Layout
8459 \begin_inset Formula $\rightleftharpoons$
8473 \begin_inset space \hspace{}
8478 \begin_inset space \hfill{}
8482 \begin_inset Tabular
8483 <lyxtabular version="3" rows="5" columns="2">
8485 <column alignment="center" valignment="top" width="0pt">
8486 <column alignment="center" valignment="top" width="0pt">
8488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8491 \begin_layout Plain Layout
8497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8500 \begin_layout Plain Layout
8508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8511 \begin_layout Plain Layout
8519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8522 \begin_layout Plain Layout
8523 \begin_inset Formula $\mapsto$
8533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8536 \begin_layout Plain Layout
8544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8547 \begin_layout Plain Layout
8548 \begin_inset Formula $\longmapsto$
8558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8561 \begin_layout Plain Layout
8569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8572 \begin_layout Plain Layout
8573 \begin_inset Formula $\leadsto$
8583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8586 \begin_layout Plain Layout
8594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8597 \begin_layout Plain Layout
8598 \begin_inset Formula $\dasharrow$
8612 \begin_inset space \hfill{}
8618 \begin_layout Standard
8619 \begin_inset VSpace medskip
8622 Arrows used as accent like e.
8623 \begin_inset space \thinspace{}
8627 \begin_inset space ~
8630 vector arrows are listed in
8631 \begin_inset CommandInset ref
8633 reference "sec:Accents"
8640 \begin_layout Standard
8641 \begin_inset VSpace bigskip
8644 Furthermore there are the labeled arrows
8648 \begin_layout Plain Layout
8664 \begin_layout Plain Layout
8682 \begin_layout Plain Layout
8689 \begin_layout Plain Layout
8704 When inserting one of these commands in a formula, an arrow with two blue
8705 boxes appear where the label can be inserted.
8706 The length of the arrow adapts to the label width.
8709 \begin_layout Standard
8711 \begin_inset Tabular
8712 <lyxtabular version="3" rows="3" columns="2">
8714 <column alignment="center" valignment="top" width="0pt">
8715 <column alignment="center" valignment="top" width="0pt">
8717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8720 \begin_layout Plain Layout
8726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8729 \begin_layout Plain Layout
8731 \begin_inset Note Note
8734 \begin_layout Plain Layout
8741 is only used as spacer.
8753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8756 \begin_layout Plain Layout
8763 \begin_layout Plain Layout
8773 \begin_inset Formula $\downarrow$
8777 \begin_inset Formula $\to$
8785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8788 \begin_layout Plain Layout
8789 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8802 \begin_layout Plain Layout
8809 \begin_layout Plain Layout
8819 \begin_inset Formula $\downarrow$
8823 \begin_inset Formula $\to$
8831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8834 \begin_layout Plain Layout
8835 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8851 \begin_layout Subsection
8852 Vertical and diagonal Arrows
8856 \begin_layout Plain Layout
8866 \begin_layout Plain Layout
8875 \begin_layout Standard
8876 \begin_inset space \hfill{}
8880 \begin_inset Tabular
8881 <lyxtabular version="3" rows="7" columns="2">
8883 <column alignment="center" valignment="top" width="0pt">
8884 <column alignment="center" valignment="top" width="0pt">
8886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8889 \begin_layout Plain Layout
8895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8898 \begin_layout Plain Layout
8906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8909 \begin_layout Plain Layout
8917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8920 \begin_layout Plain Layout
8921 \begin_inset Formula $\uparrow$
8931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8934 \begin_layout Plain Layout
8942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8945 \begin_layout Plain Layout
8946 \begin_inset Formula $\Uparrow$
8956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8959 \begin_layout Plain Layout
8967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8970 \begin_layout Plain Layout
8971 \begin_inset Formula $\updownarrow$
8981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8984 \begin_layout Plain Layout
8992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8995 \begin_layout Plain Layout
8996 \begin_inset Formula $\Updownarrow$
9006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9009 \begin_layout Plain Layout
9017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9020 \begin_layout Plain Layout
9021 \begin_inset Formula $\Downarrow$
9031 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9034 \begin_layout Plain Layout
9042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9045 \begin_layout Plain Layout
9046 \begin_inset Formula $\downarrow$
9060 \begin_inset space \hfill{}
9064 \begin_inset Tabular
9065 <lyxtabular version="3" rows="5" columns="2">
9067 <column alignment="center" valignment="top" width="0pt">
9068 <column alignment="center" valignment="top" width="0pt">
9070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9073 \begin_layout Plain Layout
9079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9082 \begin_layout Plain Layout
9090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9093 \begin_layout Plain Layout
9101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9104 \begin_layout Plain Layout
9105 \begin_inset Formula $\nearrow$
9115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9118 \begin_layout Plain Layout
9126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9129 \begin_layout Plain Layout
9130 \begin_inset Formula $\searrow$
9140 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9143 \begin_layout Plain Layout
9151 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9154 \begin_layout Plain Layout
9155 \begin_inset Formula $\swarrow$
9165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9168 \begin_layout Plain Layout
9176 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9179 \begin_layout Plain Layout
9180 \begin_inset Formula $\nwarrow$
9194 \begin_inset space \hfill{}
9200 \begin_layout Standard
9201 \begin_inset VSpace medskip
9204 Vertical arrows can be used also as delimiter together with the commands
9206 \begin_inset CommandInset ref
9208 reference "sub:Manual-Bracket-Size"
9213 \begin_inset CommandInset ref
9215 reference "sub:Automatic-Bracket-Size"
9222 \begin_layout Standard
9223 \begin_inset Newpage newpage
9229 \begin_layout Section
9231 \begin_inset CommandInset label
9241 \begin_layout Plain Layout
9250 \begin_layout Standard
9251 Accents can be inserted via the math toolbar button
9252 \begin_inset Graphics
9253 filename ../images/math/hat.png
9258 or the commands listed in the following subsections.
9261 \begin_layout Subsection
9262 Accents for one Character
9266 \begin_layout Plain Layout
9279 \begin_layout Plain Layout
9281 \begin_inset CommandInset ref
9283 reference "sub:Accents-in-Text"
9296 \begin_layout Plain Layout
9304 \begin_inset Note Note
9307 \begin_layout Plain Layout
9310 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9313 \begin_layout Plain Layout
9316 texorpdfstring is in section
9317 \begin_inset CommandInset ref
9319 reference "sub:Formulas-in-Section"
9329 \begin_inset CommandInset label
9331 name "sub:Accents-for-one"
9339 \begin_layout Plain Layout
9340 Accents ! for one character
9348 \begin_layout Standard
9349 \begin_inset space \hfill{}
9353 \begin_inset Tabular
9354 <lyxtabular version="3" rows="8" columns="2">
9356 <column alignment="center" valignment="top" width="0pt">
9357 <column alignment="center" valignment="top" width="0pt">
9359 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9362 \begin_layout Plain Layout
9368 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9371 \begin_layout Plain Layout
9373 \begin_inset Note Note
9376 \begin_layout Plain Layout
9383 is only used as spacer.
9395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9398 \begin_layout Plain Layout
9405 \begin_layout Plain Layout
9419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9422 \begin_layout Plain Layout
9423 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9436 \begin_layout Plain Layout
9443 \begin_layout Plain Layout
9457 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9460 \begin_layout Plain Layout
9461 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9471 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9474 \begin_layout Plain Layout
9481 \begin_layout Plain Layout
9495 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9498 \begin_layout Plain Layout
9499 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9509 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9512 \begin_layout Plain Layout
9520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9523 \begin_layout Plain Layout
9524 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9537 \begin_layout Plain Layout
9544 \begin_layout Plain Layout
9557 \begin_layout Plain Layout
9568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9571 \begin_layout Plain Layout
9572 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9585 \begin_layout Plain Layout
9592 \begin_layout Plain Layout
9606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9609 \begin_layout Plain Layout
9610 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9623 \begin_layout Plain Layout
9630 \begin_layout Plain Layout
9644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9647 \begin_layout Plain Layout
9648 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9662 \begin_inset space \hfill{}
9666 \begin_inset Tabular
9667 <lyxtabular version="3" rows="7" columns="2">
9669 <column alignment="center" valignment="top" width="0pt">
9670 <column alignment="center" valignment="top" width="0pt">
9672 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9675 \begin_layout Plain Layout
9681 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9684 \begin_layout Plain Layout
9692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9695 \begin_layout Plain Layout
9702 \begin_layout Plain Layout
9716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9719 \begin_layout Plain Layout
9720 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9730 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9733 \begin_layout Plain Layout
9740 \begin_layout Plain Layout
9754 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9757 \begin_layout Plain Layout
9758 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9768 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9771 \begin_layout Plain Layout
9778 \begin_layout Plain Layout
9792 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9795 \begin_layout Plain Layout
9796 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9806 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9809 \begin_layout Plain Layout
9816 \begin_layout Plain Layout
9830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9833 \begin_layout Plain Layout
9834 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9844 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9847 \begin_layout Plain Layout
9854 \begin_layout Plain Layout
9868 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9871 \begin_layout Plain Layout
9872 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9885 \begin_layout Plain Layout
9892 \begin_layout Plain Layout
9906 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9909 \begin_layout Plain Layout
9910 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9924 \begin_inset space \hfill{}
9930 \begin_layout Standard
9931 \begin_inset VSpace bigskip
9938 \begin_layout Plain Layout
9944 in formulas, a quotation mark is inserted before the vowel.
9945 These two characters are then treated by LaTeX as
9949 character when the formula part with the umlaut is marked as German.
9957 \begin_inset Quotes eld
9961 \begin_inset Quotes erd
9964 umlauts are created as demonstrated in the following example:
9967 \begin_layout Standard
9968 \begin_inset VSpace -2mm
9974 \begin_layout Standard
9976 \begin_inset Tabular
9977 <lyxtabular version="3" rows="3" columns="2">
9979 <column alignment="center" valignment="top" width="0">
9980 <column alignment="center" valignment="top" width="0">
9982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9985 \begin_layout Plain Layout
9991 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9994 \begin_layout Plain Layout
9996 \begin_inset Note Note
9999 \begin_layout Plain Layout
10006 is only used as spacer.
10018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10021 \begin_layout Plain Layout
10024 \begin_inset Quotes grd
10032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10035 \begin_layout Plain Layout
10038 \begin_inset Formula $"i$
10048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10051 \begin_layout Plain Layout
10058 \begin_layout Plain Layout
10072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10075 \begin_layout Plain Layout
10076 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10092 \begin_layout Standard
10093 Another advantage to
10099 is that umlauts can directly be converted to mathematical text because
10100 the accent commands above are
10106 in mathematical text
10109 To convert an accented character to mathematical text, only the character
10110 under the accent may be converted.
10111 This applies also for all other conversions, e.
10112 \begin_inset space \thinspace{}
10116 \begin_inset space ~
10122 \begin_layout Standard
10123 In mathematical text, umlauts and other accented characters can directly
10127 \begin_layout Subsection
10128 Accents for Operators
10132 \begin_layout Plain Layout
10133 Accents ! for operators
10141 \begin_layout Standard
10152 \begin_layout Plain Layout
10170 \begin_layout Plain Layout
10178 characters can be placed above or below an operator, respectively, to accent
10190 \begin_layout Plain Layout
10198 characters can be set before and behind an operator.
10199 The command scheme is:
10202 \begin_layout Standard
10218 \begin_layout Standard
10225 must always be before the operator that should be accented.
10226 You can accent with several characters and even with other operators and
10234 for example only characters behind an operator, write nothing between the
10235 first braces but don't omit the braces.
10238 \begin_layout Standard
10239 For example the command
10244 \begin_inset Formula $\to$
10254 \begin_inset Formula $\to$
10263 \begin_layout Plain Layout
10279 \begin_inset Formula \[
10280 \sideset{}{'}\sum_{k=1}^{n}\]
10287 \begin_layout Standard
10296 \begin_layout Plain Layout
10311 \begin_layout Plain Layout
10323 \begin_inset Formula $\uparrow$
10331 \begin_inset Formula \[
10332 \overset{a}{\maltese}\]
10336 As seen in the last example, with
10348 also symbols and characters can be accented; with
10354 this is not possible.
10357 \begin_layout Subsection
10358 Accents for several Characters
10359 \begin_inset CommandInset label
10361 name "sub:Accents-for-several"
10369 \begin_layout Plain Layout
10370 Accents ! for several characters
10378 \begin_layout Standard
10379 \begin_inset space \hfill{}
10383 \begin_inset Tabular
10384 <lyxtabular version="3" rows="5" columns="2">
10386 <column alignment="center" valignment="top" width="0pt">
10387 <column alignment="center" valignment="top" width="0pt">
10389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10392 \begin_layout Plain Layout
10398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10401 \begin_layout Plain Layout
10403 \begin_inset Note Note
10406 \begin_layout Plain Layout
10413 is only used as spacer.
10425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10428 \begin_layout Plain Layout
10435 \begin_layout Plain Layout
10449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10452 \begin_layout Plain Layout
10453 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10466 \begin_layout Plain Layout
10473 \begin_layout Plain Layout
10487 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10490 \begin_layout Plain Layout
10491 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10504 \begin_layout Plain Layout
10511 \begin_layout Plain Layout
10525 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10528 \begin_layout Plain Layout
10529 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10542 \begin_layout Plain Layout
10545 underleftrightarrow
10549 \begin_layout Plain Layout
10563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10566 \begin_layout Plain Layout
10567 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10581 \begin_inset space \hfill{}
10585 \begin_inset Tabular
10586 <lyxtabular version="3" rows="5" columns="2">
10588 <column alignment="center" valignment="top" width="0pt">
10589 <column alignment="center" valignment="top" width="0pt">
10591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10594 \begin_layout Plain Layout
10600 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10603 \begin_layout Plain Layout
10611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10614 \begin_layout Plain Layout
10621 \begin_layout Plain Layout
10635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10638 \begin_layout Plain Layout
10639 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10652 \begin_layout Plain Layout
10659 \begin_layout Plain Layout
10673 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10676 \begin_layout Plain Layout
10677 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10690 \begin_layout Plain Layout
10697 \begin_layout Plain Layout
10711 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10714 \begin_layout Plain Layout
10715 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10728 \begin_layout Plain Layout
10735 \begin_layout Plain Layout
10749 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10752 \begin_layout Plain Layout
10753 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10767 \begin_inset space \hfill{}
10773 \begin_layout Standard
10774 \begin_inset VSpace medskip
10777 With these commands as many characters as you like can be accented.
10790 will only be set in the output with a length of three characters, as shown
10791 in the following example:
10792 \begin_inset Formula \[
10793 \widetilde{A+B=C-D}\]
10800 \begin_layout Standard
10811 \begin_layout Plain Layout
10829 \begin_layout Plain Layout
10837 described in the previous subsection it is also possible to accent several
10847 \begin_layout Plain Layout
10857 \begin_inset Formula $\downarrow$
10863 \begin_inset Formula \[
10864 \underset{***}{A=B}\]
10871 \begin_layout Section
10873 \begin_inset CommandInset label
10883 \begin_layout Plain Layout
10892 \begin_layout Subsection
10894 \begin_inset CommandInset label
10896 name "sub:Predefined-Space"
10904 \begin_layout Plain Layout
10905 Space ! horizontal ! predefined
10913 \begin_layout Standard
10914 Sometimes it is necessary to insert horizontal space to a formula.
10915 This is done by inserting a protected space (shortcut
10921 \begin_inset Quotes eld
10931 \begin_layout Plain Layout
10944 \begin_inset Quotes erd
10947 appears and by pressing
10951 several times one can select one of eight different space sizes.
10952 The spaces can also be inserted using the math toolbar button
10953 \begin_inset Graphics
10954 filename ../images/math/space.png
10959 or special commands.
10960 Independent from the inserted command, one can select the size again by
10968 \begin_layout Standard
10971 \begin_inset VSpace -5mm
10975 \begin_inset Tabular
10976 <lyxtabular version="3" rows="3" columns="7">
10978 <column alignment="center" valignment="middle" width="6.8cm">
10979 <column alignment="center" valignment="top" width="0">
10980 <column alignment="center" valignment="top" width="0">
10981 <column alignment="center" valignment="top" width="0">
10982 <column alignment="center" valignment="top" width="0">
10983 <column alignment="center" valignment="top" width="0">
10984 <column alignment="center" valignment="top" width="0">
10986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10989 \begin_layout Plain Layout
10995 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10998 \begin_layout Plain Layout
11006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11009 \begin_layout Plain Layout
11017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11020 \begin_layout Plain Layout
11028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11031 \begin_layout Plain Layout
11039 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11042 \begin_layout Plain Layout
11050 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11053 \begin_layout Plain Layout
11063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11066 \begin_layout Plain Layout
11071 keystrokes after inserting the protected space
11076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11079 \begin_layout Plain Layout
11085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11088 \begin_layout Plain Layout
11094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11097 \begin_layout Plain Layout
11103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11106 \begin_layout Plain Layout
11112 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11115 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11124 \begin_layout Plain Layout
11132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11145 \begin_inset Formula $A\, B$
11153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11156 \begin_layout Plain Layout
11157 \begin_inset Formula $A\: B$
11165 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11169 \begin_inset Formula $A\; B$
11177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11180 \begin_layout Plain Layout
11181 \begin_inset Formula $A\quad B$
11189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11192 \begin_layout Plain Layout
11193 \begin_inset Formula $A\qquad B$
11201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11204 \begin_layout Plain Layout
11205 \begin_inset Formula $A\! B$
11221 \begin_layout Standard
11222 The last size seem to produce no space.
11223 It is displayed red in LyX contrary to the other sizes, because it is a
11225 There are two more negative spaces:
11228 \begin_layout Standard
11230 \begin_inset Tabular
11231 <lyxtabular version="3" rows="3" columns="3">
11233 <column alignment="center" valignment="middle" width="6.8cm">
11234 <column alignment="center" valignment="top" width="0pt">
11235 <column alignment="center" valignment="top" width="0pt">
11237 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11240 \begin_layout Plain Layout
11246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11249 \begin_layout Plain Layout
11257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11260 \begin_layout Plain Layout
11270 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11273 \begin_layout Plain Layout
11278 keystrokes after inserting the protected space
11283 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11286 \begin_layout Plain Layout
11292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11295 \begin_layout Plain Layout
11303 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11306 \begin_layout Plain Layout
11312 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11315 \begin_layout Plain Layout
11316 \begin_inset Formula $A\negmedspace B$
11324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11327 \begin_layout Plain Layout
11328 \begin_inset Formula $A\negthickspace B$
11344 \begin_layout Standard
11345 Negative spaces can lead to characters overlapping each other.
11346 Thus they can be used to enforce ligatures, what is e.
11347 \begin_inset space \thinspace{}
11351 \begin_inset space ~
11354 useful for summation operators:
11357 \begin_layout Standard
11359 \begin_inset Tabular
11360 <lyxtabular version="3" rows="3" columns="2">
11362 <column alignment="center" valignment="top" width="0">
11363 <column alignment="center" valignment="top" width="0">
11365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11368 \begin_layout Plain Layout
11374 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11377 \begin_layout Plain Layout
11379 \begin_inset Note Note
11382 \begin_layout Plain Layout
11389 is only used as spacer.
11401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11404 \begin_layout Plain Layout
11413 \begin_layout Plain Layout
11427 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11430 \begin_layout Plain Layout
11431 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11441 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11444 \begin_layout Plain Layout
11455 \begin_layout Plain Layout
11469 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11472 \begin_layout Plain Layout
11473 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11489 \begin_layout Standard
11490 Relations like for example equal signs, are always surrounded by space.
11491 To suppress this, the equal sign is placed into a TeX-brace.
11492 The following example demonstrates this:
11495 \begin_layout Standard
11497 \begin_inset Tabular
11498 <lyxtabular version="3" rows="2" columns="2">
11500 <column alignment="center" valignment="top" width="0pt">
11501 <column alignment="center" valignment="top" width="0pt">
11503 <cell alignment="center" valignment="top" usebox="none">
11506 \begin_layout Plain Layout
11512 <cell alignment="center" valignment="top" usebox="none">
11515 \begin_layout Plain Layout
11516 \begin_inset Formula $A=B$
11526 <cell alignment="center" valignment="top" usebox="none">
11529 \begin_layout Plain Layout
11530 \begin_inset Note Note
11533 \begin_layout Plain Layout
11540 is only used as spacer.
11546 \begin_inset Formula $\raisebox{5mm}{}$
11549 equation without space
11554 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11557 \begin_layout Plain Layout
11558 \begin_inset Formula $A{=}B$
11574 \begin_layout Standard
11576 The command for the last formula is:
11581 \begin_inset Formula $\to$
11587 \begin_layout Standard
11588 \begin_inset VSpace bigskip
11591 Spaces are needed for physical units, because the space between the value
11592 and the unit is the smallest one and not a normal space.
11593 For units in text, the smallest space is inserted via the menu
11595 Insert\SpecialChar \menuseparator
11596 Formatting\SpecialChar \menuseparator
11598 \begin_inset space ~
11610 \begin_layout Standard
11611 An example to visualize the difference:
11614 \begin_layout Standard
11615 \begin_inset Tabular
11616 <lyxtabular version="3" rows="2" columns="2">
11618 <column alignment="left" valignment="top" width="0">
11619 <column alignment="left" valignment="top" width="0">
11621 <cell alignment="center" valignment="top" usebox="none">
11624 \begin_layout Plain Layout
11626 \begin_inset Formula $\cdot$
11634 <cell alignment="center" valignment="top" usebox="none">
11637 \begin_layout Plain Layout
11638 space between value and unit
11645 <cell alignment="center" valignment="top" usebox="none">
11648 \begin_layout Plain Layout
11650 \begin_inset space \thinspace{}
11654 \begin_inset Formula $\cdot$
11662 <cell alignment="center" valignment="top" usebox="none">
11665 \begin_layout Plain Layout
11666 smallest space between value and unit
11679 \begin_layout Subsection
11684 \begin_layout Plain Layout
11697 \begin_layout Plain Layout
11698 for vertical space in formulas see
11699 \begin_inset CommandInset ref
11701 reference "sub:Line-Separation"
11714 \begin_layout Plain Layout
11722 \begin_inset Note Note
11725 \begin_layout Plain Layout
11728 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11731 \begin_layout Plain Layout
11734 texorpdfstring is in section
11735 \begin_inset CommandInset ref
11737 reference "sub:Formulas-in-Section"
11747 \begin_inset CommandInset label
11749 name "sub:Variable-Space"
11757 \begin_layout Plain Layout
11758 Space ! horizontal ! variable
11766 \begin_layout Standard
11767 Space with a defined length can be inserted in LyX with the command
11768 \begin_inset Newline newline
11781 \begin_layout Plain Layout
11790 For the length all units listed in
11791 \begin_inset CommandInset ref
11793 reference "tab:Available-units"
11797 are allowed, except of the unit
11798 \begin_inset Quotes eld
11802 \begin_inset Quotes erd
11806 The length may also be negative.
11807 To insert so many space that the formula uses all available space, the
11818 \begin_layout Plain Layout
11829 \begin_layout Standard
11830 \begin_inset VSpace -1mm
11836 \begin_layout Standard
11838 \begin_inset Tabular
11839 <lyxtabular version="3" rows="4" columns="2">
11841 <column alignment="center" valignment="top" width="0">
11842 <column alignment="center" valignment="top" width="0">
11844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11847 \begin_layout Plain Layout
11853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11856 \begin_layout Plain Layout
11864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11867 \begin_layout Plain Layout
11871 \begin_inset Formula $\to$
11881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11884 \begin_layout Plain Layout
11885 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11898 \begin_layout Plain Layout
11902 \begin_inset Formula $\to$
11912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11915 \begin_layout Plain Layout
11916 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11929 \begin_layout Plain Layout
11936 \begin_layout Plain Layout
11950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11953 \begin_layout Plain Layout
11954 \begin_inset Formula $A=A\hfill B=B$
11970 \begin_layout Standard
11971 In the last example the available space is given by the longest column entry
11973 In an inline formula the space depends on the length of the line in which
11981 Thus, when the line uses the full width, no space will be created.
11988 only has an effect on displayed formulas when the formula style
11993 (Formula styles are explained in
11994 \begin_inset CommandInset ref
11996 reference "sec:Formula-Styles"
12003 \begin_layout Standard
12010 , there are the commands
12022 that fill the space with a pattern, see
12023 \begin_inset CommandInset ref
12025 reference "sub:Ellipses"
12032 \begin_layout Standard
12033 For text, variable space can be inserted via the menu
12035 Insert\SpecialChar \menuseparator
12036 Formatting\SpecialChar \menuseparator
12038 \begin_inset space ~
12043 , what is not possible in formulas:
12046 \begin_layout Standard
12047 This is a line with
12048 \begin_inset space \hspace{}
12053 \begin_inset space \thinspace{}
12059 \begin_layout Standard
12060 This is a line with
12061 \begin_inset space \hfill{}
12067 \begin_layout Subsection
12068 Space besides inline Formulas
12072 \begin_layout Plain Layout
12073 Space ! besides inline formulas
12081 \begin_layout Standard
12082 The space that surrounds inline formulas can be adjusted with the length
12091 \begin_layout Plain Layout
12102 The value of a length is set with the command
12110 \begin_layout Plain Layout
12120 that has the following scheme:
12123 \begin_layout Standard
12128 setlength{length name}{value}
12131 \begin_layout Standard
12139 \begin_inset space \thinspace{}
12145 \begin_layout Standard
12155 \begin_layout Standard
12156 is inserted in TeX-mode.
12158 \begin_inset space \thinspace{}
12161 mm space will now be set around all inline formulas:
12165 \begin_layout Plain Layout
12179 \begin_layout Standard
12180 This is a line with an inline formula
12181 \begin_inset Formula $A=B$
12185 \begin_inset space \thinspace{}
12188 mm surrounding space.
12192 \begin_layout Plain Layout
12206 \begin_layout Standard
12207 To return to the predefined value,
12213 is set to the value 0
12214 \begin_inset space \thinspace{}
12220 \begin_layout Section
12225 \begin_layout Plain Layout
12235 \begin_layout Plain Layout
12240 \begin_layout Plain Layout
12251 \begin_layout Plain Layout
12266 \begin_layout Standard
12267 Boxes for text are described in chapter
12274 \begin_inset space ~
12282 \begin_layout Subsection
12284 \begin_inset CommandInset label
12286 name "sub:Boxes-with-Frame"
12294 \begin_layout Plain Layout
12303 \begin_layout Standard
12304 It is possible to frame formulas or parts of it with the commands
12314 \begin_layout Plain Layout
12332 \begin_layout Plain Layout
12343 \begin_layout Standard
12344 When one of these commands is inserted to a formula, a blue box appears
12345 within a frame to enter formula parts.
12352 an additional formula has to be created by
12360 \begin_layout Plain Layout
12361 Due to a bug in LyX it is not possible to create a new formula with
12366 \begin_inset CommandInset href
12368 name "LyX-bug #1435"
12369 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12378 , because the box content will otherwise be treated as mathematical text.
12385 is used, a new formula is automatically created inside the frame.
12388 \begin_layout Standard
12395 is not suitable to frame displayed formulas, because the formula will always
12396 be set in the size of the text.
12403 is in contrary not suitable to frame inline formulas, because the formula
12404 will always be set in the size of a displayed formula.
12407 \begin_layout Standard
12414 there is the command
12424 \begin_layout Plain Layout
12432 where additionally the frame width and the alignment can be specified.
12439 is used in the following scheme:
12442 \begin_layout Standard
12447 framebox[frame width][position]{box content}
12450 \begin_layout Standard
12451 The position can either be
12468 right aligns the formula in the box.
12469 When no position is given, the formula will be centered.
12470 \begin_inset Newline newline
12473 Is no width given, also no position can be given.
12474 In this case the frame width is adjusted to the box content like for
12483 \begin_layout Standard
12490 is inserted, a box appears containing three blue boxes.
12491 The first two boxes are surrounded by brackets and denote the two optional
12493 The third box is for formula parts like for
12502 \begin_layout Standard
12504 \begin_inset Note Note
12507 \begin_layout Plain Layout
12508 The table has been set into a minipage to make the footnote appearing.
12509 Otherwise the footnote text would not be displayed.
12515 \begin_inset FormulaMacro
12516 \newcommand{\pad}[2]{{\fboxrule0mm\fboxsep#1\boxed{\fboxrule0.4pt{}{#2}}}}
12517 {\framebox[pad][#1]{#2}}
12521 \begin_inset Box Frameless
12530 height_special "totalheight"
12533 \begin_layout Plain Layout
12535 \begin_inset Tabular
12536 <lyxtabular version="3" rows="5" columns="2">
12538 <column alignment="center" valignment="top" width="0">
12539 <column alignment="center" valignment="top" width="0">
12541 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12544 \begin_layout Plain Layout
12549 \begin_layout Plain Layout
12550 Due to a bug in LyX it is not possible to create a new formula with
12555 \begin_inset CommandInset href
12557 name "LyX-bug #1435"
12558 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12575 \begin_layout Plain Layout
12577 \begin_inset Note Note
12580 \begin_layout Plain Layout
12587 is only used as spacer.
12599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12602 \begin_layout Plain Layout
12609 \begin_layout Plain Layout
12628 \begin_layout Plain Layout
12642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12645 \begin_layout Plain Layout
12646 \begin_inset Formula $\pad{0.8ex}{\fbox{$\int A=B$}}$
12656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12659 \begin_layout Plain Layout
12666 \begin_layout Plain Layout
12681 \begin_layout Plain Layout
12695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12698 \begin_layout Plain Layout
12699 \begin_inset Formula $\pad{0.8ex}{\boxed{\int A=B}}$
12709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12712 \begin_layout Plain Layout
12719 \begin_layout Plain Layout
12733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12736 \begin_layout Plain Layout
12737 \begin_inset Formula $\pad{0.8ex}{A+\fbox{B}}$
12747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12750 \begin_layout Plain Layout
12757 \begin_layout Plain Layout
12767 \begin_inset Formula $\to$
12771 \begin_inset Formula $\to$
12784 \begin_layout Plain Layout
12794 \begin_inset Formula $\downarrow$
12802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12805 \begin_layout Plain Layout
12806 \begin_inset Formula $\pad{0.8ex}{\framebox[20mm][]{$\frac{A}{B}$}}$
12827 \begin_layout Standard
12828 The frame thickness can also be adjusted.
12829 To do this the following commands have to be inserted in TeX-mode before
12833 \begin_layout Standard
12843 \begin_inset Quotes eld
12847 \begin_inset Quotes erd
12861 \begin_inset Quotes eld
12865 \begin_inset Quotes erd
12871 \begin_layout Standard
12872 \begin_inset Quotes eld
12876 \begin_inset Quotes erd
12879 specifies the minimal distance between the frame and the first character
12881 An example for this is the following framed formula:
12885 \begin_layout Plain Layout
12897 \begin_inset Formula \[
12902 Before this formula the commands
12905 \begin_layout Standard
12927 \begin_layout Standard
12928 were inserted in TeX-mode.
12929 The given values are used for all following boxes.
12932 \begin_layout Standard
12933 To return to the standard frame size, the command
12936 \begin_layout Standard
12961 \begin_layout Plain Layout
12975 \begin_layout Standard
12976 is inserted in TeX-mode before the next formula.
12979 \begin_layout Subsection
12980 Boxes without Frame
12981 \begin_inset CommandInset label
12983 name "sub:Boxes-without-Frame"
12991 \begin_layout Plain Layout
12992 Boxes ! without frame
13000 \begin_layout Standard
13001 For boxes without a frame there are the following box commands:
13011 \begin_layout Plain Layout
13029 \begin_layout Plain Layout
13047 \begin_layout Plain Layout
13058 \begin_layout Standard
13065 a box can be super- or subscripted.
13066 But in contrary to normal super- and subscripting, the characters in the
13067 box keep their font size.
13074 is used in the following scheme:
13077 \begin_layout Standard
13082 raisebox{height}{box content}
13085 \begin_layout Standard
13086 When the box should contain a formula, an extra formula is needed like for
13096 \begin_layout Standard
13098 \begin_inset Tabular
13099 <lyxtabular version="3" rows="4" columns="2">
13101 <column alignment="center" valignment="top" width="0">
13102 <column alignment="center" valignment="top" width="0">
13104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13107 \begin_layout Plain Layout
13113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13116 \begin_layout Plain Layout
13124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13127 \begin_layout Plain Layout
13131 \begin_inset Formula $\to$
13137 \begin_inset Formula $\to$
13145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13148 \begin_layout Plain Layout
13149 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13162 \begin_layout Plain Layout
13166 \begin_inset Formula $\to$
13172 \begin_inset Formula $\to$
13180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13183 \begin_layout Plain Layout
13184 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13197 \begin_layout Plain Layout
13201 \begin_inset Formula $\to$
13216 \begin_layout Plain Layout
13230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13233 \begin_layout Plain Layout
13237 \begin_layout Plain Layout
13261 \begin_layout Standard
13262 The last formula can currently only be created using TeX-mode because LyX
13263 inserts a box instead of the needed extra formula.
13267 \begin_layout Plain Layout
13269 \begin_inset CommandInset href
13271 name "LyX-bug #1435"
13272 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13284 \begin_layout Standard
13309 , with the difference that there is no frame.
13312 \begin_layout Subsection
13314 \begin_inset CommandInset label
13316 name "sub:Colored-Boxes"
13324 \begin_layout Plain Layout
13333 \begin_layout Standard
13334 To be able to use all commands explained in this section, the LaTeX-package
13343 \begin_layout Plain Layout
13348 is part of every LaTeX standard installation.
13357 \begin_layout Plain Layout
13363 has to be loaded in the LaTeX-preamble with the line
13367 \begin_layout Plain Layout
13368 When text is colored somewhere in the document with a predefined color,
13369 LyX loads the LaTeX-package
13374 Thus it is possible that the package is loaded twice, but this doesn't
13381 \begin_inset Note Note
13384 \begin_layout Plain Layout
13385 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13394 \begin_layout Standard
13402 \begin_layout Standard
13403 \begin_inset VSpace medskip
13406 To color boxes, the command
13416 \begin_layout Plain Layout
13424 is used in the following scheme:
13427 \begin_layout Standard
13432 colorbox{color}{box content}
13435 \begin_layout Standard
13436 The box content can also be a box and a
13442 can also be part of another box (see the 2nd and 3rd example).
13443 When the box should contain a formula, an extra formula has to be created,
13454 \begin_layout Plain Layout
13455 This also applies for the command
13463 \begin_inset CommandInset href
13465 name "LyX-bug #1435"
13466 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13478 \begin_layout Standard
13479 One of the following predefined colors can be chosen:
13482 \begin_layout Standard
13516 \begin_layout Standard
13518 \begin_inset Tabular
13519 <lyxtabular version="3" rows="4" columns="2">
13521 <column alignment="center" valignment="top" width="0">
13522 <column alignment="center" valignment="top" width="0">
13524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13527 \begin_layout Plain Layout
13533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13536 \begin_layout Plain Layout
13538 \begin_inset Note Note
13541 \begin_layout Plain Layout
13548 is only used as spacer.
13560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13563 \begin_layout Plain Layout
13567 \begin_inset Formula $\to$
13577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13580 \begin_layout Plain Layout
13581 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13594 \begin_layout Plain Layout
13598 \begin_inset Formula $\to$
13609 \begin_layout Plain Layout
13623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13626 \begin_layout Plain Layout
13627 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13637 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13640 \begin_layout Plain Layout
13647 \begin_layout Plain Layout
13659 \begin_inset Formula $\to$
13669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13672 \begin_layout Plain Layout
13673 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13689 \begin_layout Standard
13696 only colors the box but not the characters in the box.
13697 To color all characters, the whole formula is highlighted and the wanted
13698 color is chosen in the
13701 \begin_inset space ~
13707 The dialog can be called with the toolbar button
13708 \begin_inset Graphics
13709 filename ../images/dialog-show_character.png
13716 Edit\SpecialChar \menuseparator
13718 \begin_inset space ~
13721 Style\SpecialChar \menuseparator
13725 The formula number has then the same color as the formula.
13726 When the formula number should get another color than the formula characters,
13727 the color must be changed within the formula.
13730 \begin_layout Standard
13734 \begin_layout Standard
13737 \begin_inset Formula \begin{equation}
13738 \int A=B\label{eq:red}\end{equation}
13745 \begin_inset Formula \begin{equation}
13746 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13753 \begin_layout Standard
13755 \begin_inset CommandInset ref
13761 is completely colored red.
13762 \begin_inset Newline newline
13766 \begin_inset CommandInset ref
13768 reference "eq:redgreen"
13772 was first completely colored green to set the color for the formula number.
13773 Subsequently the formula characters were colored red.
13776 \begin_layout Standard
13777 \begin_inset VSpace bigskip
13780 To color the frame different than the rest of the box, the command
13790 \begin_layout Plain Layout
13798 is used in the following scheme:
13801 \begin_layout Standard
13806 fcolorbox{frame color}{color}{box content}
13809 \begin_layout Standard
13816 is an extension of the command
13823 The frame width is set, like for
13846 \begin_layout Plain Layout
13858 \begin_inset Formula \[
13859 \fcolorbox{cyan}{magenta}{A=B}\]
13867 \begin_layout Plain Layout
13881 \begin_layout Standard
13882 This formula was created with the command
13883 \begin_inset Newline newline
13891 \begin_inset Formula $\to$
13897 \begin_inset Formula $\to$
13907 \begin_layout Standard
13908 \begin_inset VSpace bigskip
13911 To use other colors than the predefined ones, they have to be defined first.
13914 \begin_layout Standard
13915 One can for example define the color
13916 \begin_inset Quotes eld
13924 \begin_inset Quotes erd
13927 with the LaTeX-preamble line:
13930 \begin_layout Standard
13935 definecolor{darkgreen}{cmyk}{0.5,
13953 \begin_layout Plain Layout
13964 \begin_layout Standard
13969 is the color space that denotes the colors
13986 The four comma separated numbers are the portion factor for the corresponding
13987 colors of the color space.
13988 The factors can be in the range of 0
13989 \begin_inset space \thinspace{}
13993 \begin_inset space \thinspace{}
14001 also the color space
14005 can be used for definitions.
14022 , so that there are in this case three portion factors for the corresponding
14024 Furthermore there is the color space
14028 with one portion factor for the gray value.
14031 \begin_layout Standard
14032 As example a framed box with the new defined color
14036 where the characters have been colored
14041 \begin_inset Formula \begin{equation}
14042 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14049 \begin_layout Standard
14050 Self-defined colors can also be used for text with the help of the command
14061 \begin_layout Plain Layout
14070 \begin_layout Standard
14074 \begin_layout Plain Layout
14078 textcolor{darkgreen}{
14084 \begin_inset Quotes eld
14088 \begin_inset Quotes erd
14095 \begin_layout Plain Layout
14105 \begin_layout Standard
14116 \begin_layout Plain Layout
14124 is used in the scheme
14128 textcolor{color}{characters to color}
14133 \begin_layout Subsection
14135 \begin_inset CommandInset label
14137 name "sub:Paragraph-Boxes"
14145 \begin_layout Plain Layout
14146 Boxes ! as paragraph
14154 \begin_layout Standard
14155 A box that can contain several lines and paragraphs, a so called paragraph
14156 box (parbox), can be created with the menu
14158 Insert\SpecialChar \menuseparator
14161 or the toolbar button
14162 \begin_inset Graphics
14163 filename ../images/box-insert.png
14171 \begin_layout Standard
14172 The following example shows a framed parbox in a line:
14175 \begin_layout Standard
14176 \begin_inset VSpace medskip
14180 \begin_inset Box Boxed
14189 height_special "totalheight"
14192 \begin_layout Plain Layout
14193 This is a paragraph box.
14195 \begin_inset space \thinspace{}
14198 cm long and can also contain formulas:
14199 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14210 \begin_layout Standard
14211 \begin_inset VSpace medskip
14217 \begin_layout Standard
14218 Such a box is created by right-clicking on the gray box inset.
14219 A dialog pops up showing the box properties.
14233 \begin_inset space \thinspace{}
14238 Vertical Box Alignment
14243 \begin_layout Standard
14244 \begin_inset VSpace medskip
14247 In LaTeX a parbox is created with the command
14257 \begin_layout Plain Layout
14265 that has the following scheme:
14268 \begin_layout Standard
14273 parbox[position]{width}{box content}
14276 \begin_layout Standard
14290 for bottom means that the box is aligned within the surrounding text with
14296 for top this is done with the first line.
14297 When no position is given, the box will be vertically centered, see section
14305 \begin_inset space ~
14310 manual for examples.
14313 \begin_layout Standard
14314 \begin_inset VSpace bigskip
14317 To frame formulas completely, including the formula number, the formula
14318 must be set into a parbox.
14319 To do this, the command
14333 is inserted in TeX-mode before the formula.
14342 \begin_layout Plain Layout
14352 is hereby the line width set for the document.
14353 Because the frame is outside the parbox, 2
14354 \begin_inset space \thinspace{}
14357 times the frame separation and the frame thickness must be subtracted from
14359 As this is not automatically done by LyX due to a bug
14363 \begin_layout Plain Layout
14364 \begin_inset CommandInset href
14366 name "LyX-bug #4483"
14367 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14376 , TeX-mode has to be used.
14377 To be able to multiply and subtract in arguments, the LaTeX-package
14385 \begin_layout Plain Layout
14390 is part of every LaTeX standard installation.
14399 \begin_layout Plain Layout
14405 must be loaded in the LaTeX-preamble with the line
14408 \begin_layout Standard
14416 \begin_layout Standard
14417 Behind the formula both boxes are closed by entering
14422 Here is an example:
14426 \begin_layout Plain Layout
14440 \begin_layout Standard
14444 \begin_layout Plain Layout
14462 \begin_inset Formula \begin{equation}
14463 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14471 \begin_layout Plain Layout
14482 \begin_layout Plain Layout
14496 \begin_layout Standard
14497 \begin_inset VSpace medskip
14500 As a parbox is used as argument of
14506 , there is in this case no difference between
14521 \begin_layout Standard
14522 \begin_inset VSpace bigskip
14525 Paragraph boxes are very useful to comment formulas directly.
14532 is used in combination with the command
14546 \begin_inset CommandInset ref
14548 reference "sub:User-defined-Numbering"
14555 \begin_layout Standard
14556 An example of a formula commented with
14565 \begin_layout Standard
14569 \begin_layout Plain Layout
14582 This is a description.
14583 It is distinctly separated from the formula and multiline.
14587 \begin_layout Plain Layout
14599 \begin_layout Standard
14600 Such a formula must be inserted completely in TeX-mode because LyX does
14601 not yet support the command
14608 The formula is created with the following command sequence:
14611 \begin_layout Standard
14624 is inserted in TeX-mode.
14628 \begin_layout Plain Layout
14629 When the formula style
14641 can also be replaced by
14648 (formula styles see
14649 \begin_inset CommandInset ref
14651 reference "sec:Formula-Styles"
14660 Then the description follows as normal text, and finally
14666 is inserted in TeX-mode.
14679 hereby create a displayed formula.
14682 \begin_layout Standard
14689 can be seen in this example that was
14690 \begin_inset Quotes eld
14694 \begin_inset Quotes erd
14697 using the mathematical textmode:
14698 \begin_inset Formula \[
14699 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14706 \begin_layout Section
14711 \begin_layout Plain Layout
14720 \begin_layout Subsection
14722 \begin_inset CommandInset label
14724 name "sub:Big-Operators"
14732 \begin_layout Plain Layout
14742 \begin_layout Plain Layout
14752 \begin_layout Plain Layout
14761 \begin_layout Standard
14762 To be able to use all integral operators listed here, the option
14764 Use esint package automatically
14766 must be set in the document settings under
14769 \begin_inset space ~
14777 \begin_layout Standard
14778 \begin_inset space \hfill{}
14782 \begin_inset Tabular
14783 <lyxtabular version="3" rows="11" columns="2">
14785 <column alignment="center" valignment="top" width="0pt">
14786 <column alignment="center" valignment="top" width="0pt">
14788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14791 \begin_layout Plain Layout
14797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14800 \begin_layout Plain Layout
14808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14811 \begin_layout Plain Layout
14818 \begin_layout Plain Layout
14831 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14834 \begin_layout Plain Layout
14835 \begin_inset Formula $\sum$
14845 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14848 \begin_layout Plain Layout
14855 \begin_layout Plain Layout
14868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14871 \begin_layout Plain Layout
14872 \begin_inset Formula $\int$
14882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14885 \begin_layout Plain Layout
14893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14896 \begin_layout Plain Layout
14897 \begin_inset Formula $\intop$
14907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14910 \begin_layout Plain Layout
14918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14921 \begin_layout Plain Layout
14922 \begin_inset Formula $\oint$
14932 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14935 \begin_layout Plain Layout
14943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14946 \begin_layout Plain Layout
14947 \begin_inset Formula $\ointop$
14957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14960 \begin_layout Plain Layout
14968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14971 \begin_layout Plain Layout
14972 \begin_inset Formula $\ointctrclockwise$
14982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14985 \begin_layout Plain Layout
14993 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14996 \begin_layout Plain Layout
14997 \begin_inset Formula $\ointclockwise$
15007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15010 \begin_layout Plain Layout
15018 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15021 \begin_layout Plain Layout
15022 \begin_inset Formula $\sqint$
15032 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15035 \begin_layout Plain Layout
15043 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15046 \begin_layout Plain Layout
15047 \begin_inset Formula $\bigcap$
15057 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15060 \begin_layout Plain Layout
15068 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15071 \begin_layout Plain Layout
15072 \begin_inset Formula $\bigcup$
15086 \begin_inset space \hfill{}
15090 \begin_inset Tabular
15091 <lyxtabular version="3" rows="10" columns="2">
15093 <column alignment="center" valignment="top" width="0pt">
15094 <column alignment="center" valignment="top" width="0pt">
15096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15099 \begin_layout Plain Layout
15105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15108 \begin_layout Plain Layout
15116 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15119 \begin_layout Plain Layout
15126 \begin_layout Plain Layout
15139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15142 \begin_layout Plain Layout
15143 \begin_inset Formula $\prod$
15153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15156 \begin_layout Plain Layout
15164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15167 \begin_layout Plain Layout
15168 \begin_inset Formula $\coprod$
15178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15181 \begin_layout Plain Layout
15189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15192 \begin_layout Plain Layout
15193 \begin_inset Formula $\bigodot$
15203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15206 \begin_layout Plain Layout
15214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15217 \begin_layout Plain Layout
15218 \begin_inset Formula $\bigotimes$
15228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15231 \begin_layout Plain Layout
15239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15242 \begin_layout Plain Layout
15243 \begin_inset Formula $\bigoplus$
15253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15256 \begin_layout Plain Layout
15264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15267 \begin_layout Plain Layout
15268 \begin_inset Formula $\bigwedge$
15278 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15281 \begin_layout Plain Layout
15289 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15292 \begin_layout Plain Layout
15293 \begin_inset Formula $\bigvee$
15303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15306 \begin_layout Plain Layout
15314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15317 \begin_layout Plain Layout
15318 \begin_inset Formula $\bigsqcup$
15328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15331 \begin_layout Plain Layout
15339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15342 \begin_layout Plain Layout
15343 \begin_inset Formula $\biguplus$
15357 \begin_inset space \hfill{}
15363 \begin_layout Standard
15364 All big operators can also be inserted via the math toolbar button
15365 \begin_inset Graphics
15366 filename ../images/math/intop.png
15374 \begin_layout Standard
15375 The operators are called big because they are bigger than the sometimes
15376 equal looking binary operators.
15377 All big operators can have limits as described in the next subsection.
15380 \begin_layout Standard
15406 \begin_inset space ~
15409 in the style the operator limits are displayed, see
15410 \begin_inset CommandInset ref
15412 reference "sub:Operator-Limits"
15420 \begin_layout Subsubsection*
15421 Advices for Integrals
15424 \begin_layout Standard
15429 in an integral is an operator, that therefore has to be set upright.
15430 This is done by highlighting the
15434 and using the keyboard shortcut
15437 \begin_inset space ~
15446 \begin_layout Plain Layout
15452 \begin_inset CommandInset ref
15454 reference "sub:Font-Styles"
15464 Finally the smallest space is inserted before the
15468 , as this is usual for operators.
15472 \begin_layout Standard
15474 \begin_inset Formula $\int A(x)dx$
15478 \begin_inset Newline newline
15485 \begin_layout Plain Layout
15495 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15501 \begin_layout Standard
15502 For multiple integrals there are the following commands:
15503 \begin_inset VSpace medskip
15509 \begin_layout Standard
15510 \begin_inset space \hfill{}
15514 \begin_inset Tabular
15515 <lyxtabular version="3" rows="4" columns="2">
15517 <column alignment="center" valignment="top" width="0">
15518 <column alignment="center" valignment="top" width="0">
15520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15523 \begin_layout Plain Layout
15529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15532 \begin_layout Plain Layout
15534 \begin_inset Note Note
15537 \begin_layout Plain Layout
15544 is only used as spacer.
15556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15559 \begin_layout Plain Layout
15567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15570 \begin_layout Plain Layout
15571 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15584 \begin_layout Plain Layout
15592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15595 \begin_layout Plain Layout
15596 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15609 \begin_layout Plain Layout
15617 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15620 \begin_layout Plain Layout
15621 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15635 \begin_inset space \hfill{}
15639 \begin_inset Tabular
15640 <lyxtabular version="3" rows="4" columns="2">
15642 <column alignment="center" valignment="top" width="0">
15643 <column alignment="center" valignment="top" width="0">
15645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15648 \begin_layout Plain Layout
15654 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15657 \begin_layout Plain Layout
15665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15668 \begin_layout Plain Layout
15676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15679 \begin_layout Plain Layout
15680 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15693 \begin_layout Plain Layout
15701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15704 \begin_layout Plain Layout
15705 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15718 \begin_layout Plain Layout
15726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15729 \begin_layout Plain Layout
15730 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15744 \begin_inset space \hfill{}
15750 \begin_layout Subsection
15752 \begin_inset CommandInset label
15754 name "sub:Operator-Limits"
15762 \begin_layout Plain Layout
15771 \begin_layout Standard
15772 Limits are created by super- and subscripts:
15775 \begin_layout Standard
15777 \begin_inset Tabular
15778 <lyxtabular version="3" rows="2" columns="2">
15780 <column alignment="center" valignment="top" width="0pt">
15781 <column alignment="center" valignment="top" width="0pt">
15783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15786 \begin_layout Plain Layout
15792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15795 \begin_layout Plain Layout
15797 \begin_inset Note Note
15800 \begin_layout Plain Layout
15807 is only used as spacer.
15819 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15822 \begin_layout Plain Layout
15831 \begin_layout Plain Layout
15841 \begin_inset Formula $\to$
15845 \begin_inset Formula $\to$
15853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15856 \begin_layout Plain Layout
15857 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15873 \begin_layout Standard
15874 Limits of inline formulas are set right beside the operator.
15875 Limits in displayed formulas are set above or below the operator, except
15876 of integral limits.
15879 \begin_layout Standard
15880 To force that the limits are set beside the operator, the cursor is set
15881 directly behind the operator and the limits type is changed with the menu
15884 Edit\SpecialChar \menuseparator
15885 Math\SpecialChar \menuseparator
15897 \begin_inset space ~
15906 \begin_layout Standard
15907 The default limits type is this:
15908 \begin_inset Formula \[
15909 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15913 This is how it looks when the limits type was changed to
15920 \begin_inset Formula \[
15921 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15925 For integrals, except of
15937 , the limits are by default set beside the operator.
15938 But for multiple integrals the limits are often set below the operator.
15939 In the following example the limits type was therefore set to
15943 and so set below the integrals:
15944 \begin_inset Formula \begin{equation}
15945 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15952 \begin_layout Standard
15953 \begin_inset VSpace medskip
15956 To specify conditions for limits, the commands
15966 \begin_layout Plain Layout
15984 \begin_layout Plain Layout
15993 To create for example this expression
15994 \begin_inset Formula \begin{equation}
15995 \sum_{\begin{subarray}{c}
15997 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16004 \begin_layout Standard
16005 the following has to be done:
16006 \begin_inset Newline newline
16021 \begin_layout Plain Layout
16033 One is now in a blue box under the summation operator and insert there
16042 \begin_layout Plain Layout
16054 The blue box is now within a purple box and now several lines can be written
16056 A new line is created by inserting a line break (
16062 \begin_inset Newline newline
16067 0<k<1000 Ctrl-Return
16068 \begin_inset Newline newline
16073 is typed in, a new box appears below for the new line.
16076 \begin_layout Standard
16077 The alignment of the lines can be changed to left aligned with the
16087 Edit\SpecialChar \menuseparator
16091 To get right alignment,
16099 \begin_layout Plain Layout
16110 is inserted at the beginning of the line.
16113 \begin_layout Standard
16126 with the difference that the lines are always centered.
16129 \begin_layout Standard
16130 \begin_inset VSpace bigskip
16134 \begin_inset CommandInset ref
16136 reference "eq:substack"
16140 there can be too much space beside an operator, because the characters
16141 following the operator are set beside the limits.
16144 \begin_layout Standard
16145 To avoid this, the following macro can be used in the LaTeX-preamble:
16148 \begin_layout Standard
16162 \begin_inset Newline newline
16174 \begin_inset Newline newline
16181 mathclapinternal #1#2{
16185 mathsurround =0pt #1{#2}$}}
16188 \begin_layout Standard
16189 This defines the command
16199 \begin_layout Plain Layout
16207 that sets the width of the limit to 0
16208 \begin_inset space \thinspace{}
16212 The command scheme is
16215 \begin_layout Standard
16223 \begin_layout Standard
16224 where the limit can consist of several conditions.
16227 \begin_layout Standard
16229 \begin_inset CommandInset ref
16231 reference "eq:substack"
16235 , one uses the command
16238 \begin_layout Standard
16251 \begin_layout Plain Layout
16260 0<k<1000 Ctrl-Enter
16263 \begin_layout Standard
16264 to create the lower limit.
16265 The summand is now directly behind the summation operator:
16266 \begin_inset Formula \[
16267 \sum_{\mathclap{\substack{0<k<1000\\
16268 \\k\,\in\,\mathbb{N}}
16276 \begin_layout Standard
16277 \begin_inset VSpace bigskip
16280 How to use one limit for several operators is described in
16281 \begin_inset CommandInset ref
16283 reference "sub:Self-defined-Operators"
16290 \begin_layout Standard
16291 \begin_inset Newpage newpage
16297 \begin_layout Subsection
16299 \begin_inset CommandInset label
16301 name "sub:Binary-Operators"
16309 \begin_layout Plain Layout
16318 \begin_layout Standard
16319 Binary operators are surrounded by space when there is a character before
16321 \begin_inset VSpace medskip
16327 \begin_layout Standard
16328 \begin_inset space \hfill{}
16332 \begin_inset Tabular
16333 <lyxtabular version="3" rows="13" columns="2">
16335 <column alignment="center" valignment="top" width="0pt">
16336 <column alignment="center" valignment="top" width="0pt">
16338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16341 \begin_layout Plain Layout
16343 \begin_inset Note Note
16346 \begin_layout Plain Layout
16353 is only used as spacer.
16363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16366 \begin_layout Plain Layout
16374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16377 \begin_layout Plain Layout
16383 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16386 \begin_layout Plain Layout
16387 \begin_inset Formula $+$
16397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16400 \begin_layout Plain Layout
16406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16409 \begin_layout Plain Layout
16410 \begin_inset Formula $-$
16420 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16423 \begin_layout Plain Layout
16431 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16434 \begin_layout Plain Layout
16435 \begin_inset Formula $\pm$
16445 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16448 \begin_layout Plain Layout
16456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16459 \begin_layout Plain Layout
16460 \begin_inset Formula $\mp$
16470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16473 \begin_layout Plain Layout
16481 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16484 \begin_layout Plain Layout
16485 \begin_inset Formula $\cdot$
16495 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16498 \begin_layout Plain Layout
16506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16509 \begin_layout Plain Layout
16510 \begin_inset Formula $\times$
16520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16523 \begin_layout Plain Layout
16531 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16534 \begin_layout Plain Layout
16535 \begin_inset Formula $\div$
16545 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16548 \begin_layout Plain Layout
16552 \begin_layout Plain Layout
16565 \begin_layout Plain Layout
16577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16580 \begin_layout Plain Layout
16581 \begin_inset Formula $*$
16591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16594 \begin_layout Plain Layout
16602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16605 \begin_layout Plain Layout
16606 \begin_inset Formula $\star$
16616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16619 \begin_layout Plain Layout
16627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16630 \begin_layout Plain Layout
16631 \begin_inset Formula $\circ$
16641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16644 \begin_layout Plain Layout
16652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16655 \begin_layout Plain Layout
16656 \begin_inset Formula $\diamond$
16666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16669 \begin_layout Plain Layout
16677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16680 \begin_layout Plain Layout
16681 \begin_inset Formula $\bullet$
16695 \begin_inset space \hfill{}
16699 \begin_inset Tabular
16700 <lyxtabular version="3" rows="13" columns="2">
16702 <column alignment="center" valignment="top" width="0pt">
16703 <column alignment="center" valignment="top" width="0pt">
16705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16708 \begin_layout Plain Layout
16714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16717 \begin_layout Plain Layout
16725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16728 \begin_layout Plain Layout
16736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16739 \begin_layout Plain Layout
16740 \begin_inset Formula $\nabla$
16750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16753 \begin_layout Plain Layout
16761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16764 \begin_layout Plain Layout
16765 \begin_inset Formula $\bigtriangledown$
16775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16778 \begin_layout Plain Layout
16786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16789 \begin_layout Plain Layout
16790 \begin_inset Formula $\bigtriangleup$
16800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16803 \begin_layout Plain Layout
16811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16814 \begin_layout Plain Layout
16815 \begin_inset Formula $\Box$
16825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16828 \begin_layout Plain Layout
16836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16839 \begin_layout Plain Layout
16840 \begin_inset Formula $\cap$
16850 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16853 \begin_layout Plain Layout
16861 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16864 \begin_layout Plain Layout
16865 \begin_inset Formula $\cup$
16875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16878 \begin_layout Plain Layout
16886 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16889 \begin_layout Plain Layout
16890 \begin_inset Formula $\dagger$
16900 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16903 \begin_layout Plain Layout
16911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16914 \begin_layout Plain Layout
16915 \begin_inset Formula $\ddagger$
16925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16928 \begin_layout Plain Layout
16936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16939 \begin_layout Plain Layout
16940 \begin_inset Formula $\wr$
16950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16953 \begin_layout Plain Layout
16961 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16964 \begin_layout Plain Layout
16965 \begin_inset Formula $\bigcirc$
16975 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16978 \begin_layout Plain Layout
16986 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16989 \begin_layout Plain Layout
16990 \begin_inset Formula $\wedge$
17000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17003 \begin_layout Plain Layout
17011 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17014 \begin_layout Plain Layout
17015 \begin_inset Formula $\vee$
17029 \begin_inset space \hfill{}
17033 \begin_inset Tabular
17034 <lyxtabular version="3" rows="13" columns="2">
17036 <column alignment="center" valignment="top" width="0pt">
17037 <column alignment="center" valignment="top" width="0pt">
17039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17042 \begin_layout Plain Layout
17048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17051 \begin_layout Plain Layout
17059 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17062 \begin_layout Plain Layout
17070 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17073 \begin_layout Plain Layout
17074 \begin_inset Formula $\oplus$
17084 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17087 \begin_layout Plain Layout
17095 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17098 \begin_layout Plain Layout
17099 \begin_inset Formula $\ominus$
17109 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17112 \begin_layout Plain Layout
17120 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17123 \begin_layout Plain Layout
17124 \begin_inset Formula $\otimes$
17134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17137 \begin_layout Plain Layout
17145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17148 \begin_layout Plain Layout
17149 \begin_inset Formula $\oslash$
17159 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17162 \begin_layout Plain Layout
17170 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17173 \begin_layout Plain Layout
17174 \begin_inset Formula $\odot$
17184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17187 \begin_layout Plain Layout
17195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17198 \begin_layout Plain Layout
17199 \begin_inset Formula $\amalg$
17209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17212 \begin_layout Plain Layout
17220 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17223 \begin_layout Plain Layout
17224 \begin_inset Formula $\uplus$
17234 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17237 \begin_layout Plain Layout
17245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17248 \begin_layout Plain Layout
17249 \begin_inset Formula $\setminus$
17259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17262 \begin_layout Plain Layout
17270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17273 \begin_layout Plain Layout
17274 \begin_inset Formula $\sqcap$
17284 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17287 \begin_layout Plain Layout
17295 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17298 \begin_layout Plain Layout
17299 \begin_inset Formula $\sqcup$
17309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17312 \begin_layout Plain Layout
17320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17323 \begin_layout Plain Layout
17324 \begin_inset Formula $\triangleleft$
17334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17337 \begin_layout Plain Layout
17345 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17348 \begin_layout Plain Layout
17349 \begin_inset Formula $\triangleright$
17363 \begin_inset space \hfill{}
17369 \begin_layout Standard
17370 All binary operators can also be inserted via the math toolbar button
17371 \begin_inset Graphics
17372 filename ../images/math/pm.png
17380 \begin_layout Standard
17381 To typeset the Laplace operator also
17398 \begin_inset Formula $\nabla^{2}$
17401 ) can be used instead of
17410 \begin_layout Standard
17417 Insert\SpecialChar \menuseparator
17429 \begin_layout Subsection
17430 Self-defined Operators
17431 \begin_inset CommandInset label
17433 name "sub:Self-defined-Operators"
17441 \begin_layout Plain Layout
17442 Operators ! self-defined
17450 \begin_layout Standard
17451 With the help of the command
17455 DeclareMathOperator
17461 \begin_layout Plain Layout
17466 DeclareMathOperator
17471 custom operators can be defined in the LaTeX-preamble.
17472 Its command scheme is:
17475 \begin_layout Standard
17480 DeclareMathOperator{new command}{display}
17483 \begin_layout Standard
17484 Display can be characters or symbols that define how the operator looks
17486 To define a big operator a * is set behind the command.
17487 All self-defined big operators can have limits as described in
17488 \begin_inset CommandInset ref
17490 reference "sub:Operator-Limits"
17497 \begin_layout Standard
17498 For example the LaTeX-preamble line
17501 \begin_layout Standard
17506 DeclareMathOperator*{
17513 \begin_layout Standard
17514 defines the command
17520 , that inserts a big operator consisting of the lozenge symbol from
17521 \begin_inset CommandInset ref
17523 reference "sub:Miscellaneous-Symbols"
17528 \begin_inset Formula \[
17529 \Lozenge_{n=1}^{\infty}\]
17533 The command for this formula is:
17544 \begin_inset Formula $\to$
17550 \begin_layout Standard
17551 \begin_inset VSpace bigskip
17554 When self-defined operators are not used several times in the document,
17555 they can also be defined with the commands
17565 \begin_layout Plain Layout
17583 \begin_layout Plain Layout
17591 , which have the following scheme:
17594 \begin_layout Standard
17608 \begin_layout Standard
17615 defines big operators,
17624 \begin_layout Standard
17632 \begin_inset space \thinspace{}
17636 \begin_inset space ~
17639 be used to use one limit for several operators:
17642 \begin_layout Standard
17643 \begin_inset Formula \[
17644 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17651 \begin_layout Standard
17652 The command for the formula above is:
17653 \begin_inset Newline newline
17672 \begin_layout Plain Layout
17684 \begin_inset Formula $\to$
17693 \begin_layout Plain Layout
17707 \begin_layout Section
17712 \begin_layout Plain Layout
17721 \begin_layout Subsection
17723 \begin_inset CommandInset label
17725 name "sub:Font-Styles"
17733 \begin_layout Plain Layout
17742 \begin_layout Standard
17743 Latin letters in formulas can be set in one of the following font styles:
17744 \begin_inset VSpace -2mm
17750 \begin_layout Standard
17752 \begin_inset Tabular
17753 <lyxtabular version="3" rows="6" columns="3">
17755 <column alignment="center" valignment="top" width="0">
17756 <column alignment="center" valignment="top" width="0">
17757 <column alignment="center" valignment="top" width="0">
17759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17762 \begin_layout Plain Layout
17768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17771 \begin_layout Plain Layout
17777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17780 \begin_layout Plain Layout
17788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17791 \begin_layout Plain Layout
17800 \begin_layout Plain Layout
17816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17819 \begin_layout Plain Layout
17820 \begin_inset Formula $\mathbb{ABC}$
17828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17831 \begin_layout Plain Layout
17839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17842 \begin_layout Plain Layout
17851 \begin_layout Plain Layout
17867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17870 \begin_layout Plain Layout
17871 \begin_inset Formula $\mathbf{AbC}$
17879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17882 \begin_layout Plain Layout
17890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17893 \begin_layout Plain Layout
17902 \begin_layout Plain Layout
17918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17921 \begin_layout Plain Layout
17922 \begin_inset Formula $\boldsymbol{AbC}$
17930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17933 \begin_layout Plain Layout
17941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17944 \begin_layout Plain Layout
17953 \begin_layout Plain Layout
17969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17972 \begin_layout Plain Layout
17973 \begin_inset Formula $\mathcal{ABC}$
17981 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17984 \begin_layout Plain Layout
17992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17995 \begin_layout Plain Layout
18004 \begin_layout Plain Layout
18020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18023 \begin_layout Plain Layout
18024 \begin_inset Formula $\mathfrak{AbC}$
18032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18035 \begin_layout Plain Layout
18049 \begin_layout Standard
18051 \begin_inset Tabular
18052 <lyxtabular version="3" rows="5" columns="3">
18054 <column alignment="center" valignment="top" width="0">
18055 <column alignment="center" valignment="top" width="0">
18056 <column alignment="center" valignment="top" width="0">
18058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18061 \begin_layout Plain Layout
18067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18070 \begin_layout Plain Layout
18076 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18079 \begin_layout Plain Layout
18087 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18090 \begin_layout Plain Layout
18099 \begin_layout Plain Layout
18115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18118 \begin_layout Plain Layout
18119 \begin_inset Formula $\mathit{AbC}$
18127 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18130 \begin_layout Plain Layout
18138 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18141 \begin_layout Plain Layout
18150 \begin_layout Plain Layout
18166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18169 \begin_layout Plain Layout
18170 \begin_inset Formula $\mathrm{AbC}$
18178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18181 \begin_layout Plain Layout
18189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18192 \begin_layout Plain Layout
18201 \begin_layout Plain Layout
18217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18220 \begin_layout Plain Layout
18221 \begin_inset Formula $\mathsf{AbC}$
18229 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18232 \begin_layout Plain Layout
18240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18243 \begin_layout Plain Layout
18252 \begin_layout Plain Layout
18268 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18271 \begin_layout Plain Layout
18272 \begin_inset Formula $\mathtt{AbC}$
18280 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18283 \begin_layout Plain Layout
18297 \begin_layout Standard
18298 \begin_inset Note Greyedout
18301 \begin_layout Plain Layout
18318 can only be used for big letters.
18326 \begin_layout Standard
18327 Predefined is the style
18336 \begin_layout Standard
18337 The style commands work also for letters in mathematical constructs:
18338 \begin_inset Formula \[
18339 \mathfrak{A=\frac{b}{C}}\]
18346 \begin_layout Standard
18347 Characters in mathematical text don't appear in a math font style but in
18348 the text font style
18355 That their style can't be set correctly via the text style dialog is a
18360 \begin_layout Plain Layout
18361 \begin_inset CommandInset href
18363 name "LyX-bug #4091"
18364 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18376 \begin_layout Standard
18377 Instead of the style commands the dialog
18379 Edit\SpecialChar \menuseparator
18380 Math\SpecialChar \menuseparator
18383 or the toolbar button
18384 \begin_inset Graphics
18385 filename ../images/math/font.png
18393 \begin_layout Subsection
18395 \begin_inset CommandInset label
18397 name "sub:Bold-Formulas"
18405 \begin_layout Plain Layout
18414 \begin_layout Standard
18415 To make a complete formula bold, the command
18421 from the previous subsection cannot be used, because it doesn't work for
18422 small Greek letters.
18423 Furthermore it prints Latin letters always upright, like in the following
18427 \begin_layout Standard
18428 \begin_inset Formula \[
18429 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18436 \begin_layout Standard
18437 To display the formula correctly, the command
18444 \begin_inset Formula \[
18445 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18449 It is also possible to set the formula in a
18451 boldmath environment
18454 This environment is created by inserting the command
18462 \begin_layout Plain Layout
18473 To end the environment, the command
18481 \begin_layout Plain Layout
18491 is inserted in TeX-mode.
18495 \begin_layout Plain Layout
18505 \begin_inset Formula \[
18506 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18514 \begin_layout Plain Layout
18526 \begin_layout Subsection
18528 \begin_inset CommandInset label
18530 name "sub:Font-Sizes"
18538 \begin_layout Plain Layout
18547 \begin_layout Standard
18548 For characters in formulas there are, analog to characters in text, the
18549 following size commands:
18552 \begin_layout Standard
18596 \begin_inset Newline newline
18618 \begin_layout Standard
18619 The size produced by the commands depends on the document font size, that
18620 corresponds with the command
18627 The other commands produce smaller or larger sizes than
18634 The font size can however not exceed a certain value.
18635 Is for example the document font size 12
18636 \begin_inset space \thinspace{}
18645 switches to the same size as
18655 \begin_layout Standard
18656 A size command is inserted in TeX-mode before the formula and sets the size
18657 for all following formula and text characters.
18658 To switch back to the initial size, the command
18664 is inserted behind the formula in TeX-mode.
18667 \begin_layout Standard
18668 Within a formula the size can only be changed for symbols or letters in
18670 To do this, the size command is inserted in mathematical text.
18671 All following characters until the end of the mathematical text or until
18672 another size command will have the selected size.
18674 \begin_inset VSpace -2mm
18680 \begin_layout Standard
18684 \begin_layout Plain Layout
18694 \begin_inset Formula \[
18695 A=\frac{B}{c}\cdot\maltese\]
18700 \begin_inset Formula \[
18701 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18709 \begin_layout Plain Layout
18721 \begin_layout Standard
18722 \begin_inset VSpace medskip
18725 Before both formulas the command
18732 The command for the second formula is:
18733 \begin_inset Newline newline
18744 \begin_layout Plain Layout
18759 \begin_layout Plain Layout
18774 \begin_layout Plain Layout
18789 \begin_layout Plain Layout
18799 \begin_inset Formula $\to$
18803 \begin_inset Formula $\to$
18807 \begin_inset Newline newline
18811 \begin_inset space \hspace*{}
18825 \begin_layout Plain Layout
18840 \begin_layout Plain Layout
18855 \begin_layout Plain Layout
18867 \begin_layout Standard
18868 If a symbol cannot be displayed in different sizes, it will always be displayed
18869 in the default size.
18872 \begin_layout Section
18877 \begin_layout Plain Layout
18886 \begin_layout Standard
18887 All Greek letters can also be inserted via the toolbar button
18888 \begin_inset Graphics
18889 filename ../images/math/alpha.png
18897 \begin_layout Subsection
18899 \begin_inset CommandInset label
18901 name "sub:Small-Letters"
18909 \begin_layout Plain Layout
18910 Greek letters ! small
18918 \begin_layout Standard
18919 \begin_inset space \hfill{}
18923 \begin_inset Tabular
18924 <lyxtabular version="3" rows="11" columns="2">
18926 <column alignment="center" valignment="top" width="0pt">
18927 <column alignment="center" valignment="top" width="0pt">
18929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18932 \begin_layout Plain Layout
18938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18941 \begin_layout Plain Layout
18949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18952 \begin_layout Plain Layout
18960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18963 \begin_layout Plain Layout
18964 \begin_inset Formula $\alpha$
18974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18977 \begin_layout Plain Layout
18985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18988 \begin_layout Plain Layout
18989 \begin_inset Formula $\beta$
18999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19002 \begin_layout Plain Layout
19010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19013 \begin_layout Plain Layout
19014 \begin_inset Formula $\gamma$
19024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19027 \begin_layout Plain Layout
19035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19038 \begin_layout Plain Layout
19039 \begin_inset Formula $\delta$
19049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19052 \begin_layout Plain Layout
19060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19063 \begin_layout Plain Layout
19064 \begin_inset Formula $\epsilon$
19074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19077 \begin_layout Plain Layout
19085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19088 \begin_layout Plain Layout
19089 \begin_inset Formula $\varepsilon$
19099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19102 \begin_layout Plain Layout
19110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19113 \begin_layout Plain Layout
19114 \begin_inset Formula $\zeta$
19124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19127 \begin_layout Plain Layout
19135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19138 \begin_layout Plain Layout
19139 \begin_inset Formula $\eta$
19149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19152 \begin_layout Plain Layout
19160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19163 \begin_layout Plain Layout
19164 \begin_inset Formula $\theta$
19174 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19177 \begin_layout Plain Layout
19185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19188 \begin_layout Plain Layout
19189 \begin_inset Formula $\vartheta$
19203 \begin_inset space \hfill{}
19207 \begin_inset Tabular
19208 <lyxtabular version="3" rows="12" columns="2">
19210 <column alignment="center" valignment="top" width="0pt">
19211 <column alignment="center" valignment="top" width="0pt">
19213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19216 \begin_layout Plain Layout
19222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19225 \begin_layout Plain Layout
19233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19236 \begin_layout Plain Layout
19244 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19247 \begin_layout Plain Layout
19248 \begin_inset Formula $\iota$
19258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19261 \begin_layout Plain Layout
19269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19272 \begin_layout Plain Layout
19273 \begin_inset Formula $\kappa$
19283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19286 \begin_layout Plain Layout
19294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19297 \begin_layout Plain Layout
19298 \begin_inset Formula $\varkappa$
19308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19311 \begin_layout Plain Layout
19319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19322 \begin_layout Plain Layout
19323 \begin_inset Formula $\lambda$
19333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19336 \begin_layout Plain Layout
19344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19347 \begin_layout Plain Layout
19348 \begin_inset Formula $\mu$
19358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\nu$
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19386 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19398 \begin_inset Formula $\xi$
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19420 \begin_layout Plain Layout
19421 \begin_inset Formula $o$
19431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19434 \begin_layout Plain Layout
19442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19445 \begin_layout Plain Layout
19446 \begin_inset Formula $\pi$
19456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19459 \begin_layout Plain Layout
19467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19470 \begin_layout Plain Layout
19471 \begin_inset Formula $\varpi$
19481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19484 \begin_layout Plain Layout
19492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19495 \begin_layout Plain Layout
19496 \begin_inset Formula $\rho$
19510 \begin_inset space \hfill{}
19514 \begin_inset Tabular
19515 <lyxtabular version="3" rows="11" columns="2">
19517 <column alignment="center" valignment="top" width="0pt">
19518 <column alignment="center" valignment="top" width="0pt">
19520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19523 \begin_layout Plain Layout
19529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19532 \begin_layout Plain Layout
19540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19543 \begin_layout Plain Layout
19551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19554 \begin_layout Plain Layout
19555 \begin_inset Formula $\varrho$
19565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19568 \begin_layout Plain Layout
19576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19579 \begin_layout Plain Layout
19580 \begin_inset Formula $\sigma$
19590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19593 \begin_layout Plain Layout
19601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19604 \begin_layout Plain Layout
19605 \begin_inset Formula $\varsigma$
19615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19618 \begin_layout Plain Layout
19626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19629 \begin_layout Plain Layout
19630 \begin_inset Formula $\tau$
19640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19643 \begin_layout Plain Layout
19651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19654 \begin_layout Plain Layout
19655 \begin_inset Formula $\upsilon$
19665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19668 \begin_layout Plain Layout
19676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19679 \begin_layout Plain Layout
19680 \begin_inset Formula $\phi$
19690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19693 \begin_layout Plain Layout
19701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19704 \begin_layout Plain Layout
19705 \begin_inset Formula $\varphi$
19715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19718 \begin_layout Plain Layout
19726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19729 \begin_layout Plain Layout
19730 \begin_inset Formula $\chi$
19740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19743 \begin_layout Plain Layout
19751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19754 \begin_layout Plain Layout
19755 \begin_inset Formula $\psi$
19765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19768 \begin_layout Plain Layout
19776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19779 \begin_layout Plain Layout
19780 \begin_inset Formula $\omega$
19794 \begin_inset space \hfill{}
19800 \begin_layout Standard
19801 \begin_inset VSpace medskip
19807 \begin_layout Standard
19808 How to create upright Greek letters is explained in
19809 \begin_inset CommandInset ref
19811 reference "sub:Upright-small-Greek"
19818 \begin_layout Subsection
19823 \begin_layout Plain Layout
19824 Greek letters ! big
19832 \begin_layout Standard
19833 \begin_inset space \hfill{}
19837 \begin_inset Tabular
19838 <lyxtabular version="3" rows="7" columns="2">
19840 <column alignment="center" valignment="top" width="0pt">
19841 <column alignment="center" valignment="top" width="0pt">
19843 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19846 \begin_layout Plain Layout
19852 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19855 \begin_layout Plain Layout
19863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19866 \begin_layout Plain Layout
19874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19877 \begin_layout Plain Layout
19878 \begin_inset Formula $\Gamma$
19888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19891 \begin_layout Plain Layout
19899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19902 \begin_layout Plain Layout
19903 \begin_inset Formula $\Delta$
19913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19916 \begin_layout Plain Layout
19924 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19927 \begin_layout Plain Layout
19928 \begin_inset Formula $\Theta$
19938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19941 \begin_layout Plain Layout
19949 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19952 \begin_layout Plain Layout
19953 \begin_inset Formula $\Lambda$
19963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19966 \begin_layout Plain Layout
19974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19977 \begin_layout Plain Layout
19978 \begin_inset Formula $\Xi$
19988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19991 \begin_layout Plain Layout
19999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20002 \begin_layout Plain Layout
20003 \begin_inset Formula $\Pi$
20017 \begin_inset space \hfill{}
20021 \begin_inset Tabular
20022 <lyxtabular version="3" rows="6" columns="2">
20024 <column alignment="center" valignment="top" width="0pt">
20025 <column alignment="center" valignment="top" width="0pt">
20027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20030 \begin_layout Plain Layout
20036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20039 \begin_layout Plain Layout
20047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20050 \begin_layout Plain Layout
20058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20061 \begin_layout Plain Layout
20062 \begin_inset Formula $\Sigma$
20072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20075 \begin_layout Plain Layout
20083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20086 \begin_layout Plain Layout
20087 \begin_inset Formula $\Upsilon$
20097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20100 \begin_layout Plain Layout
20108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20111 \begin_layout Plain Layout
20112 \begin_inset Formula $\Phi$
20122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20125 \begin_layout Plain Layout
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20136 \begin_layout Plain Layout
20137 \begin_inset Formula $\Psi$
20147 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20150 \begin_layout Plain Layout
20158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20161 \begin_layout Plain Layout
20162 \begin_inset Formula $\Omega$
20176 \begin_inset space \hfill{}
20182 \begin_layout Standard
20183 \begin_inset VSpace medskip
20186 That the big Greek letters appear upright is caused by a design bug when
20188 To get correct italic big letters, begin every command with
20193 For example the command
20200 \begin_inset Formula $\varGamma$
20206 \begin_layout Subsection
20211 \begin_layout Plain Layout
20212 Greek letters ! bold
20220 \begin_layout Standard
20221 Greek letters cannot be set with different font styles like Latin letters.
20222 They can only be made bold with the command
20232 \begin_layout Plain Layout
20243 \begin_layout Standard
20245 \begin_inset Tabular
20246 <lyxtabular version="3" rows="3" columns="2">
20248 <column alignment="center" valignment="top" width="0">
20249 <column alignment="center" valignment="top" width="0">
20251 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20254 \begin_layout Plain Layout
20260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20263 \begin_layout Plain Layout
20271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20274 \begin_layout Plain Layout
20286 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20289 \begin_layout Plain Layout
20290 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20303 \begin_layout Plain Layout
20315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20318 \begin_layout Plain Layout
20319 \begin_inset Formula $\theta\boldsymbol{\theta}$
20335 \begin_layout Section
20340 \begin_layout Plain Layout
20353 \begin_layout Plain Layout
20354 A list with all symbols of most of the LaTeX-packages can be found in
20355 \begin_inset CommandInset citation
20370 \begin_layout Plain Layout
20378 \begin_inset Note Note
20381 \begin_layout Plain Layout
20384 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20387 \begin_layout Plain Layout
20390 texorpdfstring is in section
20391 \begin_inset CommandInset ref
20393 reference "sub:Formulas-in-Section"
20406 \begin_layout Plain Layout
20415 \begin_layout Standard
20416 Many of the symbols listed in this section can also be inserted via the
20418 \begin_inset Graphics
20419 filename ../images/math/nabla.png
20425 \begin_inset Graphics
20426 filename ../images/math/digamma.png
20434 \begin_layout Subsection
20435 Mathematical Symbols
20436 \begin_inset CommandInset label
20438 name "sub:Mathematical-Symbols"
20446 \begin_layout Plain Layout
20447 Symbols ! mathematical
20455 \begin_layout Standard
20456 \begin_inset space \hfill{}
20460 \begin_inset Tabular
20461 <lyxtabular version="3" rows="10" columns="2">
20463 <column alignment="center" valignment="top" width="0pt">
20464 <column alignment="center" valignment="top" width="0pt">
20466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20469 \begin_layout Plain Layout
20475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20478 \begin_layout Plain Layout
20486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20489 \begin_layout Plain Layout
20497 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20500 \begin_layout Plain Layout
20501 \begin_inset Formula $\neg$
20511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20514 \begin_layout Plain Layout
20522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20525 \begin_layout Plain Layout
20526 \begin_inset Formula $\Im$
20536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20539 \begin_layout Plain Layout
20547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20550 \begin_layout Plain Layout
20551 \begin_inset Formula $\Re$
20561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20564 \begin_layout Plain Layout
20572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20575 \begin_layout Plain Layout
20576 \begin_inset Formula $\aleph$
20586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20589 \begin_layout Plain Layout
20597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20600 \begin_layout Plain Layout
20601 \begin_inset Formula $\partial$
20611 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20614 \begin_layout Plain Layout
20622 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20625 \begin_layout Plain Layout
20626 \begin_inset Formula $\infty$
20636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20639 \begin_layout Plain Layout
20647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20650 \begin_layout Plain Layout
20651 \begin_inset Formula $\wp$
20661 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20675 \begin_layout Plain Layout
20676 \begin_inset Formula $\imath$
20686 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20689 \begin_layout Plain Layout
20697 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20700 \begin_layout Plain Layout
20701 \begin_inset Formula $\jmath$
20715 \begin_inset space \hfill{}
20719 \begin_inset Tabular
20720 <lyxtabular version="3" rows="10" columns="2">
20722 <column alignment="center" valignment="top" width="0pt">
20723 <column alignment="center" valignment="top" width="0pt">
20725 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20728 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20739 \begin_inset Note Note
20742 \begin_layout Plain Layout
20749 is only used as spacer.
20761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20764 \begin_layout Plain Layout
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20775 \begin_layout Plain Layout
20776 \begin_inset Formula $\forall$
20786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20789 \begin_layout Plain Layout
20797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20800 \begin_layout Plain Layout
20801 \begin_inset Formula $\exists$
20811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20814 \begin_layout Plain Layout
20822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20825 \begin_layout Plain Layout
20826 \begin_inset Formula $\nexists$
20836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20850 \begin_layout Plain Layout
20851 \begin_inset Formula $\emptyset$
20861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20864 \begin_layout Plain Layout
20872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20875 \begin_layout Plain Layout
20876 \begin_inset Formula $\varnothing$
20886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20889 \begin_layout Plain Layout
20897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20900 \begin_layout Plain Layout
20901 \begin_inset Formula $\dag$
20911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20914 \begin_layout Plain Layout
20922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20925 \begin_layout Plain Layout
20926 \begin_inset Formula $\ddag$
20936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20939 \begin_layout Plain Layout
20947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20950 \begin_layout Plain Layout
20954 \begin_layout Plain Layout
20964 \begin_inset Formula $\complement$
20971 \begin_layout Plain Layout
20985 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20988 \begin_layout Plain Layout
20996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20999 \begin_layout Plain Layout
21000 \begin_inset Formula $\Bbbk$
21014 \begin_inset space \hfill{}
21018 \begin_inset Tabular
21019 <lyxtabular version="3" rows="10" columns="2">
21021 <column alignment="center" valignment="top" width="0pt">
21022 <column alignment="center" valignment="top" width="0pt">
21024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21027 \begin_layout Plain Layout
21033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21036 \begin_layout Plain Layout
21044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21047 \begin_layout Plain Layout
21055 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21058 \begin_layout Plain Layout
21059 \begin_inset Formula $\prime$
21069 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21072 \begin_layout Plain Layout
21080 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21083 \begin_layout Plain Layout
21084 \begin_inset Formula $\backprime$
21094 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21097 \begin_layout Plain Layout
21105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21108 \begin_layout Plain Layout
21109 \begin_inset Formula $\mho$
21119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21122 \begin_layout Plain Layout
21130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21133 \begin_layout Plain Layout
21134 \begin_inset Formula $\triangle$
21144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21147 \begin_layout Plain Layout
21155 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21158 \begin_layout Plain Layout
21159 \begin_inset Formula $\angle$
21169 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21172 \begin_layout Plain Layout
21180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21183 \begin_layout Plain Layout
21184 \begin_inset Formula $\measuredangle$
21194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21197 \begin_layout Plain Layout
21205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21208 \begin_layout Plain Layout
21209 \begin_inset Formula $\sphericalangle$
21219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21222 \begin_layout Plain Layout
21230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21233 \begin_layout Plain Layout
21234 \begin_inset Formula $\top$
21244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21247 \begin_layout Plain Layout
21255 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21258 \begin_layout Plain Layout
21259 \begin_inset Formula $\bot$
21273 \begin_inset space \hfill{}
21279 \begin_layout Standard
21280 \begin_inset Newpage newpage
21286 \begin_layout Subsection
21287 Miscellaneous Symbols
21288 \begin_inset CommandInset label
21290 name "sub:Miscellaneous-Symbols"
21298 \begin_layout Plain Layout
21299 Symbols ! miscellaneous
21307 \begin_layout Standard
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 $\flat$
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 $\natural$
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 $\sharp$
21411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21414 \begin_layout Plain Layout
21422 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21425 \begin_layout Plain Layout
21426 \begin_inset Formula $\surd$
21436 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21439 \begin_layout Plain Layout
21447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21450 \begin_layout Plain Layout
21451 \begin_inset Formula $\checkmark$
21461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21464 \begin_layout Plain Layout
21472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21475 \begin_layout Plain Layout
21476 \begin_inset Formula $\yen$
21486 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21497 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21500 \begin_layout Plain Layout
21501 \begin_inset Formula $\pounds$
21511 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21514 \begin_layout Plain Layout
21520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21523 \begin_layout Plain Layout
21524 \begin_inset Formula $\$$
21534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21537 \begin_layout Plain Layout
21543 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21546 \begin_layout Plain Layout
21547 \begin_inset Formula $§$
21561 \begin_inset Tabular
21562 <lyxtabular version="3" rows="10" columns="2">
21564 <column alignment="center" valignment="top" width="0">
21565 <column alignment="center" valignment="top" width="0">
21567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21570 \begin_layout Plain Layout
21576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21579 \begin_layout Plain Layout
21587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21590 \begin_layout Plain Layout
21598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21601 \begin_layout Plain Layout
21602 \begin_inset Formula $\hbar$
21612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21615 \begin_layout Plain Layout
21623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21626 \begin_layout Plain Layout
21627 \begin_inset Formula $\hslash$
21637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21640 \begin_layout Plain Layout
21648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21651 \begin_layout Plain Layout
21652 \begin_inset Formula $\clubsuit$
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21665 \begin_layout Plain Layout
21673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21676 \begin_layout Plain Layout
21677 \begin_inset Formula $\spadesuit$
21687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Plain Layout
21702 \begin_inset Formula $\bigstar$
21712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21715 \begin_layout Plain Layout
21723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21726 \begin_layout Plain Layout
21727 \begin_inset Formula $\blacklozenge$
21737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21752 \begin_inset Formula $\blacktriangle$
21762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\blacktriangledown$
21787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21802 \begin_inset Formula $\bullet$
21816 \begin_inset Tabular
21817 <lyxtabular version="3" rows="10" columns="2">
21819 <column alignment="center" valignment="top" width="0pt">
21820 <column alignment="center" valignment="top" width="0pt">
21822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21825 \begin_layout Plain Layout
21831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21834 \begin_layout Plain Layout
21842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21845 \begin_layout Plain Layout
21853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21856 \begin_layout Plain Layout
21857 \begin_inset Formula $\diamondsuit$
21867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21870 \begin_layout Plain Layout
21878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21881 \begin_layout Plain Layout
21882 \begin_inset Formula $\Diamond$
21892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21895 \begin_layout Plain Layout
21903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21906 \begin_layout Plain Layout
21907 \begin_inset Formula $\heartsuit$
21917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21920 \begin_layout Plain Layout
21928 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21931 \begin_layout Plain Layout
21932 \begin_inset Formula $\P$
21942 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21945 \begin_layout Plain Layout
21953 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21956 \begin_layout Plain Layout
21957 \begin_inset Formula $\copyright$
21967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21970 \begin_layout Plain Layout
21978 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21981 \begin_layout Plain Layout
21982 \begin_inset Formula $\circledR$
21992 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21995 \begin_layout Plain Layout
22003 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22006 \begin_layout Plain Layout
22007 \begin_inset Formula $\maltese$
22017 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22020 \begin_layout Plain Layout
22028 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22031 \begin_layout Plain Layout
22032 \begin_inset Formula $\diagup$
22042 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22045 \begin_layout Plain Layout
22053 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22056 \begin_layout Plain Layout
22057 \begin_inset Formula $\diagdown$
22073 \begin_layout Standard
22074 \begin_inset VSpace medskip
22077 More symbols are listed in
22078 \begin_inset CommandInset ref
22080 reference "sub:Miscellaneous-special-Characters"
22087 \begin_layout Standard
22088 Some symbols can be displayed in different sizes, see
22089 \begin_inset CommandInset ref
22091 reference "sub:Font-Sizes"
22098 \begin_layout Subsection
22103 \begin_layout Plain Layout
22104 Symbols ! Euro-symbol
22113 \begin_layout Plain Layout
22120 \begin_layout Plain Layout
22137 \begin_layout Standard
22138 To use the Euro symbol in formulas, the LaTeX-package
22146 \begin_layout Plain Layout
22152 must be installed and loaded with the LaTeX-preamble line
22155 \begin_layout Standard
22160 usepackage[gennarrow]{eurosym}
22163 \begin_layout Standard
22164 The Euro symbol can now be inserted with the command
22174 \begin_layout Plain Layout
22185 \begin_layout Standard
22186 The Euro symbol can directly be inserted with the € key in mathematical
22187 text, without having
22202 can also be inserted in TeX-mode.
22203 The official currency symbol can then be inserted with the command
22213 \begin_layout Plain Layout
22221 , that is only available in TeX-mode.
22224 \begin_layout Standard
22228 \begin_layout Plain Layout
22238 \begin_inset Note Note
22241 \begin_layout Plain Layout
22242 The following table will only be displayed when the LaTeX-package
22254 \begin_layout Standard
22255 An overview about the different Euro symbols:
22258 \begin_layout Standard
22260 \begin_inset Tabular
22261 <lyxtabular version="3" rows="4" columns="3">
22263 <column alignment="center" valignment="top" width="0pt">
22264 <column alignment="center" valignment="top" width="0pt">
22265 <column alignment="center" valignment="top" width="0pt">
22267 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22270 \begin_layout Plain Layout
22276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22279 \begin_layout Plain Layout
22285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22288 \begin_layout Plain Layout
22296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22299 \begin_layout Plain Layout
22305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22308 \begin_layout Plain Layout
22316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22319 \begin_layout Plain Layout
22320 \begin_inset Formula $\euro$
22330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22333 \begin_layout Plain Layout
22339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22342 \begin_layout Plain Layout
22348 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22351 \begin_layout Plain Layout
22352 \begin_inset Formula $\mbox{€}$
22362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22365 \begin_layout Plain Layout
22371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22374 \begin_layout Plain Layout
22382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22385 \begin_layout Plain Layout
22389 \begin_layout Plain Layout
22411 \begin_layout Standard
22415 \begin_layout Plain Layout
22425 \begin_inset Note Note
22428 \begin_layout Plain Layout
22429 The following will be displayed when the LaTeX-package
22441 \begin_layout Standard
22442 You need to install the LaTeX-package
22446 to see the rest of this subsection in the output.
22449 \begin_layout Standard
22453 \begin_layout Plain Layout
22465 \begin_layout Section
22467 \begin_inset CommandInset label
22469 name "sec:Relations"
22477 \begin_layout Plain Layout
22487 \begin_layout Plain Layout
22492 \begin_layout Plain Layout
22503 \begin_layout Plain Layout
22518 \begin_layout Standard
22519 All relations can also be inserted via the toolbar button
22520 \begin_inset Graphics
22521 filename ../images/math/leq.png
22529 \begin_layout Standard
22530 \begin_inset space \hfill{}
22534 \begin_inset Tabular
22535 <lyxtabular version="3" rows="17" columns="2">
22537 <column alignment="center" valignment="top" width="0pt">
22538 <column alignment="center" valignment="top" width="0pt">
22540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22543 \begin_layout Plain Layout
22549 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22552 \begin_layout Plain Layout
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22563 \begin_layout Plain Layout
22569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22572 \begin_layout Plain Layout
22573 \begin_inset Formula $<$
22583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22586 \begin_layout Plain Layout
22594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22597 \begin_layout Plain Layout
22598 \begin_inset Formula $\le$
22608 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22611 \begin_layout Plain Layout
22619 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22622 \begin_layout Plain Layout
22623 \begin_inset Formula $\ll$
22633 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22636 \begin_layout Plain Layout
22644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22647 \begin_layout Plain Layout
22648 \begin_inset Formula $\prec$
22658 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22661 \begin_layout Plain Layout
22669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22672 \begin_layout Plain Layout
22673 \begin_inset Formula $\preceq$
22683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22686 \begin_layout Plain Layout
22694 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22697 \begin_layout Plain Layout
22698 \begin_inset Formula $\subset$
22708 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22711 \begin_layout Plain Layout
22719 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22722 \begin_layout Plain Layout
22723 \begin_inset Formula $\subseteq$
22733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22736 \begin_layout Plain Layout
22744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22747 \begin_layout Plain Layout
22748 \begin_inset Formula $\sqsubseteq$
22758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22761 \begin_layout Plain Layout
22769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22772 \begin_layout Plain Layout
22773 \begin_inset Formula $\in$
22783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22786 \begin_layout Plain Layout
22794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22797 \begin_layout Plain Layout
22798 \begin_inset Formula $\vdash$
22808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22811 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22822 \begin_layout Plain Layout
22823 \begin_inset Formula $\smile$
22833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22847 \begin_layout Plain Layout
22848 \begin_inset Formula $\lhd$
22858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22861 \begin_layout Plain Layout
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22872 \begin_layout Plain Layout
22873 \begin_inset Formula $\unlhd$
22883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22886 \begin_layout Plain Layout
22894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22897 \begin_layout Plain Layout
22898 \begin_inset Formula $\gtrless$
22908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22922 \begin_layout Plain Layout
22923 \begin_inset Formula $\mid$
22933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22944 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22947 \begin_layout Plain Layout
22948 \begin_inset Formula $\nmid$
22962 \begin_inset space \hfill{}
22966 \begin_inset Tabular
22967 <lyxtabular version="3" rows="17" columns="2">
22969 <column alignment="center" valignment="top" width="0pt">
22970 <column alignment="center" valignment="top" width="0pt">
22972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22975 \begin_layout Plain Layout
22981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22984 \begin_layout Plain Layout
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22995 \begin_layout Plain Layout
23001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23004 \begin_layout Plain Layout
23005 \begin_inset Formula $=$
23015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23018 \begin_layout Plain Layout
23026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23029 \begin_layout Plain Layout
23030 \begin_inset Formula $\not=$
23040 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23043 \begin_layout Plain Layout
23051 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23054 \begin_layout Plain Layout
23055 \begin_inset Formula $\equiv$
23065 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23068 \begin_layout Plain Layout
23076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23079 \begin_layout Plain Layout
23080 \begin_inset Formula $\sim$
23090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23093 \begin_layout Plain Layout
23101 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23104 \begin_layout Plain Layout
23105 \begin_inset Formula $\simeq$
23115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23118 \begin_layout Plain Layout
23126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23129 \begin_layout Plain Layout
23130 \begin_inset Formula $\approx$
23140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23143 \begin_layout Plain Layout
23151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23154 \begin_layout Plain Layout
23155 \begin_inset Formula $\cong$
23165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23168 \begin_layout Plain Layout
23176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23179 \begin_layout Plain Layout
23180 \begin_inset Formula $\bowtie$
23190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23193 \begin_layout Plain Layout
23201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23204 \begin_layout Plain Layout
23205 \begin_inset Formula $\notin$
23215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23218 \begin_layout Plain Layout
23226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23229 \begin_layout Plain Layout
23230 \begin_inset Formula $\perp$
23240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23243 \begin_layout Plain Layout
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23254 \begin_layout Plain Layout
23255 \begin_inset Formula $\propto$
23265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23268 \begin_layout Plain Layout
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23279 \begin_layout Plain Layout
23280 \begin_inset Formula $\asymp$
23290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23293 \begin_layout Plain Layout
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23304 \begin_layout Plain Layout
23305 \begin_inset Formula $\doteq$
23315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23318 \begin_layout Plain Layout
23326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23329 \begin_layout Plain Layout
23330 \begin_inset Formula $\circeq$
23340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23343 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23354 \begin_layout Plain Layout
23355 \begin_inset Formula $\models$
23365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23368 \begin_layout Plain Layout
23376 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23379 \begin_layout Plain Layout
23380 \begin_inset Formula $\widehat{=}$
23394 \begin_inset space \hfill{}
23398 \begin_inset Tabular
23399 <lyxtabular version="3" rows="17" columns="2">
23401 <column alignment="center" valignment="top" width="0pt">
23402 <column alignment="center" valignment="top" width="0pt">
23404 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23407 \begin_layout Plain Layout
23413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23427 \begin_layout Plain Layout
23433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23436 \begin_layout Plain Layout
23437 \begin_inset Formula $>$
23447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23450 \begin_layout Plain Layout
23458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23461 \begin_layout Plain Layout
23462 \begin_inset Formula $\ge$
23472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23475 \begin_layout Plain Layout
23483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23486 \begin_layout Plain Layout
23487 \begin_inset Formula $\gg$
23497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23500 \begin_layout Plain Layout
23508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23511 \begin_layout Plain Layout
23512 \begin_inset Formula $\succ$
23522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23525 \begin_layout Plain Layout
23533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23536 \begin_layout Plain Layout
23537 \begin_inset Formula $\succeq$
23547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23550 \begin_layout Plain Layout
23558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23561 \begin_layout Plain Layout
23562 \begin_inset Formula $\supset$
23572 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23575 \begin_layout Plain Layout
23583 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23586 \begin_layout Plain Layout
23587 \begin_inset Formula $\supseteq$
23597 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23600 \begin_layout Plain Layout
23608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23611 \begin_layout Plain Layout
23612 \begin_inset Formula $\sqsupseteq$
23622 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23625 \begin_layout Plain Layout
23633 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23636 \begin_layout Plain Layout
23637 \begin_inset Formula $\ni$
23647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23650 \begin_layout Plain Layout
23658 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23661 \begin_layout Plain Layout
23662 \begin_inset Formula $\dashv$
23672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23675 \begin_layout Plain Layout
23683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23686 \begin_layout Plain Layout
23687 \begin_inset Formula $\frown$
23697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23700 \begin_layout Plain Layout
23708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23711 \begin_layout Plain Layout
23712 \begin_inset Formula $\rhd$
23722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23725 \begin_layout Plain Layout
23733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23736 \begin_layout Plain Layout
23737 \begin_inset Formula $\unrhd$
23747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23750 \begin_layout Plain Layout
23758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23761 \begin_layout Plain Layout
23762 \begin_inset Formula $\lessgtr$
23772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23775 \begin_layout Plain Layout
23783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23786 \begin_layout Plain Layout
23787 \begin_inset Formula $\parallel$
23797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23800 \begin_layout Plain Layout
23808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23811 \begin_layout Plain Layout
23812 \begin_inset Formula $\nparallel$
23826 \begin_inset space \hfill{}
23832 \begin_layout Standard
23833 \begin_inset VSpace medskip
23848 are bigger than the equal looking operators
23863 \begin_layout Standard
23864 Relations are, in contrary to symbols, always surrounded by space.
23867 \begin_layout Standard
23868 Relations with labels can be created with the command
23878 \begin_layout Plain Layout
23889 \begin_layout Standard
23891 \begin_inset Tabular
23892 <lyxtabular version="3" rows="2" columns="2">
23894 <column alignment="center" valignment="top" width="0">
23895 <column alignment="center" valignment="top" width="0">
23897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23900 \begin_layout Plain Layout
23906 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23909 \begin_layout Plain Layout
23911 \begin_inset Note Note
23914 \begin_layout Plain Layout
23921 is only used as spacer.
23933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23936 \begin_layout Plain Layout
23943 \begin_layout Plain Layout
23960 \begin_layout Plain Layout
23970 \begin_inset Formula $\downarrow$
23979 \begin_layout Plain Layout
23992 \begin_layout Plain Layout
24006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24009 \begin_layout Plain Layout
24010 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24026 \begin_layout Section
24030 \begin_layout Subsection
24031 Predefined Functions
24032 \begin_inset CommandInset label
24034 name "sub:Predefined-Functions"
24042 \begin_layout Plain Layout
24043 Functions ! predefined
24051 \begin_layout Standard
24052 In general, variables are set
24056 in mathematical expressions, but not function names, because
24057 \begin_inset Formula $sin$
24060 could be misunderstood as
24061 \begin_inset Formula $s\cdot i\cdot n$
24065 Therefore there are predefined functions, that are additionally a bit separated
24067 They are inserted as commands starting with a backslash before their name.
24070 \begin_layout Standard
24072 \begin_inset Tabular
24073 <lyxtabular version="3" rows="2" columns="4">
24075 <column alignment="center" valignment="top" width="0pt">
24076 <column alignment="center" valignment="top" width="0pt">
24077 <column alignment="center" valignment="top" width="0pt">
24078 <column alignment="center" valignment="top" width="0pt">
24080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24083 \begin_layout Plain Layout
24089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24092 \begin_layout Plain Layout
24098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24101 \begin_layout Plain Layout
24107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24110 \begin_layout Plain Layout
24118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24121 \begin_layout Plain Layout
24127 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24130 \begin_layout Plain Layout
24131 \begin_inset Formula $Asin(x)+B$
24139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24142 \begin_layout Plain Layout
24150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24153 \begin_layout Plain Layout
24154 \begin_inset Formula $A\sin(x)+B$
24168 \begin_inset Newpage pagebreak
24174 \begin_layout Standard
24175 The following functions are predefined:
24178 \begin_layout Standard
24179 \begin_inset VSpace -2mm
24185 \begin_layout Standard
24187 \begin_inset Tabular
24188 <lyxtabular version="3" rows="9" columns="4">
24190 <column alignment="center" valignment="top" width="0pt">
24191 <column alignment="center" valignment="top" width="0pt">
24192 <column alignment="center" valignment="top" width="0pt">
24193 <column alignment="center" valignment="top" width="0pt">
24195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24204 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24207 \begin_layout Plain Layout
24213 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24216 \begin_layout Plain Layout
24222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24225 \begin_layout Plain Layout
24233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24236 \begin_layout Plain Layout
24244 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24247 \begin_layout Plain Layout
24255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24258 \begin_layout Plain Layout
24266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24269 \begin_layout Plain Layout
24279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24282 \begin_layout Plain Layout
24290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24293 \begin_layout Plain Layout
24301 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24304 \begin_layout Plain Layout
24312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24315 \begin_layout Plain Layout
24325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24328 \begin_layout Plain Layout
24336 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24339 \begin_layout Plain Layout
24347 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24350 \begin_layout Plain Layout
24358 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24361 \begin_layout Plain Layout
24371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24374 \begin_layout Plain Layout
24382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24385 \begin_layout Plain Layout
24393 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24396 \begin_layout Plain Layout
24404 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24407 \begin_layout Plain Layout
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24431 \begin_layout Plain Layout
24439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24442 \begin_layout Plain Layout
24450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24453 \begin_layout Plain Layout
24463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24466 \begin_layout Plain Layout
24474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24477 \begin_layout Plain Layout
24485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24488 \begin_layout Plain Layout
24496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24499 \begin_layout Plain Layout
24509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24512 \begin_layout Plain Layout
24520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24523 \begin_layout Plain Layout
24531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24534 \begin_layout Plain Layout
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24545 \begin_layout Plain Layout
24555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24558 \begin_layout Plain Layout
24566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24569 \begin_layout Plain Layout
24577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24580 \begin_layout Plain Layout
24588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24591 \begin_layout Plain Layout
24607 \begin_layout Standard
24608 They can also be inserted with the math toolbar button
24609 \begin_inset Graphics
24610 filename ../images/math/functions.png
24618 \begin_layout Subsection
24619 Self-defined Functions
24623 \begin_layout Plain Layout
24624 Functions ! self-defined
24632 \begin_layout Standard
24633 To use a function that is not predefined, like for example the sign function
24634 sgn(x), there are two possibilities:
24637 \begin_layout Itemize
24638 Define the function by inserting the following line to the LaTeX-preamble
24642 \begin_layout Plain Layout
24647 DeclareMathOperator
24650 \begin_inset CommandInset ref
24652 reference "sub:Self-defined-Operators"
24662 \begin_inset Newline newline
24666 \begin_inset VSpace -3mm
24670 \begin_inset Newline newline
24677 DeclareMathOperator{
24685 \begin_layout Plain Layout
24690 DeclareMathOperator
24696 \begin_inset Newline newline
24700 \begin_inset VSpace -2mm
24704 \begin_inset Newline newline
24707 Now the new defined function can be called with the command
24716 \begin_layout Itemize
24717 Write the the formula as usual, mark the formula name, in our example the
24722 , and change it to mathematical text.
24723 At last a space is inserted between prefactor and function.
24726 \begin_layout Standard
24727 The result is the same with both methods as with a predefined function
24731 \begin_layout Plain Layout
24732 In LyX self-defined functions are displayed red, predefined ones black.
24740 \begin_layout Standard
24742 \begin_inset Tabular
24743 <lyxtabular version="3" rows="3" columns="2">
24745 <column alignment="center" valignment="top" width="0pt">
24746 <column alignment="center" valignment="top" width="0pt">
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24751 \begin_layout Plain Layout
24757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24760 \begin_layout Plain Layout
24768 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24771 \begin_layout Plain Layout
24779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24782 \begin_layout Plain Layout
24783 \begin_inset Formula $A\sgn(x)+B$
24793 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24796 \begin_layout Plain Layout
24800 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24811 \begin_layout Plain Layout
24812 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24828 \begin_layout Standard
24829 The first method is more suitable when the self-defined function should
24830 be used several times.
24833 \begin_layout Subsection
24838 \begin_layout Plain Layout
24847 \begin_layout Standard
24848 For limits there are defined besides
24858 \begin_layout Plain Layout
24878 furthermore the following functions:
24881 \begin_layout Standard
24883 \begin_inset Tabular
24884 <lyxtabular version="3" rows="5" columns="2">
24886 <column alignment="center" valignment="top" width="0">
24887 <column alignment="center" valignment="top" width="0">
24889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24892 \begin_layout Plain Layout
24898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24901 \begin_layout Plain Layout
24903 \begin_inset Note Note
24906 \begin_layout Plain Layout
24913 is only used as spacer.
24925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24928 \begin_layout Plain Layout
24936 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24939 \begin_layout Plain Layout
24940 \begin_inset Formula $\varliminf$
24950 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24953 \begin_layout Plain Layout
24961 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24964 \begin_layout Plain Layout
24965 \begin_inset Formula $\varlimsup$
24975 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24978 \begin_layout Plain Layout
24986 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24989 \begin_layout Plain Layout
24990 \begin_inset Formula $\varprojlim$
25000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25003 \begin_layout Plain Layout
25011 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25014 \begin_layout Plain Layout
25015 \begin_inset Formula $\varinjlim$
25019 \begin_inset Formula $\raisebox{-2.5mm}{}$
25035 \begin_layout Standard
25036 \begin_inset VSpace medskip
25039 The limit is created by inserting a subscript.
25040 It is set right beside the function in an inline formula:
25043 \begin_layout Standard
25045 \begin_inset Tabular
25046 <lyxtabular version="3" rows="2" columns="2">
25048 <column alignment="center" valignment="top" width="0pt">
25049 <column alignment="center" valignment="top" width="0pt">
25051 <cell alignment="center" valignment="top" usebox="none">
25054 \begin_layout Plain Layout
25060 <cell alignment="center" valignment="top" usebox="none">
25063 \begin_layout Plain Layout
25064 \begin_inset space \hspace{}
25069 \begin_inset Note Note
25072 \begin_layout Plain Layout
25085 are used here as spacer.
25097 <cell alignment="center" valignment="top" usebox="none">
25100 \begin_layout Plain Layout
25109 \begin_layout Plain Layout
25122 \begin_layout Plain Layout
25136 <cell alignment="center" valignment="top" usebox="none">
25139 \begin_layout Plain Layout
25140 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25156 \begin_layout Standard
25157 In a displayed formula the limit is set below the formula, as usual:
25158 \begin_inset Formula \[
25166 \begin_layout Subsection
25171 \begin_layout Plain Layout
25172 Functions ! modulo-
25180 \begin_layout Standard
25181 The modulo-function is special, because it exists in four variants.
25184 \begin_layout Standard
25185 The variants in a displayed formula:
25186 \begin_inset Formula \begin{align*}
25187 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25188 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25189 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25190 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25191 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25198 \begin_layout Standard
25199 In an inline formula less space is set before the function names for all
25203 \begin_layout Section
25208 \begin_layout Plain Layout
25217 \begin_layout Subsection
25218 Special Characters in Mathematical Text
25221 \begin_layout Standard
25222 The following commands can only be used in mathematical text or in TeX-mode:
25225 \begin_layout Standard
25226 \begin_inset space \hfill{}
25230 \begin_inset Tabular
25231 <lyxtabular version="3" rows="8" columns="2">
25233 <column alignment="block" valignment="top" width="0">
25234 <column alignment="block" valignment="top" width="0">
25236 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25239 \begin_layout Plain Layout
25245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25248 \begin_layout Plain Layout
25256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25259 \begin_layout Plain Layout
25267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25270 \begin_layout Plain Layout
25271 \begin_inset Formula $\textrm{œ}$
25281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25284 \begin_layout Plain Layout
25292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25295 \begin_layout Plain Layout
25296 \begin_inset Formula $\textrm{Œ}$
25306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25309 \begin_layout Plain Layout
25317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25320 \begin_layout Plain Layout
25321 \begin_inset Formula $\textrm{æ}$
25331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25334 \begin_layout Plain Layout
25342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25345 \begin_layout Plain Layout
25346 \begin_inset Formula $\textrm{Æ}$
25356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25359 \begin_layout Plain Layout
25367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25370 \begin_layout Plain Layout
25371 \begin_inset Formula $\textrm{\aa}$
25381 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25384 \begin_layout Plain Layout
25391 \begin_layout Plain Layout
25398 \begin_layout Plain Layout
25419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25422 \begin_layout Plain Layout
25423 \begin_inset Formula $\textrm{Å}$
25433 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25436 \begin_layout Plain Layout
25444 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25447 \begin_layout Plain Layout
25448 \begin_inset Formula $\textrm{ı}$
25462 \begin_inset space \hfill{}
25466 \begin_inset Tabular
25467 <lyxtabular version="3" rows="8" columns="2">
25469 <column alignment="block" valignment="top" width="0">
25470 <column alignment="center" valignment="top" width="0">
25472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25475 \begin_layout Plain Layout
25477 \begin_inset Note Note
25480 \begin_layout Plain Layout
25487 is used for separation, because otherwise the output will be ¡ and ¿ respective
25498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25501 \begin_layout Plain Layout
25509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25512 \begin_layout Plain Layout
25520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25523 \begin_layout Plain Layout
25524 \begin_inset Formula $\textrm{ø}$
25534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25537 \begin_layout Plain Layout
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25548 \begin_layout Plain Layout
25549 \begin_inset Formula $\textrm{Ø}$
25559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25562 \begin_layout Plain Layout
25570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25573 \begin_layout Plain Layout
25574 \begin_inset Formula $\textrm{ł}$
25584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25587 \begin_layout Plain Layout
25595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25598 \begin_layout Plain Layout
25599 \begin_inset Formula $\textrm{Ł}$
25609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25612 \begin_layout Plain Layout
25614 \begin_inset space \hspace{}
25622 \begin_layout Plain Layout
25636 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25639 \begin_layout Plain Layout
25640 \begin_inset Formula $\textrm{!`}$
25650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25653 \begin_layout Plain Layout
25655 \begin_inset space \hspace{}
25663 \begin_layout Plain Layout
25677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25680 \begin_layout Plain Layout
25681 \begin_inset Formula $\textrm{?`}$
25691 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25694 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25705 \begin_layout Plain Layout
25706 \begin_inset Formula $\textrm{ȷ}$
25720 \begin_inset space \hfill{}
25726 \begin_layout Standard
25728 \begin_inset Formula $\textrm{\textrm{Å}}$
25732 \begin_inset Formula $\textrm{\textrm{Ø}}$
25735 can also be inserted via the math toolbar button
25736 \begin_inset Graphics
25737 filename ../images/math/digamma.png
25745 \begin_layout Standard
25746 An exception are the commands
25749 \begin_inset space \hspace{}
25758 \begin_inset space \hspace{}
25764 , because they can be inserted in LyX directly to text.
25767 \begin_layout Subsection
25769 \begin_inset CommandInset label
25771 name "sub:Accents-in-Text"
25779 \begin_layout Plain Layout
25788 \begin_layout Standard
25789 With the following commands all letters can be accented.
25790 The commands must be inserted in TeX-mode.
25793 \begin_layout Standard
25794 \begin_inset space \hfill{}
25798 \begin_inset Tabular
25799 <lyxtabular version="3" rows="8" columns="2">
25801 <column alignment="block" valignment="top" width="0">
25802 <column alignment="block" valignment="top" width="0">
25804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25807 \begin_layout Plain Layout
25813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25816 \begin_layout Plain Layout
25824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25827 \begin_layout Plain Layout
25831 \begin_inset Quotes grd
25839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25842 \begin_layout Plain Layout
25846 \begin_layout Plain Layout
25862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25865 \begin_layout Plain Layout
25873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25876 \begin_layout Plain Layout
25880 \begin_layout Plain Layout
25896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25899 \begin_layout Plain Layout
25906 \begin_layout Plain Layout
25920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25923 \begin_layout Plain Layout
25927 \begin_layout Plain Layout
25943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25946 \begin_layout Plain Layout
25954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25957 \begin_layout Plain Layout
25961 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25980 \begin_layout Plain Layout
25987 \begin_layout Plain Layout
26001 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26004 \begin_layout Plain Layout
26008 \begin_layout Plain Layout
26024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26027 \begin_layout Plain Layout
26034 \begin_layout Plain Layout
26048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26051 \begin_layout Plain Layout
26055 \begin_layout Plain Layout
26071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26074 \begin_layout Plain Layout
26081 \begin_layout Plain Layout
26095 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26098 \begin_layout Plain Layout
26102 \begin_layout Plain Layout
26122 \begin_inset space \hfill{}
26126 \begin_inset Tabular
26127 <lyxtabular version="3" rows="8" columns="2">
26129 <column alignment="block" valignment="top" width="0">
26130 <column alignment="center" valignment="top" width="0">
26132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26135 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26144 \begin_layout Plain Layout
26152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26155 \begin_layout Plain Layout
26162 \begin_layout Plain Layout
26176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26179 \begin_layout Plain Layout
26183 \begin_layout Plain Layout
26199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26202 \begin_layout Plain Layout
26210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26213 \begin_layout Plain Layout
26217 \begin_layout Plain Layout
26233 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26236 \begin_layout Plain Layout
26243 \begin_layout Plain Layout
26254 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26257 \begin_layout Plain Layout
26261 \begin_layout Plain Layout
26277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26280 \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
26405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26408 \begin_layout Plain Layout
26415 \begin_layout Plain Layout
26429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26432 \begin_layout Plain Layout
26436 \begin_layout Plain Layout
26456 \begin_inset space \hfill{}
26462 \begin_layout Standard
26463 \begin_inset VSpace medskip
26472 also two different characters can be accented.
26481 \begin_layout Plain Layout
26496 \begin_layout Plain Layout
26508 \begin_layout Standard
26521 can in combination with vowels directly be inserted with the keyboard without
26523 The same applies for the tilde
26527 \begin_layout Plain Layout
26528 This only applies for keyboards where the tilde is defined as accent.
26537 in combination with
26552 \begin_layout Standard
26595 , and accents inserted directly with the keyboard are also available in
26597 For the other accents there are special math commands to be used in formulas,
26599 \begin_inset CommandInset ref
26601 reference "sub:Accents-for-one"
26608 \begin_layout Standard
26609 \begin_inset VSpace bigskip
26612 Furthermore, with the command
26622 \begin_layout Plain Layout
26630 all numbers and letters can be set into a circle, quasi accented with a
26631 circle, similar to the the copyright symbol.
26634 \begin_layout Standard
26636 \begin_inset Tabular
26637 <lyxtabular version="3" rows="3" columns="2">
26639 <column alignment="center" valignment="top" width="0">
26640 <column alignment="center" valignment="top" width="0">
26642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26645 \begin_layout Plain Layout
26651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26654 \begin_layout Plain Layout
26656 \begin_inset Note Note
26659 \begin_layout Plain Layout
26666 is only used as spacer.
26678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26681 \begin_layout Plain Layout
26689 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26692 \begin_layout Plain Layout
26696 \begin_layout Plain Layout
26712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26715 \begin_layout Plain Layout
26726 raisebox{-1.5pt}{W}}
26731 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26734 \begin_layout Plain Layout
26735 \begin_inset Formula $\raisebox{4.5mm}{}$
26742 \begin_layout Plain Layout
26760 \begin_inset Formula $\raisebox{-2mm}{}$
26776 \begin_layout Standard
26777 One has to take care that the character fits in the circle.
26788 \begin_layout Plain Layout
26790 \begin_inset CommandInset ref
26792 reference "sub:Font-Sizes"
26801 specifies thereby the size of the circle.
26812 \begin_layout Plain Layout
26814 \begin_inset CommandInset ref
26816 reference "sub:Boxes-without-Frame"
26825 the character can be centered.
26828 \begin_layout Subsection
26833 \begin_layout Plain Layout
26842 \begin_layout Standard
26843 Minuscule numbers are created with the command
26853 \begin_layout Plain Layout
26862 The command can be used in formulas and in TeX-mode.
26863 The command scheme is:
26866 \begin_layout Standard
26871 oldstylenums{number}
26874 \begin_layout Standard
26879 oldstylenums{0123456789
26882 \begin_inset Formula $\oldstylenums{0123456789}$
26888 \begin_layout Subsection
26889 Miscellaneous special Characters
26890 \begin_inset CommandInset label
26892 name "sub:Miscellaneous-special-Characters"
26900 \begin_layout Plain Layout
26901 Special characters ! miscellaneous
26909 \begin_layout Standard
26910 The following characters can only be inserted to formulas by using commands:
26913 \begin_layout Standard
26915 \begin_inset Tabular
26916 <lyxtabular version="3" rows="4" columns="2">
26918 <column alignment="center" valignment="top" width="0">
26919 <column alignment="center" valignment="top" width="0">
26921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26924 \begin_layout Plain Layout
26930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26933 \begin_layout Plain Layout
26941 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26944 \begin_layout Plain Layout
26951 \begin_layout Plain Layout
26965 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26968 \begin_layout Plain Layout
26969 \begin_inset Formula $\mathcircumflex$
26979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26982 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26994 \begin_inset Formula $\_$
27004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27007 \begin_layout Plain Layout
27012 \begin_layout Plain Layout
27027 \begin_layout Plain Layout
27038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27041 \begin_layout Plain Layout
27042 \begin_inset Formula $^{\circ}$
27058 \begin_layout Standard
27059 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27060 contains the following line
27064 \begin_layout Plain Layout
27065 More about this is described in
27066 \begin_inset CommandInset ref
27068 reference "sub:Text-Characters-in"
27080 \begin_layout Standard
27085 DeclareInputtext{176}{
27098 \begin_layout Section
27100 \begin_inset CommandInset label
27102 name "sec:Formula-Styles"
27110 \begin_layout Plain Layout
27119 \begin_layout Itemize
27120 There are two different alignment styles:
27124 \begin_layout Description
27125 Centered is the predefined standard
27128 \begin_layout Description
27129 Indented for this the option
27133 must be inserted in the menu
27135 Document\SpecialChar \menuseparator
27141 \begin_inset space ~
27147 \begin_layout Standard
27152 is used, the indentation can be adjusted with the length
27162 \begin_layout Plain Layout
27171 Should the distance be 15
27172 \begin_inset space \thinspace{}
27175 mm, the following command line is inserted in the LaTeX-preamble
27178 \begin_layout Standard
27188 \begin_layout Standard
27189 When no length is specified, the predefined value of 30
27190 \begin_inset space \thinspace{}
27197 \begin_layout Itemize
27198 And two different numbering styles:
27202 \begin_layout Description
27203 Right is the predefined standard
27206 \begin_layout Description
27207 Left for this the option
27211 must be inserted in the menu
27213 Document\SpecialChar \menuseparator
27219 \begin_inset space ~
27226 \begin_layout Standard
27235 can also be used together.
27236 In this case both options are inserted, separated by a comma.
27239 \begin_layout Standard
27240 The chosen styles are used for all displayed formulas of the document.
27241 When both, centered and indented formulas should be created in a document,
27247 The indented formulas are then set in a flalign environment, see
27248 \begin_inset CommandInset ref
27250 reference "sub:Flalign-Environment"
27257 \begin_layout Section
27259 \begin_inset CommandInset label
27261 name "sec:Multiline-Formulas"
27269 \begin_layout Plain Layout
27270 Formula ! multiline
27278 \begin_layout Subsection
27282 \begin_layout Standard
27283 In LyX multiline formulas are created by pressing
27290 This creates either an
27292 eqnarray environment
27294 that is described in
27295 \begin_inset CommandInset ref
27297 reference "sub:Eqnarray-Environment"
27301 or, when the option
27303 Use AMS math package
27305 in the document settings is selected, an
27309 that is described in
27310 \begin_inset CommandInset ref
27312 reference "sub:Standard-align-Environment"
27319 \begin_layout Standard
27320 There are other multiline formula environments that can be created via the
27323 Insert\SpecialChar \menuseparator
27327 These environments are described in the following sections.
27330 \begin_layout Standard
27331 In all multiline formula environments a new line is created by pressing
27337 To add or delete lines, the math toolbar buttons
27338 \begin_inset Graphics
27339 filename ../images/tabular-feature_append-row.png
27345 \begin_inset Graphics
27346 filename ../images/tabular-feature_delete-row.png
27351 , respectively, or the menu
27353 Edit\SpecialChar \menuseparator
27359 \begin_layout Subsubsection
27361 \begin_inset CommandInset label
27363 name "sub:Line-Separation"
27371 \begin_layout Plain Layout
27372 Formula ! multiline ! Line separation
27380 \begin_layout Standard
27381 There is sometimes not enough space in multiline formulas between the lines:
27382 \begin_inset Formula \begin{eqnarray*}
27383 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}\\
27384 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*}
27391 \begin_layout Standard
27392 In LaTeX additional line space is specified as optional argument of the
27394 This is not yet possible in LyX
27398 \begin_layout Plain Layout
27400 \begin_inset CommandInset href
27402 name "LyX-bug #1505"
27403 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27412 , therefore the whole formula must be inserted in TeX-mode.
27413 To add in our example space, the command
27421 is inserted at the end of the first line.
27426 \begin_layout Plain Layout
27433 \begin_layout Plain Layout
27435 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27438 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27445 \begin_layout Plain Layout
27449 left(B^{2}+x_{0}^{2}
27457 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27462 \begin_layout Plain Layout
27474 \begin_layout Standard
27475 \begin_inset VSpace bigskip
27478 To set the the line separation for all lines in a formula, the length
27488 \begin_layout Plain Layout
27498 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27509 \begin_inset space \thinspace{}
27514 \begin_inset space \thinspace{}
27517 mm additional line separation as in the previous example, the command
27520 \begin_layout Standard
27530 \begin_layout Standard
27531 is inserted in TeX-mode before the formula.
27532 This requires that the LaTeX-package
27540 \begin_layout Plain Layout
27545 is part of every LaTeX standard installation.
27554 \begin_layout Plain Layout
27560 was loaded in LaTeX-preamble with the line
27563 \begin_layout Standard
27571 \begin_layout Standard
27576 \begin_layout Plain Layout
27588 \begin_inset Formula \begin{eqnarray*}
27589 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}\\
27590 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*}
27597 \begin_layout Standard
27601 \begin_layout Plain Layout
27612 To get back to the predefined distance,
27618 is set to the value 3
27619 \begin_inset space \thinspace{}
27625 \begin_layout Subsubsection
27627 \begin_inset CommandInset label
27629 name "sub:Column-Separation"
27637 \begin_layout Plain Layout
27638 Formula ! multiline ! Column separation
27646 \begin_layout Standard
27647 Multiline formulas form a matrix.
27648 A formula in the eqnarray environment is for example a matrix with three
27650 By changing the column separation in this environment, the space beside
27651 the relation sign can be changed.
27654 \begin_layout Standard
27655 The column separation is specified with the length
27665 \begin_layout Plain Layout
27674 \begin_inset Newline newline
27677 column separation = 2
27678 \begin_inset space \thinspace{}
27688 \begin_inset Newline newline
27694 \begin_layout Standard
27704 \begin_layout Standard
27705 inserted in TeX-mode, sets for all following formulas a column separation
27707 \begin_inset space \thinspace{}
27711 To get back to the predefined distance,
27718 \begin_inset space \thinspace{}
27724 \begin_layout Standard
27726 \begin_inset space \thinspace{}
27729 cm column separation:
27733 \begin_layout Plain Layout
27745 \begin_inset Formula \begin{eqnarray*}
27747 C & \ne & A\end{eqnarray*}
27751 A formula with the predefined column separation for matrices of 10
27752 \begin_inset space \thinspace{}
27759 \begin_layout Plain Layout
27771 \begin_inset Formula \begin{eqnarray*}
27773 C & \ne & A\end{eqnarray*}
27780 \begin_layout Subsubsection
27785 \begin_layout Plain Layout
27794 \begin_layout Standard
27795 Long formulas can be typeset using these methods:
27798 \begin_layout Itemize
27799 When one side of the equation is much shorther than the line width, this
27800 one is chosen for the left side and the right side is typeset over two
27805 \begin_layout Plain Layout
27815 \begin_inset Formula \begin{eqnarray}
27816 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 \\
27817 & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
27825 \begin_layout Plain Layout
27835 \begin_inset Newline newline
27838 The minus sign at the beginning of the second line does normally not appear
27839 as operator because it is the first character of the line.
27840 Thus it would not be surrounded by space and could not be distinguished
27841 from the fraction bar.
27842 To avoid this, space was inserted behind the minus sign with the command
27853 \begin_layout Plain Layout
27861 \begin_inset CommandInset ref
27863 reference "sub:Variable-Space"
27876 \begin_layout Plain Layout
27887 \begin_layout Itemize
27888 When both sides of the equation are too long, the command
27898 \begin_layout Plain Layout
27907 It is inserted to the first column of the first line and effects that all
27908 further insertions overwrite the following columns:
27912 \begin_layout Plain Layout
27922 \begin_inset Formula \begin{eqnarray}
27923 \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 \\
27924 & & -\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 \\
27925 & & =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}
27933 \begin_layout Plain Layout
27943 \begin_inset Newline newline
27946 After the insertion of
27952 , the cursor is in a purple box that is a bit shifted to the left from the
27954 In this the formula is inserted.
27958 \begin_layout Plain Layout
27968 \begin_inset Newline newline
27971 The content of the further lines is inserted to the second or another formula
27973 The greater the column number where it was inserted, the larger the indentation.
27977 \begin_layout Plain Layout
27987 \begin_inset Newline newline
27991 \begin_inset Note Greyedout
27994 \begin_layout Plain Layout
27995 Note the following when using
28004 \begin_layout Itemize
28005 The formula doesn't use the full page width.
28007 \begin_inset space \thinspace{}
28011 \begin_inset space ~
28015 \begin_inset Formula $-B^{2}$
28018 is added to the first line in the above example, it would have been outside
28020 To better use the width, negative space can be inserted at the beginning
28024 \begin_layout Itemize
28025 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28030 \begin_layout Plain Layout
28031 \begin_inset CommandInset href
28033 name "LyX-bug #1429"
28034 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28043 One can only set the cursor at the beginning of the line and move it with
28052 \begin_layout Itemize
28053 Other methods to set long formulas are offered by the environments described
28055 \begin_inset CommandInset ref
28057 reference "sub:Multline-Environment"
28062 \begin_inset CommandInset ref
28064 reference "sub:Multiline-Formula-Parts"
28071 \begin_layout Subsubsection
28073 \begin_inset CommandInset label
28075 name "sub:Multiline-Brackets"
28083 \begin_layout Plain Layout
28084 Brackets ! for multiline expressions
28092 \begin_layout Standard
28093 For brackets spanning multiple lines the following problem occurs:
28094 \begin_inset Formula \begin{eqnarray*}
28095 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28096 & & \left.\cdots+B-D\right]\end{eqnarray*}
28103 \begin_layout Standard
28104 The closing bracket is smaller than the opening bracket because brackets
28105 with variable size may not span multiple lines.
28108 \begin_layout Standard
28109 To set the bracket size for the second line correctly, the first line is
28120 \begin_layout Plain Layout
28128 and the second line with
28136 \begin_layout Plain Layout
28150 \begin_inset CommandInset ref
28152 reference "sub:Automatic-Bracket-Size"
28167 \begin_layout Plain Layout
28193 \begin_layout Plain Layout
28212 \begin_layout Plain Layout
28231 \begin_layout Plain Layout
28243 \begin_inset Formula $\downarrow$
28252 \begin_layout Plain Layout
28260 is inserted, because the multiplication operator with its limits is the
28261 largest symbol in the first line and this should be the size for the bracket
28262 in the second line.
28265 \begin_layout Standard
28266 The result is this:
28267 \begin_inset Formula \begin{eqnarray*}
28268 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28269 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28276 \begin_layout Subsection
28280 \begin_layout Standard
28281 Align environments can be used for every kind of multiline formulas.
28282 They are specially useful to set several formulas side by side.
28285 \begin_layout Standard
28286 Align environments consist of columns.
28287 The odd columns are right aligned, the even ones left aligned.
28288 Every line in an Align environment can be numbered.
28291 \begin_layout Standard
28292 Align environments are created via the menu
28294 Insert\SpecialChar \menuseparator
28300 Edit\SpecialChar \menuseparator
28301 Math\SpecialChar \menuseparator
28302 Change Formula Type
28304 already existing formulas can be converted to Align environments.
28307 \begin_layout Standard
28308 To add or delete columns, the math toolbar buttons
28309 \begin_inset Graphics
28310 filename ../images/tabular-feature_append-column.png
28316 \begin_inset Graphics
28317 filename ../images/tabular-feature_delete-column.png
28322 , respectively, or the menu
28324 Edit\SpecialChar \menuseparator
28330 \begin_layout Subsubsection
28331 Standard align Environment
28332 \begin_inset CommandInset label
28334 name "sub:Standard-align-Environment"
28342 \begin_layout Plain Layout
28343 Formula ! multiline ! align environment
28351 \begin_layout Standard
28352 This Align environment is created by presssing
28356 in a formula or by the menu
28358 Insert\SpecialChar \menuseparator
28359 Math\SpecialChar \menuseparator
28360 AMS align Environment
28365 \begin_layout Standard
28366 An example for two formulas set side by side, that are created with a four
28367 column align environment:
28368 \begin_inset Formula \begin{align*}
28369 A & =\sin(B) & C & =D\\
28370 C & \ne A & B & \ne D\end{align*}
28374 As it can be seen, the formulas in this environment are placed so as if
28383 \begin_layout Plain Layout
28391 \begin_inset CommandInset ref
28393 reference "sub:Variable-Space"
28404 before the first and after every even column.
28405 When the formula style
28411 \begin_layout Plain Layout
28413 \begin_inset CommandInset ref
28415 reference "sec:Formula-Styles"
28426 is used, the formula is set without the
28432 before the first column.
28435 \begin_layout Subsubsection
28436 Alignat Environment
28440 \begin_layout Plain Layout
28441 Formula ! multiline ! alignat environment
28449 \begin_layout Standard
28450 The alignat environment has no predefined column separation.
28451 It can be inserted manually with the spaces that are described
28452 \begin_inset CommandInset ref
28454 reference "sub:Space"
28461 \begin_layout Standard
28462 The above example in the alignat environment where 1
28463 \begin_inset space \thinspace{}
28466 cm space was inserted at the beginning of the second formula:
28467 \begin_inset Formula \begin{alignat*}{2}
28468 A & =\sin(B) & \hspace{1cm}C & =D\\
28469 C & \ne A & B & \ne D\end{alignat*}
28473 Because the column separation can be set separately for every column, this
28474 environment is especially suitable to set three and more formulas side
28478 \begin_layout Subsubsection
28479 Flalign Environment
28480 \begin_inset CommandInset label
28482 name "sub:Flalign-Environment"
28490 \begin_layout Plain Layout
28491 Formula ! multiline ! flalign environment
28499 \begin_layout Standard
28500 In this environment the first two columns are always set as much as possible
28501 to the left and the last two ones to the right.
28503 \begin_inset Formula \begin{flalign*}
28504 A & =1 & B & =2 & C & =3\\
28505 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28512 \begin_layout Standard
28513 By creating a flalign environment with an odd number of columns where an
28514 empty TeX-brace is inserted to the last column, several formulas in a document
28515 can be set to the left, although the formula style
28520 As example the indented formula
28521 \begin_inset CommandInset ref
28523 reference "eq:VolInt"
28528 \begin_inset Formula \begin{flalign}
28529 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28533 The first two columns contain the formula.
28534 To indent it as with the formula style
28539 \begin_inset space \thinspace{}
28542 pt space was inserted at the beginning of the first column.
28545 \begin_layout Subsection
28546 Eqnarray Environment
28547 \begin_inset CommandInset label
28549 name "sub:Eqnarray-Environment"
28557 \begin_layout Plain Layout
28558 Formula ! multiline ! eqnarray environment
28566 \begin_layout Standard
28567 When this environment has been created, three blue boxes appear.
28568 The content of the first box is right aligned, the content of the last
28570 The content of the middle box appears centered and a bit smaller, because
28571 it is designed to insert there only relation characters.
28572 \begin_inset Formula \begin{eqnarray*}
28573 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28575 A & = & A\end{eqnarray*}
28582 \begin_layout Subsection
28587 \begin_layout Plain Layout
28588 Formula ! multiline ! gather environment
28596 \begin_layout Standard
28597 This environment consists of only one centered column.
28598 Every line can be numbered.
28599 \begin_inset Formula \begin{gather}
28601 X=\textrm{-}1\end{gather}
28608 \begin_layout Subsection
28609 Multline Environment
28610 \begin_inset CommandInset label
28612 name "sub:Multline-Environment"
28620 \begin_layout Plain Layout
28621 Formula ! multiline ! multline environment
28629 \begin_layout Standard
28630 The multline environment consists, like the gather environment, of only
28632 But the first line is left aligned, the last one right aligned.
28633 All other lines are centered.
28634 Therefore this environment is suitable for long formulas.
28636 \begin_inset CommandInset ref
28638 reference "eq:lefteqn"
28642 in the multline environment:
28643 \begin_inset Formula \begin{multline}
28644 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}\\
28645 -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}\\
28646 =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}
28653 \begin_layout Standard
28654 In the output only the last (first) line of a multline environment appears
28655 numbered when the document numbering is right (left).
28659 \begin_layout Plain Layout
28660 numbering styles see
28661 \begin_inset CommandInset ref
28663 reference "sec:Formula-Styles"
28675 \begin_layout Standard
28684 \begin_layout Plain Layout
28702 \begin_layout Plain Layout
28712 a centered line can be right or left aligned, respectively.
28713 The commands are used as follows:
28716 \begin_layout Standard
28721 shoveright{line content}
28727 shoveleft{line content}
28730 \begin_layout Standard
28731 \begin_inset VSpace medskip
28742 \begin_layout Plain Layout
28752 specifies the distance of the first line from the left page margin.
28753 Predefined is the length 0
28754 \begin_inset space \thinspace{}
28760 \begin_layout Standard
28761 As example the above formula where the command
28764 \begin_layout Standard
28774 \begin_layout Standard
28775 was inserted in TeX-mode before:
28779 \begin_layout Plain Layout
28791 \begin_inset Formula \begin{multline}
28792 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}\\
28793 \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}}\\
28794 =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}
28802 \begin_layout Plain Layout
28813 The second line was left aligned using
28822 \begin_layout Subsection
28823 Multiline Formula Parts
28824 \begin_inset CommandInset label
28826 name "sub:Multiline-Formula-Parts"
28834 \begin_layout Plain Layout
28835 Formula ! multiline ! formula parts
28843 \begin_layout Standard
28844 To display only parts of a formula with multiple lines, one of the following
28845 environments are used:
28862 They can be inserted via the menu
28864 Insert\SpecialChar \menuseparator
28867 or by using the commands described in this section.
28870 \begin_layout Standard
28871 The first three have the same properties as the corresponding multiline
28872 formula environments, but it is possible to set further formula parts beside
28875 \begin_inset Formula \[
28876 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28877 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28878 \right\} \textrm{Uncertainty relations}\]
28885 \begin_layout Standard
28886 To get this formula, a displayed formula is created where the command
28894 \begin_layout Plain Layout
28905 A purple box appears around the blue formula box where now columns and
28906 lines can be added.
28907 Outside the multiline environment other formula parts can be set, like
28911 \begin_layout Standard
28912 The aligned environment is also suitable for long formulas whose lines are
28913 horizontally aligned.
28914 Using aligned in a displayed formula has the advantage that the formula
28915 number is vertically centered behind the lines.
28917 \begin_inset CommandInset ref
28919 reference "eq:kurzlang"
28923 in the aligned environment:
28924 \begin_inset Formula \begin{equation}
28925 \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}|}\\
28926 & -\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}
28934 \begin_layout Standard
28935 To use the environments
28957 \begin_layout Plain Layout
28975 \begin_layout Plain Layout
28993 \begin_layout Plain Layout
29001 are inserted, respectively.
29002 The split environment has the same properties as the aligned environment
29003 but it can only have two columns.
29006 \begin_layout Subsection
29007 Text in multiline Formulas
29008 \begin_inset CommandInset label
29010 name "sub:Text-in-multiline"
29018 \begin_layout Plain Layout
29028 \begin_layout Plain Layout
29029 Formula ! multiline ! text
29037 \begin_layout Standard
29038 In the Align environments, and the multline and gather environment, text
29039 can be inserted that will appear in a separate line and doesn't affect
29040 the column alignment.
29041 To do this, the command
29049 \begin_layout Plain Layout
29059 is used in the following scheme:
29062 \begin_layout Standard
29070 \begin_layout Standard
29071 The text should not be longer than a line because it cannot be hyphenated.
29072 As LyX doesn't yet support
29078 directly, the text is written as mathematical text.
29085 must hereby be at the beginning of a line and appears in the output above
29087 An example where the text was inserted at the beginning of the second line:
29088 \begin_inset Formula \begin{align}
29089 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29090 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29097 \begin_layout Section
29102 \begin_layout Plain Layout
29112 \begin_layout Plain Layout
29113 Formula ! numbering|see
29117 \begin_layout Plain Layout
29128 \begin_layout Plain Layout
29143 \begin_layout Subsection
29147 \begin_layout Standard
29148 Numbered formulas can be created with the menu
29150 Insert\SpecialChar \menuseparator
29151 Math\SpecialChar \menuseparator
29153 \begin_inset space ~
29161 \begin_inset space ~
29167 Existing formulas can be numbered with the menu
29169 Edit\SpecialChar \menuseparator
29170 Math\SpecialChar \menuseparator
29172 \begin_inset space ~
29180 \begin_inset space ~
29186 The formula number is displayed in LyX behind the formula as number sign
29188 The number sign is replaced in the output by the formula number.
29191 \begin_layout Standard
29192 When numbering is turned on in multiline formulas, all lines will be numbered.
29193 But the numbering can be controlled with the menu
29195 Edit\SpecialChar \menuseparator
29196 Math\SpecialChar \menuseparator
29198 \begin_inset space ~
29202 \begin_inset space ~
29206 \begin_inset space ~
29214 \begin_inset space ~
29222 \begin_layout Standard
29223 Except of inline formulas, all formulas can be numbered with two different
29225 \begin_inset CommandInset ref
29227 reference "sec:Formula-Styles"
29234 \begin_layout Subsection
29236 \begin_inset CommandInset label
29238 name "sub:Cross-References"
29246 \begin_layout Plain Layout
29247 Cross-references ! to formulas
29255 \begin_layout Standard
29256 All labeled formulas can be cross-referenced.
29257 A label is added by the menu
29259 Insert\SpecialChar \menuseparator
29262 or the toolbar button
29263 \begin_inset Graphics
29264 filename ../images/label-insert.png
29270 The cursor must hereby be inside a displayed formula.
29271 A dialog pops up displaying the prefix
29276 The label is inserted there behind the prefix.
29277 The predefined prefix means
29278 \begin_inset Quotes eld
29282 \begin_inset Quotes erd
29285 and makes it easier to find labels in large documents because it marks
29286 it as formula label to divide it from e.
29287 \begin_inset space \thinspace{}
29291 \begin_inset space ~
29295 To change a label, the menu
29297 Insert\SpecialChar \menuseparator
29303 \begin_layout Standard
29304 The name of the label is displayed in LyX within two parentheses behind
29306 A formula with a label is always numbered.
29309 \begin_layout Standard
29310 Cross-references are inserted via the menu
29312 Insert\SpecialChar \menuseparator
29315 or with the toolbar button
29316 \begin_inset Graphics
29317 filename ../images/dialog-show-new-inset_ref.png
29323 A formula cross-reference appears in the output as formula number.
29324 When in the cross-reference dialog window the format
29328 is chosen, the cross-reference appears in the output as formula number
29330 \begin_inset Newline newline
29333 By right-clicking on a cross-reference in LyX, one jumps to the formula
29334 that is referenced.
29337 \begin_layout Standard
29338 Here are as examples cross-references to formulas of the following subsections:
29339 \begin_inset Note Note
29342 \begin_layout Plain Layout
29343 Note the different cross-reference types.
29351 \begin_layout Standard
29353 \begin_inset CommandInset ref
29360 \begin_inset CommandInset ref
29368 \begin_inset CommandInset ref
29374 ) big Latin letters are used for the numbering in contrary to (
29375 \begin_inset CommandInset ref
29384 \begin_layout Standard
29385 \begin_inset VSpace medskip
29388 When the argument of
29396 \begin_layout Plain Layout
29404 \begin_inset CommandInset ref
29406 reference "sub:User-defined-Numbering"
29417 contains a box like in
29418 \begin_inset CommandInset ref
29420 reference "sub:Paragraph-Boxes"
29424 , the formula cannot be referenced.
29427 \begin_layout Subsection
29432 \begin_layout Plain Layout
29433 Formula numbering ! subnumbering
29441 \begin_layout Standard
29442 With the help of the commands
29446 begin{subequations}
29454 formulas can be subnumbered.
29455 Both commands are inserted in TeX-mode.
29458 \begin_layout Standard
29460 \begin_inset Formula \begin{equation}
29461 A=C-B\label{eq:a}\end{equation}
29469 \begin_layout Plain Layout
29473 addtocounter{equation}{-1}
29482 \begin_layout Plain Layout
29486 begin{subequations}
29492 \begin_inset VSpace -5mm
29496 \begin_inset Formula \begin{equation}
29497 B=C-A\label{eq:b}\end{equation}
29502 \begin_inset Formula \begin{equation}
29503 C=A+B\label{eq:c}\end{equation}
29510 \begin_layout Standard
29514 \begin_layout Plain Layout
29526 \begin_layout Standard
29527 To create the example, the following is done:
29530 \begin_layout Enumerate
29531 first formula is inserted
29534 \begin_layout Enumerate
29539 addtocounter{equation}{-1}
29541 begin{subequations}
29545 \begin_layout Plain Layout
29554 \begin_inset Newline newline
29559 is inserted after the first formula
29562 \begin_layout Enumerate
29563 second formula is inserted
29566 \begin_layout Enumerate
29567 third formula is inserted
29570 \begin_layout Enumerate
29577 is inserted after the third formula
29580 \begin_layout Standard
29581 Every formula between the commands
29593 is subnumbered as a, b,
29594 \begin_inset Newline linebreak
29597 c, \SpecialChar \ldots{}
29598 For multiline formulas every line will be subnumbered.
29599 All subnumbered formulas are treated as
29604 But as every numbered formula increases the counter
29608 by one, the command
29614 is needed to decrease it.
29615 Otherwise the formulas
29616 \begin_inset CommandInset ref
29623 \begin_inset CommandInset ref
29630 \begin_inset CommandInset ref
29636 would be numbered as
29637 \begin_inset CommandInset ref
29644 \begin_inset CommandInset ref
29651 \begin_inset CommandInset ref
29660 \begin_layout Standard
29661 By inserting the commands in TeX-mode, a space is created between the first
29664 \begin_inset space \thinspace{}
29667 mm vertical space is inserted after the command
29671 begin{subequations}
29674 When the formula style
29680 \begin_layout Plain Layout
29682 \begin_inset CommandInset ref
29684 reference "sec:Formula-Styles"
29696 \begin_inset space \thinspace{}
29699 mm space is inserted instead.
29702 \begin_layout Standard
29703 Here is an example for a multiline formula where the numbering was turned
29704 off for the second line:
29708 \begin_layout Plain Layout
29712 begin{subequations}
29718 \begin_inset Formula \begin{eqnarray}
29719 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29720 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29721 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29729 \begin_layout Plain Layout
29741 \begin_layout Subsection
29742 User-defined Numbering
29743 \begin_inset CommandInset label
29745 name "sub:User-defined-Numbering"
29753 \begin_layout Plain Layout
29754 Formula numbering ! user-defined
29762 \begin_layout Standard
29766 \begin_layout Plain Layout
29767 Formula numbering ! self-defined delimiters
29772 With the standard numbering parentheses are set around the formula number.
29773 To replace the parentheses for example by vertical bars, the following
29774 line is added to the LaTeX-preamble:
29777 \begin_layout Standard
29789 \begin_inset Note Note
29792 \begin_layout Plain Layout
29793 This macro is already declared in the LaTeX-preamble for testing.
29794 To activate it, remove the percent sign at the beginning.
29802 \begin_layout Standard
29803 To use other characters, the vertical bars besides the
29807 are replaced by one ore more characters.
29808 To get only the formula number the vertical bars are omitted.
29811 \begin_layout Standard
29812 \begin_inset VSpace bigskip
29815 When there should be an expression of your choice instead of the consecutive
29816 formula number in parentheses behind the formula, the command
29826 \begin_layout Plain Layout
29835 \begin_inset Formula \begin{equation}
29836 A+B=C\tag{something}\label{eq:tag}\end{equation}
29840 In this example the command
29848 \begin_layout Plain Layout
29859 was inserted to the formula.
29862 \begin_layout Standard
29871 \begin_layout Plain Layout
29882 is inserted instead, the star prevents the parentheses around the expression:
29883 \begin_inset Formula \[
29884 A+B=C\tag*{something}\]
29891 \begin_layout Standard
29892 \begin_inset VSpace bigskip
29895 To restart the formula numbering with new document parts or sections, the
29896 following command is used:
29899 \begin_layout Standard
29904 @addtoreset{equation}{part}
29910 \begin_layout Plain Layout
29915 \begin_layout Plain Layout
29926 \begin_layout Plain Layout
29939 \begin_layout Plain Layout
29950 \begin_layout Plain Layout
29963 \begin_inset Newline newline
29967 \begin_inset Newline newline
29974 @addtoreset{equation}{section}
29977 \begin_layout Standard
29978 To be able to use these commands in TeX-mode, the
29979 \begin_inset Quotes eld
29983 \begin_inset Quotes erd
29986 character has to be made
29987 \begin_inset Quotes eld
29991 \begin_inset Quotes erd
29994 for LaTeX using the command
30008 So the command sequence in TeX-mode is:
30011 \begin_layout Standard
30017 \begin_inset Newline newline
30022 @addtoreset{equation}{section}
30023 \begin_inset Newline newline
30031 \begin_layout Standard
30032 In the LaTeX-preamble
30044 can be omitted as they are automatically internally inserted by LyX.
30047 \begin_layout Standard
30062 \begin_layout Plain Layout
30067 is part of the LaTeX-package
30075 \begin_layout Plain Layout
30076 Packages ! carlisle
30081 that is part of every LaTeX standard installation.
30090 \begin_layout Plain Layout
30091 Packages ! remreset
30096 has to be loaded in the LaTeX-preamble with the line
30099 \begin_layout Standard
30104 usepackage{remreset}
30107 \begin_layout Standard
30118 \begin_layout Plain Layout
30123 \begin_layout Plain Layout
30134 \begin_layout Plain Layout
30147 \begin_layout Plain Layout
30158 \begin_layout Plain Layout
30170 can be used with the same scheme as
30179 \begin_layout Standard
30180 \begin_inset VSpace bigskip
30183 Sometimes formulas should be numbered in the following form:
30186 \begin_layout Standard
30189 (section number.formula number)
30192 \begin_layout Standard
30193 The formula number should start with every section with
30194 \begin_inset Quotes eld
30198 \begin_inset Quotes erd
30204 \begin_layout Standard
30205 For this case there is the command
30215 \begin_layout Plain Layout
30223 , which is used with the following scheme:
30226 \begin_layout Standard
30231 numberwithin{counter}{sectioning}
30234 \begin_layout Standard
30235 Counter denotes what kind of numbering is affected, sectioning denotes what
30236 number is before the dot.
30239 \begin_layout Standard
30240 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30243 \begin_layout Standard
30248 numberwithin{equation}{section}
30251 \begin_layout Standard
30252 This is the result:
30256 \begin_layout Plain Layout
30260 numberwithin{equation}{section}
30266 \begin_inset Formula \begin{equation}
30267 A+B=C\end{equation}
30274 \begin_layout Standard
30276 \begin_inset space \thinspace{}
30280 \begin_inset space ~
30283 tables so that the number of the part is the sectioning,
30284 \begin_inset Newline newline
30291 numberwithin{table}{part}
30296 \begin_layout Standard
30297 To go back to the standard numbering or to prevent this kind of numbering
30298 when it is defined by the document class, the following command is inserted
30299 as TeX-Code or to the LaTeX-preamble:
30302 \begin_layout Standard
30315 \begin_layout Plain Layout
30329 \begin_layout Plain Layout
30345 \begin_inset Newline newline
30353 \begin_inset Newline newline
30365 \begin_layout Standard
30372 uses internally the command
30378 , described above, that also needs to be reverted.
30382 \begin_layout Plain Layout
30389 \begin_layout Plain Layout
30393 @removefromreset{equation}{section}
30396 \begin_layout Plain Layout
30408 \begin_layout Subsection
30409 Numbering with Roman Numbers and Letters
30410 \begin_inset CommandInset label
30412 name "sub:Numbering-with-Roman"
30420 \begin_layout Plain Layout
30421 Formula numbering ! with letters
30430 \begin_layout Plain Layout
30431 Formula numbering ! with Roman numbers
30439 \begin_layout Standard
30440 Formulas can also be numbered with Roman numbers and Latin letters.
30441 To number for example with small Roman numbers, the command
30444 \begin_layout Standard
30456 \begin_layout Standard
30457 is inserted before the formula in TeX-mode.
30468 \begin_layout Plain Layout
30476 redefines the predefined command
30492 \begin_layout Plain Layout
30499 has the same scheme like the command
30505 that is described in
30506 \begin_inset CommandInset ref
30508 reference "sec:User-defined-Commands"
30522 is the formula counter.
30529 is used as prefix for a counter, the value of the counter is output as
30531 When a formula is numbered, LaTeX sets internally the command
30537 behind the formula.
30546 \begin_layout Plain Layout
30556 outputs the counter as small Roman number.
30559 \begin_layout Standard
30560 All formulas behind the command
30570 are now numbered Roman.
30571 To switch to numbering with big Roman numbers, the command is inserted
30588 \begin_layout Plain Layout
30600 \begin_inset Quotes eld
30604 \begin_inset Quotes erd
30607 with small Latin letters there is the command
30617 \begin_layout Plain Layout
30625 , for big ones there is the command
30635 \begin_layout Plain Layout
30648 \begin_layout Standard
30649 \begin_inset Note Greyedout
30652 \begin_layout Plain Layout
30657 Only maximal 26 formulas can be numbered with Latin letters in one document.
30665 \begin_layout Standard
30669 \begin_layout Plain Layout
30685 \begin_layout Standard
30686 \begin_inset Formula \begin{equation}
30687 A=\textrm{small roman}\label{eq:rom}\end{equation}
30695 \begin_layout Plain Layout
30709 \begin_inset Formula \begin{equation}
30710 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30718 \begin_layout Plain Layout
30732 \begin_inset Formula \begin{equation}
30733 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30741 \begin_layout Plain Layout
30755 \begin_inset Formula \begin{equation}
30756 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30763 \begin_layout Standard
30764 To switch back to the default numbering, insert the command:
30767 \begin_layout Standard
30780 \begin_layout Plain Layout
30791 \begin_layout Standard
30795 \begin_layout Plain Layout
30809 \begin_inset Formula \begin{equation}
30810 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30817 \begin_layout Standard
30818 \begin_inset VSpace medskip
30821 As you see, formulas are numbered serially independent from the numbering
30823 When then numbering should start with
30824 \begin_inset Quotes eld
30828 \begin_inset Quotes erd
30831 when the style is changed, new equation counters have to be defined.
30832 A description about this can be found in the file
30833 \begin_inset CommandInset href
30835 target "Formula-numbering.lyx"
30842 \begin_layout Section
30843 User-defined Commands
30844 \begin_inset CommandInset label
30846 name "sec:User-defined-Commands"
30854 \begin_layout Plain Layout
30855 User-defined commands
30863 \begin_layout Standard
30864 Many LaTeX-commands are too long to be used frequently.
30865 But it is possible to define with the command
30875 \begin_layout Plain Layout
30883 new shorter commands.
30886 \begin_layout Standard
30887 The command scheme of
30896 \begin_layout Standard
30901 newcommand{new command name}[number of arguments][optional
30906 \begin_inset Newline newline
30913 \begin_layout Plain Layout
30928 \begin_layout Plain Layout
30935 {command definition}
30938 \begin_layout Standard
30939 \begin_inset Note Greyedout
30942 \begin_layout Plain Layout
30947 Assure that the name of the new command is not already used in your document
30948 or by LaTeX-packages that you use.
30949 When you for example define the command
30961 , you get an error message because
30967 is already defined as command for
30968 \begin_inset Quotes eld
30972 \begin_inset Formula $\le$
30976 \begin_inset Quotes erd
30987 \begin_layout Standard
30988 \begin_inset Note Greyedout
30991 \begin_layout Plain Layout
30996 The names of user-defined commands may only consist of Latin letters.
31004 \begin_layout Standard
31005 The number of arguments is an integer in the range 0
31006 \begin_inset space \thinspace{}
31010 \begin_inset space \thinspace{}
31013 9 and specifies how many arguments the new command should have.
31014 With the optional value a value for an optional argument can be predefined.
31015 When this is done, the
31023 rgument of the new command is automatically an optional one.
31026 \begin_layout Standard
31027 Here are some examples:
31030 \begin_layout Itemize
31031 To define the command
31043 , the LaTeX-preamble line is:
31047 \begin_layout Plain Layout
31059 \begin_inset Newline newline
31071 \begin_layout Itemize
31072 To define the command
31084 , the argument (that should be underlined) must be taken into account.
31085 For this the preamble line is:
31089 \begin_layout Plain Layout
31101 \begin_inset Newline newline
31116 \begin_layout Plain Layout
31128 \begin_inset Newline newline
31137 acts as argument placeholder, the
31141 behind it denotes that it is the placeholder for the first argument.
31144 \begin_layout Itemize
31152 \begin_inset space \thinspace{}
31156 \begin_inset space ~
31169 \begin_layout Plain Layout
31181 \begin_inset Newline newline
31190 framebox#1#2{$#3$}}
31196 \begin_layout Plain Layout
31208 \begin_inset Newline newline
31213 The two Dollar signs creates the extra formula needed for
31220 \begin_inset CommandInset ref
31222 reference "sub:Boxes-with-Frame"
31229 \begin_layout Itemize
31230 To create a new command for
31236 where the color for the box needn't to be specified, the argument for the
31237 color is defined optional:
31241 \begin_layout Plain Layout
31253 \begin_inset Newline newline
31262 fcolorbox{#2}{#1}{$#3$}}
31268 \begin_layout Plain Layout
31278 \begin_inset Newline newline
31281 When the color is not specified when using
31287 , the predefined color
31294 \begin_layout Standard
31295 A test of the new defined commands:
31298 \begin_layout Standard
31300 \begin_inset Tabular
31301 <lyxtabular version="3" rows="6" columns="2">
31303 <column alignment="center" valignment="top" width="0">
31304 <column alignment="center" valignment="top" width="0">
31306 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31309 \begin_layout Plain Layout
31315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31318 \begin_layout Plain Layout
31320 \begin_inset Note Note
31323 \begin_layout Plain Layout
31330 is only used as spacer.
31342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31345 \begin_layout Plain Layout
31352 \begin_layout Plain Layout
31366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31369 \begin_layout Plain Layout
31370 \begin_inset Formula $A\gr B$
31380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31383 \begin_layout Plain Layout
31391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31394 \begin_layout Plain Layout
31395 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31408 \begin_layout Plain Layout
31412 \begin_inset Formula $\to$
31418 \begin_inset Formula $\to$
31429 \begin_layout Plain Layout
31443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31446 \begin_layout Plain Layout
31447 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31460 \begin_layout Plain Layout
31464 \begin_inset Formula $\to$
31475 \begin_layout Plain Layout
31489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31492 \begin_layout Plain Layout
31493 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31506 \begin_layout Plain Layout
31512 \begin_inset Formula $\to$
31523 \begin_layout Plain Layout
31537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31540 \begin_layout Plain Layout
31541 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31557 \begin_layout Section
31561 \begin_layout Standard
31562 LyX supports two types of commutative diagrams:
31570 that are explained in the following.
31573 \begin_layout Subsection
31578 \begin_layout Plain Layout
31587 \begin_layout Standard
31588 Diagrams of this type visualize relations by vertical and horizontal lines
31590 \begin_inset Formula \[
31591 \begin{CD}A@>>>B@>>>C\\
31593 F@<<<E@<<<D\end{CD}\]
31600 \begin_layout Standard
31601 To get them, the command
31609 \begin_layout Plain Layout
31619 is inserted to a formula.
31620 A blue box appears with two dashed lines where further commands can be
31626 a new line is created.
31627 Horizontal relations are inserted in odd, vertical in even formula lines.
31630 \begin_layout Standard
31631 To create the relations there are the following commands:
31634 \begin_layout Itemize
31639 creates a left arrow,
31650 \begin_layout Itemize
31655 creates an up arrow,
31663 a vertical equal sign
31666 \begin_layout Itemize
31672 is a placeholder for non-existent relations
31675 \begin_layout Standard
31676 All arrows can be labeled as follows:
31679 \begin_layout Itemize
31680 Is text inserted between the first and second < or >, resp., it is placed
31682 When it is inserted between the second and third one, it appears under
31686 \begin_layout Itemize
31687 When text for vertical arrows is inserted between the first and second A
31688 or V, resp., it is placed left beside the arrow.
31689 When it is inserted between the second and third one, it appears right
31691 If the text contains an A or V, these letters must be set into a TeX-brace.
31694 \begin_layout Standard
31695 As example a diagram with all possible relations:
31698 \begin_layout Standard
31699 \begin_inset Formula \[
31700 \begin{CD}A@>j>>B@>>k>C@=F\\
31702 D@<<j<E@>k>>F@=C\end{CD}\]
31709 \begin_layout Standard
31710 The command for this is:
31711 \begin_inset Newline newline
31722 \begin_layout Plain Layout
31731 A@>j>>B@>>k>C@=F Ctrl-Enter
31732 \begin_inset Newline newline
31739 \begin_layout Plain Layout
31754 \begin_layout Plain Layout
31767 \begin_layout Plain Layout
31779 \begin_inset Formula $\to$
31785 \begin_inset Newline newline
31792 \begin_layout Plain Layout
31807 \begin_layout Plain Layout
31820 \begin_layout Plain Layout
31830 \begin_layout Subsection
31835 \begin_layout Plain Layout
31836 Diagrams ! xymatrix
31844 \begin_layout Standard
31845 To be able to use xymatrices, the LaTeX-package
31850 A xymatrix is created by inserting the command
31857 Then you are able to add new matrix columns and rows like for normal matrices,
31859 \begin_inset CommandInset ref
31861 reference "sec:Matrices"
31868 \begin_layout Standard
31869 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31871 All possibilities to create commutative diagrams and decorations are explained
31872 in detail in this manual:
31873 \begin_inset CommandInset href
31875 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31882 \begin_layout Standard
31883 \begin_inset Newpage newpage
31889 \begin_layout Section
31894 \begin_layout Plain Layout
31907 \begin_layout Plain Layout
31908 Other useful math tips can be found in
31909 \begin_inset CommandInset citation
31924 \begin_layout Plain Layout
31932 \begin_inset Note Note
31935 \begin_layout Plain Layout
31938 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31941 \begin_layout Plain Layout
31944 texorpdfstring is in section
31945 \begin_inset CommandInset ref
31947 reference "sub:Formulas-in-Section"
31960 \begin_layout Plain Layout
31970 \begin_layout Plain Layout
31975 \begin_layout Plain Layout
31982 Chemical characters
31986 \begin_layout Plain Layout
32001 \begin_layout Subsection
32002 Chemical Symbols and Equations
32003 \begin_inset CommandInset label
32005 name "sub:Chemical-Symbols-and"
32013 \begin_layout Plain Layout
32014 Chemical characters ! Symbols
32023 \begin_layout Plain Layout
32033 \begin_layout Plain Layout
32042 \begin_layout Standard
32043 An example text from chemistry:
32046 \begin_layout Quote
32048 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32051 -ion reacts with two
32052 \begin_inset Formula $\mathrm{Na^{+}}$
32055 -ions to sodium sulfate
32056 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32060 The chemical equation for this is:
32061 \begin_inset Formula \[
32062 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32069 \begin_layout Standard
32070 This chemical equation can directly be created as formula.
32071 To avoid that the symbols appear italic, everything is highlighted and
32072 changed by the shortcut
32075 \begin_inset space ~
32080 to the upright font style.
32084 \begin_layout Plain Layout
32090 \begin_inset CommandInset ref
32092 reference "sub:Font-Styles"
32104 \begin_layout Subsection
32109 \begin_layout Plain Layout
32118 \begin_layout Standard
32119 Negative numbers often look ugly in formulas because the minus sign before
32120 the number is set with the same length as the minus operator sign.
32121 When writing the negative number in normal text, the minus sign appears
32125 \begin_layout Standard
32126 Thus, the problem disappears when converting the minus sign to mathematical
32130 \begin_layout Standard
32131 An example to visualize the problem:
32134 \begin_layout Standard
32136 \begin_inset Tabular
32137 <lyxtabular version="3" rows="3" columns="2">
32139 <column alignment="right" valignment="top" width="0">
32140 <column alignment="left" valignment="top" width="0">
32142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32145 \begin_layout Plain Layout
32151 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32154 \begin_layout Plain Layout
32162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32165 \begin_layout Plain Layout
32171 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32174 \begin_layout Plain Layout
32175 \begin_inset Formula $x=-2$
32185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32188 \begin_layout Plain Layout
32194 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32197 \begin_layout Plain Layout
32198 \begin_inset Formula $x=\textrm{-}2$
32214 \begin_layout Subsection
32215 Comma as decimal Separator
32219 \begin_layout Plain Layout
32228 \begin_layout Standard
32229 In LaTeX a comma inside a formula is used, according to the English convention,
32230 as number group separator.
32231 So there will be space added behind all commas in formulas.
32234 \begin_layout Standard
32235 To avoid this, the comma is highlighted and changed to mathematical text
32239 \begin_inset space ~
32247 \begin_layout Standard
32248 To use all formula commas in the document as decimal separator, the file
32257 \begin_layout Plain Layout
32262 is part of the LaTeX-package
32270 \begin_layout Plain Layout
32275 \begin_layout Plain Layout
32298 \begin_layout Plain Layout
32304 is loaded with the LaTeX-preamble line
32307 \begin_layout Standard
32315 \begin_layout Subsection
32317 \begin_inset CommandInset label
32319 name "sub:Physical-Vectors"
32327 \begin_layout Plain Layout
32336 \begin_layout Standard
32337 Predefined vectors are offered by the LaTeX-package
32345 \begin_layout Plain Layout
32350 should be part of every LaTeX standard installation.
32359 \begin_layout Plain Layout
32365 that is loaded with the LaTeX-preamble line
32368 \begin_layout Standard
32376 \begin_layout Standard
32380 \begin_layout Plain Layout
32390 \begin_inset Note Note
32393 \begin_layout Plain Layout
32394 The following table will only be displayed when the LaTeX-package
32403 The following commands are defined:
32406 \begin_layout Standard
32408 \begin_inset Tabular
32409 <lyxtabular version="3" rows="4" columns="2">
32411 <column alignment="center" valignment="top" width="0">
32412 <column alignment="center" valignment="top" width="0">
32414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32417 \begin_layout Plain Layout
32423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32426 \begin_layout Plain Layout
32434 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32437 \begin_layout Plain Layout
32447 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32450 \begin_layout Plain Layout
32451 \begin_inset Formula $\Bra{\psi}$
32461 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32464 \begin_layout Plain Layout
32474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32477 \begin_layout Plain Layout
32478 \begin_inset Formula $\Ket{\psi}$
32488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32491 \begin_layout Plain Layout
32503 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32506 \begin_layout Plain Layout
32507 \begin_inset Formula $\Braket{\psi|\phi}$
32523 \begin_layout Standard
32530 assures that all vertical bars are set in the size of the surrounding brackets:
32531 \begin_inset Formula \[
32532 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32540 \begin_layout Plain Layout
32550 \begin_inset Note Note
32553 \begin_layout Plain Layout
32554 The following will be displayed when the LaTeX-package
32566 \begin_layout Standard
32567 You need to install the LaTeX-package
32571 to see the rest of this subsection in the output.
32574 \begin_layout Standard
32578 \begin_layout Plain Layout
32590 \begin_layout Standard
32597 can also be achieved using the command
32603 , that is described in
32604 \begin_inset CommandInset ref
32606 reference "sub:Automatic-Bracket-Size"
32613 \begin_layout Subsection
32614 Self-defined Fractions
32615 \begin_inset CommandInset label
32617 name "sub:Self-defined-Fractions"
32625 \begin_layout Plain Layout
32626 Fractions ! self-defined
32634 \begin_layout Standard
32635 To define custom commands for fractions, the command
32645 \begin_layout Plain Layout
32653 is used in the following scheme:
32656 \begin_layout Standard
32669 bracket}{fraction bar thickness}{style}
32670 \begin_inset Newline newline
32677 \begin_layout Plain Layout
32692 \begin_layout Plain Layout
32699 {numerator}{denominator}
32702 \begin_layout Standard
32703 The style is a number in the range of 0
32704 \begin_inset space \thinspace{}
32708 \begin_inset space \thinspace{}
32714 \begin_layout Standard
32716 \begin_inset Tabular
32717 <lyxtabular version="3" rows="5" columns="2">
32719 <column alignment="center" valignment="top" width="0">
32720 <column alignment="center" valignment="top" width="0">
32722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32725 \begin_layout Plain Layout
32731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32734 \begin_layout Plain Layout
32742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32745 \begin_layout Plain Layout
32751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32754 \begin_layout Plain Layout
32755 display style formula
32762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32765 \begin_layout Plain Layout
32771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32774 \begin_layout Plain Layout
32782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32785 \begin_layout Plain Layout
32791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32794 \begin_layout Plain Layout
32802 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32805 \begin_layout Plain Layout
32811 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32814 \begin_layout Plain Layout
32828 \begin_layout Standard
32829 When no style is given, the size is adjusted to the surrounding environment
32830 like for the command
32839 \begin_layout Standard
32840 When no fraction bar thickness is given, the predefined value of 0.4
32841 \begin_inset space \thinspace{}
32847 \begin_layout Standard
32848 \begin_inset VSpace medskip
32851 For example, the commands
32864 \begin_inset CommandInset ref
32866 reference "sub:Fractions"
32870 are defined with the commands
32873 \begin_layout Standard
32882 genfrac{}{}{}{0}{#1}{#2}}
32885 \begin_layout Standard
32889 \begin_layout Standard
32898 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32901 \begin_layout Standard
32902 \begin_inset VSpace medskip
32905 To define a fraction where the fraction bar thickness can be given as optional
32906 argument, the following line is inserted to the LaTeX-preamble:
32909 \begin_layout Standard
32918 genfrac{}{}{#1}{}{#2}{#3}}
32921 \begin_layout Standard
32923 \begin_inset Formula \begin{align*}
32924 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32925 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32929 As one can see, the distance of the numerator and the denominator to the
32930 fraction bar is round about three times the bar thickness.
32933 \begin_layout Subsection
32935 \begin_inset CommandInset label
32937 name "sub:Canceled-Formulas"
32945 \begin_layout Plain Layout
32954 \begin_layout Standard
32955 To cancel formulas or formula parts, the LaTeX-package
32963 \begin_layout Plain Layout
32968 is part of every LaTeX standard installation.
32977 \begin_layout Plain Layout
32983 has to be loaded with the LaTeX-preamble line
32986 \begin_layout Standard
32991 usepackage[samesize]{cancel}
32994 \begin_layout Standard
32995 There are four ways to cancel formulas:
32998 \begin_layout Standard
33000 \begin_inset Tabular
33001 <lyxtabular version="3" rows="5" columns="2">
33003 <column alignment="center" valignment="top" width="0">
33004 <column alignment="center" valignment="top" width="0">
33006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33009 \begin_layout Plain Layout
33015 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33018 \begin_layout Plain Layout
33020 \begin_inset Note Note
33023 \begin_layout Plain Layout
33036 are used here as spacer.
33048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33051 \begin_layout Plain Layout
33060 \begin_layout Plain Layout
33074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33077 \begin_layout Plain Layout
33078 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33091 \begin_layout Plain Layout
33100 \begin_layout Plain Layout
33114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33117 \begin_layout Plain Layout
33118 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33131 \begin_layout Plain Layout
33140 \begin_layout Plain Layout
33154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33157 \begin_layout Plain Layout
33158 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33168 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33171 \begin_layout Plain Layout
33175 \begin_inset Formula $\to$
33186 \begin_layout Plain Layout
33200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33203 \begin_layout Plain Layout
33204 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33220 \begin_layout Standard
33227 is especially suitable to visualize the reduction of fractions within formulas:
33228 \begin_inset Formula \[
33229 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33236 \begin_layout Subsection
33237 Formulas in Section Headings
33238 \begin_inset CommandInset label
33240 name "sub:Formulas-in-Section"
33248 \begin_layout Plain Layout
33249 Formula ! in section headings
33257 \begin_layout Standard
33258 When formulas are used in section headings, the following has to be taken
33262 \begin_layout Standard
33263 \begin_inset Note Greyedout
33266 \begin_layout Plain Layout
33275 \begin_layout Plain Layout
33276 Packages ! hyperref
33281 support is enabled in the document settings dialog under
33284 \begin_inset space ~
33289 , PDF-bookmarks are created for every section heading in the table of contents.
33290 If a section heading contains formulas, they are incorrectly displayed
33291 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33300 \begin_layout Standard
33301 Both problems can be solved by inserting at the end of the section heading
33302 a short title with the menu
33304 Insert\SpecialChar \menuseparator
33306 \begin_inset space ~
33312 Short titles are used as alternative for multiline section headings to
33313 keep the table of contents clearly arranged.
33314 Only the short title appears in the table of contents and therefore also
33315 in the PDF-bookmark.
33318 \begin_layout Standard
33319 When formulas should be used in the table of contents but
33323 is used, one can use the following command in TeX-mode:
33326 \begin_layout Standard
33331 texorpdfstring{part}{alternative}
33335 \begin_layout Plain Layout
33346 \begin_layout Standard
33347 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33348 This can be characters, formulas, footnotes, but also cross-references.
33349 The alternative is used instead of the part for the bookmark.
33352 \begin_layout Standard
33353 Here are two example headings:
33354 \begin_inset VSpace -3mm
33361 \begin_layout Plain Layout
33373 \begin_layout Subsubsection
33374 Heading without formula in table of contents
33375 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33379 \begin_inset OptArg
33382 \begin_layout Plain Layout
33383 Heading without formula in table of contents
33391 \begin_layout Subsubsection
33392 Heading with formula in table of contents
33396 \begin_layout Plain Layout
33406 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33413 \begin_layout Plain Layout
33423 \begin_layout Standard
33427 \begin_layout Plain Layout
33436 In the first heading a short title was used, in the second one
33445 \begin_layout Standard
33446 To get the same formatting as for the other headings, the complete heading
33455 \begin_layout Plain Layout
33457 \begin_inset CommandInset ref
33459 reference "sub:Bold-Formulas"
33471 \begin_layout Subsection
33472 Formulas in multi-column Text
33476 \begin_layout Plain Layout
33477 Formula ! in multi-column text
33485 \begin_layout Standard
33486 Formulas in multi-column text are often too wide to fit into a column and
33487 thus need to be set over the whole page width.
33488 This is done by using the LaTeX-package
33496 \begin_layout Plain Layout
33501 is part of every LaTeX standard installation.
33510 \begin_layout Plain Layout
33511 Packages ! multicol
33516 , that is loaded with the LaTeX-preamble line
33519 \begin_layout Standard
33524 usepackage{multicol}
33527 \begin_layout Standard
33528 \begin_inset Note Greyedout
33531 \begin_layout Plain Layout
33532 Note herby that the setting
33535 \begin_inset space ~
33542 Document\SpecialChar \menuseparator
33548 \begin_inset space ~
33568 \begin_layout Standard
33569 Before the multi-column text the command
33572 \begin_layout Standard
33577 begin{multicols}{column number}
33580 \begin_layout Standard
33581 is written in TeX-mode.
33582 The column number is a number in the range of 2
33583 \begin_inset space \thinspace{}
33587 \begin_inset space \thinspace{}
33591 Before the formula the multi-column text is ended by inserting the command
33594 \begin_layout Standard
33602 \begin_layout Standard
33606 \begin_layout Standard
33607 Due to the command some space is automatically added before the formula.
33609 \begin_inset space \thinspace{}
33612 mm vertical space is inserted before the formula.
33613 When the formula style
33619 \begin_layout Plain Layout
33621 \begin_inset CommandInset ref
33623 reference "sec:Formula-Styles"
33635 \begin_inset space \thinspace{}
33638 mm space is inserted instead.
33641 \begin_layout Standard
33642 As example a multi-column text with a displayed formula:
33645 \begin_layout Standard
33649 \begin_layout Plain Layout
33653 begin{multicols}{2}
33658 Das Spektrum wird fouriertransformiert.
33659 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33660 , Lösungsmittel) zu trennen.
33661 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33662 nun das Aussehen des Ausgangssignals.
33663 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33664 über alle Phasen integrieren muss.
33666 \begin_inset Formula $S$
33669 unser normiertes Ausgangssignal and
33670 \begin_inset Formula $P$
33673 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33677 \begin_layout Plain Layout
33687 \begin_inset VSpace -6mm
33691 \begin_inset Formula \begin{equation}
33692 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33700 \begin_layout Plain Layout
33704 begin{multicols}{2}
33710 \begin_inset Formula $S_{0}$
33713 das Signal ohne Gradient ist and the Normierungsbedingung
33714 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33718 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33720 \begin_inset Formula $\nicefrac{\pi}{2}$
33724 \begin_inset space \thinspace{}
33727 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33728 das Signal zusätzlich abschwächt.
33729 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33731 \begin_inset Formula $T_{2}$
33737 \begin_layout Standard
33741 \begin_layout Plain Layout
33753 \begin_layout Subsection
33754 Formulas with Description of Variables
33758 \begin_layout Plain Layout
33759 Formula ! with description of variables
33767 \begin_layout Standard
33768 To describe variables within a formula, like in formula
33769 \begin_inset CommandInset ref
33771 reference "eq:within"
33780 \begin_inset Formula $n$
33784 \begin_inset space ~
33787 matrix is used with left aligned columns for the
33788 \begin_inset Formula $n$
33795 \begin_layout Plain Layout
33797 \begin_inset CommandInset ref
33799 reference "sec:Matrices"
33808 To set the description in a smaller size, before the matrix e.
33809 \begin_inset space \thinspace{}
33813 \begin_inset space ~
33826 \begin_layout Plain Layout
33828 \begin_inset CommandInset ref
33830 reference "sub:Font-Sizes"
33842 \begin_layout Standard
33843 When the formula style
33849 \begin_layout Plain Layout
33851 \begin_inset CommandInset ref
33853 reference "sec:Formula-Styles"
33874 \begin_layout Plain Layout
33881 only works in formulas with the style
33886 \begin_inset CommandInset ref
33888 reference "sub:Variable-Space"
33897 is inserted before and after the matrix to have the same separation of
33898 the matrix from the equation and the side margin.
33901 \begin_layout Standard
33902 When the formula style
33906 is used, the method described in
33907 \begin_inset CommandInset ref
33909 reference "sub:Flalign-Environment"
33913 is used to indent formulas.
33915 \begin_inset CommandInset ref
33917 reference "eq:within"
33921 consists of five columns whereas in the first two columns contain the equation,
33922 the third the matrix, and the last one an empty TeX-brace.
33923 \begin_inset Formula \begin{flalign}
33924 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33925 \rho & \textrm{density}\\
33926 V & \textrm{volume}\\
33927 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33934 \begin_layout Subsection
33935 Upright small Greek Letters
33936 \begin_inset CommandInset label
33938 name "sub:Upright-small-Greek"
33946 \begin_layout Plain Layout
33947 Greek letters ! upright
33955 \begin_layout Standard
33956 Most of the math fonts only provide italic small Greek letters.
33957 But for symbols of elementary particles like pions and neutrinos, upright
33958 Greek letters are needed.
33967 \begin_layout Plain Layout
33972 is part of the LaTeX-package
33980 \begin_layout Plain Layout
33985 \begin_layout Plain Layout
34008 \begin_layout Plain Layout
34014 that is loaded with the LaTeX-preamble line
34017 \begin_layout Standard
34022 usepackage{upgreek}
34025 \begin_layout Standard
34031 \begin_layout Plain Layout
34041 \begin_inset Note Note
34044 \begin_layout Plain Layout
34045 The following table will only be displayed when the LaTeX-package
34054 They are created when the command for a small Greek letters is started
34060 For example the command
34067 \begin_inset Formula $\uptau$
34073 \begin_layout Standard
34074 With these commands reactions of elementary particles can be typeset:
34075 \begin_inset Formula \[
34076 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34083 \begin_layout Standard
34084 The upright letters are more bold and wider than the italic ones.
34085 They should therefore not be used for units like
34086 \begin_inset Quotes eld
34090 \begin_inset Quotes erd
34096 \begin_layout Standard
34100 \begin_layout Plain Layout
34110 \begin_inset Note Note
34113 \begin_layout Plain Layout
34114 The following will be displayed when the LaTeX-package
34126 \begin_layout Standard
34127 You need to install the LaTeX-package
34131 to see the rest of this subsection in the output.
34134 \begin_layout Standard
34138 \begin_layout Plain Layout
34150 \begin_layout Subsection
34151 Text Characters in Formulas
34152 \begin_inset CommandInset label
34154 name "sub:Text-Characters-in"
34162 \begin_layout Plain Layout
34171 \begin_layout Standard
34172 In some cases you might want to insert text characters directly into formulas.
34173 When for example the centered dot · is often used in formulas like
34174 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34177 , one would have to insert the command
34187 \begin_layout Plain Layout
34189 \begin_inset CommandInset ref
34191 reference "sub:Binary-Operators"
34200 all the time, because this character is defined in all encodings as text
34202 But the encoding can be changed by this LaTeX-preamble line:
34205 \begin_layout Standard
34210 Declare Inputtext{183}{
34220 f\SpecialChar \textcompwordmark{}
34224 \begin_layout Standard
34225 The character encoding (menu
34227 Document\SpecialChar \menuseparator
34228 Settings\SpecialChar \menuseparator
34231 ) specifies what character appears when a keyboard key is pressed.
34232 When the key for the character '·' is pressed, internally the command
34239 But this command is not available in a formula so that you would get LaTeX-erro
34241 With the changed encoding the right command is chosen automatically, depending
34242 on if the character was inserted into a formula or not.
34245 \begin_layout Standard
34246 The encoding of several characters is saved in definition files.
34247 Fore example the encoding
34251 is defined in the file
34255 that is in the installation folder of LaTeX.
34256 Encodings should only be changed via the LaTeX-preamble and not in the
34258 Otherwise own documents could not be edited by other LyX users working
34259 on other computers.
34262 \begin_layout Standard
34263 \begin_inset VSpace medskip
34266 Besides the centered dot, in this document the degree sign ° is defined
34267 with the following LaTeX-preamble line so that it can directly be inserted
34271 \begin_layout Standard
34276 DeclareInputtext{176}{
34286 f\SpecialChar \textcompwordmark{}
34290 \begin_layout Standard
34291 \begin_inset Newpage newpage
34297 \begin_layout Section
34303 \begin_layout Plain Layout
34312 \begin_layout Standard
34313 This section is a summary of the most important typographic rules, listed
34318 \begin_layout Plain Layout
34319 This collection was partly taken from the German semi-official dictionary
34321 \begin_inset Quotes eld
34325 \begin_inset Quotes erd
34329 \begin_inset CommandInset citation
34335 that lists some of the ISO rules.
34343 \begin_layout Itemize
34352 \begin_layout Plain Layout
34353 done with font styles, see
34354 \begin_inset CommandInset ref
34356 reference "sub:Font-Styles"
34366 \begin_inset space \thinspace{}
34370 \begin_inset Newline newline
34373 Between the value and the unit is the smallest space, see
34374 \begin_inset CommandInset ref
34376 reference "sub:Predefined-Space"
34381 \begin_inset Newline newline
34384 This convention is automatically fulfilled when the command
34391 When it is entered to a formula, two boxes appear.
34392 In the first one the value is inserted, in the second one the unit, and
34394 \begin_inset Formula $\unit[30]{km/h}$
34398 \begin_inset space \thinspace{}
34408 is not a real LaTeX command but the command
34414 , therefore you cannot use it in TeX code.
34417 \begin_layout Itemize
34418 Percent and perthousand signs are set like physical units:
34419 \begin_inset Newline newline
34423 \begin_inset space \thinspace{}
34429 \begin_layout Itemize
34430 The degree sign follows directly on the value: 15°, but not when it is used
34432 \begin_inset space \thinspace{}
34438 \begin_layout Itemize
34439 In numbers with more than four digits the smallest space is inserted before
34440 every third digit to group them:
34450 \begin_inset space \thinspace{}
34454 \begin_inset space \thinspace{}
34460 \begin_layout Itemize
34461 For dimensions like 120×90×40
34462 \begin_inset space \thinspace{}
34465 cm the multiplication sign
34466 \begin_inset Quotes eld
34470 \begin_inset Quotes erd
34474 It is available with the LaTeX-command
34480 , but can also directly be inserted with some keyboard definitions.
34483 \begin_layout Itemize
34484 Functions with names consisting of several letters are set upright to avoid
34486 \begin_inset CommandInset ref
34488 reference "sub:Predefined-Functions"
34495 \begin_layout Itemize
34496 Indices consisting of several letters, are set upright:
34497 \begin_inset Formula $E_{\mathrm{kin}}$
34501 \begin_inset Newline newline
34504 Components of matrices are set italic:
34505 \begin_inset Formula $\hat{H}_{kl}$
34511 \begin_layout Itemize
34512 The differentiation/integration operator 'd', the Euler's number 'e', and
34513 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34517 \begin_layout Standard
34518 \begin_inset Newpage newpage
34524 \begin_layout Section
34529 \begin_layout Plain Layout
34538 \begin_layout Standard
34539 Some characters and symbols can be created with several commands.
34540 Here is a list of the synonym commands:
34543 \begin_layout Standard
34544 \begin_inset VSpace bigskip
34548 \begin_inset space \hfill{}
34552 \begin_inset Tabular
34553 <lyxtabular version="3" rows="12" columns="2">
34555 <column alignment="center" valignment="top" width="0pt">
34556 <column alignment="center" valignment="top" width="0pt">
34558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34561 \begin_layout Plain Layout
34567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34570 \begin_layout Plain Layout
34572 \begin_inset Note Note
34575 \begin_layout Plain Layout
34582 is only used as spacer.
34594 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34597 \begin_layout Plain Layout
34605 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34608 \begin_layout Plain Layout
34612 \begin_layout Plain Layout
34625 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34642 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34653 \begin_layout Plain Layout
34663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34666 \begin_layout Plain Layout
34674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34677 \begin_layout Plain Layout
34687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34690 \begin_layout Plain Layout
34698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34701 \begin_layout Plain Layout
34709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34712 \begin_layout Plain Layout
34720 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34723 \begin_layout Plain Layout
34731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34734 \begin_layout Plain Layout
34742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34745 \begin_layout Plain Layout
34755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34758 \begin_layout Plain Layout
34766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34769 \begin_layout Plain Layout
34779 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34782 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34793 \begin_layout Plain Layout
34803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34806 \begin_layout Plain Layout
34814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34817 \begin_layout Plain Layout
34827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34830 \begin_layout Plain Layout
34838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34841 \begin_layout Plain Layout
34849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34852 \begin_layout Plain Layout
34860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34863 \begin_layout Plain Layout
34875 \begin_inset space \hfill{}
34879 \begin_inset Tabular
34880 <lyxtabular version="3" rows="12" columns="2">
34882 <column alignment="center" valignment="top" width="0pt">
34883 <column alignment="center" valignment="top" width="0pt">
34885 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34888 \begin_layout Plain Layout
34894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34897 \begin_layout Plain Layout
34905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34908 \begin_layout Plain Layout
34916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34919 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34934 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34945 \begin_layout Plain Layout
34955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34958 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34969 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34982 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34993 \begin_layout Plain Layout
35001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35004 \begin_layout Plain Layout
35012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35015 \begin_layout Plain Layout
35023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35026 \begin_layout Plain Layout
35034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35037 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35050 \begin_layout Plain Layout
35058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35061 \begin_layout Plain Layout
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35074 \begin_layout Plain Layout
35082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35085 \begin_layout Plain Layout
35095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35098 \begin_layout Plain Layout
35106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35109 \begin_layout Plain Layout
35119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35122 \begin_layout Plain Layout
35130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35133 \begin_layout Plain Layout
35143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35146 \begin_layout Plain Layout
35154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35157 \begin_layout Plain Layout
35171 \begin_inset space \hfill{}
35177 \begin_layout Standard
35178 \begin_inset Newpage newpage
35184 \begin_layout Bibliography
35185 \begin_inset CommandInset bibitem
35186 LatexCommand bibitem
35198 The LaTeX Companion
35201 Addison Wesley, 2004
35204 \begin_layout Bibliography
35205 \begin_inset CommandInset bibitem
35206 LatexCommand bibitem
35212 \begin_inset CommandInset href
35215 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35219 of LaTeX's math abilities
35222 \begin_layout Bibliography
35223 \begin_inset CommandInset bibitem
35224 LatexCommand bibitem
35229 LaTeX tips and tricks-
35230 \begin_inset CommandInset href
35233 target "http://tug.org/TeXnik/"
35240 \begin_layout Bibliography
35241 \begin_inset CommandInset bibitem
35242 LatexCommand bibitem
35248 \begin_inset CommandInset href
35251 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35259 \begin_layout Plain Layout
35271 \begin_layout Bibliography
35272 \begin_inset CommandInset bibitem
35273 LatexCommand bibitem
35279 \begin_inset CommandInset href
35282 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35286 of all symbols available with LaTeX-packages
35289 \begin_layout Bibliography
35290 \begin_inset CommandInset bibitem
35291 LatexCommand bibitem
35297 \begin_inset CommandInset href
35299 name "Documentation"
35300 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35304 of the LaTeX-package
35312 \begin_layout Plain Layout
35313 Packages ! hyperref
35321 \begin_layout Bibliography
35322 \begin_inset CommandInset bibitem
35323 LatexCommand bibitem
35329 \begin_inset CommandInset href
35332 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35343 \begin_inset CommandInset ref
35345 reference "sub:Operator-Limits"
35353 \begin_layout Plain Layout
35364 \begin_layout Bibliography
35365 \begin_inset CommandInset bibitem
35366 LatexCommand bibitem
35377 Auflage, Duden 2001
35380 \begin_layout Subsubsection*
35381 \begin_inset CommandInset index_print
35382 LatexCommand printindex