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 Box Frameless
12524 height_special "totalheight"
12527 \begin_layout Plain Layout
12529 \begin_inset Tabular
12530 <lyxtabular version="3" rows="5" columns="2">
12532 <column alignment="center" valignment="top" width="0">
12533 <column alignment="center" valignment="top" width="0">
12535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12538 \begin_layout Plain Layout
12543 \begin_layout Plain Layout
12544 Due to a bug in LyX it is not possible to create a new formula with
12549 \begin_inset CommandInset href
12551 name "LyX-bug #1435"
12552 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12569 \begin_layout Plain Layout
12571 \begin_inset Note Note
12574 \begin_layout Plain Layout
12581 is only used as spacer.
12593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12596 \begin_layout Plain Layout
12603 \begin_layout Plain Layout
12622 \begin_layout Plain Layout
12636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12639 \begin_layout Plain Layout
12640 \begin_inset Formula $\raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}$
12650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12653 \begin_layout Plain Layout
12660 \begin_layout Plain Layout
12675 \begin_layout Plain Layout
12689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12692 \begin_layout Plain Layout
12693 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12706 \begin_layout Plain Layout
12713 \begin_layout Plain Layout
12727 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12730 \begin_layout Plain Layout
12731 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12744 \begin_layout Plain Layout
12751 \begin_layout Plain Layout
12761 \begin_inset Formula $\to$
12765 \begin_inset Formula $\to$
12778 \begin_layout Plain Layout
12788 \begin_inset Formula $\downarrow$
12796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12799 \begin_layout Plain Layout
12800 \begin_inset Formula $\raisebox{6mm}{}$
12804 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12808 \begin_inset Formula $\raisebox{-4mm}{}$
12829 \begin_layout Standard
12830 The frame thickness can also be adjusted.
12831 To do this the following commands have to be inserted in TeX-mode before
12835 \begin_layout Standard
12845 \begin_inset Quotes eld
12849 \begin_inset Quotes erd
12863 \begin_inset Quotes eld
12867 \begin_inset Quotes erd
12873 \begin_layout Standard
12874 \begin_inset Quotes eld
12878 \begin_inset Quotes erd
12881 specifies the minimal distance between the frame and the first character
12883 An example for this is the following framed formula:
12887 \begin_layout Plain Layout
12899 \begin_inset Formula \[
12904 Before this formula the commands
12907 \begin_layout Standard
12929 \begin_layout Standard
12930 were inserted in TeX-mode.
12931 The given values are used for all following boxes.
12934 \begin_layout Standard
12935 To return to the standard frame size, the command
12938 \begin_layout Standard
12963 \begin_layout Plain Layout
12977 \begin_layout Standard
12978 is inserted in TeX-mode before the next formula.
12981 \begin_layout Subsection
12982 Boxes without Frame
12983 \begin_inset CommandInset label
12985 name "sub:Boxes-without-Frame"
12993 \begin_layout Plain Layout
12994 Boxes ! without frame
13002 \begin_layout Standard
13003 For boxes without a frame there are the following box commands:
13013 \begin_layout Plain Layout
13031 \begin_layout Plain Layout
13049 \begin_layout Plain Layout
13060 \begin_layout Standard
13067 a box can be super- or subscripted.
13068 But in contrary to normal super- and subscripting, the characters in the
13069 box keep their font size.
13076 is used in the following scheme:
13079 \begin_layout Standard
13084 raisebox{height}{box content}
13087 \begin_layout Standard
13088 When the box should contain a formula, an extra formula is needed like for
13098 \begin_layout Standard
13100 \begin_inset Tabular
13101 <lyxtabular version="3" rows="4" columns="2">
13103 <column alignment="center" valignment="top" width="0">
13104 <column alignment="center" valignment="top" width="0">
13106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13109 \begin_layout Plain Layout
13115 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13118 \begin_layout Plain Layout
13126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13129 \begin_layout Plain Layout
13133 \begin_inset Formula $\to$
13139 \begin_inset Formula $\to$
13147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13150 \begin_layout Plain Layout
13151 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13164 \begin_layout Plain Layout
13168 \begin_inset Formula $\to$
13174 \begin_inset Formula $\to$
13182 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13185 \begin_layout Plain Layout
13186 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13199 \begin_layout Plain Layout
13203 \begin_inset Formula $\to$
13218 \begin_layout Plain Layout
13232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13235 \begin_layout Plain Layout
13239 \begin_layout Plain Layout
13263 \begin_layout Standard
13264 The last formula can currently only be created using TeX-mode because LyX
13265 inserts a box instead of the needed extra formula.
13269 \begin_layout Plain Layout
13271 \begin_inset CommandInset href
13273 name "LyX-bug #1435"
13274 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13286 \begin_layout Standard
13311 , with the difference that there is no frame.
13314 \begin_layout Subsection
13316 \begin_inset CommandInset label
13318 name "sub:Colored-Boxes"
13326 \begin_layout Plain Layout
13335 \begin_layout Standard
13336 To be able to use all commands explained in this section, the LaTeX-package
13345 \begin_layout Plain Layout
13350 is part of every LaTeX standard installation.
13359 \begin_layout Plain Layout
13365 has to be loaded in the LaTeX-preamble with the line
13369 \begin_layout Plain Layout
13370 When text is colored somewhere in the document with a predefined color,
13371 LyX loads the LaTeX-package
13376 Thus it is possible that the package is loaded twice, but this doesn't
13383 \begin_inset Note Note
13386 \begin_layout Plain Layout
13387 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13396 \begin_layout Standard
13404 \begin_layout Standard
13405 \begin_inset VSpace medskip
13408 To color boxes, the command
13418 \begin_layout Plain Layout
13426 is used in the following scheme:
13429 \begin_layout Standard
13434 colorbox{color}{box content}
13437 \begin_layout Standard
13438 The box content can also be a box and a
13444 can also be part of another box (see the 2nd and 3rd example).
13445 When the box should contain a formula, an extra formula has to be created,
13456 \begin_layout Plain Layout
13457 This also applies for the command
13465 \begin_inset CommandInset href
13467 name "LyX-bug #1435"
13468 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13480 \begin_layout Standard
13481 One of the following predefined colors can be chosen:
13484 \begin_layout Standard
13518 \begin_layout Standard
13520 \begin_inset Tabular
13521 <lyxtabular version="3" rows="4" columns="2">
13523 <column alignment="center" valignment="top" width="0">
13524 <column alignment="center" valignment="top" width="0">
13526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13529 \begin_layout Plain Layout
13535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13538 \begin_layout Plain Layout
13540 \begin_inset Note Note
13543 \begin_layout Plain Layout
13550 is only used as spacer.
13562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13565 \begin_layout Plain Layout
13569 \begin_inset Formula $\to$
13579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13582 \begin_layout Plain Layout
13583 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13596 \begin_layout Plain Layout
13600 \begin_inset Formula $\to$
13611 \begin_layout Plain Layout
13625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13628 \begin_layout Plain Layout
13629 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13642 \begin_layout Plain Layout
13649 \begin_layout Plain Layout
13661 \begin_inset Formula $\to$
13671 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13674 \begin_layout Plain Layout
13675 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13691 \begin_layout Standard
13698 only colors the box but not the characters in the box.
13699 To color all characters, the whole formula is highlighted and the wanted
13700 color is chosen in the
13703 \begin_inset space ~
13709 The dialog can be called with the toolbar button
13710 \begin_inset Graphics
13711 filename ../images/dialog-show_character.png
13718 Edit\SpecialChar \menuseparator
13720 \begin_inset space ~
13723 Style\SpecialChar \menuseparator
13727 The formula number has then the same color as the formula.
13728 When the formula number should get another color than the formula characters,
13729 the color must be changed within the formula.
13732 \begin_layout Standard
13736 \begin_layout Standard
13739 \begin_inset Formula \begin{equation}
13740 \int A=B\label{eq:red}\end{equation}
13747 \begin_inset Formula \begin{equation}
13748 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13755 \begin_layout Standard
13757 \begin_inset CommandInset ref
13763 is completely colored red.
13764 \begin_inset Newline newline
13768 \begin_inset CommandInset ref
13770 reference "eq:redgreen"
13774 was first completely colored green to set the color for the formula number.
13775 Subsequently the formula characters were colored red.
13778 \begin_layout Standard
13779 \begin_inset VSpace bigskip
13782 To color the frame different than the rest of the box, the command
13792 \begin_layout Plain Layout
13800 is used in the following scheme:
13803 \begin_layout Standard
13808 fcolorbox{frame color}{color}{box content}
13811 \begin_layout Standard
13818 is an extension of the command
13825 The frame width is set, like for
13848 \begin_layout Plain Layout
13860 \begin_inset Formula \[
13861 \fcolorbox{cyan}{magenta}{A=B}\]
13869 \begin_layout Plain Layout
13883 \begin_layout Standard
13884 This formula was created with the command
13885 \begin_inset Newline newline
13893 \begin_inset Formula $\to$
13899 \begin_inset Formula $\to$
13909 \begin_layout Standard
13910 \begin_inset VSpace bigskip
13913 To use other colors than the predefined ones, they have to be defined first.
13916 \begin_layout Standard
13917 One can for example define the color
13918 \begin_inset Quotes eld
13926 \begin_inset Quotes erd
13929 with the LaTeX-preamble line:
13932 \begin_layout Standard
13937 definecolor{darkgreen}{cmyk}{0.5,
13955 \begin_layout Plain Layout
13966 \begin_layout Standard
13971 is the color space that denotes the colors
13988 The four comma separated numbers are the portion factor for the corresponding
13989 colors of the color space.
13990 The factors can be in the range of 0
13991 \begin_inset space \thinspace{}
13995 \begin_inset space \thinspace{}
14003 also the color space
14007 can be used for definitions.
14024 , so that there are in this case three portion factors for the corresponding
14026 Furthermore there is the color space
14030 with one portion factor for the gray value.
14033 \begin_layout Standard
14034 As example a framed box with the new defined color
14038 where the characters have been colored
14043 \begin_inset Formula \begin{equation}
14044 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
14051 \begin_layout Standard
14052 Self-defined colors can also be used for text with the help of the command
14063 \begin_layout Plain Layout
14072 \begin_layout Standard
14076 \begin_layout Plain Layout
14080 textcolor{darkgreen}{
14086 \begin_inset Quotes eld
14090 \begin_inset Quotes erd
14097 \begin_layout Plain Layout
14107 \begin_layout Standard
14118 \begin_layout Plain Layout
14126 is used in the scheme
14130 textcolor{color}{characters to color}
14135 \begin_layout Subsection
14137 \begin_inset CommandInset label
14139 name "sub:Paragraph-Boxes"
14147 \begin_layout Plain Layout
14148 Boxes ! as paragraph
14156 \begin_layout Standard
14157 A box that can contain several lines and paragraphs, a so called paragraph
14158 box (parbox), can be created with the menu
14160 Insert\SpecialChar \menuseparator
14163 or the toolbar button
14164 \begin_inset Graphics
14165 filename ../images/box-insert.png
14173 \begin_layout Standard
14174 The following example shows a framed parbox in a line:
14177 \begin_layout Standard
14178 \begin_inset VSpace medskip
14182 \begin_inset Box Boxed
14191 height_special "totalheight"
14194 \begin_layout Plain Layout
14195 This is a paragraph box.
14197 \begin_inset space \thinspace{}
14200 cm long and can also contain formulas:
14201 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14212 \begin_layout Standard
14213 \begin_inset VSpace medskip
14219 \begin_layout Standard
14220 Such a box is created by right-clicking on the gray box inset.
14221 A dialog pops up showing the box properties.
14235 \begin_inset space \thinspace{}
14240 Vertical Box Alignment
14245 \begin_layout Standard
14246 \begin_inset VSpace medskip
14249 In LaTeX a parbox is created with the command
14259 \begin_layout Plain Layout
14267 that has the following scheme:
14270 \begin_layout Standard
14275 parbox[position]{width}{box content}
14278 \begin_layout Standard
14292 for bottom means that the box is aligned within the surrounding text with
14298 for top this is done with the first line.
14299 When no position is given, the box will be vertically centered, see section
14307 \begin_inset space ~
14312 manual for examples.
14315 \begin_layout Standard
14316 \begin_inset VSpace bigskip
14319 To frame formulas completely, including the formula number, the formula
14320 must be set into a parbox.
14321 To do this, the command
14335 is inserted in TeX-mode before the formula.
14344 \begin_layout Plain Layout
14354 is hereby the line width set for the document.
14355 Because the frame is outside the parbox, 2
14356 \begin_inset space \thinspace{}
14359 times the frame separation and the frame thickness must be subtracted from
14361 As this is not automatically done by LyX due to a bug
14365 \begin_layout Plain Layout
14366 \begin_inset CommandInset href
14368 name "LyX-bug #4483"
14369 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14378 , TeX-mode has to be used.
14379 To be able to multiply and subtract in arguments, the LaTeX-package
14387 \begin_layout Plain Layout
14392 is part of every LaTeX standard installation.
14401 \begin_layout Plain Layout
14407 must be loaded in the LaTeX-preamble with the line
14410 \begin_layout Standard
14418 \begin_layout Standard
14419 Behind the formula both boxes are closed by entering
14424 Here is an example:
14428 \begin_layout Plain Layout
14442 \begin_layout Standard
14446 \begin_layout Plain Layout
14464 \begin_inset Formula \begin{equation}
14465 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14473 \begin_layout Plain Layout
14484 \begin_layout Plain Layout
14498 \begin_layout Standard
14499 \begin_inset VSpace medskip
14502 As a parbox is used as argument of
14508 , there is in this case no difference between
14523 \begin_layout Standard
14524 \begin_inset VSpace bigskip
14527 Paragraph boxes are very useful to comment formulas directly.
14534 is used in combination with the command
14548 \begin_inset CommandInset ref
14550 reference "sub:User-defined-Numbering"
14557 \begin_layout Standard
14558 An example of a formula commented with
14567 \begin_layout Standard
14571 \begin_layout Plain Layout
14584 This is a description.
14585 It is distinctly separated from the formula and multiline.
14589 \begin_layout Plain Layout
14601 \begin_layout Standard
14602 Such a formula must be inserted completely in TeX-mode because LyX does
14603 not yet support the command
14610 The formula is created with the following command sequence:
14613 \begin_layout Standard
14626 is inserted in TeX-mode.
14630 \begin_layout Plain Layout
14631 When the formula style
14643 can also be replaced by
14650 (formula styles see
14651 \begin_inset CommandInset ref
14653 reference "sec:Formula-Styles"
14662 Then the description follows as normal text, and finally
14668 is inserted in TeX-mode.
14681 hereby create a displayed formula.
14684 \begin_layout Standard
14691 can be seen in this example that was
14692 \begin_inset Quotes eld
14696 \begin_inset Quotes erd
14699 using the mathematical textmode:
14700 \begin_inset Formula \[
14701 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14708 \begin_layout Section
14713 \begin_layout Plain Layout
14722 \begin_layout Subsection
14724 \begin_inset CommandInset label
14726 name "sub:Big-Operators"
14734 \begin_layout Plain Layout
14744 \begin_layout Plain Layout
14754 \begin_layout Plain Layout
14763 \begin_layout Standard
14764 To be able to use all integral operators listed here, the option
14766 Use esint package automatically
14768 must be set in the document settings under
14771 \begin_inset space ~
14779 \begin_layout Standard
14780 \begin_inset space \hfill{}
14784 \begin_inset Tabular
14785 <lyxtabular version="3" rows="11" columns="2">
14787 <column alignment="center" valignment="top" width="0pt">
14788 <column alignment="center" valignment="top" width="0pt">
14790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14793 \begin_layout Plain Layout
14799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14802 \begin_layout Plain Layout
14810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14813 \begin_layout Plain Layout
14820 \begin_layout Plain Layout
14833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14836 \begin_layout Plain Layout
14837 \begin_inset Formula $\sum$
14847 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14850 \begin_layout Plain Layout
14857 \begin_layout Plain Layout
14870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14873 \begin_layout Plain Layout
14874 \begin_inset Formula $\int$
14884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14887 \begin_layout Plain Layout
14895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14898 \begin_layout Plain Layout
14899 \begin_inset Formula $\intop$
14909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14912 \begin_layout Plain Layout
14920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14923 \begin_layout Plain Layout
14924 \begin_inset Formula $\oint$
14934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14937 \begin_layout Plain Layout
14945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14948 \begin_layout Plain Layout
14949 \begin_inset Formula $\ointop$
14959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14962 \begin_layout Plain Layout
14970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14973 \begin_layout Plain Layout
14974 \begin_inset Formula $\ointctrclockwise$
14984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14987 \begin_layout Plain Layout
14995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14998 \begin_layout Plain Layout
14999 \begin_inset Formula $\ointclockwise$
15009 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15012 \begin_layout Plain Layout
15020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15023 \begin_layout Plain Layout
15024 \begin_inset Formula $\sqint$
15034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15037 \begin_layout Plain Layout
15045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15048 \begin_layout Plain Layout
15049 \begin_inset Formula $\bigcap$
15059 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15062 \begin_layout Plain Layout
15070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15073 \begin_layout Plain Layout
15074 \begin_inset Formula $\bigcup$
15088 \begin_inset space \hfill{}
15092 \begin_inset Tabular
15093 <lyxtabular version="3" rows="10" columns="2">
15095 <column alignment="center" valignment="top" width="0pt">
15096 <column alignment="center" valignment="top" width="0pt">
15098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15101 \begin_layout Plain Layout
15107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15110 \begin_layout Plain Layout
15118 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15121 \begin_layout Plain Layout
15128 \begin_layout Plain Layout
15141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15144 \begin_layout Plain Layout
15145 \begin_inset Formula $\prod$
15155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15158 \begin_layout Plain Layout
15166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15169 \begin_layout Plain Layout
15170 \begin_inset Formula $\coprod$
15180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15183 \begin_layout Plain Layout
15191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15194 \begin_layout Plain Layout
15195 \begin_inset Formula $\bigodot$
15205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15208 \begin_layout Plain Layout
15216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15219 \begin_layout Plain Layout
15220 \begin_inset Formula $\bigotimes$
15230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15233 \begin_layout Plain Layout
15241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15244 \begin_layout Plain Layout
15245 \begin_inset Formula $\bigoplus$
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15258 \begin_layout Plain Layout
15266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15269 \begin_layout Plain Layout
15270 \begin_inset Formula $\bigwedge$
15280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15283 \begin_layout Plain Layout
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15294 \begin_layout Plain Layout
15295 \begin_inset Formula $\bigvee$
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15319 \begin_layout Plain Layout
15320 \begin_inset Formula $\bigsqcup$
15330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15333 \begin_layout Plain Layout
15341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15344 \begin_layout Plain Layout
15345 \begin_inset Formula $\biguplus$
15359 \begin_inset space \hfill{}
15365 \begin_layout Standard
15366 All big operators can also be inserted via the math toolbar button
15367 \begin_inset Graphics
15368 filename ../images/math/intop.png
15376 \begin_layout Standard
15377 The operators are called big because they are bigger than the sometimes
15378 equal looking binary operators.
15379 All big operators can have limits as described in the next subsection.
15382 \begin_layout Standard
15408 \begin_inset space ~
15411 in the style the operator limits are displayed, see
15412 \begin_inset CommandInset ref
15414 reference "sub:Operator-Limits"
15422 \begin_layout Subsubsection*
15423 Advices for Integrals
15426 \begin_layout Standard
15431 in an integral is an operator, that therefore has to be set upright.
15432 This is done by highlighting the
15436 and using the keyboard shortcut
15439 \begin_inset space ~
15448 \begin_layout Plain Layout
15454 \begin_inset CommandInset ref
15456 reference "sub:Font-Styles"
15466 Finally the smallest space is inserted before the
15470 , as this is usual for operators.
15474 \begin_layout Standard
15476 \begin_inset Formula $\int A(x)dx$
15480 \begin_inset Newline newline
15487 \begin_layout Plain Layout
15497 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15503 \begin_layout Standard
15504 For multiple integrals there are the following commands:
15505 \begin_inset VSpace medskip
15511 \begin_layout Standard
15512 \begin_inset space \hfill{}
15516 \begin_inset Tabular
15517 <lyxtabular version="3" rows="4" columns="2">
15519 <column alignment="center" valignment="top" width="0">
15520 <column alignment="center" valignment="top" width="0">
15522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15525 \begin_layout Plain Layout
15531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15534 \begin_layout Plain Layout
15536 \begin_inset Note Note
15539 \begin_layout Plain Layout
15546 is only used as spacer.
15558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15561 \begin_layout Plain Layout
15569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15572 \begin_layout Plain Layout
15573 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15583 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15586 \begin_layout Plain Layout
15594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15597 \begin_layout Plain Layout
15598 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15611 \begin_layout Plain Layout
15619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15622 \begin_layout Plain Layout
15623 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15637 \begin_inset space \hfill{}
15641 \begin_inset Tabular
15642 <lyxtabular version="3" rows="4" columns="2">
15644 <column alignment="center" valignment="top" width="0">
15645 <column alignment="center" valignment="top" width="0">
15647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15650 \begin_layout Plain Layout
15656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15659 \begin_layout Plain Layout
15667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15670 \begin_layout Plain Layout
15678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15681 \begin_layout Plain Layout
15682 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15695 \begin_layout Plain Layout
15703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15706 \begin_layout Plain Layout
15707 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15720 \begin_layout Plain Layout
15728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15731 \begin_layout Plain Layout
15732 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15746 \begin_inset space \hfill{}
15752 \begin_layout Subsection
15754 \begin_inset CommandInset label
15756 name "sub:Operator-Limits"
15764 \begin_layout Plain Layout
15773 \begin_layout Standard
15774 Limits are created by super- and subscripts:
15777 \begin_layout Standard
15779 \begin_inset Tabular
15780 <lyxtabular version="3" rows="2" columns="2">
15782 <column alignment="center" valignment="top" width="0pt">
15783 <column alignment="center" valignment="top" width="0pt">
15785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15788 \begin_layout Plain Layout
15794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15797 \begin_layout Plain Layout
15799 \begin_inset Note Note
15802 \begin_layout Plain Layout
15809 is only used as spacer.
15821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15824 \begin_layout Plain Layout
15833 \begin_layout Plain Layout
15843 \begin_inset Formula $\to$
15847 \begin_inset Formula $\to$
15855 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15858 \begin_layout Plain Layout
15859 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15875 \begin_layout Standard
15876 Limits of inline formulas are set right beside the operator.
15877 Limits in displayed formulas are set above or below the operator, except
15878 of integral limits.
15881 \begin_layout Standard
15882 To force that the limits are set beside the operator, the cursor is set
15883 directly behind the operator and the limits type is changed with the menu
15886 Edit\SpecialChar \menuseparator
15887 Math\SpecialChar \menuseparator
15899 \begin_inset space ~
15908 \begin_layout Standard
15909 The default limits type is this:
15910 \begin_inset Formula \[
15911 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15915 This is how it looks when the limits type was changed to
15922 \begin_inset Formula \[
15923 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15927 For integrals, except of
15939 , the limits are by default set beside the operator.
15940 But for multiple integrals the limits are often set below the operator.
15941 In the following example the limits type was therefore set to
15945 and so set below the integrals:
15946 \begin_inset Formula \begin{equation}
15947 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15954 \begin_layout Standard
15955 \begin_inset VSpace medskip
15958 To specify conditions for limits, the commands
15968 \begin_layout Plain Layout
15986 \begin_layout Plain Layout
15995 To create for example this expression
15996 \begin_inset Formula \begin{equation}
15997 \sum_{\begin{subarray}{c}
15999 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
16006 \begin_layout Standard
16007 the following has to be done:
16008 \begin_inset Newline newline
16023 \begin_layout Plain Layout
16035 One is now in a blue box under the summation operator and insert there
16044 \begin_layout Plain Layout
16056 The blue box is now within a purple box and now several lines can be written
16058 A new line is created by inserting a line break (
16064 \begin_inset Newline newline
16069 0<k<1000 Ctrl-Return
16070 \begin_inset Newline newline
16075 is typed in, a new box appears below for the new line.
16078 \begin_layout Standard
16079 The alignment of the lines can be changed to left aligned with the
16089 Edit\SpecialChar \menuseparator
16093 To get right alignment,
16101 \begin_layout Plain Layout
16112 is inserted at the beginning of the line.
16115 \begin_layout Standard
16128 with the difference that the lines are always centered.
16131 \begin_layout Standard
16132 \begin_inset VSpace bigskip
16136 \begin_inset CommandInset ref
16138 reference "eq:substack"
16142 there can be too much space beside an operator, because the characters
16143 following the operator are set beside the limits.
16146 \begin_layout Standard
16147 To avoid this, the following macro can be used in the LaTeX-preamble:
16150 \begin_layout Standard
16164 \begin_inset Newline newline
16176 \begin_inset Newline newline
16183 mathclapinternal #1#2{
16187 mathsurround =0pt #1{#2}$}}
16190 \begin_layout Standard
16191 This defines the command
16201 \begin_layout Plain Layout
16209 that sets the width of the limit to 0
16210 \begin_inset space \thinspace{}
16214 The command scheme is
16217 \begin_layout Standard
16225 \begin_layout Standard
16226 where the limit can consist of several conditions.
16229 \begin_layout Standard
16231 \begin_inset CommandInset ref
16233 reference "eq:substack"
16237 , one uses the command
16240 \begin_layout Standard
16253 \begin_layout Plain Layout
16262 0<k<1000 Ctrl-Enter
16265 \begin_layout Standard
16266 to create the lower limit.
16267 The summand is now directly behind the summation operator:
16268 \begin_inset Formula \[
16269 \sum_{\mathclap{\substack{0<k<1000\\
16270 \\k\,\in\,\mathbb{N}}
16278 \begin_layout Standard
16279 \begin_inset VSpace bigskip
16282 How to use one limit for several operators is described in
16283 \begin_inset CommandInset ref
16285 reference "sub:Self-defined-Operators"
16292 \begin_layout Standard
16293 \begin_inset Newpage newpage
16299 \begin_layout Subsection
16301 \begin_inset CommandInset label
16303 name "sub:Binary-Operators"
16311 \begin_layout Plain Layout
16320 \begin_layout Standard
16321 Binary operators are surrounded by space when there is a character before
16323 \begin_inset VSpace medskip
16329 \begin_layout Standard
16330 \begin_inset space \hfill{}
16334 \begin_inset Tabular
16335 <lyxtabular version="3" rows="13" columns="2">
16337 <column alignment="center" valignment="top" width="0pt">
16338 <column alignment="center" valignment="top" width="0pt">
16340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16343 \begin_layout Plain Layout
16345 \begin_inset Note Note
16348 \begin_layout Plain Layout
16355 is only used as spacer.
16365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16368 \begin_layout Plain Layout
16376 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16379 \begin_layout Plain Layout
16385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16388 \begin_layout Plain Layout
16389 \begin_inset Formula $+$
16399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16402 \begin_layout Plain Layout
16408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16411 \begin_layout Plain Layout
16412 \begin_inset Formula $-$
16422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16425 \begin_layout Plain Layout
16433 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16436 \begin_layout Plain Layout
16437 \begin_inset Formula $\pm$
16447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16450 \begin_layout Plain Layout
16458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16461 \begin_layout Plain Layout
16462 \begin_inset Formula $\mp$
16472 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16475 \begin_layout Plain Layout
16483 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16486 \begin_layout Plain Layout
16487 \begin_inset Formula $\cdot$
16497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16500 \begin_layout Plain Layout
16508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16511 \begin_layout Plain Layout
16512 \begin_inset Formula $\times$
16522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16525 \begin_layout Plain Layout
16533 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16536 \begin_layout Plain Layout
16537 \begin_inset Formula $\div$
16547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16550 \begin_layout Plain Layout
16554 \begin_layout Plain Layout
16567 \begin_layout Plain Layout
16579 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16582 \begin_layout Plain Layout
16583 \begin_inset Formula $*$
16593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16596 \begin_layout Plain Layout
16604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16607 \begin_layout Plain Layout
16608 \begin_inset Formula $\star$
16618 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16621 \begin_layout Plain Layout
16629 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16632 \begin_layout Plain Layout
16633 \begin_inset Formula $\circ$
16643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16646 \begin_layout Plain Layout
16654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16657 \begin_layout Plain Layout
16658 \begin_inset Formula $\diamond$
16668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16671 \begin_layout Plain Layout
16679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16682 \begin_layout Plain Layout
16683 \begin_inset Formula $\bullet$
16697 \begin_inset space \hfill{}
16701 \begin_inset Tabular
16702 <lyxtabular version="3" rows="13" columns="2">
16704 <column alignment="center" valignment="top" width="0pt">
16705 <column alignment="center" valignment="top" width="0pt">
16707 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16710 \begin_layout Plain Layout
16716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16719 \begin_layout Plain Layout
16727 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16730 \begin_layout Plain Layout
16738 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16741 \begin_layout Plain Layout
16742 \begin_inset Formula $\nabla$
16752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16755 \begin_layout Plain Layout
16763 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16766 \begin_layout Plain Layout
16767 \begin_inset Formula $\bigtriangledown$
16777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16780 \begin_layout Plain Layout
16788 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16791 \begin_layout Plain Layout
16792 \begin_inset Formula $\bigtriangleup$
16802 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16805 \begin_layout Plain Layout
16813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16816 \begin_layout Plain Layout
16817 \begin_inset Formula $\Box$
16827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16830 \begin_layout Plain Layout
16838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16841 \begin_layout Plain Layout
16842 \begin_inset Formula $\cap$
16852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16855 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16867 \begin_inset Formula $\cup$
16877 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16880 \begin_layout Plain Layout
16888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16891 \begin_layout Plain Layout
16892 \begin_inset Formula $\dagger$
16902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16905 \begin_layout Plain Layout
16913 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16916 \begin_layout Plain Layout
16917 \begin_inset Formula $\ddagger$
16927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16930 \begin_layout Plain Layout
16938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16941 \begin_layout Plain Layout
16942 \begin_inset Formula $\wr$
16952 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16955 \begin_layout Plain Layout
16963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16966 \begin_layout Plain Layout
16967 \begin_inset Formula $\bigcirc$
16977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16980 \begin_layout Plain Layout
16988 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16991 \begin_layout Plain Layout
16992 \begin_inset Formula $\wedge$
17002 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17005 \begin_layout Plain Layout
17013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17016 \begin_layout Plain Layout
17017 \begin_inset Formula $\vee$
17031 \begin_inset space \hfill{}
17035 \begin_inset Tabular
17036 <lyxtabular version="3" rows="13" columns="2">
17038 <column alignment="center" valignment="top" width="0pt">
17039 <column alignment="center" valignment="top" width="0pt">
17041 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17044 \begin_layout Plain Layout
17050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17053 \begin_layout Plain Layout
17061 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17064 \begin_layout Plain Layout
17072 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17075 \begin_layout Plain Layout
17076 \begin_inset Formula $\oplus$
17086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17089 \begin_layout Plain Layout
17097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17100 \begin_layout Plain Layout
17101 \begin_inset Formula $\ominus$
17111 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17114 \begin_layout Plain Layout
17122 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17125 \begin_layout Plain Layout
17126 \begin_inset Formula $\otimes$
17136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17139 \begin_layout Plain Layout
17147 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17150 \begin_layout Plain Layout
17151 \begin_inset Formula $\oslash$
17161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17164 \begin_layout Plain Layout
17172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17175 \begin_layout Plain Layout
17176 \begin_inset Formula $\odot$
17186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17189 \begin_layout Plain Layout
17197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17200 \begin_layout Plain Layout
17201 \begin_inset Formula $\amalg$
17211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17214 \begin_layout Plain Layout
17222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17225 \begin_layout Plain Layout
17226 \begin_inset Formula $\uplus$
17236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17239 \begin_layout Plain Layout
17247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17250 \begin_layout Plain Layout
17251 \begin_inset Formula $\setminus$
17261 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17264 \begin_layout Plain Layout
17272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17275 \begin_layout Plain Layout
17276 \begin_inset Formula $\sqcap$
17286 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17289 \begin_layout Plain Layout
17297 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17300 \begin_layout Plain Layout
17301 \begin_inset Formula $\sqcup$
17311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17314 \begin_layout Plain Layout
17322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17325 \begin_layout Plain Layout
17326 \begin_inset Formula $\triangleleft$
17336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17339 \begin_layout Plain Layout
17347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17350 \begin_layout Plain Layout
17351 \begin_inset Formula $\triangleright$
17365 \begin_inset space \hfill{}
17371 \begin_layout Standard
17372 All binary operators can also be inserted via the math toolbar button
17373 \begin_inset Graphics
17374 filename ../images/math/pm.png
17382 \begin_layout Standard
17383 To typeset the Laplace operator also
17400 \begin_inset Formula $\nabla^{2}$
17403 ) can be used instead of
17412 \begin_layout Standard
17419 Insert\SpecialChar \menuseparator
17431 \begin_layout Subsection
17432 Self-defined Operators
17433 \begin_inset CommandInset label
17435 name "sub:Self-defined-Operators"
17443 \begin_layout Plain Layout
17444 Operators ! self-defined
17452 \begin_layout Standard
17453 With the help of the command
17457 DeclareMathOperator
17463 \begin_layout Plain Layout
17468 DeclareMathOperator
17473 custom operators can be defined in the LaTeX-preamble.
17474 Its command scheme is:
17477 \begin_layout Standard
17482 DeclareMathOperator{new command}{display}
17485 \begin_layout Standard
17486 Display can be characters or symbols that define how the operator looks
17488 To define a big operator a * is set behind the command.
17489 All self-defined big operators can have limits as described in
17490 \begin_inset CommandInset ref
17492 reference "sub:Operator-Limits"
17499 \begin_layout Standard
17500 For example the LaTeX-preamble line
17503 \begin_layout Standard
17508 DeclareMathOperator*{
17515 \begin_layout Standard
17516 defines the command
17522 , that inserts a big operator consisting of the lozenge symbol from
17523 \begin_inset CommandInset ref
17525 reference "sub:Miscellaneous-Symbols"
17530 \begin_inset Formula \[
17531 \Lozenge_{n=1}^{\infty}\]
17535 The command for this formula is:
17546 \begin_inset Formula $\to$
17552 \begin_layout Standard
17553 \begin_inset VSpace bigskip
17556 When self-defined operators are not used several times in the document,
17557 they can also be defined with the commands
17567 \begin_layout Plain Layout
17585 \begin_layout Plain Layout
17593 , which have the following scheme:
17596 \begin_layout Standard
17610 \begin_layout Standard
17617 defines big operators,
17626 \begin_layout Standard
17634 \begin_inset space \thinspace{}
17638 \begin_inset space ~
17641 be used to use one limit for several operators:
17644 \begin_layout Standard
17645 \begin_inset Formula \[
17646 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17653 \begin_layout Standard
17654 The command for the formula above is:
17655 \begin_inset Newline newline
17674 \begin_layout Plain Layout
17686 \begin_inset Formula $\to$
17695 \begin_layout Plain Layout
17709 \begin_layout Section
17714 \begin_layout Plain Layout
17723 \begin_layout Subsection
17725 \begin_inset CommandInset label
17727 name "sub:Font-Styles"
17735 \begin_layout Plain Layout
17744 \begin_layout Standard
17745 Latin letters in formulas can be set in one of the following font styles:
17746 \begin_inset VSpace -2mm
17752 \begin_layout Standard
17754 \begin_inset Tabular
17755 <lyxtabular version="3" rows="6" columns="3">
17757 <column alignment="center" valignment="top" width="0">
17758 <column alignment="center" valignment="top" width="0">
17759 <column alignment="center" valignment="top" width="0">
17761 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17764 \begin_layout Plain Layout
17770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17773 \begin_layout Plain Layout
17779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17782 \begin_layout Plain Layout
17790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17793 \begin_layout Plain Layout
17802 \begin_layout Plain Layout
17818 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17821 \begin_layout Plain Layout
17822 \begin_inset Formula $\mathbb{ABC}$
17830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17833 \begin_layout Plain Layout
17841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17844 \begin_layout Plain Layout
17853 \begin_layout Plain Layout
17869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17872 \begin_layout Plain Layout
17873 \begin_inset Formula $\mathbf{AbC}$
17881 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17884 \begin_layout Plain Layout
17892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17895 \begin_layout Plain Layout
17904 \begin_layout Plain Layout
17920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17924 \begin_inset Formula $\boldsymbol{AbC}$
17932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17935 \begin_layout Plain Layout
17943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17946 \begin_layout Plain Layout
17955 \begin_layout Plain Layout
17971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17974 \begin_layout Plain Layout
17975 \begin_inset Formula $\mathcal{ABC}$
17983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17986 \begin_layout Plain Layout
17994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17997 \begin_layout Plain Layout
18006 \begin_layout Plain Layout
18022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18025 \begin_layout Plain Layout
18026 \begin_inset Formula $\mathfrak{AbC}$
18034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18037 \begin_layout Plain Layout
18051 \begin_layout Standard
18053 \begin_inset Tabular
18054 <lyxtabular version="3" rows="5" columns="3">
18056 <column alignment="center" valignment="top" width="0">
18057 <column alignment="center" valignment="top" width="0">
18058 <column alignment="center" valignment="top" width="0">
18060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18063 \begin_layout Plain Layout
18069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18072 \begin_layout Plain Layout
18078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18081 \begin_layout Plain Layout
18089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18092 \begin_layout Plain Layout
18101 \begin_layout Plain Layout
18117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18120 \begin_layout Plain Layout
18121 \begin_inset Formula $\mathit{AbC}$
18129 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18132 \begin_layout Plain Layout
18140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18143 \begin_layout Plain Layout
18152 \begin_layout Plain Layout
18168 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18171 \begin_layout Plain Layout
18172 \begin_inset Formula $\mathrm{AbC}$
18180 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18183 \begin_layout Plain Layout
18191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18194 \begin_layout Plain Layout
18203 \begin_layout Plain Layout
18219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18222 \begin_layout Plain Layout
18223 \begin_inset Formula $\mathsf{AbC}$
18231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18234 \begin_layout Plain Layout
18242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18245 \begin_layout Plain Layout
18254 \begin_layout Plain Layout
18270 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18273 \begin_layout Plain Layout
18274 \begin_inset Formula $\mathtt{AbC}$
18282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18285 \begin_layout Plain Layout
18299 \begin_layout Standard
18300 \begin_inset Note Greyedout
18303 \begin_layout Plain Layout
18320 can only be used for big letters.
18328 \begin_layout Standard
18329 Predefined is the style
18338 \begin_layout Standard
18339 The style commands work also for letters in mathematical constructs:
18340 \begin_inset Formula \[
18341 \mathfrak{A=\frac{b}{C}}\]
18348 \begin_layout Standard
18349 Characters in mathematical text don't appear in a math font style but in
18350 the text font style
18357 That their style can't be set correctly via the text style dialog is a
18362 \begin_layout Plain Layout
18363 \begin_inset CommandInset href
18365 name "LyX-bug #4091"
18366 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18378 \begin_layout Standard
18379 Instead of the style commands the dialog
18381 Edit\SpecialChar \menuseparator
18382 Math\SpecialChar \menuseparator
18385 or the toolbar button
18386 \begin_inset Graphics
18387 filename ../images/math/font.png
18395 \begin_layout Subsection
18397 \begin_inset CommandInset label
18399 name "sub:Bold-Formulas"
18407 \begin_layout Plain Layout
18416 \begin_layout Standard
18417 To make a complete formula bold, the command
18423 from the previous subsection cannot be used, because it doesn't work for
18424 small Greek letters.
18425 Furthermore it prints Latin letters always upright, like in the following
18429 \begin_layout Standard
18430 \begin_inset Formula \[
18431 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18438 \begin_layout Standard
18439 To display the formula correctly, the command
18446 \begin_inset Formula \[
18447 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18451 It is also possible to set the formula in a
18453 boldmath environment
18456 This environment is created by inserting the command
18464 \begin_layout Plain Layout
18475 To end the environment, the command
18483 \begin_layout Plain Layout
18493 is inserted in TeX-mode.
18497 \begin_layout Plain Layout
18507 \begin_inset Formula \[
18508 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18516 \begin_layout Plain Layout
18528 \begin_layout Subsection
18530 \begin_inset CommandInset label
18532 name "sub:Font-Sizes"
18540 \begin_layout Plain Layout
18549 \begin_layout Standard
18550 For characters in formulas there are, analog to characters in text, the
18551 following size commands:
18554 \begin_layout Standard
18598 \begin_inset Newline newline
18620 \begin_layout Standard
18621 The size produced by the commands depends on the document font size, that
18622 corresponds with the command
18629 The other commands produce smaller or larger sizes than
18636 The font size can however not exceed a certain value.
18637 Is for example the document font size 12
18638 \begin_inset space \thinspace{}
18647 switches to the same size as
18657 \begin_layout Standard
18658 A size command is inserted in TeX-mode before the formula and sets the size
18659 for all following formula and text characters.
18660 To switch back to the initial size, the command
18666 is inserted behind the formula in TeX-mode.
18669 \begin_layout Standard
18670 Within a formula the size can only be changed for symbols or letters in
18672 To do this, the size command is inserted in mathematical text.
18673 All following characters until the end of the mathematical text or until
18674 another size command will have the selected size.
18676 \begin_inset VSpace -2mm
18682 \begin_layout Standard
18686 \begin_layout Plain Layout
18696 \begin_inset Formula \[
18697 A=\frac{B}{c}\cdot\maltese\]
18702 \begin_inset Formula \[
18703 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18711 \begin_layout Plain Layout
18723 \begin_layout Standard
18724 \begin_inset VSpace medskip
18727 Before both formulas the command
18734 The command for the second formula is:
18735 \begin_inset Newline newline
18746 \begin_layout Plain Layout
18761 \begin_layout Plain Layout
18776 \begin_layout Plain Layout
18791 \begin_layout Plain Layout
18801 \begin_inset Formula $\to$
18805 \begin_inset Formula $\to$
18809 \begin_inset Newline newline
18813 \begin_inset space \hspace*{}
18827 \begin_layout Plain Layout
18842 \begin_layout Plain Layout
18857 \begin_layout Plain Layout
18869 \begin_layout Standard
18870 If a symbol cannot be displayed in different sizes, it will always be displayed
18871 in the default size.
18874 \begin_layout Section
18879 \begin_layout Plain Layout
18888 \begin_layout Standard
18889 All Greek letters can also be inserted via the toolbar button
18890 \begin_inset Graphics
18891 filename ../images/math/alpha.png
18899 \begin_layout Subsection
18901 \begin_inset CommandInset label
18903 name "sub:Small-Letters"
18911 \begin_layout Plain Layout
18912 Greek letters ! small
18920 \begin_layout Standard
18921 \begin_inset space \hfill{}
18925 \begin_inset Tabular
18926 <lyxtabular version="3" rows="11" columns="2">
18928 <column alignment="center" valignment="top" width="0pt">
18929 <column alignment="center" valignment="top" width="0pt">
18931 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18934 \begin_layout Plain Layout
18940 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18943 \begin_layout Plain Layout
18951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18954 \begin_layout Plain Layout
18962 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18965 \begin_layout Plain Layout
18966 \begin_inset Formula $\alpha$
18976 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18979 \begin_layout Plain Layout
18987 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18990 \begin_layout Plain Layout
18991 \begin_inset Formula $\beta$
19001 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19004 \begin_layout Plain Layout
19012 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19015 \begin_layout Plain Layout
19016 \begin_inset Formula $\gamma$
19026 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19029 \begin_layout Plain Layout
19037 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19040 \begin_layout Plain Layout
19041 \begin_inset Formula $\delta$
19051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19054 \begin_layout Plain Layout
19062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19065 \begin_layout Plain Layout
19066 \begin_inset Formula $\epsilon$
19076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19079 \begin_layout Plain Layout
19087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19090 \begin_layout Plain Layout
19091 \begin_inset Formula $\varepsilon$
19101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19104 \begin_layout Plain Layout
19112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19115 \begin_layout Plain Layout
19116 \begin_inset Formula $\zeta$
19126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19129 \begin_layout Plain Layout
19137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19140 \begin_layout Plain Layout
19141 \begin_inset Formula $\eta$
19151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19154 \begin_layout Plain Layout
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19165 \begin_layout Plain Layout
19166 \begin_inset Formula $\theta$
19176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19179 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19191 \begin_inset Formula $\vartheta$
19205 \begin_inset space \hfill{}
19209 \begin_inset Tabular
19210 <lyxtabular version="3" rows="12" columns="2">
19212 <column alignment="center" valignment="top" width="0pt">
19213 <column alignment="center" valignment="top" width="0pt">
19215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19218 \begin_layout Plain Layout
19224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19227 \begin_layout Plain Layout
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19238 \begin_layout Plain Layout
19246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19249 \begin_layout Plain Layout
19250 \begin_inset Formula $\iota$
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19263 \begin_layout Plain Layout
19271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19274 \begin_layout Plain Layout
19275 \begin_inset Formula $\kappa$
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19288 \begin_layout Plain Layout
19296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19299 \begin_layout Plain Layout
19300 \begin_inset Formula $\varkappa$
19310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19313 \begin_layout Plain Layout
19321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19324 \begin_layout Plain Layout
19325 \begin_inset Formula $\lambda$
19335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19338 \begin_layout Plain Layout
19346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19349 \begin_layout Plain Layout
19350 \begin_inset Formula $\mu$
19360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19363 \begin_layout Plain Layout
19371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19374 \begin_layout Plain Layout
19375 \begin_inset Formula $\nu$
19385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19388 \begin_layout Plain Layout
19396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19399 \begin_layout Plain Layout
19400 \begin_inset Formula $\xi$
19410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19413 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $o$
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\pi$
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Plain Layout
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Plain Layout
19473 \begin_inset Formula $\varpi$
19483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19486 \begin_layout Plain Layout
19494 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Plain Layout
19498 \begin_inset Formula $\rho$
19512 \begin_inset space \hfill{}
19516 \begin_inset Tabular
19517 <lyxtabular version="3" rows="11" columns="2">
19519 <column alignment="center" valignment="top" width="0pt">
19520 <column alignment="center" valignment="top" width="0pt">
19522 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19525 \begin_layout Plain Layout
19531 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19534 \begin_layout Plain Layout
19542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19545 \begin_layout Plain Layout
19553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19556 \begin_layout Plain Layout
19557 \begin_inset Formula $\varrho$
19567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19570 \begin_layout Plain Layout
19578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19581 \begin_layout Plain Layout
19582 \begin_inset Formula $\sigma$
19592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19595 \begin_layout Plain Layout
19603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19606 \begin_layout Plain Layout
19607 \begin_inset Formula $\varsigma$
19617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19620 \begin_layout Plain Layout
19628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19631 \begin_layout Plain Layout
19632 \begin_inset Formula $\tau$
19642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19645 \begin_layout Plain Layout
19653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19656 \begin_layout Plain Layout
19657 \begin_inset Formula $\upsilon$
19667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19670 \begin_layout Plain Layout
19678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19681 \begin_layout Plain Layout
19682 \begin_inset Formula $\phi$
19692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19695 \begin_layout Plain Layout
19703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19706 \begin_layout Plain Layout
19707 \begin_inset Formula $\varphi$
19717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19720 \begin_layout Plain Layout
19728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19731 \begin_layout Plain Layout
19732 \begin_inset Formula $\chi$
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19745 \begin_layout Plain Layout
19753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19756 \begin_layout Plain Layout
19757 \begin_inset Formula $\psi$
19767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19770 \begin_layout Plain Layout
19778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19781 \begin_layout Plain Layout
19782 \begin_inset Formula $\omega$
19796 \begin_inset space \hfill{}
19802 \begin_layout Standard
19803 \begin_inset VSpace medskip
19809 \begin_layout Standard
19810 How to create upright Greek letters is explained in
19811 \begin_inset CommandInset ref
19813 reference "sub:Upright-small-Greek"
19820 \begin_layout Subsection
19825 \begin_layout Plain Layout
19826 Greek letters ! big
19834 \begin_layout Standard
19835 \begin_inset space \hfill{}
19839 \begin_inset Tabular
19840 <lyxtabular version="3" rows="7" columns="2">
19842 <column alignment="center" valignment="top" width="0pt">
19843 <column alignment="center" valignment="top" width="0pt">
19845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\Gamma$
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\Delta$
19915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\Theta$
19940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\Lambda$
19965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\Xi$
19990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19993 \begin_layout Plain Layout
20001 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20004 \begin_layout Plain Layout
20005 \begin_inset Formula $\Pi$
20019 \begin_inset space \hfill{}
20023 \begin_inset Tabular
20024 <lyxtabular version="3" rows="6" columns="2">
20026 <column alignment="center" valignment="top" width="0pt">
20027 <column alignment="center" valignment="top" width="0pt">
20029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20032 \begin_layout Plain Layout
20038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20041 \begin_layout Plain Layout
20049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20052 \begin_layout Plain Layout
20060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20063 \begin_layout Plain Layout
20064 \begin_inset Formula $\Sigma$
20074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20077 \begin_layout Plain Layout
20085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20088 \begin_layout Plain Layout
20089 \begin_inset Formula $\Upsilon$
20099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20102 \begin_layout Plain Layout
20110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20113 \begin_layout Plain Layout
20114 \begin_inset Formula $\Phi$
20124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20127 \begin_layout Plain Layout
20135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20138 \begin_layout Plain Layout
20139 \begin_inset Formula $\Psi$
20149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20152 \begin_layout Plain Layout
20160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20163 \begin_layout Plain Layout
20164 \begin_inset Formula $\Omega$
20178 \begin_inset space \hfill{}
20184 \begin_layout Standard
20185 \begin_inset VSpace medskip
20188 That the big Greek letters appear upright is caused by a design bug when
20190 To get correct italic big letters, begin every command with
20195 For example the command
20202 \begin_inset Formula $\varGamma$
20208 \begin_layout Subsection
20213 \begin_layout Plain Layout
20214 Greek letters ! bold
20222 \begin_layout Standard
20223 Greek letters cannot be set with different font styles like Latin letters.
20224 They can only be made bold with the command
20234 \begin_layout Plain Layout
20245 \begin_layout Standard
20247 \begin_inset Tabular
20248 <lyxtabular version="3" rows="3" columns="2">
20250 <column alignment="center" valignment="top" width="0">
20251 <column alignment="center" valignment="top" width="0">
20253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20256 \begin_layout Plain Layout
20262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20265 \begin_layout Plain Layout
20273 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20276 \begin_layout Plain Layout
20288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20291 \begin_layout Plain Layout
20292 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20305 \begin_layout Plain Layout
20317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20320 \begin_layout Plain Layout
20321 \begin_inset Formula $\theta\boldsymbol{\theta}$
20337 \begin_layout Section
20342 \begin_layout Plain Layout
20355 \begin_layout Plain Layout
20356 A list with all symbols of most of the LaTeX-packages can be found in
20357 \begin_inset CommandInset citation
20372 \begin_layout Plain Layout
20380 \begin_inset Note Note
20383 \begin_layout Plain Layout
20386 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20389 \begin_layout Plain Layout
20392 texorpdfstring is in section
20393 \begin_inset CommandInset ref
20395 reference "sub:Formulas-in-Section"
20408 \begin_layout Plain Layout
20417 \begin_layout Standard
20418 Many of the symbols listed in this section can also be inserted via the
20420 \begin_inset Graphics
20421 filename ../images/math/nabla.png
20427 \begin_inset Graphics
20428 filename ../images/math/digamma.png
20436 \begin_layout Subsection
20437 Mathematical Symbols
20438 \begin_inset CommandInset label
20440 name "sub:Mathematical-Symbols"
20448 \begin_layout Plain Layout
20449 Symbols ! mathematical
20457 \begin_layout Standard
20458 \begin_inset space \hfill{}
20462 \begin_inset Tabular
20463 <lyxtabular version="3" rows="10" columns="2">
20465 <column alignment="center" valignment="top" width="0pt">
20466 <column alignment="center" valignment="top" width="0pt">
20468 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20471 \begin_layout Plain Layout
20477 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20480 \begin_layout Plain Layout
20488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20491 \begin_layout Plain Layout
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20502 \begin_layout Plain Layout
20503 \begin_inset Formula $\neg$
20513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20516 \begin_layout Plain Layout
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20527 \begin_layout Plain Layout
20528 \begin_inset Formula $\Im$
20538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20541 \begin_layout Plain Layout
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20552 \begin_layout Plain Layout
20553 \begin_inset Formula $\Re$
20563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20566 \begin_layout Plain Layout
20574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20577 \begin_layout Plain Layout
20578 \begin_inset Formula $\aleph$
20588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20591 \begin_layout Plain Layout
20599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20602 \begin_layout Plain Layout
20603 \begin_inset Formula $\partial$
20613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20616 \begin_layout Plain Layout
20624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20627 \begin_layout Plain Layout
20628 \begin_inset Formula $\infty$
20638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20641 \begin_layout Plain Layout
20649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20652 \begin_layout Plain Layout
20653 \begin_inset Formula $\wp$
20663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20666 \begin_layout Plain Layout
20674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20677 \begin_layout Plain Layout
20678 \begin_inset Formula $\imath$
20688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20691 \begin_layout Plain Layout
20699 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20702 \begin_layout Plain Layout
20703 \begin_inset Formula $\jmath$
20717 \begin_inset space \hfill{}
20721 \begin_inset Tabular
20722 <lyxtabular version="3" rows="10" columns="2">
20724 <column alignment="center" valignment="top" width="0pt">
20725 <column alignment="center" valignment="top" width="0pt">
20727 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20730 \begin_layout Plain Layout
20736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20739 \begin_layout Plain Layout
20741 \begin_inset Note Note
20744 \begin_layout Plain Layout
20751 is only used as spacer.
20763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20766 \begin_layout Plain Layout
20774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20777 \begin_layout Plain Layout
20778 \begin_inset Formula $\forall$
20788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20791 \begin_layout Plain Layout
20799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20802 \begin_layout Plain Layout
20803 \begin_inset Formula $\exists$
20813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20816 \begin_layout Plain Layout
20824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20827 \begin_layout Plain Layout
20828 \begin_inset Formula $\nexists$
20838 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20841 \begin_layout Plain Layout
20849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20852 \begin_layout Plain Layout
20853 \begin_inset Formula $\emptyset$
20863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20866 \begin_layout Plain Layout
20874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20877 \begin_layout Plain Layout
20878 \begin_inset Formula $\varnothing$
20888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20891 \begin_layout Plain Layout
20899 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20902 \begin_layout Plain Layout
20903 \begin_inset Formula $\dag$
20913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20916 \begin_layout Plain Layout
20924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20927 \begin_layout Plain Layout
20928 \begin_inset Formula $\ddag$
20938 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20941 \begin_layout Plain Layout
20949 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20952 \begin_layout Plain Layout
20956 \begin_layout Plain Layout
20966 \begin_inset Formula $\complement$
20973 \begin_layout Plain Layout
20987 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20990 \begin_layout Plain Layout
20998 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21001 \begin_layout Plain Layout
21002 \begin_inset Formula $\Bbbk$
21016 \begin_inset space \hfill{}
21020 \begin_inset Tabular
21021 <lyxtabular version="3" rows="10" columns="2">
21023 <column alignment="center" valignment="top" width="0pt">
21024 <column alignment="center" valignment="top" width="0pt">
21026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21029 \begin_layout Plain Layout
21035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21038 \begin_layout Plain Layout
21046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21049 \begin_layout Plain Layout
21057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21060 \begin_layout Plain Layout
21061 \begin_inset Formula $\prime$
21071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21074 \begin_layout Plain Layout
21082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21085 \begin_layout Plain Layout
21086 \begin_inset Formula $\backprime$
21096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21099 \begin_layout Plain Layout
21107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21110 \begin_layout Plain Layout
21111 \begin_inset Formula $\mho$
21121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21124 \begin_layout Plain Layout
21132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21135 \begin_layout Plain Layout
21136 \begin_inset Formula $\triangle$
21146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21149 \begin_layout Plain Layout
21157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21160 \begin_layout Plain Layout
21161 \begin_inset Formula $\angle$
21171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21174 \begin_layout Plain Layout
21182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21185 \begin_layout Plain Layout
21186 \begin_inset Formula $\measuredangle$
21196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21199 \begin_layout Plain Layout
21207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21210 \begin_layout Plain Layout
21211 \begin_inset Formula $\sphericalangle$
21221 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21224 \begin_layout Plain Layout
21232 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21235 \begin_layout Plain Layout
21236 \begin_inset Formula $\top$
21246 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21249 \begin_layout Plain Layout
21257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21260 \begin_layout Plain Layout
21261 \begin_inset Formula $\bot$
21275 \begin_inset space \hfill{}
21281 \begin_layout Standard
21282 \begin_inset Newpage newpage
21288 \begin_layout Subsection
21289 Miscellaneous Symbols
21290 \begin_inset CommandInset label
21292 name "sub:Miscellaneous-Symbols"
21300 \begin_layout Plain Layout
21301 Symbols ! miscellaneous
21309 \begin_layout Standard
21312 \begin_inset Tabular
21313 <lyxtabular version="3" rows="10" columns="2">
21315 <column alignment="center" valignment="top" width="0pt">
21316 <column alignment="center" valignment="top" width="0pt">
21318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21321 \begin_layout Plain Layout
21327 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21330 \begin_layout Plain Layout
21338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21341 \begin_layout Plain Layout
21349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21352 \begin_layout Plain Layout
21353 \begin_inset Formula $\flat$
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\natural$
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\sharp$
21413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21424 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21427 \begin_layout Plain Layout
21428 \begin_inset Formula $\surd$
21438 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $\checkmark$
21463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\yen$
21488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\pounds$
21513 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21516 \begin_layout Plain Layout
21522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21525 \begin_layout Plain Layout
21526 \begin_inset Formula $\$$
21536 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21539 \begin_layout Plain Layout
21545 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21548 \begin_layout Plain Layout
21549 \begin_inset Formula $§$
21563 \begin_inset Tabular
21564 <lyxtabular version="3" rows="10" columns="2">
21566 <column alignment="center" valignment="top" width="0">
21567 <column alignment="center" valignment="top" width="0">
21569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21572 \begin_layout Plain Layout
21578 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21581 \begin_layout Plain Layout
21589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21592 \begin_layout Plain Layout
21600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21603 \begin_layout Plain Layout
21604 \begin_inset Formula $\hbar$
21614 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21617 \begin_layout Plain Layout
21625 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21628 \begin_layout Plain Layout
21629 \begin_inset Formula $\hslash$
21639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21642 \begin_layout Plain Layout
21650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21653 \begin_layout Plain Layout
21654 \begin_inset Formula $\clubsuit$
21664 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21667 \begin_layout Plain Layout
21675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21678 \begin_layout Plain Layout
21679 \begin_inset Formula $\spadesuit$
21689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21692 \begin_layout Plain Layout
21700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21703 \begin_layout Plain Layout
21704 \begin_inset Formula $\bigstar$
21714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21717 \begin_layout Plain Layout
21725 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21728 \begin_layout Plain Layout
21729 \begin_inset Formula $\blacklozenge$
21739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21742 \begin_layout Plain Layout
21750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21753 \begin_layout Plain Layout
21754 \begin_inset Formula $\blacktriangle$
21764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21767 \begin_layout Plain Layout
21775 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21778 \begin_layout Plain Layout
21779 \begin_inset Formula $\blacktriangledown$
21789 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21792 \begin_layout Plain Layout
21800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21803 \begin_layout Plain Layout
21804 \begin_inset Formula $\bullet$
21818 \begin_inset Tabular
21819 <lyxtabular version="3" rows="10" columns="2">
21821 <column alignment="center" valignment="top" width="0pt">
21822 <column alignment="center" valignment="top" width="0pt">
21824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21827 \begin_layout Plain Layout
21833 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21836 \begin_layout Plain Layout
21844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21847 \begin_layout Plain Layout
21855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21858 \begin_layout Plain Layout
21859 \begin_inset Formula $\diamondsuit$
21869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21872 \begin_layout Plain Layout
21880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21883 \begin_layout Plain Layout
21884 \begin_inset Formula $\Diamond$
21894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21897 \begin_layout Plain Layout
21905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21908 \begin_layout Plain Layout
21909 \begin_inset Formula $\heartsuit$
21919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21922 \begin_layout Plain Layout
21930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21933 \begin_layout Plain Layout
21934 \begin_inset Formula $\P$
21944 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21947 \begin_layout Plain Layout
21955 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21958 \begin_layout Plain Layout
21959 \begin_inset Formula $\copyright$
21969 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21972 \begin_layout Plain Layout
21980 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21983 \begin_layout Plain Layout
21984 \begin_inset Formula $\circledR$
21994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21997 \begin_layout Plain Layout
22005 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22008 \begin_layout Plain Layout
22009 \begin_inset Formula $\maltese$
22019 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22022 \begin_layout Plain Layout
22030 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22033 \begin_layout Plain Layout
22034 \begin_inset Formula $\diagup$
22044 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22047 \begin_layout Plain Layout
22055 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22058 \begin_layout Plain Layout
22059 \begin_inset Formula $\diagdown$
22075 \begin_layout Standard
22076 \begin_inset VSpace medskip
22079 More symbols are listed in
22080 \begin_inset CommandInset ref
22082 reference "sub:Miscellaneous-special-Characters"
22089 \begin_layout Standard
22090 Some symbols can be displayed in different sizes, see
22091 \begin_inset CommandInset ref
22093 reference "sub:Font-Sizes"
22100 \begin_layout Subsection
22105 \begin_layout Plain Layout
22106 Symbols ! Euro-symbol
22115 \begin_layout Plain Layout
22122 \begin_layout Plain Layout
22139 \begin_layout Standard
22140 To use the Euro symbol in formulas, the LaTeX-package
22148 \begin_layout Plain Layout
22154 must be installed and loaded with the LaTeX-preamble line
22157 \begin_layout Standard
22162 usepackage[gennarrow]{eurosym}
22165 \begin_layout Standard
22166 The Euro symbol can now be inserted with the command
22176 \begin_layout Plain Layout
22187 \begin_layout Standard
22188 The Euro symbol can directly be inserted with the € key in mathematical
22189 text, without having
22204 can also be inserted in TeX-mode.
22205 The official currency symbol can then be inserted with the command
22215 \begin_layout Plain Layout
22223 , that is only available in TeX-mode.
22226 \begin_layout Standard
22230 \begin_layout Plain Layout
22240 \begin_inset Note Note
22243 \begin_layout Plain Layout
22244 The following table will only be displayed when the LaTeX-package
22256 \begin_layout Standard
22257 An overview about the different Euro symbols:
22260 \begin_layout Standard
22262 \begin_inset Tabular
22263 <lyxtabular version="3" rows="4" columns="3">
22265 <column alignment="center" valignment="top" width="0pt">
22266 <column alignment="center" valignment="top" width="0pt">
22267 <column alignment="center" valignment="top" width="0pt">
22269 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22272 \begin_layout Plain Layout
22278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22281 \begin_layout Plain Layout
22287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22290 \begin_layout Plain Layout
22298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22301 \begin_layout Plain Layout
22307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22310 \begin_layout Plain Layout
22318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22321 \begin_layout Plain Layout
22322 \begin_inset Formula $\euro$
22332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22335 \begin_layout Plain Layout
22341 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22344 \begin_layout Plain Layout
22350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22353 \begin_layout Plain Layout
22354 \begin_inset Formula $\mbox{€}$
22364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22367 \begin_layout Plain Layout
22373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22376 \begin_layout Plain Layout
22384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22387 \begin_layout Plain Layout
22391 \begin_layout Plain Layout
22413 \begin_layout Standard
22417 \begin_layout Plain Layout
22427 \begin_inset Note Note
22430 \begin_layout Plain Layout
22431 The following will be displayed when the LaTeX-package
22443 \begin_layout Standard
22444 You need to install the LaTeX-package
22448 to see the rest of this subsection in the output.
22451 \begin_layout Standard
22455 \begin_layout Plain Layout
22467 \begin_layout Section
22469 \begin_inset CommandInset label
22471 name "sec:Relations"
22479 \begin_layout Plain Layout
22489 \begin_layout Plain Layout
22494 \begin_layout Plain Layout
22505 \begin_layout Plain Layout
22520 \begin_layout Standard
22521 All relations can also be inserted via the toolbar button
22522 \begin_inset Graphics
22523 filename ../images/math/leq.png
22531 \begin_layout Standard
22532 \begin_inset space \hfill{}
22536 \begin_inset Tabular
22537 <lyxtabular version="3" rows="17" columns="2">
22539 <column alignment="center" valignment="top" width="0pt">
22540 <column alignment="center" valignment="top" width="0pt">
22542 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22551 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22554 \begin_layout Plain Layout
22562 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22565 \begin_layout Plain Layout
22571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22574 \begin_layout Plain Layout
22575 \begin_inset Formula $<$
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22588 \begin_layout Plain Layout
22596 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22599 \begin_layout Plain Layout
22600 \begin_inset Formula $\le$
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22613 \begin_layout Plain Layout
22621 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22624 \begin_layout Plain Layout
22625 \begin_inset Formula $\ll$
22635 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22638 \begin_layout Plain Layout
22646 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22649 \begin_layout Plain Layout
22650 \begin_inset Formula $\prec$
22660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22663 \begin_layout Plain Layout
22671 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22674 \begin_layout Plain Layout
22675 \begin_inset Formula $\preceq$
22685 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22688 \begin_layout Plain Layout
22696 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22699 \begin_layout Plain Layout
22700 \begin_inset Formula $\subset$
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22713 \begin_layout Plain Layout
22721 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22724 \begin_layout Plain Layout
22725 \begin_inset Formula $\subseteq$
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22738 \begin_layout Plain Layout
22746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22749 \begin_layout Plain Layout
22750 \begin_inset Formula $\sqsubseteq$
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22763 \begin_layout Plain Layout
22771 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22774 \begin_layout Plain Layout
22775 \begin_inset Formula $\in$
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22788 \begin_layout Plain Layout
22796 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22799 \begin_layout Plain Layout
22800 \begin_inset Formula $\vdash$
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22821 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22824 \begin_layout Plain Layout
22825 \begin_inset Formula $\smile$
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22838 \begin_layout Plain Layout
22846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22849 \begin_layout Plain Layout
22850 \begin_inset Formula $\lhd$
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22863 \begin_layout Plain Layout
22871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22874 \begin_layout Plain Layout
22875 \begin_inset Formula $\unlhd$
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22888 \begin_layout Plain Layout
22896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22899 \begin_layout Plain Layout
22900 \begin_inset Formula $\gtrless$
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22913 \begin_layout Plain Layout
22921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22924 \begin_layout Plain Layout
22925 \begin_inset Formula $\mid$
22935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22938 \begin_layout Plain Layout
22946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22949 \begin_layout Plain Layout
22950 \begin_inset Formula $\nmid$
22964 \begin_inset space \hfill{}
22968 \begin_inset Tabular
22969 <lyxtabular version="3" rows="17" columns="2">
22971 <column alignment="center" valignment="top" width="0pt">
22972 <column alignment="center" valignment="top" width="0pt">
22974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22986 \begin_layout Plain Layout
22994 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22997 \begin_layout Plain Layout
23003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23006 \begin_layout Plain Layout
23007 \begin_inset Formula $=$
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23020 \begin_layout Plain Layout
23028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23031 \begin_layout Plain Layout
23032 \begin_inset Formula $\not=$
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23045 \begin_layout Plain Layout
23053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23056 \begin_layout Plain Layout
23057 \begin_inset Formula $\equiv$
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23070 \begin_layout Plain Layout
23078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23081 \begin_layout Plain Layout
23082 \begin_inset Formula $\sim$
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23095 \begin_layout Plain Layout
23103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23106 \begin_layout Plain Layout
23107 \begin_inset Formula $\simeq$
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23120 \begin_layout Plain Layout
23128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23131 \begin_layout Plain Layout
23132 \begin_inset Formula $\approx$
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23145 \begin_layout Plain Layout
23153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23156 \begin_layout Plain Layout
23157 \begin_inset Formula $\cong$
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23170 \begin_layout Plain Layout
23178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23181 \begin_layout Plain Layout
23182 \begin_inset Formula $\bowtie$
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23195 \begin_layout Plain Layout
23203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23206 \begin_layout Plain Layout
23207 \begin_inset Formula $\notin$
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23220 \begin_layout Plain Layout
23228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23231 \begin_layout Plain Layout
23232 \begin_inset Formula $\perp$
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23245 \begin_layout Plain Layout
23253 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23256 \begin_layout Plain Layout
23257 \begin_inset Formula $\propto$
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23270 \begin_layout Plain Layout
23278 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23281 \begin_layout Plain Layout
23282 \begin_inset Formula $\asymp$
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23295 \begin_layout Plain Layout
23303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23306 \begin_layout Plain Layout
23307 \begin_inset Formula $\doteq$
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23320 \begin_layout Plain Layout
23328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23331 \begin_layout Plain Layout
23332 \begin_inset Formula $\circeq$
23342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23345 \begin_layout Plain Layout
23353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23356 \begin_layout Plain Layout
23357 \begin_inset Formula $\models$
23367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23370 \begin_layout Plain Layout
23378 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23381 \begin_layout Plain Layout
23382 \begin_inset Formula $\widehat{=}$
23396 \begin_inset space \hfill{}
23400 \begin_inset Tabular
23401 <lyxtabular version="3" rows="17" columns="2">
23403 <column alignment="center" valignment="top" width="0pt">
23404 <column alignment="center" valignment="top" width="0pt">
23406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23415 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23418 \begin_layout Plain Layout
23426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23429 \begin_layout Plain Layout
23435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23438 \begin_layout Plain Layout
23439 \begin_inset Formula $>$
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23452 \begin_layout Plain Layout
23460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23463 \begin_layout Plain Layout
23464 \begin_inset Formula $\ge$
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23477 \begin_layout Plain Layout
23485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23488 \begin_layout Plain Layout
23489 \begin_inset Formula $\gg$
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23502 \begin_layout Plain Layout
23510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23513 \begin_layout Plain Layout
23514 \begin_inset Formula $\succ$
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23527 \begin_layout Plain Layout
23535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23538 \begin_layout Plain Layout
23539 \begin_inset Formula $\succeq$
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23552 \begin_layout Plain Layout
23560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23563 \begin_layout Plain Layout
23564 \begin_inset Formula $\supset$
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23577 \begin_layout Plain Layout
23585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23588 \begin_layout Plain Layout
23589 \begin_inset Formula $\supseteq$
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23602 \begin_layout Plain Layout
23610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23613 \begin_layout Plain Layout
23614 \begin_inset Formula $\sqsupseteq$
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23627 \begin_layout Plain Layout
23635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23638 \begin_layout Plain Layout
23639 \begin_inset Formula $\ni$
23649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23652 \begin_layout Plain Layout
23660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23663 \begin_layout Plain Layout
23664 \begin_inset Formula $\dashv$
23674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23677 \begin_layout Plain Layout
23685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23688 \begin_layout Plain Layout
23689 \begin_inset Formula $\frown$
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23702 \begin_layout Plain Layout
23710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23713 \begin_layout Plain Layout
23714 \begin_inset Formula $\rhd$
23724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23727 \begin_layout Plain Layout
23735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23738 \begin_layout Plain Layout
23739 \begin_inset Formula $\unrhd$
23749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23752 \begin_layout Plain Layout
23760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23763 \begin_layout Plain Layout
23764 \begin_inset Formula $\lessgtr$
23774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23777 \begin_layout Plain Layout
23785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23788 \begin_layout Plain Layout
23789 \begin_inset Formula $\parallel$
23799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23802 \begin_layout Plain Layout
23810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23813 \begin_layout Plain Layout
23814 \begin_inset Formula $\nparallel$
23828 \begin_inset space \hfill{}
23834 \begin_layout Standard
23835 \begin_inset VSpace medskip
23850 are bigger than the equal looking operators
23865 \begin_layout Standard
23866 Relations are, in contrary to symbols, always surrounded by space.
23869 \begin_layout Standard
23870 Relations with labels can be created with the command
23880 \begin_layout Plain Layout
23891 \begin_layout Standard
23893 \begin_inset Tabular
23894 <lyxtabular version="3" rows="2" columns="2">
23896 <column alignment="center" valignment="top" width="0">
23897 <column alignment="center" valignment="top" width="0">
23899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23902 \begin_layout Plain Layout
23908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23911 \begin_layout Plain Layout
23913 \begin_inset Note Note
23916 \begin_layout Plain Layout
23923 is only used as spacer.
23935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23938 \begin_layout Plain Layout
23945 \begin_layout Plain Layout
23962 \begin_layout Plain Layout
23972 \begin_inset Formula $\downarrow$
23981 \begin_layout Plain Layout
23994 \begin_layout Plain Layout
24008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24011 \begin_layout Plain Layout
24012 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24028 \begin_layout Section
24032 \begin_layout Subsection
24033 Predefined Functions
24034 \begin_inset CommandInset label
24036 name "sub:Predefined-Functions"
24044 \begin_layout Plain Layout
24045 Functions ! predefined
24053 \begin_layout Standard
24054 In general, variables are set
24058 in mathematical expressions, but not function names, because
24059 \begin_inset Formula $sin$
24062 could be misunderstood as
24063 \begin_inset Formula $s\cdot i\cdot n$
24067 Therefore there are predefined functions, that are additionally a bit separated
24069 They are inserted as commands starting with a backslash before their name.
24072 \begin_layout Standard
24074 \begin_inset Tabular
24075 <lyxtabular version="3" rows="2" columns="4">
24077 <column alignment="center" valignment="top" width="0pt">
24078 <column alignment="center" valignment="top" width="0pt">
24079 <column alignment="center" valignment="top" width="0pt">
24080 <column alignment="center" valignment="top" width="0pt">
24082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24085 \begin_layout Plain Layout
24091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24094 \begin_layout Plain Layout
24100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24103 \begin_layout Plain Layout
24109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24112 \begin_layout Plain Layout
24120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24123 \begin_layout Plain Layout
24129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24132 \begin_layout Plain Layout
24133 \begin_inset Formula $Asin(x)+B$
24141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24144 \begin_layout Plain Layout
24152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24155 \begin_layout Plain Layout
24156 \begin_inset Formula $A\sin(x)+B$
24170 \begin_inset Newpage pagebreak
24176 \begin_layout Standard
24177 The following functions are predefined:
24180 \begin_layout Standard
24181 \begin_inset VSpace -2mm
24187 \begin_layout Standard
24189 \begin_inset Tabular
24190 <lyxtabular version="3" rows="9" columns="4">
24192 <column alignment="center" valignment="top" width="0pt">
24193 <column alignment="center" valignment="top" width="0pt">
24194 <column alignment="center" valignment="top" width="0pt">
24195 <column alignment="center" valignment="top" width="0pt">
24197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24200 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24215 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24218 \begin_layout Plain Layout
24224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24227 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24238 \begin_layout Plain Layout
24246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24249 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24260 \begin_layout Plain Layout
24268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24271 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24284 \begin_layout Plain Layout
24292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24295 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24306 \begin_layout Plain Layout
24314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24317 \begin_layout Plain Layout
24327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24330 \begin_layout Plain Layout
24338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24352 \begin_layout Plain Layout
24360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24363 \begin_layout Plain Layout
24373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24387 \begin_layout Plain Layout
24395 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24398 \begin_layout Plain Layout
24406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24409 \begin_layout Plain Layout
24419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24422 \begin_layout Plain Layout
24430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24433 \begin_layout Plain Layout
24441 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24444 \begin_layout Plain Layout
24452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24455 \begin_layout Plain Layout
24465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24468 \begin_layout Plain Layout
24476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24479 \begin_layout Plain Layout
24487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24490 \begin_layout Plain Layout
24498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24501 \begin_layout Plain Layout
24511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24514 \begin_layout Plain Layout
24522 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24525 \begin_layout Plain Layout
24533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24536 \begin_layout Plain Layout
24544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24547 \begin_layout Plain Layout
24557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24560 \begin_layout Plain Layout
24568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24571 \begin_layout Plain Layout
24579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24582 \begin_layout Plain Layout
24590 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24593 \begin_layout Plain Layout
24609 \begin_layout Standard
24610 They can also be inserted with the math toolbar button
24611 \begin_inset Graphics
24612 filename ../images/math/functions.png
24620 \begin_layout Subsection
24621 Self-defined Functions
24625 \begin_layout Plain Layout
24626 Functions ! self-defined
24634 \begin_layout Standard
24635 To use a function that is not predefined, like for example the sign function
24636 sgn(x), there are two possibilities:
24639 \begin_layout Itemize
24640 Define the function by inserting the following line to the LaTeX-preamble
24644 \begin_layout Plain Layout
24649 DeclareMathOperator
24652 \begin_inset CommandInset ref
24654 reference "sub:Self-defined-Operators"
24664 \begin_inset Newline newline
24668 \begin_inset VSpace -3mm
24672 \begin_inset Newline newline
24679 DeclareMathOperator{
24687 \begin_layout Plain Layout
24692 DeclareMathOperator
24698 \begin_inset Newline newline
24702 \begin_inset VSpace -2mm
24706 \begin_inset Newline newline
24709 Now the new defined function can be called with the command
24718 \begin_layout Itemize
24719 Write the the formula as usual, mark the formula name, in our example the
24724 , and change it to mathematical text.
24725 At last a space is inserted between prefactor and function.
24728 \begin_layout Standard
24729 The result is the same with both methods as with a predefined function
24733 \begin_layout Plain Layout
24734 In LyX self-defined functions are displayed red, predefined ones black.
24742 \begin_layout Standard
24744 \begin_inset Tabular
24745 <lyxtabular version="3" rows="3" columns="2">
24747 <column alignment="center" valignment="top" width="0pt">
24748 <column alignment="center" valignment="top" width="0pt">
24750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24753 \begin_layout Plain Layout
24759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24762 \begin_layout Plain Layout
24770 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24773 \begin_layout Plain Layout
24781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24784 \begin_layout Plain Layout
24785 \begin_inset Formula $A\sgn(x)+B$
24795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24798 \begin_layout Plain Layout
24802 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24813 \begin_layout Plain Layout
24814 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24830 \begin_layout Standard
24831 The first method is more suitable when the self-defined function should
24832 be used several times.
24835 \begin_layout Subsection
24840 \begin_layout Plain Layout
24849 \begin_layout Standard
24850 For limits there are defined besides
24860 \begin_layout Plain Layout
24880 furthermore the following functions:
24883 \begin_layout Standard
24885 \begin_inset Tabular
24886 <lyxtabular version="3" rows="5" columns="2">
24888 <column alignment="center" valignment="top" width="0">
24889 <column alignment="center" valignment="top" width="0">
24891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24900 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24903 \begin_layout Plain Layout
24905 \begin_inset Note Note
24908 \begin_layout Plain Layout
24915 is only used as spacer.
24927 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24930 \begin_layout Plain Layout
24938 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24941 \begin_layout Plain Layout
24942 \begin_inset Formula $\varliminf$
24952 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24955 \begin_layout Plain Layout
24963 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24966 \begin_layout Plain Layout
24967 \begin_inset Formula $\varlimsup$
24977 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24991 \begin_layout Plain Layout
24992 \begin_inset Formula $\varprojlim$
25002 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25005 \begin_layout Plain Layout
25013 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25016 \begin_layout Plain Layout
25017 \begin_inset Formula $\varinjlim$
25021 \begin_inset Formula $\raisebox{-2.5mm}{}$
25037 \begin_layout Standard
25038 \begin_inset VSpace medskip
25041 The limit is created by inserting a subscript.
25042 It is set right beside the function in an inline formula:
25045 \begin_layout Standard
25047 \begin_inset Tabular
25048 <lyxtabular version="3" rows="2" columns="2">
25050 <column alignment="center" valignment="top" width="0pt">
25051 <column alignment="center" valignment="top" width="0pt">
25053 <cell alignment="center" valignment="top" usebox="none">
25056 \begin_layout Plain Layout
25062 <cell alignment="center" valignment="top" usebox="none">
25065 \begin_layout Plain Layout
25066 \begin_inset space \hspace{}
25071 \begin_inset Note Note
25074 \begin_layout Plain Layout
25087 are used here as spacer.
25099 <cell alignment="center" valignment="top" usebox="none">
25102 \begin_layout Plain Layout
25111 \begin_layout Plain Layout
25124 \begin_layout Plain Layout
25138 <cell alignment="center" valignment="top" usebox="none">
25141 \begin_layout Plain Layout
25142 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25158 \begin_layout Standard
25159 In a displayed formula the limit is set below the formula, as usual:
25160 \begin_inset Formula \[
25168 \begin_layout Subsection
25173 \begin_layout Plain Layout
25174 Functions ! modulo-
25182 \begin_layout Standard
25183 The modulo-function is special, because it exists in four variants.
25186 \begin_layout Standard
25187 The variants in a displayed formula:
25188 \begin_inset Formula \begin{align*}
25189 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25190 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25191 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25192 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25193 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25200 \begin_layout Standard
25201 In an inline formula less space is set before the function names for all
25205 \begin_layout Section
25210 \begin_layout Plain Layout
25219 \begin_layout Subsection
25220 Special Characters in Mathematical Text
25223 \begin_layout Standard
25224 The following commands can only be used in mathematical text or in TeX-mode:
25227 \begin_layout Standard
25228 \begin_inset space \hfill{}
25232 \begin_inset Tabular
25233 <lyxtabular version="3" rows="8" columns="2">
25235 <column alignment="block" valignment="top" width="0">
25236 <column alignment="block" valignment="top" width="0">
25238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25241 \begin_layout Plain Layout
25247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25261 \begin_layout Plain Layout
25269 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25272 \begin_layout Plain Layout
25273 \begin_inset Formula $\textrm{œ}$
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25286 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25297 \begin_layout Plain Layout
25298 \begin_inset Formula $\textrm{Œ}$
25308 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25311 \begin_layout Plain Layout
25319 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25322 \begin_layout Plain Layout
25323 \begin_inset Formula $\textrm{æ}$
25333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25336 \begin_layout Plain Layout
25344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25347 \begin_layout Plain Layout
25348 \begin_inset Formula $\textrm{Æ}$
25358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25361 \begin_layout Plain Layout
25369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25372 \begin_layout Plain Layout
25373 \begin_inset Formula $\textrm{\aa}$
25383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25386 \begin_layout Plain Layout
25393 \begin_layout Plain Layout
25400 \begin_layout Plain Layout
25421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25424 \begin_layout Plain Layout
25425 \begin_inset Formula $\textrm{Å}$
25435 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25438 \begin_layout Plain Layout
25446 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25449 \begin_layout Plain Layout
25450 \begin_inset Formula $\textrm{ı}$
25464 \begin_inset space \hfill{}
25468 \begin_inset Tabular
25469 <lyxtabular version="3" rows="8" columns="2">
25471 <column alignment="block" valignment="top" width="0">
25472 <column alignment="center" valignment="top" width="0">
25474 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25477 \begin_layout Plain Layout
25479 \begin_inset Note Note
25482 \begin_layout Plain Layout
25489 is used for separation, because otherwise the output will be ¡ and ¿ respective
25500 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25503 \begin_layout Plain Layout
25511 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25514 \begin_layout Plain Layout
25522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25525 \begin_layout Plain Layout
25526 \begin_inset Formula $\textrm{ø}$
25536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25539 \begin_layout Plain Layout
25547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25550 \begin_layout Plain Layout
25551 \begin_inset Formula $\textrm{Ø}$
25561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25564 \begin_layout Plain Layout
25572 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25575 \begin_layout Plain Layout
25576 \begin_inset Formula $\textrm{ł}$
25586 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25589 \begin_layout Plain Layout
25597 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25600 \begin_layout Plain Layout
25601 \begin_inset Formula $\textrm{Ł}$
25611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25614 \begin_layout Plain Layout
25616 \begin_inset space \hspace{}
25624 \begin_layout Plain Layout
25638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25641 \begin_layout Plain Layout
25642 \begin_inset Formula $\textrm{!`}$
25652 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25655 \begin_layout Plain Layout
25657 \begin_inset space \hspace{}
25665 \begin_layout Plain Layout
25679 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25682 \begin_layout Plain Layout
25683 \begin_inset Formula $\textrm{?`}$
25693 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25696 \begin_layout Plain Layout
25704 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25707 \begin_layout Plain Layout
25708 \begin_inset Formula $\textrm{ȷ}$
25722 \begin_inset space \hfill{}
25728 \begin_layout Standard
25730 \begin_inset Formula $\textrm{\textrm{Å}}$
25734 \begin_inset Formula $\textrm{\textrm{Ø}}$
25737 can also be inserted via the math toolbar button
25738 \begin_inset Graphics
25739 filename ../images/math/digamma.png
25747 \begin_layout Standard
25748 An exception are the commands
25751 \begin_inset space \hspace{}
25760 \begin_inset space \hspace{}
25766 , because they can be inserted in LyX directly to text.
25769 \begin_layout Subsection
25771 \begin_inset CommandInset label
25773 name "sub:Accents-in-Text"
25781 \begin_layout Plain Layout
25790 \begin_layout Standard
25791 With the following commands all letters can be accented.
25792 The commands must be inserted in TeX-mode.
25795 \begin_layout Standard
25796 \begin_inset space \hfill{}
25800 \begin_inset Tabular
25801 <lyxtabular version="3" rows="8" columns="2">
25803 <column alignment="block" valignment="top" width="0">
25804 <column alignment="block" valignment="top" width="0">
25806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25809 \begin_layout Plain Layout
25815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25818 \begin_layout Plain Layout
25826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25829 \begin_layout Plain Layout
25833 \begin_inset Quotes grd
25841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25848 \begin_layout Plain Layout
25864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25867 \begin_layout Plain Layout
25875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25878 \begin_layout Plain Layout
25882 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25901 \begin_layout Plain Layout
25908 \begin_layout Plain Layout
25922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25925 \begin_layout Plain Layout
25929 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25948 \begin_layout Plain Layout
25956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25959 \begin_layout Plain Layout
25963 \begin_layout Plain Layout
25979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25982 \begin_layout Plain Layout
25989 \begin_layout Plain Layout
26003 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26006 \begin_layout Plain Layout
26010 \begin_layout Plain Layout
26026 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26029 \begin_layout Plain Layout
26036 \begin_layout Plain Layout
26050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26053 \begin_layout Plain Layout
26057 \begin_layout Plain Layout
26073 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26076 \begin_layout Plain Layout
26083 \begin_layout Plain Layout
26097 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26100 \begin_layout Plain Layout
26104 \begin_layout Plain Layout
26124 \begin_inset space \hfill{}
26128 \begin_inset Tabular
26129 <lyxtabular version="3" rows="8" columns="2">
26131 <column alignment="block" valignment="top" width="0">
26132 <column alignment="center" valignment="top" width="0">
26134 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26137 \begin_layout Plain Layout
26143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26146 \begin_layout Plain Layout
26154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26157 \begin_layout Plain Layout
26164 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26185 \begin_layout Plain Layout
26201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26204 \begin_layout Plain Layout
26212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26215 \begin_layout Plain Layout
26219 \begin_layout Plain Layout
26235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26238 \begin_layout Plain Layout
26245 \begin_layout Plain Layout
26256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26259 \begin_layout Plain Layout
26263 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26282 \begin_layout Plain Layout
26290 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26293 \begin_layout Plain Layout
26297 \begin_layout Plain Layout
26313 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26316 \begin_layout Plain Layout
26323 \begin_layout Plain Layout
26337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26340 \begin_layout Plain Layout
26344 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26363 \begin_layout Plain Layout
26370 \begin_layout Plain Layout
26384 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26387 \begin_layout Plain Layout
26391 \begin_layout Plain Layout
26407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26410 \begin_layout Plain Layout
26417 \begin_layout Plain Layout
26431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26434 \begin_layout Plain Layout
26438 \begin_layout Plain Layout
26458 \begin_inset space \hfill{}
26464 \begin_layout Standard
26465 \begin_inset VSpace medskip
26474 also two different characters can be accented.
26483 \begin_layout Plain Layout
26498 \begin_layout Plain Layout
26510 \begin_layout Standard
26523 can in combination with vowels directly be inserted with the keyboard without
26525 The same applies for the tilde
26529 \begin_layout Plain Layout
26530 This only applies for keyboards where the tilde is defined as accent.
26539 in combination with
26554 \begin_layout Standard
26597 , and accents inserted directly with the keyboard are also available in
26599 For the other accents there are special math commands to be used in formulas,
26601 \begin_inset CommandInset ref
26603 reference "sub:Accents-for-one"
26610 \begin_layout Standard
26611 \begin_inset VSpace bigskip
26614 Furthermore, with the command
26624 \begin_layout Plain Layout
26632 all numbers and letters can be set into a circle, quasi accented with a
26633 circle, similar to the the copyright symbol.
26636 \begin_layout Standard
26638 \begin_inset Tabular
26639 <lyxtabular version="3" rows="3" columns="2">
26641 <column alignment="center" valignment="top" width="0">
26642 <column alignment="center" valignment="top" width="0">
26644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26647 \begin_layout Plain Layout
26653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26656 \begin_layout Plain Layout
26658 \begin_inset Note Note
26661 \begin_layout Plain Layout
26668 is only used as spacer.
26680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26683 \begin_layout Plain Layout
26691 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26694 \begin_layout Plain Layout
26698 \begin_layout Plain Layout
26714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26717 \begin_layout Plain Layout
26728 raisebox{-1.5pt}{W}}
26733 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26736 \begin_layout Plain Layout
26737 \begin_inset Formula $\raisebox{4.5mm}{}$
26744 \begin_layout Plain Layout
26762 \begin_inset Formula $\raisebox{-2mm}{}$
26778 \begin_layout Standard
26779 One has to take care that the character fits in the circle.
26790 \begin_layout Plain Layout
26792 \begin_inset CommandInset ref
26794 reference "sub:Font-Sizes"
26803 specifies thereby the size of the circle.
26814 \begin_layout Plain Layout
26816 \begin_inset CommandInset ref
26818 reference "sub:Boxes-without-Frame"
26827 the character can be centered.
26830 \begin_layout Subsection
26835 \begin_layout Plain Layout
26844 \begin_layout Standard
26845 Minuscule numbers are created with the command
26855 \begin_layout Plain Layout
26864 The command can be used in formulas and in TeX-mode.
26865 The command scheme is:
26868 \begin_layout Standard
26873 oldstylenums{number}
26876 \begin_layout Standard
26881 oldstylenums{0123456789
26884 \begin_inset Formula $\oldstylenums{0123456789}$
26890 \begin_layout Subsection
26891 Miscellaneous special Characters
26892 \begin_inset CommandInset label
26894 name "sub:Miscellaneous-special-Characters"
26902 \begin_layout Plain Layout
26903 Special characters ! miscellaneous
26911 \begin_layout Standard
26912 The following characters can only be inserted to formulas by using commands:
26915 \begin_layout Standard
26917 \begin_inset Tabular
26918 <lyxtabular version="3" rows="4" columns="2">
26920 <column alignment="center" valignment="top" width="0">
26921 <column alignment="center" valignment="top" width="0">
26923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26926 \begin_layout Plain Layout
26932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26935 \begin_layout Plain Layout
26943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26946 \begin_layout Plain Layout
26953 \begin_layout Plain Layout
26967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26971 \begin_inset Formula $\mathcircumflex$
26981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26984 \begin_layout Plain Layout
26992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26995 \begin_layout Plain Layout
26996 \begin_inset Formula $\_$
27006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27009 \begin_layout Plain Layout
27014 \begin_layout Plain Layout
27029 \begin_layout Plain Layout
27040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27043 \begin_layout Plain Layout
27044 \begin_inset Formula $^{\circ}$
27060 \begin_layout Standard
27061 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27062 contains the following line
27066 \begin_layout Plain Layout
27067 More about this is described in
27068 \begin_inset CommandInset ref
27070 reference "sub:Text-Characters-in"
27082 \begin_layout Standard
27087 DeclareInputtext{176}{
27100 \begin_layout Section
27102 \begin_inset CommandInset label
27104 name "sec:Formula-Styles"
27112 \begin_layout Plain Layout
27121 \begin_layout Itemize
27122 There are two different alignment styles:
27126 \begin_layout Description
27127 Centered is the predefined standard
27130 \begin_layout Description
27131 Indented for this the option
27135 must be inserted in the menu
27137 Document\SpecialChar \menuseparator
27143 \begin_inset space ~
27149 \begin_layout Standard
27154 is used, the indentation can be adjusted with the length
27164 \begin_layout Plain Layout
27173 Should the distance be 15
27174 \begin_inset space \thinspace{}
27177 mm, the following command line is inserted in the LaTeX-preamble
27180 \begin_layout Standard
27190 \begin_layout Standard
27191 When no length is specified, the predefined value of 30
27192 \begin_inset space \thinspace{}
27199 \begin_layout Itemize
27200 And two different numbering styles:
27204 \begin_layout Description
27205 Right is the predefined standard
27208 \begin_layout Description
27209 Left for this the option
27213 must be inserted in the menu
27215 Document\SpecialChar \menuseparator
27221 \begin_inset space ~
27228 \begin_layout Standard
27237 can also be used together.
27238 In this case both options are inserted, separated by a comma.
27241 \begin_layout Standard
27242 The chosen styles are used for all displayed formulas of the document.
27243 When both, centered and indented formulas should be created in a document,
27249 The indented formulas are then set in a flalign environment, see
27250 \begin_inset CommandInset ref
27252 reference "sub:Flalign-Environment"
27259 \begin_layout Section
27261 \begin_inset CommandInset label
27263 name "sec:Multiline-Formulas"
27271 \begin_layout Plain Layout
27272 Formula ! multiline
27280 \begin_layout Subsection
27284 \begin_layout Standard
27285 In LyX multiline formulas are created by pressing
27292 This creates either an
27294 eqnarray environment
27296 that is described in
27297 \begin_inset CommandInset ref
27299 reference "sub:Eqnarray-Environment"
27303 or, when the option
27305 Use AMS math package
27307 in the document settings is selected, an
27311 that is described in
27312 \begin_inset CommandInset ref
27314 reference "sub:Standard-align-Environment"
27321 \begin_layout Standard
27322 There are other multiline formula environments that can be created via the
27325 Insert\SpecialChar \menuseparator
27329 These environments are described in the following sections.
27332 \begin_layout Standard
27333 In all multiline formula environments a new line is created by pressing
27339 To add or delete lines, the math toolbar buttons
27340 \begin_inset Graphics
27341 filename ../images/tabular-feature_append-row.png
27347 \begin_inset Graphics
27348 filename ../images/tabular-feature_delete-row.png
27353 , respectively, or the menu
27355 Edit\SpecialChar \menuseparator
27361 \begin_layout Subsubsection
27363 \begin_inset CommandInset label
27365 name "sub:Line-Separation"
27373 \begin_layout Plain Layout
27374 Formula ! multiline ! Line separation
27382 \begin_layout Standard
27383 There is sometimes not enough space in multiline formulas between the lines:
27384 \begin_inset Formula \begin{eqnarray*}
27385 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}\\
27386 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*}
27393 \begin_layout Standard
27394 In LaTeX additional line space is specified as optional argument of the
27396 This is not yet possible in LyX
27400 \begin_layout Plain Layout
27402 \begin_inset CommandInset href
27404 name "LyX-bug #1505"
27405 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27414 , therefore the whole formula must be inserted in TeX-mode.
27415 To add in our example space, the command
27423 is inserted at the end of the first line.
27428 \begin_layout Plain Layout
27435 \begin_layout Plain Layout
27437 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27440 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27447 \begin_layout Plain Layout
27451 left(B^{2}+x_{0}^{2}
27459 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27464 \begin_layout Plain Layout
27476 \begin_layout Standard
27477 \begin_inset VSpace bigskip
27480 To set the the line separation for all lines in a formula, the length
27490 \begin_layout Plain Layout
27500 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27511 \begin_inset space \thinspace{}
27516 \begin_inset space \thinspace{}
27519 mm additional line separation as in the previous example, the command
27522 \begin_layout Standard
27532 \begin_layout Standard
27533 is inserted in TeX-mode before the formula.
27534 This requires that the LaTeX-package
27542 \begin_layout Plain Layout
27547 is part of every LaTeX standard installation.
27556 \begin_layout Plain Layout
27562 was loaded in LaTeX-preamble with the line
27565 \begin_layout Standard
27573 \begin_layout Standard
27578 \begin_layout Plain Layout
27590 \begin_inset Formula \begin{eqnarray*}
27591 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}\\
27592 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*}
27599 \begin_layout Standard
27603 \begin_layout Plain Layout
27614 To get back to the predefined distance,
27620 is set to the value 3
27621 \begin_inset space \thinspace{}
27627 \begin_layout Subsubsection
27629 \begin_inset CommandInset label
27631 name "sub:Column-Separation"
27639 \begin_layout Plain Layout
27640 Formula ! multiline ! Column separation
27648 \begin_layout Standard
27649 Multiline formulas form a matrix.
27650 A formula in the eqnarray environment is for example a matrix with three
27652 By changing the column separation in this environment, the space beside
27653 the relation sign can be changed.
27656 \begin_layout Standard
27657 The column separation is specified with the length
27667 \begin_layout Plain Layout
27676 \begin_inset Newline newline
27679 column separation = 2
27680 \begin_inset space \thinspace{}
27690 \begin_inset Newline newline
27696 \begin_layout Standard
27706 \begin_layout Standard
27707 inserted in TeX-mode, sets for all following formulas a column separation
27709 \begin_inset space \thinspace{}
27713 To get back to the predefined distance,
27720 \begin_inset space \thinspace{}
27726 \begin_layout Standard
27728 \begin_inset space \thinspace{}
27731 cm column separation:
27735 \begin_layout Plain Layout
27747 \begin_inset Formula \begin{eqnarray*}
27749 C & \ne & A\end{eqnarray*}
27753 A formula with the predefined column separation for matrices of 10
27754 \begin_inset space \thinspace{}
27761 \begin_layout Plain Layout
27773 \begin_inset Formula \begin{eqnarray*}
27775 C & \ne & A\end{eqnarray*}
27782 \begin_layout Subsubsection
27787 \begin_layout Plain Layout
27796 \begin_layout Standard
27797 Long formulas can be typeset using these methods:
27800 \begin_layout Itemize
27801 When one side of the equation is much shorther than the line width, this
27802 one is chosen for the left side and the right side is typeset over two
27807 \begin_layout Plain Layout
27817 \begin_inset Formula \begin{eqnarray}
27818 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 \\
27819 & & -\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}
27827 \begin_layout Plain Layout
27837 \begin_inset Newline newline
27840 The minus sign at the beginning of the second line does normally not appear
27841 as operator because it is the first character of the line.
27842 Thus it would not be surrounded by space and could not be distinguished
27843 from the fraction bar.
27844 To avoid this, space was inserted behind the minus sign with the command
27855 \begin_layout Plain Layout
27863 \begin_inset CommandInset ref
27865 reference "sub:Variable-Space"
27878 \begin_layout Plain Layout
27889 \begin_layout Itemize
27890 When both sides of the equation are too long, the command
27900 \begin_layout Plain Layout
27909 It is inserted to the first column of the first line and effects that all
27910 further insertions overwrite the following columns:
27914 \begin_layout Plain Layout
27924 \begin_inset Formula \begin{eqnarray}
27925 \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 \\
27926 & & -\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 \\
27927 & & =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}
27935 \begin_layout Plain Layout
27945 \begin_inset Newline newline
27948 After the insertion of
27954 , the cursor is in a purple box that is a bit shifted to the left from the
27956 In this the formula is inserted.
27960 \begin_layout Plain Layout
27970 \begin_inset Newline newline
27973 The content of the further lines is inserted to the second or another formula
27975 The greater the column number where it was inserted, the larger the indentation.
27979 \begin_layout Plain Layout
27989 \begin_inset Newline newline
27993 \begin_inset Note Greyedout
27996 \begin_layout Plain Layout
27997 Note the following when using
28006 \begin_layout Itemize
28007 The formula doesn't use the full page width.
28009 \begin_inset space \thinspace{}
28013 \begin_inset space ~
28017 \begin_inset Formula $-B^{2}$
28020 is added to the first line in the above example, it would have been outside
28022 To better use the width, negative space can be inserted at the beginning
28026 \begin_layout Itemize
28027 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28032 \begin_layout Plain Layout
28033 \begin_inset CommandInset href
28035 name "LyX-bug #1429"
28036 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28045 One can only set the cursor at the beginning of the line and move it with
28054 \begin_layout Itemize
28055 Other methods to set long formulas are offered by the environments described
28057 \begin_inset CommandInset ref
28059 reference "sub:Multline-Environment"
28064 \begin_inset CommandInset ref
28066 reference "sub:Multiline-Formula-Parts"
28073 \begin_layout Subsubsection
28075 \begin_inset CommandInset label
28077 name "sub:Multiline-Brackets"
28085 \begin_layout Plain Layout
28086 Brackets ! for multiline expressions
28094 \begin_layout Standard
28095 For brackets spanning multiple lines the following problem occurs:
28096 \begin_inset Formula \begin{eqnarray*}
28097 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28098 & & \left.\cdots+B-D\right]\end{eqnarray*}
28105 \begin_layout Standard
28106 The closing bracket is smaller than the opening bracket because brackets
28107 with variable size may not span multiple lines.
28110 \begin_layout Standard
28111 To set the bracket size for the second line correctly, the first line is
28122 \begin_layout Plain Layout
28130 and the second line with
28138 \begin_layout Plain Layout
28152 \begin_inset CommandInset ref
28154 reference "sub:Automatic-Bracket-Size"
28169 \begin_layout Plain Layout
28195 \begin_layout Plain Layout
28214 \begin_layout Plain Layout
28233 \begin_layout Plain Layout
28245 \begin_inset Formula $\downarrow$
28254 \begin_layout Plain Layout
28262 is inserted, because the multiplication operator with its limits is the
28263 largest symbol in the first line and this should be the size for the bracket
28264 in the second line.
28267 \begin_layout Standard
28268 The result is this:
28269 \begin_inset Formula \begin{eqnarray*}
28270 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28271 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28278 \begin_layout Subsection
28282 \begin_layout Standard
28283 Align environments can be used for every kind of multiline formulas.
28284 They are specially useful to set several formulas side by side.
28287 \begin_layout Standard
28288 Align environments consist of columns.
28289 The odd columns are right aligned, the even ones left aligned.
28290 Every line in an Align environment can be numbered.
28293 \begin_layout Standard
28294 Align environments are created via the menu
28296 Insert\SpecialChar \menuseparator
28302 Edit\SpecialChar \menuseparator
28303 Math\SpecialChar \menuseparator
28304 Change Formula Type
28306 already existing formulas can be converted to Align environments.
28309 \begin_layout Standard
28310 To add or delete columns, the math toolbar buttons
28311 \begin_inset Graphics
28312 filename ../images/tabular-feature_append-column.png
28318 \begin_inset Graphics
28319 filename ../images/tabular-feature_delete-column.png
28324 , respectively, or the menu
28326 Edit\SpecialChar \menuseparator
28332 \begin_layout Subsubsection
28333 Standard align Environment
28334 \begin_inset CommandInset label
28336 name "sub:Standard-align-Environment"
28344 \begin_layout Plain Layout
28345 Formula ! multiline ! align environment
28353 \begin_layout Standard
28354 This Align environment is created by presssing
28358 in a formula or by the menu
28360 Insert\SpecialChar \menuseparator
28361 Math\SpecialChar \menuseparator
28362 AMS align Environment
28367 \begin_layout Standard
28368 An example for two formulas set side by side, that are created with a four
28369 column align environment:
28370 \begin_inset Formula \begin{align*}
28371 A & =\sin(B) & C & =D\\
28372 C & \ne A & B & \ne D\end{align*}
28376 As it can be seen, the formulas in this environment are placed so as if
28385 \begin_layout Plain Layout
28393 \begin_inset CommandInset ref
28395 reference "sub:Variable-Space"
28406 before the first and after every even column.
28407 When the formula style
28413 \begin_layout Plain Layout
28415 \begin_inset CommandInset ref
28417 reference "sec:Formula-Styles"
28428 is used, the formula is set without the
28434 before the first column.
28437 \begin_layout Subsubsection
28438 Alignat Environment
28442 \begin_layout Plain Layout
28443 Formula ! multiline ! alignat environment
28451 \begin_layout Standard
28452 The alignat environment has no predefined column separation.
28453 It can be inserted manually with the spaces that are described
28454 \begin_inset CommandInset ref
28456 reference "sub:Space"
28463 \begin_layout Standard
28464 The above example in the alignat environment where 1
28465 \begin_inset space \thinspace{}
28468 cm space was inserted at the beginning of the second formula:
28469 \begin_inset Formula \begin{alignat*}{2}
28470 A & =\sin(B) & \hspace{1cm}C & =D\\
28471 C & \ne A & B & \ne D\end{alignat*}
28475 Because the column separation can be set separately for every column, this
28476 environment is especially suitable to set three and more formulas side
28480 \begin_layout Subsubsection
28481 Flalign Environment
28482 \begin_inset CommandInset label
28484 name "sub:Flalign-Environment"
28492 \begin_layout Plain Layout
28493 Formula ! multiline ! flalign environment
28501 \begin_layout Standard
28502 In this environment the first two columns are always set as much as possible
28503 to the left and the last two ones to the right.
28505 \begin_inset Formula \begin{flalign*}
28506 A & =1 & B & =2 & C & =3\\
28507 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28514 \begin_layout Standard
28515 By creating a flalign environment with an odd number of columns where an
28516 empty TeX-brace is inserted to the last column, several formulas in a document
28517 can be set to the left, although the formula style
28522 As example the indented formula
28523 \begin_inset CommandInset ref
28525 reference "eq:VolInt"
28530 \begin_inset Formula \begin{flalign}
28531 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28535 The first two columns contain the formula.
28536 To indent it as with the formula style
28541 \begin_inset space \thinspace{}
28544 pt space was inserted at the beginning of the first column.
28547 \begin_layout Subsection
28548 Eqnarray Environment
28549 \begin_inset CommandInset label
28551 name "sub:Eqnarray-Environment"
28559 \begin_layout Plain Layout
28560 Formula ! multiline ! eqnarray environment
28568 \begin_layout Standard
28569 When this environment has been created, three blue boxes appear.
28570 The content of the first box is right aligned, the content of the last
28572 The content of the middle box appears centered and a bit smaller, because
28573 it is designed to insert there only relation characters.
28574 \begin_inset Formula \begin{eqnarray*}
28575 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28577 A & = & A\end{eqnarray*}
28584 \begin_layout Subsection
28589 \begin_layout Plain Layout
28590 Formula ! multiline ! gather environment
28598 \begin_layout Standard
28599 This environment consists of only one centered column.
28600 Every line can be numbered.
28601 \begin_inset Formula \begin{gather}
28603 X=\textrm{-}1\end{gather}
28610 \begin_layout Subsection
28611 Multline Environment
28612 \begin_inset CommandInset label
28614 name "sub:Multline-Environment"
28622 \begin_layout Plain Layout
28623 Formula ! multiline ! multline environment
28631 \begin_layout Standard
28632 The multline environment consists, like the gather environment, of only
28634 But the first line is left aligned, the last one right aligned.
28635 All other lines are centered.
28636 Therefore this environment is suitable for long formulas.
28638 \begin_inset CommandInset ref
28640 reference "eq:lefteqn"
28644 in the multline environment:
28645 \begin_inset Formula \begin{multline}
28646 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}\\
28647 -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}\\
28648 =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}
28655 \begin_layout Standard
28656 In the output only the last (first) line of a multline environment appears
28657 numbered when the document numbering is right (left).
28661 \begin_layout Plain Layout
28662 numbering styles see
28663 \begin_inset CommandInset ref
28665 reference "sec:Formula-Styles"
28677 \begin_layout Standard
28686 \begin_layout Plain Layout
28704 \begin_layout Plain Layout
28714 a centered line can be right or left aligned, respectively.
28715 The commands are used as follows:
28718 \begin_layout Standard
28723 shoveright{line content}
28729 shoveleft{line content}
28732 \begin_layout Standard
28733 \begin_inset VSpace medskip
28744 \begin_layout Plain Layout
28754 specifies the distance of the first line from the left page margin.
28755 Predefined is the length 0
28756 \begin_inset space \thinspace{}
28762 \begin_layout Standard
28763 As example the above formula where the command
28766 \begin_layout Standard
28776 \begin_layout Standard
28777 was inserted in TeX-mode before:
28781 \begin_layout Plain Layout
28793 \begin_inset Formula \begin{multline}
28794 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}\\
28795 \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}}\\
28796 =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}
28804 \begin_layout Plain Layout
28815 The second line was left aligned using
28824 \begin_layout Subsection
28825 Multiline Formula Parts
28826 \begin_inset CommandInset label
28828 name "sub:Multiline-Formula-Parts"
28836 \begin_layout Plain Layout
28837 Formula ! multiline ! formula parts
28845 \begin_layout Standard
28846 To display only parts of a formula with multiple lines, one of the following
28847 environments are used:
28864 They can be inserted via the menu
28866 Insert\SpecialChar \menuseparator
28869 or by using the commands described in this section.
28872 \begin_layout Standard
28873 The first three have the same properties as the corresponding multiline
28874 formula environments, but it is possible to set further formula parts beside
28877 \begin_inset Formula \[
28878 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28879 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28880 \right\} \textrm{Uncertainty relations}\]
28887 \begin_layout Standard
28888 To get this formula, a displayed formula is created where the command
28896 \begin_layout Plain Layout
28907 A purple box appears around the blue formula box where now columns and
28908 lines can be added.
28909 Outside the multiline environment other formula parts can be set, like
28913 \begin_layout Standard
28914 The aligned environment is also suitable for long formulas whose lines are
28915 horizontally aligned.
28916 Using aligned in a displayed formula has the advantage that the formula
28917 number is vertically centered behind the lines.
28919 \begin_inset CommandInset ref
28921 reference "eq:kurzlang"
28925 in the aligned environment:
28926 \begin_inset Formula \begin{equation}
28927 \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}|}\\
28928 & -\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}
28936 \begin_layout Standard
28937 To use the environments
28959 \begin_layout Plain Layout
28977 \begin_layout Plain Layout
28995 \begin_layout Plain Layout
29003 are inserted, respectively.
29004 The split environment has the same properties as the aligned environment
29005 but it can only have two columns.
29008 \begin_layout Subsection
29009 Text in multiline Formulas
29010 \begin_inset CommandInset label
29012 name "sub:Text-in-multiline"
29020 \begin_layout Plain Layout
29030 \begin_layout Plain Layout
29031 Formula ! multiline ! text
29039 \begin_layout Standard
29040 In the Align environments, and the multline and gather environment, text
29041 can be inserted that will appear in a separate line and doesn't affect
29042 the column alignment.
29043 To do this, the command
29051 \begin_layout Plain Layout
29061 is used in the following scheme:
29064 \begin_layout Standard
29072 \begin_layout Standard
29073 The text should not be longer than a line because it cannot be hyphenated.
29074 As LyX doesn't yet support
29080 directly, the text is written as mathematical text.
29087 must hereby be at the beginning of a line and appears in the output above
29089 An example where the text was inserted at the beginning of the second line:
29090 \begin_inset Formula \begin{align}
29091 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29092 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29099 \begin_layout Section
29104 \begin_layout Plain Layout
29114 \begin_layout Plain Layout
29115 Formula ! numbering|see
29119 \begin_layout Plain Layout
29130 \begin_layout Plain Layout
29145 \begin_layout Subsection
29149 \begin_layout Standard
29150 Numbered formulas can be created with the menu
29152 Insert\SpecialChar \menuseparator
29153 Math\SpecialChar \menuseparator
29155 \begin_inset space ~
29163 \begin_inset space ~
29169 Existing formulas can be numbered with the menu
29171 Edit\SpecialChar \menuseparator
29172 Math\SpecialChar \menuseparator
29174 \begin_inset space ~
29182 \begin_inset space ~
29188 The formula number is displayed in LyX behind the formula as number sign
29190 The number sign is replaced in the output by the formula number.
29193 \begin_layout Standard
29194 When numbering is turned on in multiline formulas, all lines will be numbered.
29195 But the numbering can be controlled with the menu
29197 Edit\SpecialChar \menuseparator
29198 Math\SpecialChar \menuseparator
29200 \begin_inset space ~
29204 \begin_inset space ~
29208 \begin_inset space ~
29216 \begin_inset space ~
29224 \begin_layout Standard
29225 Except of inline formulas, all formulas can be numbered with two different
29227 \begin_inset CommandInset ref
29229 reference "sec:Formula-Styles"
29236 \begin_layout Subsection
29238 \begin_inset CommandInset label
29240 name "sub:Cross-References"
29248 \begin_layout Plain Layout
29249 Cross-references ! to formulas
29257 \begin_layout Standard
29258 All labeled formulas can be cross-referenced.
29259 A label is added by the menu
29261 Insert\SpecialChar \menuseparator
29264 or the toolbar button
29265 \begin_inset Graphics
29266 filename ../images/label-insert.png
29272 The cursor must hereby be inside a displayed formula.
29273 A dialog pops up displaying the prefix
29278 The label is inserted there behind the prefix.
29279 The predefined prefix means
29280 \begin_inset Quotes eld
29284 \begin_inset Quotes erd
29287 and makes it easier to find labels in large documents because it marks
29288 it as formula label to divide it from e.
29289 \begin_inset space \thinspace{}
29293 \begin_inset space ~
29297 To change a label, the menu
29299 Insert\SpecialChar \menuseparator
29305 \begin_layout Standard
29306 The name of the label is displayed in LyX within two parentheses behind
29308 A formula with a label is always numbered.
29311 \begin_layout Standard
29312 Cross-references are inserted via the menu
29314 Insert\SpecialChar \menuseparator
29317 or with the toolbar button
29318 \begin_inset Graphics
29319 filename ../images/dialog-show-new-inset_ref.png
29325 A formula cross-reference appears in the output as formula number.
29326 When in the cross-reference dialog window the format
29330 is chosen, the cross-reference appears in the output as formula number
29332 \begin_inset Newline newline
29335 By right-clicking on a cross-reference in LyX, one jumps to the formula
29336 that is referenced.
29339 \begin_layout Standard
29340 Here are as examples cross-references to formulas of the following subsections:
29341 \begin_inset Note Note
29344 \begin_layout Plain Layout
29345 Note the different cross-reference types.
29353 \begin_layout Standard
29355 \begin_inset CommandInset ref
29362 \begin_inset CommandInset ref
29370 \begin_inset CommandInset ref
29376 ) big Latin letters are used for the numbering in contrary to (
29377 \begin_inset CommandInset ref
29386 \begin_layout Standard
29387 \begin_inset VSpace medskip
29390 When the argument of
29398 \begin_layout Plain Layout
29406 \begin_inset CommandInset ref
29408 reference "sub:User-defined-Numbering"
29419 contains a box like in
29420 \begin_inset CommandInset ref
29422 reference "sub:Paragraph-Boxes"
29426 , the formula cannot be referenced.
29429 \begin_layout Subsection
29434 \begin_layout Plain Layout
29435 Formula numbering ! subnumbering
29443 \begin_layout Standard
29444 With the help of the commands
29448 begin{subequations}
29456 formulas can be subnumbered.
29457 Both commands are inserted in TeX-mode.
29460 \begin_layout Standard
29462 \begin_inset Formula \begin{equation}
29463 A=C-B\label{eq:a}\end{equation}
29471 \begin_layout Plain Layout
29475 addtocounter{equation}{-1}
29484 \begin_layout Plain Layout
29488 begin{subequations}
29494 \begin_inset VSpace -5mm
29498 \begin_inset Formula \begin{equation}
29499 B=C-A\label{eq:b}\end{equation}
29504 \begin_inset Formula \begin{equation}
29505 C=A+B\label{eq:c}\end{equation}
29512 \begin_layout Standard
29516 \begin_layout Plain Layout
29528 \begin_layout Standard
29529 To create the example, the following is done:
29532 \begin_layout Enumerate
29533 first formula is inserted
29536 \begin_layout Enumerate
29541 addtocounter{equation}{-1}
29543 begin{subequations}
29547 \begin_layout Plain Layout
29556 \begin_inset Newline newline
29561 is inserted after the first formula
29564 \begin_layout Enumerate
29565 second formula is inserted
29568 \begin_layout Enumerate
29569 third formula is inserted
29572 \begin_layout Enumerate
29579 is inserted after the third formula
29582 \begin_layout Standard
29583 Every formula between the commands
29595 is subnumbered as a, b,
29596 \begin_inset Newline linebreak
29599 c, \SpecialChar \ldots{}
29600 For multiline formulas every line will be subnumbered.
29601 All subnumbered formulas are treated as
29606 But as every numbered formula increases the counter
29610 by one, the command
29616 is needed to decrease it.
29617 Otherwise the formulas
29618 \begin_inset CommandInset ref
29625 \begin_inset CommandInset ref
29632 \begin_inset CommandInset ref
29638 would be numbered as
29639 \begin_inset CommandInset ref
29646 \begin_inset CommandInset ref
29653 \begin_inset CommandInset ref
29662 \begin_layout Standard
29663 By inserting the commands in TeX-mode, a space is created between the first
29666 \begin_inset space \thinspace{}
29669 mm vertical space is inserted after the command
29673 begin{subequations}
29676 When the formula style
29682 \begin_layout Plain Layout
29684 \begin_inset CommandInset ref
29686 reference "sec:Formula-Styles"
29698 \begin_inset space \thinspace{}
29701 mm space is inserted instead.
29704 \begin_layout Standard
29705 Here is an example for a multiline formula where the numbering was turned
29706 off for the second line:
29710 \begin_layout Plain Layout
29714 begin{subequations}
29720 \begin_inset Formula \begin{eqnarray}
29721 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29722 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29723 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29731 \begin_layout Plain Layout
29743 \begin_layout Subsection
29744 User-defined Numbering
29745 \begin_inset CommandInset label
29747 name "sub:User-defined-Numbering"
29755 \begin_layout Plain Layout
29756 Formula numbering ! user-defined
29764 \begin_layout Standard
29768 \begin_layout Plain Layout
29769 Formula numbering ! self-defined delimiters
29774 With the standard numbering parentheses are set around the formula number.
29775 To replace the parentheses for example by vertical bars, the following
29776 line is added to the LaTeX-preamble:
29779 \begin_layout Standard
29791 \begin_inset Note Note
29794 \begin_layout Plain Layout
29795 This macro is already declared in the LaTeX-preamble for testing.
29796 To activate it, remove the percent sign at the beginning.
29804 \begin_layout Standard
29805 To use other characters, the vertical bars besides the
29809 are replaced by one ore more characters.
29810 To get only the formula number the vertical bars are omitted.
29813 \begin_layout Standard
29814 \begin_inset VSpace bigskip
29817 When there should be an expression of your choice instead of the consecutive
29818 formula number in parentheses behind the formula, the command
29828 \begin_layout Plain Layout
29837 \begin_inset Formula \begin{equation}
29838 A+B=C\tag{something}\label{eq:tag}\end{equation}
29842 In this example the command
29850 \begin_layout Plain Layout
29861 was inserted to the formula.
29864 \begin_layout Standard
29873 \begin_layout Plain Layout
29884 is inserted instead, the star prevents the parentheses around the expression:
29885 \begin_inset Formula \[
29886 A+B=C\tag*{something}\]
29893 \begin_layout Standard
29894 \begin_inset VSpace bigskip
29897 To restart the formula numbering with new document parts or sections, the
29898 following command is used:
29901 \begin_layout Standard
29906 @addtoreset{equation}{part}
29912 \begin_layout Plain Layout
29917 \begin_layout Plain Layout
29928 \begin_layout Plain Layout
29941 \begin_layout Plain Layout
29952 \begin_layout Plain Layout
29965 \begin_inset Newline newline
29969 \begin_inset Newline newline
29976 @addtoreset{equation}{section}
29979 \begin_layout Standard
29980 To be able to use these commands in TeX-mode, the
29981 \begin_inset Quotes eld
29985 \begin_inset Quotes erd
29988 character has to be made
29989 \begin_inset Quotes eld
29993 \begin_inset Quotes erd
29996 for LaTeX using the command
30010 So the command sequence in TeX-mode is:
30013 \begin_layout Standard
30019 \begin_inset Newline newline
30024 @addtoreset{equation}{section}
30025 \begin_inset Newline newline
30033 \begin_layout Standard
30034 In the LaTeX-preamble
30046 can be omitted as they are automatically internally inserted by LyX.
30049 \begin_layout Standard
30064 \begin_layout Plain Layout
30069 is part of the LaTeX-package
30077 \begin_layout Plain Layout
30078 Packages ! carlisle
30083 that is part of every LaTeX standard installation.
30092 \begin_layout Plain Layout
30093 Packages ! remreset
30098 has to be loaded in the LaTeX-preamble with the line
30101 \begin_layout Standard
30106 usepackage{remreset}
30109 \begin_layout Standard
30120 \begin_layout Plain Layout
30125 \begin_layout Plain Layout
30136 \begin_layout Plain Layout
30149 \begin_layout Plain Layout
30160 \begin_layout Plain Layout
30172 can be used with the same scheme as
30181 \begin_layout Standard
30182 \begin_inset VSpace bigskip
30185 Sometimes formulas should be numbered in the following form:
30188 \begin_layout Standard
30191 (section number.formula number)
30194 \begin_layout Standard
30195 The formula number should start with every section with
30196 \begin_inset Quotes eld
30200 \begin_inset Quotes erd
30206 \begin_layout Standard
30207 For this case there is the command
30217 \begin_layout Plain Layout
30225 , which is used with the following scheme:
30228 \begin_layout Standard
30233 numberwithin{counter}{sectioning}
30236 \begin_layout Standard
30237 Counter denotes what kind of numbering is affected, sectioning denotes what
30238 number is before the dot.
30241 \begin_layout Standard
30242 Thus in our case the following LaTeX-preamble or TeX-Code line is used:
30245 \begin_layout Standard
30250 numberwithin{equation}{section}
30253 \begin_layout Standard
30254 This is the result:
30258 \begin_layout Plain Layout
30262 numberwithin{equation}{section}
30268 \begin_inset Formula \begin{equation}
30269 A+B=C\end{equation}
30276 \begin_layout Standard
30278 \begin_inset space \thinspace{}
30282 \begin_inset space ~
30285 tables so that the number of the part is the sectioning,
30286 \begin_inset Newline newline
30293 numberwithin{table}{part}
30298 \begin_layout Standard
30299 To go back to the standard numbering or to prevent this kind of numbering
30300 when it is defined by the document class, the following command is inserted
30301 as TeX-Code or to the LaTeX-preamble:
30304 \begin_layout Standard
30317 \begin_layout Plain Layout
30331 \begin_layout Plain Layout
30347 \begin_inset Newline newline
30355 \begin_inset Newline newline
30367 \begin_layout Standard
30374 uses internally the command
30380 , described above, that also needs to be reverted.
30384 \begin_layout Plain Layout
30391 \begin_layout Plain Layout
30395 @removefromreset{equation}{section}
30398 \begin_layout Plain Layout
30410 \begin_layout Subsection
30411 Numbering with Roman Numbers and Letters
30412 \begin_inset CommandInset label
30414 name "sub:Numbering-with-Roman"
30422 \begin_layout Plain Layout
30423 Formula numbering ! with letters
30432 \begin_layout Plain Layout
30433 Formula numbering ! with Roman numbers
30441 \begin_layout Standard
30442 Formulas can also be numbered with Roman numbers and Latin letters.
30443 To number for example with small Roman numbers, the command
30446 \begin_layout Standard
30458 \begin_layout Standard
30459 is inserted before the formula in TeX-mode.
30470 \begin_layout Plain Layout
30478 redefines the predefined command
30494 \begin_layout Plain Layout
30501 has the same scheme like the command
30507 that is described in
30508 \begin_inset CommandInset ref
30510 reference "sec:User-defined-Commands"
30524 is the formula counter.
30531 is used as prefix for a counter, the value of the counter is output as
30533 When a formula is numbered, LaTeX sets internally the command
30539 behind the formula.
30548 \begin_layout Plain Layout
30558 outputs the counter as small Roman number.
30561 \begin_layout Standard
30562 All formulas behind the command
30572 are now numbered Roman.
30573 To switch to numbering with big Roman numbers, the command is inserted
30590 \begin_layout Plain Layout
30602 \begin_inset Quotes eld
30606 \begin_inset Quotes erd
30609 with small Latin letters there is the command
30619 \begin_layout Plain Layout
30627 , for big ones there is the command
30637 \begin_layout Plain Layout
30650 \begin_layout Standard
30651 \begin_inset Note Greyedout
30654 \begin_layout Plain Layout
30659 Only maximal 26 formulas can be numbered with Latin letters in one document.
30667 \begin_layout Standard
30671 \begin_layout Plain Layout
30687 \begin_layout Standard
30688 \begin_inset Formula \begin{equation}
30689 A=\textrm{small roman}\label{eq:rom}\end{equation}
30697 \begin_layout Plain Layout
30711 \begin_inset Formula \begin{equation}
30712 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30720 \begin_layout Plain Layout
30734 \begin_inset Formula \begin{equation}
30735 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30743 \begin_layout Plain Layout
30757 \begin_inset Formula \begin{equation}
30758 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30765 \begin_layout Standard
30766 To switch back to the default numbering, insert the command:
30769 \begin_layout Standard
30782 \begin_layout Plain Layout
30793 \begin_layout Standard
30797 \begin_layout Plain Layout
30811 \begin_inset Formula \begin{equation}
30812 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30819 \begin_layout Standard
30820 \begin_inset VSpace medskip
30823 As you see, formulas are numbered serially independent from the numbering
30825 When then numbering should start with
30826 \begin_inset Quotes eld
30830 \begin_inset Quotes erd
30833 when the style is changed, new equation counters have to be defined.
30834 A description about this can be found in the file
30835 \begin_inset CommandInset href
30837 target "Formula-numbering.lyx"
30844 \begin_layout Section
30845 User-defined Commands
30846 \begin_inset CommandInset label
30848 name "sec:User-defined-Commands"
30856 \begin_layout Plain Layout
30857 User-defined commands
30865 \begin_layout Standard
30866 Many LaTeX-commands are too long to be used frequently.
30867 But it is possible to define with the command
30877 \begin_layout Plain Layout
30885 new shorter commands.
30888 \begin_layout Standard
30889 The command scheme of
30898 \begin_layout Standard
30903 newcommand{new command name}[number of arguments][optional
30908 \begin_inset Newline newline
30915 \begin_layout Plain Layout
30930 \begin_layout Plain Layout
30937 {command definition}
30940 \begin_layout Standard
30941 \begin_inset Note Greyedout
30944 \begin_layout Plain Layout
30949 Assure that the name of the new command is not already used in your document
30950 or by LaTeX-packages that you use.
30951 When you for example define the command
30963 , you get an error message because
30969 is already defined as command for
30970 \begin_inset Quotes eld
30974 \begin_inset Formula $\le$
30978 \begin_inset Quotes erd
30989 \begin_layout Standard
30990 \begin_inset Note Greyedout
30993 \begin_layout Plain Layout
30998 The names of user-defined commands may only consist of Latin letters.
31006 \begin_layout Standard
31007 The number of arguments is an integer in the range 0
31008 \begin_inset space \thinspace{}
31012 \begin_inset space \thinspace{}
31015 9 and specifies how many arguments the new command should have.
31016 With the optional value a value for an optional argument can be predefined.
31017 When this is done, the
31025 rgument of the new command is automatically an optional one.
31028 \begin_layout Standard
31029 Here are some examples:
31032 \begin_layout Itemize
31033 To define the command
31045 , the LaTeX-preamble line is:
31049 \begin_layout Plain Layout
31061 \begin_inset Newline newline
31073 \begin_layout Itemize
31074 To define the command
31086 , the argument (that should be underlined) must be taken into account.
31087 For this the preamble line is:
31091 \begin_layout Plain Layout
31103 \begin_inset Newline newline
31118 \begin_layout Plain Layout
31130 \begin_inset Newline newline
31139 acts as argument placeholder, the
31143 behind it denotes that it is the placeholder for the first argument.
31146 \begin_layout Itemize
31154 \begin_inset space \thinspace{}
31158 \begin_inset space ~
31171 \begin_layout Plain Layout
31183 \begin_inset Newline newline
31192 framebox#1#2{$#3$}}
31198 \begin_layout Plain Layout
31210 \begin_inset Newline newline
31215 The two Dollar signs creates the extra formula needed for
31222 \begin_inset CommandInset ref
31224 reference "sub:Boxes-with-Frame"
31231 \begin_layout Itemize
31232 To create a new command for
31238 where the color for the box needn't to be specified, the argument for the
31239 color is defined optional:
31243 \begin_layout Plain Layout
31255 \begin_inset Newline newline
31264 fcolorbox{#2}{#1}{$#3$}}
31270 \begin_layout Plain Layout
31280 \begin_inset Newline newline
31283 When the color is not specified when using
31289 , the predefined color
31296 \begin_layout Standard
31297 A test of the new defined commands:
31300 \begin_layout Standard
31302 \begin_inset Tabular
31303 <lyxtabular version="3" rows="6" columns="2">
31305 <column alignment="center" valignment="top" width="0">
31306 <column alignment="center" valignment="top" width="0">
31308 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31311 \begin_layout Plain Layout
31317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31320 \begin_layout Plain Layout
31322 \begin_inset Note Note
31325 \begin_layout Plain Layout
31332 is only used as spacer.
31344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31347 \begin_layout Plain Layout
31354 \begin_layout Plain Layout
31368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31371 \begin_layout Plain Layout
31372 \begin_inset Formula $A\gr B$
31382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31385 \begin_layout Plain Layout
31393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31396 \begin_layout Plain Layout
31397 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31410 \begin_layout Plain Layout
31414 \begin_inset Formula $\to$
31420 \begin_inset Formula $\to$
31431 \begin_layout Plain Layout
31445 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31448 \begin_layout Plain Layout
31449 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31462 \begin_layout Plain Layout
31466 \begin_inset Formula $\to$
31477 \begin_layout Plain Layout
31491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31494 \begin_layout Plain Layout
31495 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31508 \begin_layout Plain Layout
31514 \begin_inset Formula $\to$
31525 \begin_layout Plain Layout
31539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31542 \begin_layout Plain Layout
31543 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31559 \begin_layout Section
31563 \begin_layout Standard
31564 LyX supports two types of commutative diagrams:
31572 that are explained in the following.
31575 \begin_layout Subsection
31580 \begin_layout Plain Layout
31589 \begin_layout Standard
31590 Diagrams of this type visualize relations by vertical and horizontal lines
31592 \begin_inset Formula \[
31593 \begin{CD}A@>>>B@>>>C\\
31595 F@<<<E@<<<D\end{CD}\]
31602 \begin_layout Standard
31603 To get them, the command
31611 \begin_layout Plain Layout
31621 is inserted to a formula.
31622 A blue box appears with two dashed lines where further commands can be
31628 a new line is created.
31629 Horizontal relations are inserted in odd, vertical in even formula lines.
31632 \begin_layout Standard
31633 To create the relations there are the following commands:
31636 \begin_layout Itemize
31641 creates a left arrow,
31652 \begin_layout Itemize
31657 creates an up arrow,
31665 a vertical equal sign
31668 \begin_layout Itemize
31674 is a placeholder for non-existent relations
31677 \begin_layout Standard
31678 All arrows can be labeled as follows:
31681 \begin_layout Itemize
31682 Is text inserted between the first and second < or >, resp., it is placed
31684 When it is inserted between the second and third one, it appears under
31688 \begin_layout Itemize
31689 When text for vertical arrows is inserted between the first and second A
31690 or V, resp., it is placed left beside the arrow.
31691 When it is inserted between the second and third one, it appears right
31693 If the text contains an A or V, these letters must be set into a TeX-brace.
31696 \begin_layout Standard
31697 As example a diagram with all possible relations:
31700 \begin_layout Standard
31701 \begin_inset Formula \[
31702 \begin{CD}A@>j>>B@>>k>C@=F\\
31704 D@<<j<E@>k>>F@=C\end{CD}\]
31711 \begin_layout Standard
31712 The command for this is:
31713 \begin_inset Newline newline
31724 \begin_layout Plain Layout
31733 A@>j>>B@>>k>C@=F Ctrl-Enter
31734 \begin_inset Newline newline
31741 \begin_layout Plain Layout
31756 \begin_layout Plain Layout
31769 \begin_layout Plain Layout
31781 \begin_inset Formula $\to$
31787 \begin_inset Newline newline
31794 \begin_layout Plain Layout
31809 \begin_layout Plain Layout
31822 \begin_layout Plain Layout
31832 \begin_layout Subsection
31837 \begin_layout Plain Layout
31838 Diagrams ! xymatrix
31846 \begin_layout Standard
31847 To be able to use xymatrices, the LaTeX-package
31852 A xymatrix is created by inserting the command
31859 Then you are able to add new matrix columns and rows like for normal matrices,
31861 \begin_inset CommandInset ref
31863 reference "sec:Matrices"
31870 \begin_layout Standard
31871 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
31873 All possibilities to create commutative diagrams and decorations are explained
31874 in detail in this manual:
31875 \begin_inset CommandInset href
31877 target "http://wiki.lyx.org/LyX/XY-pic#xy-manual"
31884 \begin_layout Standard
31885 \begin_inset Newpage newpage
31891 \begin_layout Section
31896 \begin_layout Plain Layout
31909 \begin_layout Plain Layout
31910 Other useful math tips can be found in
31911 \begin_inset CommandInset citation
31926 \begin_layout Plain Layout
31934 \begin_inset Note Note
31937 \begin_layout Plain Layout
31940 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31943 \begin_layout Plain Layout
31946 texorpdfstring is in section
31947 \begin_inset CommandInset ref
31949 reference "sub:Formulas-in-Section"
31962 \begin_layout Plain Layout
31972 \begin_layout Plain Layout
31977 \begin_layout Plain Layout
31984 Chemical characters
31988 \begin_layout Plain Layout
32003 \begin_layout Subsection
32004 Chemical Symbols and Equations
32005 \begin_inset CommandInset label
32007 name "sub:Chemical-Symbols-and"
32015 \begin_layout Plain Layout
32016 Chemical characters ! Symbols
32025 \begin_layout Plain Layout
32035 \begin_layout Plain Layout
32044 \begin_layout Standard
32045 An example text from chemistry:
32048 \begin_layout Quote
32050 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32053 -ion reacts with two
32054 \begin_inset Formula $\mathrm{Na^{+}}$
32057 -ions to sodium sulfate
32058 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32062 The chemical equation for this is:
32063 \begin_inset Formula \[
32064 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32071 \begin_layout Standard
32072 This chemical equation can directly be created as formula.
32073 To avoid that the symbols appear italic, everything is highlighted and
32074 changed by the shortcut
32077 \begin_inset space ~
32082 to the upright font style.
32086 \begin_layout Plain Layout
32092 \begin_inset CommandInset ref
32094 reference "sub:Font-Styles"
32106 \begin_layout Subsection
32111 \begin_layout Plain Layout
32120 \begin_layout Standard
32121 Negative numbers often look ugly in formulas because the minus sign before
32122 the number is set with the same length as the minus operator sign.
32123 When writing the negative number in normal text, the minus sign appears
32127 \begin_layout Standard
32128 Thus, the problem disappears when converting the minus sign to mathematical
32132 \begin_layout Standard
32133 An example to visualize the problem:
32136 \begin_layout Standard
32138 \begin_inset Tabular
32139 <lyxtabular version="3" rows="3" columns="2">
32141 <column alignment="right" valignment="top" width="0">
32142 <column alignment="left" valignment="top" width="0">
32144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32147 \begin_layout Plain Layout
32153 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32156 \begin_layout Plain Layout
32164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32167 \begin_layout Plain Layout
32173 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32176 \begin_layout Plain Layout
32177 \begin_inset Formula $x=-2$
32187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32190 \begin_layout Plain Layout
32196 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32199 \begin_layout Plain Layout
32200 \begin_inset Formula $x=\textrm{-}2$
32216 \begin_layout Subsection
32217 Comma as decimal Separator
32221 \begin_layout Plain Layout
32230 \begin_layout Standard
32231 In LaTeX a comma inside a formula is used, according to the English convention,
32232 as number group separator.
32233 So there will be space added behind all commas in formulas.
32236 \begin_layout Standard
32237 To avoid this, the comma is highlighted and changed to mathematical text
32241 \begin_inset space ~
32249 \begin_layout Standard
32250 To use all formula commas in the document as decimal separator, the file
32259 \begin_layout Plain Layout
32264 is part of the LaTeX-package
32272 \begin_layout Plain Layout
32277 \begin_layout Plain Layout
32300 \begin_layout Plain Layout
32306 is loaded with the LaTeX-preamble line
32309 \begin_layout Standard
32317 \begin_layout Subsection
32319 \begin_inset CommandInset label
32321 name "sub:Physical-Vectors"
32329 \begin_layout Plain Layout
32338 \begin_layout Standard
32339 Predefined vectors are offered by the LaTeX-package
32347 \begin_layout Plain Layout
32352 should be part of every LaTeX standard installation.
32361 \begin_layout Plain Layout
32367 that is loaded with the LaTeX-preamble line
32370 \begin_layout Standard
32378 \begin_layout Standard
32382 \begin_layout Plain Layout
32392 \begin_inset Note Note
32395 \begin_layout Plain Layout
32396 The following table will only be displayed when the LaTeX-package
32405 The following commands are defined:
32408 \begin_layout Standard
32410 \begin_inset Tabular
32411 <lyxtabular version="3" rows="4" columns="2">
32413 <column alignment="center" valignment="top" width="0">
32414 <column alignment="center" valignment="top" width="0">
32416 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32419 \begin_layout Plain Layout
32425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32428 \begin_layout Plain Layout
32436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32439 \begin_layout Plain Layout
32449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32452 \begin_layout Plain Layout
32453 \begin_inset Formula $\Bra{\psi}$
32463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32466 \begin_layout Plain Layout
32476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32479 \begin_layout Plain Layout
32480 \begin_inset Formula $\Ket{\psi}$
32490 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32493 \begin_layout Plain Layout
32505 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32508 \begin_layout Plain Layout
32509 \begin_inset Formula $\Braket{\psi|\phi}$
32525 \begin_layout Standard
32532 assures that all vertical bars are set in the size of the surrounding brackets:
32533 \begin_inset Formula \[
32534 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32542 \begin_layout Plain Layout
32552 \begin_inset Note Note
32555 \begin_layout Plain Layout
32556 The following will be displayed when the LaTeX-package
32568 \begin_layout Standard
32569 You need to install the LaTeX-package
32573 to see the rest of this subsection in the output.
32576 \begin_layout Standard
32580 \begin_layout Plain Layout
32592 \begin_layout Standard
32599 can also be achieved using the command
32605 , that is described in
32606 \begin_inset CommandInset ref
32608 reference "sub:Automatic-Bracket-Size"
32615 \begin_layout Subsection
32616 Self-defined Fractions
32617 \begin_inset CommandInset label
32619 name "sub:Self-defined-Fractions"
32627 \begin_layout Plain Layout
32628 Fractions ! self-defined
32636 \begin_layout Standard
32637 To define custom commands for fractions, the command
32647 \begin_layout Plain Layout
32655 is used in the following scheme:
32658 \begin_layout Standard
32671 bracket}{fraction bar thickness}{style}
32672 \begin_inset Newline newline
32679 \begin_layout Plain Layout
32694 \begin_layout Plain Layout
32701 {numerator}{denominator}
32704 \begin_layout Standard
32705 The style is a number in the range of 0
32706 \begin_inset space \thinspace{}
32710 \begin_inset space \thinspace{}
32716 \begin_layout Standard
32718 \begin_inset Tabular
32719 <lyxtabular version="3" rows="5" columns="2">
32721 <column alignment="center" valignment="top" width="0">
32722 <column alignment="center" valignment="top" width="0">
32724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32727 \begin_layout Plain Layout
32733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32736 \begin_layout Plain Layout
32744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32747 \begin_layout Plain Layout
32753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32756 \begin_layout Plain Layout
32757 display style formula
32764 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32767 \begin_layout Plain Layout
32773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32776 \begin_layout Plain Layout
32784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32787 \begin_layout Plain Layout
32793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32796 \begin_layout Plain Layout
32804 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32807 \begin_layout Plain Layout
32813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32816 \begin_layout Plain Layout
32830 \begin_layout Standard
32831 When no style is given, the size is adjusted to the surrounding environment
32832 like for the command
32841 \begin_layout Standard
32842 When no fraction bar thickness is given, the predefined value of 0.4
32843 \begin_inset space \thinspace{}
32849 \begin_layout Standard
32850 \begin_inset VSpace medskip
32853 For example, the commands
32866 \begin_inset CommandInset ref
32868 reference "sub:Fractions"
32872 are defined with the commands
32875 \begin_layout Standard
32884 genfrac{}{}{}{0}{#1}{#2}}
32887 \begin_layout Standard
32891 \begin_layout Standard
32900 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32903 \begin_layout Standard
32904 \begin_inset VSpace medskip
32907 To define a fraction where the fraction bar thickness can be given as optional
32908 argument, the following line is inserted to the LaTeX-preamble:
32911 \begin_layout Standard
32920 genfrac{}{}{#1}{}{#2}{#3}}
32923 \begin_layout Standard
32925 \begin_inset Formula \begin{align*}
32926 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32927 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32931 As one can see, the distance of the numerator and the denominator to the
32932 fraction bar is round about three times the bar thickness.
32935 \begin_layout Subsection
32937 \begin_inset CommandInset label
32939 name "sub:Canceled-Formulas"
32947 \begin_layout Plain Layout
32956 \begin_layout Standard
32957 To cancel formulas or formula parts, the LaTeX-package
32965 \begin_layout Plain Layout
32970 is part of every LaTeX standard installation.
32979 \begin_layout Plain Layout
32985 has to be loaded with the LaTeX-preamble line
32988 \begin_layout Standard
32993 usepackage[samesize]{cancel}
32996 \begin_layout Standard
32997 There are four ways to cancel formulas:
33000 \begin_layout Standard
33002 \begin_inset Tabular
33003 <lyxtabular version="3" rows="5" columns="2">
33005 <column alignment="center" valignment="top" width="0">
33006 <column alignment="center" valignment="top" width="0">
33008 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33011 \begin_layout Plain Layout
33017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33020 \begin_layout Plain Layout
33022 \begin_inset Note Note
33025 \begin_layout Plain Layout
33038 are used here as spacer.
33050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33053 \begin_layout Plain Layout
33062 \begin_layout Plain Layout
33076 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33079 \begin_layout Plain Layout
33080 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33090 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33093 \begin_layout Plain Layout
33102 \begin_layout Plain Layout
33116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33119 \begin_layout Plain Layout
33120 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33133 \begin_layout Plain Layout
33142 \begin_layout Plain Layout
33156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33159 \begin_layout Plain Layout
33160 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33173 \begin_layout Plain Layout
33177 \begin_inset Formula $\to$
33188 \begin_layout Plain Layout
33202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33205 \begin_layout Plain Layout
33206 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33222 \begin_layout Standard
33229 is especially suitable to visualize the reduction of fractions within formulas:
33230 \begin_inset Formula \[
33231 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33238 \begin_layout Subsection
33239 Formulas in Section Headings
33240 \begin_inset CommandInset label
33242 name "sub:Formulas-in-Section"
33250 \begin_layout Plain Layout
33251 Formula ! in section headings
33259 \begin_layout Standard
33260 When formulas are used in section headings, the following has to be taken
33264 \begin_layout Standard
33265 \begin_inset Note Greyedout
33268 \begin_layout Plain Layout
33277 \begin_layout Plain Layout
33278 Packages ! hyperref
33283 support is enabled in the document settings dialog under
33286 \begin_inset space ~
33291 , PDF-bookmarks are created for every section heading in the table of contents.
33292 If a section heading contains formulas, they are incorrectly displayed
33293 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33302 \begin_layout Standard
33303 Both problems can be solved by inserting at the end of the section heading
33304 a short title with the menu
33306 Insert\SpecialChar \menuseparator
33308 \begin_inset space ~
33314 Short titles are used as alternative for multiline section headings to
33315 keep the table of contents clearly arranged.
33316 Only the short title appears in the table of contents and therefore also
33317 in the PDF-bookmark.
33320 \begin_layout Standard
33321 When formulas should be used in the table of contents but
33325 is used, one can use the following command in TeX-mode:
33328 \begin_layout Standard
33333 texorpdfstring{part}{alternative}
33337 \begin_layout Plain Layout
33348 \begin_layout Standard
33349 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33350 This can be characters, formulas, footnotes, but also cross-references.
33351 The alternative is used instead of the part for the bookmark.
33354 \begin_layout Standard
33355 Here are two example headings:
33356 \begin_inset VSpace -3mm
33363 \begin_layout Plain Layout
33375 \begin_layout Subsubsection
33376 Heading without formula in table of contents
33377 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33381 \begin_inset OptArg
33384 \begin_layout Plain Layout
33385 Heading without formula in table of contents
33393 \begin_layout Subsubsection
33394 Heading with formula in table of contents
33398 \begin_layout Plain Layout
33408 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33415 \begin_layout Plain Layout
33425 \begin_layout Standard
33429 \begin_layout Plain Layout
33438 In the first heading a short title was used, in the second one
33447 \begin_layout Standard
33448 To get the same formatting as for the other headings, the complete heading
33457 \begin_layout Plain Layout
33459 \begin_inset CommandInset ref
33461 reference "sub:Bold-Formulas"
33473 \begin_layout Subsection
33474 Formulas in multi-column Text
33478 \begin_layout Plain Layout
33479 Formula ! in multi-column text
33487 \begin_layout Standard
33488 Formulas in multi-column text are often too wide to fit into a column and
33489 thus need to be set over the whole page width.
33490 This is done by using the LaTeX-package
33498 \begin_layout Plain Layout
33503 is part of every LaTeX standard installation.
33512 \begin_layout Plain Layout
33513 Packages ! multicol
33518 , that is loaded with the LaTeX-preamble line
33521 \begin_layout Standard
33526 usepackage{multicol}
33529 \begin_layout Standard
33530 \begin_inset Note Greyedout
33533 \begin_layout Plain Layout
33534 Note herby that the setting
33537 \begin_inset space ~
33544 Document\SpecialChar \menuseparator
33550 \begin_inset space ~
33570 \begin_layout Standard
33571 Before the multi-column text the command
33574 \begin_layout Standard
33579 begin{multicols}{column number}
33582 \begin_layout Standard
33583 is written in TeX-mode.
33584 The column number is a number in the range of 2
33585 \begin_inset space \thinspace{}
33589 \begin_inset space \thinspace{}
33593 Before the formula the multi-column text is ended by inserting the command
33596 \begin_layout Standard
33604 \begin_layout Standard
33608 \begin_layout Standard
33609 Due to the command some space is automatically added before the formula.
33611 \begin_inset space \thinspace{}
33614 mm vertical space is inserted before the formula.
33615 When the formula style
33621 \begin_layout Plain Layout
33623 \begin_inset CommandInset ref
33625 reference "sec:Formula-Styles"
33637 \begin_inset space \thinspace{}
33640 mm space is inserted instead.
33643 \begin_layout Standard
33644 As example a multi-column text with a displayed formula:
33647 \begin_layout Standard
33651 \begin_layout Plain Layout
33655 begin{multicols}{2}
33660 Das Spektrum wird fouriertransformiert.
33661 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33662 , Lösungsmittel) zu trennen.
33663 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33664 nun das Aussehen des Ausgangssignals.
33665 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33666 über alle Phasen integrieren muss.
33668 \begin_inset Formula $S$
33671 unser normiertes Ausgangssignal and
33672 \begin_inset Formula $P$
33675 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33679 \begin_layout Plain Layout
33689 \begin_inset VSpace -6mm
33693 \begin_inset Formula \begin{equation}
33694 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33702 \begin_layout Plain Layout
33706 begin{multicols}{2}
33712 \begin_inset Formula $S_{0}$
33715 das Signal ohne Gradient ist and the Normierungsbedingung
33716 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33720 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33722 \begin_inset Formula $\nicefrac{\pi}{2}$
33726 \begin_inset space \thinspace{}
33729 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33730 das Signal zusätzlich abschwächt.
33731 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33733 \begin_inset Formula $T_{2}$
33739 \begin_layout Standard
33743 \begin_layout Plain Layout
33755 \begin_layout Subsection
33756 Formulas with Description of Variables
33760 \begin_layout Plain Layout
33761 Formula ! with description of variables
33769 \begin_layout Standard
33770 To describe variables within a formula, like in formula
33771 \begin_inset CommandInset ref
33773 reference "eq:within"
33782 \begin_inset Formula $n$
33786 \begin_inset space ~
33789 matrix is used with left aligned columns for the
33790 \begin_inset Formula $n$
33797 \begin_layout Plain Layout
33799 \begin_inset CommandInset ref
33801 reference "sec:Matrices"
33810 To set the description in a smaller size, before the matrix e.
33811 \begin_inset space \thinspace{}
33815 \begin_inset space ~
33828 \begin_layout Plain Layout
33830 \begin_inset CommandInset ref
33832 reference "sub:Font-Sizes"
33844 \begin_layout Standard
33845 When the formula style
33851 \begin_layout Plain Layout
33853 \begin_inset CommandInset ref
33855 reference "sec:Formula-Styles"
33876 \begin_layout Plain Layout
33883 only works in formulas with the style
33888 \begin_inset CommandInset ref
33890 reference "sub:Variable-Space"
33899 is inserted before and after the matrix to have the same separation of
33900 the matrix from the equation and the side margin.
33903 \begin_layout Standard
33904 When the formula style
33908 is used, the method described in
33909 \begin_inset CommandInset ref
33911 reference "sub:Flalign-Environment"
33915 is used to indent formulas.
33917 \begin_inset CommandInset ref
33919 reference "eq:within"
33923 consists of five columns whereas in the first two columns contain the equation,
33924 the third the matrix, and the last one an empty TeX-brace.
33925 \begin_inset Formula \begin{flalign}
33926 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33927 \rho & \textrm{density}\\
33928 V & \textrm{volume}\\
33929 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33936 \begin_layout Subsection
33937 Upright small Greek Letters
33938 \begin_inset CommandInset label
33940 name "sub:Upright-small-Greek"
33948 \begin_layout Plain Layout
33949 Greek letters ! upright
33957 \begin_layout Standard
33958 Most of the math fonts only provide italic small Greek letters.
33959 But for symbols of elementary particles like pions and neutrinos, upright
33960 Greek letters are needed.
33969 \begin_layout Plain Layout
33974 is part of the LaTeX-package
33982 \begin_layout Plain Layout
33987 \begin_layout Plain Layout
34010 \begin_layout Plain Layout
34016 that is loaded with the LaTeX-preamble line
34019 \begin_layout Standard
34024 usepackage{upgreek}
34027 \begin_layout Standard
34033 \begin_layout Plain Layout
34043 \begin_inset Note Note
34046 \begin_layout Plain Layout
34047 The following table will only be displayed when the LaTeX-package
34056 They are created when the command for a small Greek letters is started
34062 For example the command
34069 \begin_inset Formula $\uptau$
34075 \begin_layout Standard
34076 With these commands reactions of elementary particles can be typeset:
34077 \begin_inset Formula \[
34078 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34085 \begin_layout Standard
34086 The upright letters are more bold and wider than the italic ones.
34087 They should therefore not be used for units like
34088 \begin_inset Quotes eld
34092 \begin_inset Quotes erd
34098 \begin_layout Standard
34102 \begin_layout Plain Layout
34112 \begin_inset Note Note
34115 \begin_layout Plain Layout
34116 The following will be displayed when the LaTeX-package
34128 \begin_layout Standard
34129 You need to install the LaTeX-package
34133 to see the rest of this subsection in the output.
34136 \begin_layout Standard
34140 \begin_layout Plain Layout
34152 \begin_layout Subsection
34153 Text Characters in Formulas
34154 \begin_inset CommandInset label
34156 name "sub:Text-Characters-in"
34164 \begin_layout Plain Layout
34173 \begin_layout Standard
34174 In some cases you might want to insert text characters directly into formulas.
34175 When for example the centered dot · is often used in formulas like
34176 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34179 , one would have to insert the command
34189 \begin_layout Plain Layout
34191 \begin_inset CommandInset ref
34193 reference "sub:Binary-Operators"
34202 all the time, because this character is defined in all encodings as text
34204 But the encoding can be changed by this LaTeX-preamble line:
34207 \begin_layout Standard
34212 Declare Inputtext{183}{
34222 f\SpecialChar \textcompwordmark{}
34226 \begin_layout Standard
34227 The character encoding (menu
34229 Document\SpecialChar \menuseparator
34230 Settings\SpecialChar \menuseparator
34233 ) specifies what character appears when a keyboard key is pressed.
34234 When the key for the character '·' is pressed, internally the command
34241 But this command is not available in a formula so that you would get LaTeX-erro
34243 With the changed encoding the right command is chosen automatically, depending
34244 on if the character was inserted into a formula or not.
34247 \begin_layout Standard
34248 The encoding of several characters is saved in definition files.
34249 Fore example the encoding
34253 is defined in the file
34257 that is in the installation folder of LaTeX.
34258 Encodings should only be changed via the LaTeX-preamble and not in the
34260 Otherwise own documents could not be edited by other LyX users working
34261 on other computers.
34264 \begin_layout Standard
34265 \begin_inset VSpace medskip
34268 Besides the centered dot, in this document the degree sign ° is defined
34269 with the following LaTeX-preamble line so that it can directly be inserted
34273 \begin_layout Standard
34278 DeclareInputtext{176}{
34288 f\SpecialChar \textcompwordmark{}
34292 \begin_layout Standard
34293 \begin_inset Newpage newpage
34299 \begin_layout Section
34305 \begin_layout Plain Layout
34314 \begin_layout Standard
34315 This section is a summary of the most important typographic rules, listed
34320 \begin_layout Plain Layout
34321 This collection was partly taken from the German semi-official dictionary
34323 \begin_inset Quotes eld
34327 \begin_inset Quotes erd
34331 \begin_inset CommandInset citation
34337 that lists some of the ISO rules.
34345 \begin_layout Itemize
34354 \begin_layout Plain Layout
34355 done with font styles, see
34356 \begin_inset CommandInset ref
34358 reference "sub:Font-Styles"
34368 \begin_inset space \thinspace{}
34372 \begin_inset Newline newline
34375 Between the value and the unit is the smallest space, see
34376 \begin_inset CommandInset ref
34378 reference "sub:Predefined-Space"
34383 \begin_inset Newline newline
34386 This convention is automatically fulfilled when the command
34393 When it is entered to a formula, two boxes appear.
34394 In the first one the value is inserted, in the second one the unit, and
34396 \begin_inset Formula $\unit[30]{km/h}$
34400 \begin_inset space \thinspace{}
34410 is not a real LaTeX command but the command
34416 , therefore you cannot use it in TeX code.
34419 \begin_layout Itemize
34420 Percent and perthousand signs are set like physical units:
34421 \begin_inset Newline newline
34425 \begin_inset space \thinspace{}
34431 \begin_layout Itemize
34432 The degree sign follows directly on the value: 15°, but not when it is used
34434 \begin_inset space \thinspace{}
34440 \begin_layout Itemize
34441 In numbers with more than four digits the smallest space is inserted before
34442 every third digit to group them:
34452 \begin_inset space \thinspace{}
34456 \begin_inset space \thinspace{}
34462 \begin_layout Itemize
34463 For dimensions like 120×90×40
34464 \begin_inset space \thinspace{}
34467 cm the multiplication sign
34468 \begin_inset Quotes eld
34472 \begin_inset Quotes erd
34476 It is available with the LaTeX-command
34482 , but can also directly be inserted with some keyboard definitions.
34485 \begin_layout Itemize
34486 Functions with names consisting of several letters are set upright to avoid
34488 \begin_inset CommandInset ref
34490 reference "sub:Predefined-Functions"
34497 \begin_layout Itemize
34498 Indices consisting of several letters, are set upright:
34499 \begin_inset Formula $E_{\mathrm{kin}}$
34503 \begin_inset Newline newline
34506 Components of matrices are set italic:
34507 \begin_inset Formula $\hat{H}_{kl}$
34513 \begin_layout Itemize
34514 The differentiation/integration operator 'd', the Euler's number 'e', and
34515 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34519 \begin_layout Standard
34520 \begin_inset Newpage newpage
34526 \begin_layout Section
34531 \begin_layout Plain Layout
34540 \begin_layout Standard
34541 Some characters and symbols can be created with several commands.
34542 Here is a list of the synonym commands:
34545 \begin_layout Standard
34546 \begin_inset VSpace bigskip
34550 \begin_inset space \hfill{}
34554 \begin_inset Tabular
34555 <lyxtabular version="3" rows="12" columns="2">
34557 <column alignment="center" valignment="top" width="0pt">
34558 <column alignment="center" valignment="top" width="0pt">
34560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34563 \begin_layout Plain Layout
34569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34572 \begin_layout Plain Layout
34574 \begin_inset Note Note
34577 \begin_layout Plain Layout
34584 is only used as spacer.
34596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34599 \begin_layout Plain Layout
34607 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34610 \begin_layout Plain Layout
34614 \begin_layout Plain Layout
34627 \begin_layout Plain Layout
34641 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34644 \begin_layout Plain Layout
34652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34655 \begin_layout Plain Layout
34665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34668 \begin_layout Plain Layout
34676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34679 \begin_layout Plain Layout
34689 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34692 \begin_layout Plain Layout
34700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34703 \begin_layout Plain Layout
34711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34714 \begin_layout Plain Layout
34722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34725 \begin_layout Plain Layout
34733 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34736 \begin_layout Plain Layout
34744 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34747 \begin_layout Plain Layout
34757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34760 \begin_layout Plain Layout
34768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34771 \begin_layout Plain Layout
34781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34784 \begin_layout Plain Layout
34792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34795 \begin_layout Plain Layout
34805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34808 \begin_layout Plain Layout
34816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34819 \begin_layout Plain Layout
34829 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34832 \begin_layout Plain Layout
34840 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34843 \begin_layout Plain Layout
34851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34854 \begin_layout Plain Layout
34862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34865 \begin_layout Plain Layout
34877 \begin_inset space \hfill{}
34881 \begin_inset Tabular
34882 <lyxtabular version="3" rows="12" columns="2">
34884 <column alignment="center" valignment="top" width="0pt">
34885 <column alignment="center" valignment="top" width="0pt">
34887 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34890 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34910 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34936 \begin_layout Plain Layout
34944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34947 \begin_layout Plain Layout
34957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34960 \begin_layout Plain Layout
34968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34971 \begin_layout Plain Layout
34981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34984 \begin_layout Plain Layout
34992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34995 \begin_layout Plain Layout
35003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35006 \begin_layout Plain Layout
35014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35017 \begin_layout Plain Layout
35025 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35028 \begin_layout Plain Layout
35036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35039 \begin_layout Plain Layout
35049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35052 \begin_layout Plain Layout
35060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35063 \begin_layout Plain Layout
35073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35076 \begin_layout Plain Layout
35084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35087 \begin_layout Plain Layout
35097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35100 \begin_layout Plain Layout
35108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35111 \begin_layout Plain Layout
35121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35124 \begin_layout Plain Layout
35132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35135 \begin_layout Plain Layout
35145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35148 \begin_layout Plain Layout
35156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35159 \begin_layout Plain Layout
35173 \begin_inset space \hfill{}
35179 \begin_layout Standard
35180 \begin_inset Newpage newpage
35186 \begin_layout Bibliography
35187 \begin_inset CommandInset bibitem
35188 LatexCommand bibitem
35200 The LaTeX Companion
35203 Addison Wesley, 2004
35206 \begin_layout Bibliography
35207 \begin_inset CommandInset bibitem
35208 LatexCommand bibitem
35214 \begin_inset CommandInset href
35217 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35221 of LaTeX's math abilities
35224 \begin_layout Bibliography
35225 \begin_inset CommandInset bibitem
35226 LatexCommand bibitem
35231 LaTeX tips and tricks-
35232 \begin_inset CommandInset href
35235 target "http://tug.org/TeXnik/"
35242 \begin_layout Bibliography
35243 \begin_inset CommandInset bibitem
35244 LatexCommand bibitem
35250 \begin_inset CommandInset href
35253 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35261 \begin_layout Plain Layout
35273 \begin_layout Bibliography
35274 \begin_inset CommandInset bibitem
35275 LatexCommand bibitem
35281 \begin_inset CommandInset href
35284 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35288 of all symbols available with LaTeX-packages
35291 \begin_layout Bibliography
35292 \begin_inset CommandInset bibitem
35293 LatexCommand bibitem
35299 \begin_inset CommandInset href
35301 name "Documentation"
35302 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35306 of the LaTeX-package
35314 \begin_layout Plain Layout
35315 Packages ! hyperref
35323 \begin_layout Bibliography
35324 \begin_inset CommandInset bibitem
35325 LatexCommand bibitem
35331 \begin_inset CommandInset href
35334 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35345 \begin_inset CommandInset ref
35347 reference "sub:Operator-Limits"
35355 \begin_layout Plain Layout
35366 \begin_layout Bibliography
35367 \begin_inset CommandInset bibitem
35368 LatexCommand bibitem
35379 Auflage, Duden 2001
35382 \begin_layout Subsubsection*
35383 \begin_inset CommandInset index_print
35384 LatexCommand printindex