1 #LyX 1.6.0svn 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,
43 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
46 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
48 \settowidth{\abc}{\space}
49 \renewcommand{\equationautorefname}{\hspace{-\abc}}
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]{Contents}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
78 \usepackage[samesize]{cancel}
80 % enables calculation of values,
83 % for multiple table row and column cells
93 % center multirows (e.g. in sec. 13.3)
94 \renewcommand{\multirowsetup}{\centering}
96 % define a color, used in sec.9.3
97 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
99 % declare operators (see sec. 10.4 and sec. 15.2)
100 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
101 \DeclareMathOperator{\sgn}{sgn}
103 \newcommand{\spce}{\textvisiblespace}
105 % example definitions for sec. 20.1
106 \newcommand{\gr}{\Longrightarrow}
107 \newcommand{\us}[1]{\underline{#1}}
108 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
109 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
110 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
112 % example macro from sec. 19.4
113 %\def\tagform@#1{\maketag@@@{|#1|}}
115 % macro from sec. 10.2
116 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
117 \def\mathclap {\mathpalette \mathclapinternal}
118 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
120 % redefine the greyed out note
121 \renewenvironment{lyxgreyedout}
122 {\textcolor{blue}\bgroup}{\egroup}
124 % check for package eurosym
125 % used for the Euro symbol
127 \IfFileExists{eurosym.sty}
128 {\usepackage[gennarrow]{eurosym}
129 \setboolean{eurosym}{true}}
130 {\setboolean{eurosym}{false}}
132 % needed in sec. 22.4
133 % check for package braket
135 \IfFileExists{braket.sty}
137 \setboolean{braket}{true}}
138 {\setboolean{braket}{false}}
140 % needed in sec. 22.10
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
153 \font_typewriter default
154 \font_default_family default
164 \pdf_title "LyX's Math Manual"
165 \pdf_author "LyX Team, Uwe Stöhr"
166 \pdf_subject "LyX-documentation about math"
167 \pdf_keywords "LyX, Mathed"
169 \pdf_bookmarksnumbered true
170 \pdf_bookmarksopen true
171 \pdf_bookmarksopenlevel 1
172 \pdf_breaklinks false
176 \pdf_pagebackref false
177 \pdf_pdfusetitle false
178 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
185 \paperorientation portrait
188 \paragraph_separation skip
190 \quotes_language english
193 \paperpagestyle plain
197 \tracking_changes false
198 \output_changes false
206 LyX's detailed Math manual
214 \begin_layout Plain Layout
216 If you have comments or error corrections, please send them to the LyX Documenta
220 \begin_inset CommandInset href
222 name "lyx-docs@lists.lyx.org"
223 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
234 \begin_inset Note Note
237 \begin_layout Plain Layout
244 \begin_inset Newline newline
248 \begin_inset Newline newline
256 \begin_layout Standard
257 \begin_inset CommandInset toc
258 LatexCommand tableofcontents
265 \begin_layout Standard
266 \begin_inset Note Note
269 \begin_layout Plain Layout
270 To export this document to PDF, PS, or DVI the LaTeX-packages
283 If they are not installed you can export the document anyway but the sections
284 where the packages are required won't appear in the output.
287 \begin_layout Plain Layout
288 The latest PDF-version of this document can be found here:
289 \begin_inset Newline newline
294 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
302 \begin_layout Standard
303 \begin_inset Newpage newpage
309 \begin_layout Section
311 \begin_inset CommandInset label
313 name "sec:Introduction"
320 \begin_layout Standard
321 This document explains LyX's math features and is furthermore a collection
322 of LaTeX-commands used for mathematical characters and constructs.
323 The explanations are designed for the usage of commands.
324 It is therefore required that you have read the section
335 \begin_layout Standard
336 Most of the characters and many constructs explained in this manual are
337 also accessible via the menu
341 \SpecialChar \menuseparator
357 But everybody who has to write lots of formulas will notice that it is
358 much faster to use commands instead of the math toolbar.
359 Therefore this manual is focused on commands but also mentions the correspondin
360 g toolbar buttons when available.
363 \begin_layout Standard
364 If not specially mentioned the commands are only available within formulas.
365 To be able to use all commands explained in this document, the option
369 must be used in the document settings (menu
371 Document\SpecialChar \menuseparator
372 Settings\SpecialChar \menuseparator
383 \begin_layout Plain Layout
386 Use AMS math package automatically
392 \begin_layout Plain Layout
401 -math when math constructs are found that are supported by LyX.
409 \begin_layout Standard
410 This document doesn't list all
414 \begin_layout Plain Layout
427 \begin_layout Plain Layout
432 \begin_layout Plain Layout
441 -math commands is in the file
444 \begin_inset CommandInset href
447 target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps"
453 , which is part of every LaTeX standard installation.
458 for lucidity reasons.
461 \begin_layout Section
463 \begin_inset CommandInset label
465 name "sec:General-Instructions"
472 \begin_layout Standard
473 To create an inline formula
477 \begin_layout Plain Layout
483 that is embedded into a text line, press
487 or the toolbar button
488 \begin_inset Graphics
489 filename ../images/math-mode.png
495 \begin_inset Newline newline
498 To create a display style formula
502 \begin_layout Plain Layout
503 Formula ! display style
508 that will appear bigger and in an own paragraph, press
515 \begin_layout Standard
516 To change a display style formula to an inline formula, set the cursor into
517 the formula and press
523 Edit\SpecialChar \menuseparator
524 Math\SpecialChar \menuseparator
528 The same way is used to change an inline formula to a display style formula.
531 \begin_layout Standard
532 To display parts of an inline formula in the size of a display style formula,
541 \begin_layout Plain Layout
552 Then a new blue box appears in which the desired formula part is inserted.
555 \begin_layout Standard
556 Only inline formulas are allowed inside tables.
559 \begin_layout Standard
564 can be turned on in the menu
566 View\SpecialChar \menuseparator
570 When you click there on
571 \begin_inset Quotes eld
575 \begin_inset Quotes erd
578 the toolbar will be shown permanently at the bottom; this state is visualized
583 menu with a checkmark.
584 When you click in this state again on
585 \begin_inset Quotes eld
589 \begin_inset Quotes erd
600 is only shown when the cursor is within a formula; this state is visualized
601 by the renaming of the menu entry from
602 \begin_inset Quotes eld
606 \begin_inset Quotes erd
610 \begin_inset Quotes eld
618 \begin_inset Quotes erd
624 \begin_layout Standard
629 \begin_layout Plain Layout
634 \begin_layout Plain Layout
642 \begin_layout Plain Layout
653 \begin_layout Plain Layout
670 is invoked by pressing the toolbar button
671 \begin_inset Graphics
672 filename ../images/ert-insert.png
679 Insert\SpecialChar \menuseparator
684 \begin_layout Plain Layout
695 \begin_layout Plain Layout
709 \begin_inset Note Note
712 \begin_layout Plain Layout
713 In LyX there are three
714 \begin_inset Quotes eld
718 \begin_inset Quotes erd
721 that appear in the output with sub- and superscript letters: TeX, LaTeX,
725 \begin_layout Plain Layout
726 To avoid that these names are recognized as proper names, TeX-braces are
727 set around one of the letters of the name.
735 \begin_layout Standard
736 To change the LaTeX-preamble
740 \begin_layout Plain Layout
748 Document\SpecialChar \menuseparator
749 Settings\SpecialChar \menuseparator
754 \begin_layout Plain Layout
765 \begin_layout Plain Layout
781 \begin_layout Standard
782 To edit matrices, case differentiations, and multiline formulas subsequently,
785 Edit\SpecialChar \menuseparator
790 Edit\SpecialChar \menuseparator
792 \begin_inset space \thinspace{}
796 \begin_inset space \thinspace{}
806 When lines and columns are swapped via the menu, the column or line where
807 the cursor is in is exchanged with the column to the right or the line
809 Is the cursor in the last column or row, the exchange is done with the
810 column to the left or the line above.
813 \begin_layout Standard
814 To write text in formulas
818 \begin_layout Plain Layout
819 For multiline formulas the command
826 \begin_inset CommandInset ref
828 reference "sub:Text-in-multiline"
845 \begin_layout Plain Layout
855 \begin_layout Plain Layout
862 This mode is invoked with the the shortcut
870 or by the insertion of the command
878 \begin_layout Plain Layout
889 The text appears black in LyX and can therefore be distinguished from the
890 other formula parts that appear blue.
891 In the output mathematical text is set upright, in contrary to other formula
895 \begin_layout Subsection*
899 \begin_layout Standard
900 Most of the LaTeX-commands for math constructs have the following scheme:
903 \begin_layout Standard
919 \begin_layout Standard
920 A command starts always with a backslash
921 \begin_inset Quotes gld
931 \begin_inset Quotes grd
935 To omit optional arguments, also omit the associated brackets.
936 The braces around the required arguments are named in this document as
941 \begin_layout Plain Layout
946 \begin_layout Plain Layout
954 \begin_layout Plain Layout
965 \begin_layout Plain Layout
983 If you add in a formula a left brace to a command name, LyX creates automatical
985 In all other cases TeX-braces are created in formulas with the command
993 TeX-braces appear red in LyX, in contrary to normal braces that appear
995 In TeX-mode no command is needed to get TeX-braces.
996 TeX-braces don't appear in the output.
999 \begin_layout Standard
1000 When commands without arguments, like commands for symbols are entered in
1001 TeX-mode, a space character must
1005 be behind the command to end it.
1006 This space doesn't appear in the output.
1007 When the space should appear in the output, the space must be followed
1008 by a protected space in normal text.
1011 \begin_layout Standard
1012 A protected space is inserted with
1019 \begin_layout Subsection*
1020 \begin_inset Newpage newpage
1026 \begin_layout Itemize
1031 \begin_layout Plain Layout
1032 This visible space character can be created with the command
1042 \begin_layout Plain Layout
1050 , inserted in TeX-mode.
1059 \begin_layout Plain Layout
1069 \begin_inset space ~
1072 denotes a space character to be input.
1075 \begin_layout Itemize
1077 \begin_inset Formula $\to$
1080 denotes the usage of the corresponding arrow key on the keyboard.
1083 \begin_layout Subsection*
1087 \begin_layout Standard
1089 \begin_inset Float table
1095 \begin_layout Plain Layout
1097 \begin_inset Caption
1099 \begin_layout Plain Layout
1100 \begin_inset CommandInset label
1102 name "tab:Used-units"
1114 \begin_layout Plain Layout
1116 \begin_inset Tabular
1117 <lyxtabular version="3" rows="13" columns="2">
1119 <column alignment="center" valignment="top" width="0">
1120 <column alignment="center" valignment="top" width="0">
1122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1125 \begin_layout Plain Layout
1131 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1134 \begin_layout Plain Layout
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
1162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1165 \begin_layout Plain Layout
1171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1174 \begin_layout Plain Layout
1182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1185 \begin_layout Plain Layout
1191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1194 \begin_layout Plain Layout
1196 \begin_inset space \thinspace{}
1200 \begin_inset space \thinspace{}
1210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1213 \begin_layout Plain Layout
1219 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1222 \begin_layout Plain Layout
1224 \begin_inset space \thinspace{}
1228 \begin_inset space \thinspace{}
1238 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1241 \begin_layout Plain Layout
1247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1250 \begin_layout Plain Layout
1252 \begin_inset space \thinspace{}
1256 \begin_inset space \thinspace{}
1266 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1269 \begin_layout Plain Layout
1275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1278 \begin_layout Plain Layout
1280 \begin_inset space \thinspace{}
1284 \begin_inset space \thinspace{}
1294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1297 \begin_layout Plain Layout
1303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1306 \begin_layout Plain Layout
1308 \begin_inset space \thinspace{}
1312 \begin_inset space \thinspace{}
1322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1325 \begin_layout Plain Layout
1331 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1334 \begin_layout Plain Layout
1336 \begin_inset space \thinspace{}
1340 \begin_inset Formula $\approx$
1344 \begin_inset space \thinspace{}
1354 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1357 \begin_layout Plain Layout
1363 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1366 \begin_layout Plain Layout
1368 \begin_inset space \thinspace{}
1372 \begin_inset space \thinspace{}
1382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1385 \begin_layout Plain Layout
1391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1394 \begin_layout Plain Layout
1398 \begin_inset Quotes eld
1404 \begin_inset Quotes erd
1414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1417 \begin_layout Plain Layout
1423 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1426 \begin_layout Plain Layout
1428 \begin_inset Quotes eld
1436 \begin_inset Quotes erd
1446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1449 \begin_layout Plain Layout
1455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1458 \begin_layout Plain Layout
1460 \begin_inset space \thinspace{}
1464 \begin_inset Formula $\nicefrac{1}{18}$
1468 \begin_inset space \thinspace{}
1489 \begin_layout Standard
1490 \begin_inset Newpage newpage
1496 \begin_layout Section
1500 \begin_layout Subsection
1505 \begin_layout Plain Layout
1515 \begin_layout Plain Layout
1525 \begin_layout Plain Layout
1530 \begin_layout Plain Layout
1541 \begin_layout Plain Layout
1557 \begin_layout Plain Layout
1562 \begin_layout Plain Layout
1573 \begin_layout Plain Layout
1588 \begin_layout Standard
1589 Indices are created with an underscore
1590 \begin_inset Quotes eld
1594 \begin_inset Quotes erd
1597 or via the math toolbar button
1598 \begin_inset Graphics
1599 filename ../images/math-subscript.png
1604 , exponents with a caret
1605 \begin_inset Quotes eld
1609 \begin_inset Quotes erd
1612 or via the math toolbar button
1613 \begin_inset Graphics
1614 filename ../images/math-superscript.png
1622 \begin_layout Standard
1624 \begin_inset Tabular
1625 <lyxtabular version="3" rows="4" columns="2">
1627 <column alignment="center" valignment="top" width="0pt">
1628 <column alignment="center" valignment="top" width="0pt">
1630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1633 \begin_layout Plain Layout
1639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1642 \begin_layout Plain Layout
1644 \begin_inset Note Note
1647 \begin_layout Plain Layout
1654 is only used as spacer.
1666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1669 \begin_layout Plain Layout
1675 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1678 \begin_layout Plain Layout
1679 \begin_inset Formula $B_{V}$
1689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1692 \begin_layout Plain Layout
1698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1701 \begin_layout Plain Layout
1702 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1712 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1715 \begin_layout Plain Layout
1720 \begin_layout Plain Layout
1734 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1737 \begin_layout Plain Layout
1738 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1754 \begin_layout Standard
1755 As the caret is in some languages an accent, vowels will be accentuated
1756 in this case and not set as exponents
1760 \begin_layout Plain Layout
1761 Depending on the used keyboard settings this can also happen for other character
1768 To get in this case exponents, press
1772 after the caret as in the last example.
1775 \begin_layout Subsection
1777 \begin_inset CommandInset label
1779 name "sub:Fractions"
1787 \begin_layout Plain Layout
1796 \begin_layout Standard
1797 Fractions are generated with the command
1807 \begin_layout Plain Layout
1815 or via the math toolbar button
1816 \begin_inset Graphics
1817 filename ../images/math/frac.png
1823 The font size is adjusted automatically, depending on whether the fraction
1824 is in an inline or display style formula.
1825 With the math toolbar button
1826 \begin_inset Graphics
1827 filename ../images/math/frac-square.png
1832 you can select different fraction types.
1835 \begin_layout Standard
1844 \begin_layout Plain Layout
1854 a fraction can be created that has in any case the size of a display style
1864 \begin_layout Plain Layout
1874 the fraction appears always with the size of an inline formula.
1878 \begin_layout Standard
1879 A line with the fraction
1880 \begin_inset Formula $\frac{1}{2}$
1883 that was created with the command
1892 \begin_layout Standard
1893 A line with the fraction
1894 \begin_inset Formula $\dfrac{1}{2}$
1897 that was created with the command
1906 \begin_layout Standard
1908 \begin_inset Tabular
1909 <lyxtabular version="3" rows="4" columns="2">
1911 <column alignment="center" valignment="top" width="0pt">
1912 <column alignment="center" valignment="top" width="0pt">
1914 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1917 \begin_layout Plain Layout
1923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1926 \begin_layout Plain Layout
1928 \begin_inset Note Note
1931 \begin_layout Plain Layout
1938 is only used as spacer.
1950 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1953 \begin_layout Plain Layout
1960 \begin_layout Plain Layout
1970 \begin_inset Formula $\downarrow$
1978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1981 \begin_layout Plain Layout
1982 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1992 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1995 \begin_layout Plain Layout
2002 \begin_layout Plain Layout
2012 \begin_inset Formula $\downarrow$
2020 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2023 \begin_layout Plain Layout
2024 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
2034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2037 \begin_layout Plain Layout
2044 \begin_layout Plain Layout
2057 \begin_layout Plain Layout
2072 \begin_layout Plain Layout
2082 \begin_inset Formula $\downarrow$
2086 \begin_inset Formula $\downarrow\downarrow$
2094 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2097 \begin_layout Plain Layout
2098 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2114 \begin_layout Standard
2115 \begin_inset VSpace bigskip
2119 \begin_inset Newpage newpage
2122 For nested fractions the command
2132 \begin_layout Plain Layout
2142 \begin_inset VSpace -3mm
2148 \begin_layout Standard
2149 \begin_inset Formula \begin{align*}
2150 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2151 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2158 \begin_layout Standard
2159 The command for the example above is:
2162 \begin_layout Standard
2168 \begin_inset Formula $\to$
2178 \begin_inset Formula $\to$
2184 \begin_inset Formula $\to\to$
2192 \begin_layout Standard
2193 \begin_inset VSpace medskip
2199 \begin_layout Standard
2206 sets the fraction always in the size of a displayed formula, also when
2207 it is part of another fraction.
2214 has the following command scheme:
2217 \begin_layout Standard
2222 cfrac[numerator position]{numerator}{denominator}
2225 \begin_layout Standard
2226 The numerator position can be
2239 l or r aligns the numerator to the left or right, resp.
2240 \begin_inset space ~
2243 with the fraction stroke.
2248 or no position is given, the numerator appears centered.
2249 These fractions demonstrate the different alignments:
2250 \begin_inset Newline newline
2256 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2260 \begin_inset Formula $\cfrac{A}{B+C}$
2264 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2270 \begin_layout Standard
2271 \begin_inset VSpace medskip
2274 It is often advantageous to combine
2287 \begin_inset Formula \[
2288 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2295 \begin_layout Standard
2296 For inline fractions with a sloped fraction stroke you can use the command
2305 \begin_layout Plain Layout
2316 \begin_inset Formula $\nicefrac{5}{31}$
2322 \begin_layout Standard
2323 How to define own fractions where the fraction stroke can be changed, is
2325 \begin_inset CommandInset ref
2327 reference "sub:Self-defined-Fractions"
2334 \begin_layout Subsection
2339 \begin_layout Plain Layout
2348 \begin_layout Standard
2349 Square roots are created with
2359 \begin_layout Plain Layout
2367 or the math toolbar button
2368 \begin_inset Graphics
2369 filename ../images/math/sqrt.png
2374 , all other roots with the command
2384 \begin_layout Plain Layout
2392 or with the math toolbar button
2393 \begin_inset Graphics
2394 filename ../images/math/root.png
2402 \begin_layout Standard
2404 \begin_inset Tabular
2405 <lyxtabular version="3" rows="3" columns="2">
2407 <column alignment="center" valignment="top" width="0pt">
2408 <column alignment="center" valignment="top" width="0pt">
2410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2413 \begin_layout Plain Layout
2419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2422 \begin_layout Plain Layout
2424 \begin_inset Note Note
2427 \begin_layout Plain Layout
2434 is only used as spacer.
2446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2449 \begin_layout Plain Layout
2456 \begin_layout Plain Layout
2470 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2473 \begin_layout Plain Layout
2474 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2484 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2487 \begin_layout Plain Layout
2494 \begin_layout Plain Layout
2504 \begin_inset Formula $\downarrow$
2512 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2532 \begin_layout Standard
2533 A square root can also be created with
2539 when the root index field is left empty.
2542 \begin_layout Standard
2543 With certain indices the distance to the root is too small, like in this
2545 \begin_inset Formula $\sqrt[\beta]{B}$
2549 \begin_inset Newline newline
2553 \begin_inset Formula $\beta$
2557 To avoid this, the commands
2567 \begin_layout Plain Layout
2585 \begin_layout Plain Layout
2593 are used with the following scheme:
2596 \begin_layout Standard
2610 \begin_layout Standard
2611 Distance is the number of Big Points (unit bp;
2612 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2615 ), that the index should be moved to the left or top, resp..
2616 The commands are written to the index.
2617 This way the command
2618 \begin_inset Newline newline
2628 \begin_inset Formula $\to$
2634 \begin_inset Formula $\to$
2643 \begin_layout Plain Layout
2653 \begin_inset Formula $\to$
2657 \begin_inset Newline newline
2662 produces a correct typeset formula:
2663 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2669 \begin_layout Subsection
2670 Binomial coefficients
2674 \begin_layout Plain Layout
2675 Binomial coefficient s
2683 \begin_layout Standard
2684 Binomial coefficients are inserted with the command
2694 \begin_layout Plain Layout
2702 or with the submenu of the math toolbar button
2703 \begin_inset Graphics
2704 filename ../images/math/frac-square.png
2710 Analog to fractions (
2730 \begin_layout Plain Layout
2750 \begin_layout Plain Layout
2759 For other brackets around binomial coeficients there are the commands
2769 \begin_layout Plain Layout
2787 \begin_layout Plain Layout
2798 \begin_layout Standard
2800 \begin_inset Tabular
2801 <lyxtabular version="3" rows="6" columns="2">
2803 <column alignment="center" valignment="top" width="0pt">
2804 <column alignment="center" valignment="top" width="0pt">
2806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2809 \begin_layout Plain Layout
2815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2818 \begin_layout Plain Layout
2820 \begin_inset Note Note
2823 \begin_layout Plain Layout
2830 is only used as spacer.
2842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2845 \begin_layout Plain Layout
2852 \begin_layout Plain Layout
2862 \begin_inset Formula $\downarrow$
2870 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2873 \begin_layout Plain Layout
2874 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2887 \begin_layout Plain Layout
2894 \begin_layout Plain Layout
2904 \begin_inset Formula $\downarrow$
2912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2915 \begin_layout Plain Layout
2916 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2929 \begin_layout Plain Layout
2936 \begin_layout Plain Layout
2946 \begin_inset Formula $\downarrow$
2954 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2957 \begin_layout Plain Layout
2958 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2971 \begin_layout Plain Layout
2978 \begin_layout Plain Layout
2988 \begin_inset Formula $\downarrow$
2996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2999 \begin_layout Plain Layout
3000 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3013 \begin_layout Plain Layout
3020 \begin_layout Plain Layout
3030 \begin_inset Formula $\downarrow$
3038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3041 \begin_layout Plain Layout
3042 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3058 \begin_layout Subsection
3059 Case differentiations
3063 \begin_layout Plain Layout
3064 Case differentiations
3072 \begin_layout Standard
3074 \begin_inset Tabular
3075 <lyxtabular version="3" rows="3" columns="2">
3077 <column alignment="center" valignment="top" width="0pt">
3078 <column alignment="center" valignment="top" width="0pt">
3080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3083 \begin_layout Plain Layout
3089 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3092 \begin_layout Plain Layout
3100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3103 \begin_layout Plain Layout
3110 \begin_layout Plain Layout
3120 \begin_inset Formula $\to$
3127 \begin_layout Plain Layout
3140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3143 \begin_layout Plain Layout
3144 \begin_inset Formula $\begin{cases}
3155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3158 \begin_layout Plain Layout
3165 \begin_layout Plain Layout
3179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3182 \begin_layout Plain Layout
3183 \begin_inset Formula $\begin{cases}
3184 A & \textrm{for }x>0\\
3185 B & \textrm{for }x=0\end{cases}$
3201 \begin_layout Standard
3208 or the usage of the math toolbar button
3209 \begin_inset Graphics
3210 filename ../images/math/cases.png
3215 you can create new lines with the shortcut
3219 or the table toolbar button
3220 \begin_inset Graphics
3221 filename ../images/tabular-feature_append-row.png
3229 \begin_layout Standard
3236 is also available via the menu
3238 Insert\SpecialChar \menuseparator
3239 Math\SpecialChar \menuseparator
3245 \begin_layout Subsection
3250 \begin_layout Plain Layout
3259 \begin_layout Standard
3270 \begin_layout Plain Layout
3278 every character can be displayed canceled.
3279 The characters are quasi accentuated by a slash.
3282 \begin_layout Standard
3284 \begin_inset Tabular
3285 <lyxtabular version="3" rows="4" columns="2">
3287 <column alignment="center" valignment="top" width="0pt">
3288 <column alignment="center" valignment="top" width="0pt">
3290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3293 \begin_layout Plain Layout
3299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3302 \begin_layout Plain Layout
3310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3313 \begin_layout Plain Layout
3321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3324 \begin_layout Plain Layout
3325 \begin_inset Formula $\not=$
3335 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3338 \begin_layout Plain Layout
3348 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3351 \begin_layout Plain Layout
3352 \begin_inset Formula $\not\le$
3362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3365 \begin_layout Plain Layout
3375 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3378 \begin_layout Plain Layout
3379 \begin_inset Formula $\not\parallel$
3395 \begin_layout Standard
3396 The last example shows, that not all negations look good.
3397 Therefore there are for some negations special commands (see
3398 \begin_inset CommandInset ref
3400 reference "sub:Mathematical-Symbols"
3405 \begin_inset CommandInset ref
3407 reference "sec:Relations"
3414 \begin_layout Subsection
3416 \begin_inset CommandInset label
3418 name "sub:Placeholders"
3426 \begin_layout Plain Layout
3436 \begin_layout Plain Layout
3437 Chemical characters ! Isotopes
3446 \begin_layout Plain Layout
3451 \begin_layout Plain Layout
3462 \begin_layout Plain Layout
3477 \begin_layout Standard
3479 \begin_inset space \thinspace{}
3483 \begin_inset space ~
3490 \begin_layout Plain Layout
3491 More about chemical symbols is written in
3492 \begin_inset CommandInset ref
3494 reference "sub:Chemical-Symbols-and"
3503 the following problem occurs:
3506 \begin_layout Standard
3508 \begin_inset Tabular
3509 <lyxtabular version="3" rows="2" columns="2">
3511 <column alignment="center" valignment="top" width="0pt">
3512 <column alignment="center" valignment="top" width="0pt">
3514 <cell alignment="center" valignment="top" usebox="none">
3517 \begin_layout Plain Layout
3518 Indices created with sub- and superscripts:
3523 <cell alignment="center" valignment="top" usebox="none">
3526 \begin_layout Plain Layout
3527 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3537 <cell alignment="center" valignment="top" usebox="none">
3540 \begin_layout Plain Layout
3546 <cell alignment="center" valignment="top" usebox="none">
3549 \begin_layout Plain Layout
3550 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3564 \begin_inset Note Note
3567 \begin_layout Plain Layout
3574 is only used as spacer.
3582 \begin_layout Standard
3583 The shorter index is by default placed below or above the first character
3584 of the longer index.
3585 To avoid this there is the command
3595 \begin_layout Plain Layout
3603 or the math toolbar button
3604 \begin_inset space \thinspace{}
3611 \begin_layout Plain Layout
3612 can be found in the submenu of the toolbar button
3613 \begin_inset Graphics
3614 filename ../images/math/space.png
3625 \begin_inset Graphics
3626 filename ../images/math/phantom.png
3631 that creates one or more phantom characters.
3638 a small blue box appears that is superposed with two red arrows.
3639 The arrows indicate that the complete width and height of the box content
3640 will be created as placeholder.
3641 Phantom characters are accordingly placeholders with the size of the characters.
3644 \begin_layout Standard
3646 \begin_inset Tabular
3647 <lyxtabular version="3" rows="4" columns="2">
3649 <column alignment="center" valignment="top" width="0">
3650 <column alignment="center" valignment="top" width="0">
3652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3655 \begin_layout Plain Layout
3661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3664 \begin_layout Plain Layout
3666 \begin_inset Note Note
3669 \begin_layout Plain Layout
3676 is only used as spacer.
3688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3691 \begin_layout Plain Layout
3696 \begin_layout Plain Layout
3711 \begin_layout Plain Layout
3721 \begin_inset Formula $\to$
3728 \begin_layout Plain Layout
3742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3745 \begin_layout Plain Layout
3746 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3759 \begin_layout Plain Layout
3764 \begin_layout Plain Layout
3779 \begin_layout Plain Layout
3789 \begin_inset Formula $\to$
3796 \begin_layout Plain Layout
3810 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3813 \begin_layout Plain Layout
3814 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3827 \begin_layout Plain Layout
3834 \begin_layout Plain Layout
3849 \begin_layout Plain Layout
3859 \begin_inset Formula $\to$
3866 \begin_layout Plain Layout
3880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3883 \begin_layout Plain Layout
3884 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3900 \begin_layout Standard
3901 Furthermore there are the commands
3911 \begin_layout Plain Layout
3920 \begin_inset space ~
3924 \begin_inset Graphics
3925 filename ../images/math/vphantom.png
3940 \begin_layout Plain Layout
3949 \begin_inset space ~
3953 \begin_inset Graphics
3954 filename ../images/math/hphantom.png
3966 creates only space for the maximal height of the characters in the box
3967 but not for its width.
3974 creates only space for the width of the box content.
3975 Therefore the boxes of both commands have only one red arrow.
3978 \begin_layout Standard
3989 \begin_layout Plain Layout
4004 space for the height of the integral sign,
4008 \begin_layout Plain Layout
4015 creates an integral sign, see
4016 \begin_inset CommandInset ref
4018 reference "sub:Big-Operators"
4027 because this is the larger character.
4028 An example application is in
4029 \begin_inset CommandInset ref
4031 reference "sub:Multiline-Brackets"
4038 \begin_layout Subsection
4043 \begin_layout Plain Layout
4053 \begin_layout Plain Layout
4054 Formula ! underlined
4062 \begin_layout Standard
4064 \begin_inset Tabular
4065 <lyxtabular version="3" rows="4" columns="2">
4067 <column alignment="center" valignment="top" width="0pt">
4068 <column alignment="center" valignment="top" width="0pt">
4070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4073 \begin_layout Plain Layout
4079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4082 \begin_layout Plain Layout
4084 \begin_inset Note Note
4087 \begin_layout Plain Layout
4094 is only used as spacer.
4106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4109 \begin_layout Plain Layout
4116 \begin_layout Plain Layout
4129 \begin_layout Plain Layout
4142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4145 \begin_layout Plain Layout
4146 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4156 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4159 \begin_layout Plain Layout
4166 \begin_layout Plain Layout
4179 \begin_layout Plain Layout
4192 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4195 \begin_layout Plain Layout
4196 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4206 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4209 \begin_layout Plain Layout
4216 \begin_layout Plain Layout
4231 \begin_layout Plain Layout
4245 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4248 \begin_layout Plain Layout
4249 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4265 \begin_layout Standard
4266 In the last example it doesn't matter if first
4281 \begin_layout Standard
4282 To double underline e.
4283 \begin_inset space \thinspace{}
4296 \begin_layout Standard
4297 It is possible to place up to 6 lines above or below characters.
4300 \begin_layout Subsection
4305 \begin_layout Plain Layout
4314 \begin_layout Standard
4315 There are different types of ellipses available.
4319 \begin_layout Plain Layout
4320 In the math toolbar in the submenu of the button
4321 \begin_inset Graphics
4322 filename ../images/math/ldots.png
4332 For listings dots at the baseline are used (
4342 \begin_layout Plain Layout
4350 ), while for operations dots are needed that are on the same height as the
4361 \begin_layout Plain Layout
4370 When using the command
4380 \begin_layout Plain Layout
4388 , LaTeX decides on the basis of the next character what type is used.
4391 \begin_layout Standard
4393 \begin_inset Tabular
4394 <lyxtabular version="3" rows="8" columns="2">
4396 <column alignment="center" valignment="top" width="0pt">
4397 <column alignment="center" valignment="top" width="0pt">
4399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4402 \begin_layout Plain Layout
4408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4411 \begin_layout Plain Layout
4419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4422 \begin_layout Plain Layout
4427 \begin_layout Plain Layout
4442 \begin_layout Plain Layout
4456 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4459 \begin_layout Plain Layout
4460 \begin_inset Formula $A_{1},\dots,A_{n}$
4470 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4473 \begin_layout Plain Layout
4478 \begin_layout Plain Layout
4493 \begin_layout Plain Layout
4507 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4510 \begin_layout Plain Layout
4511 \begin_inset Formula $A_{1}+\dots+A_{n}$
4521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4524 \begin_layout Plain Layout
4529 \begin_layout Plain Layout
4544 \begin_layout Plain Layout
4558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4561 \begin_layout Plain Layout
4562 \begin_inset Formula $A_{1},\ldots,A_{n}$
4572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4575 \begin_layout Plain Layout
4580 \begin_layout Plain Layout
4595 \begin_layout Plain Layout
4609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4612 \begin_layout Plain Layout
4613 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4626 \begin_layout Plain Layout
4634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4637 \begin_layout Plain Layout
4638 \begin_inset Formula $\vdots$
4648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4651 \begin_layout Plain Layout
4659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4662 \begin_layout Plain Layout
4663 \begin_inset Formula $\ddots$
4673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4676 \begin_layout Plain Layout
4678 \begin_inset space \thinspace{}
4681 matrix with the different dots
4686 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4689 \begin_layout Plain Layout
4690 \begin_inset Formula $\begin{array}{ccc}
4691 A_{11} & \cdots & A_{1m}\\
4692 \vdots & \ddots & \vdots\\
4693 A_{n1} & \cdots & A_{nm}\end{array}$
4709 \begin_layout Standard
4710 The ellipses available in menu
4712 Insert\SpecialChar \menuseparator
4714 \begin_inset space ~
4728 \begin_layout Standard
4729 \begin_inset VSpace medskip
4732 Specially for matrices there are ellipses that span over several columns.
4733 They are created with the command
4743 \begin_layout Plain Layout
4751 , that has the following scheme:
4754 \begin_layout Standard
4759 hdotsfor[distance]{number of columns}
4762 \begin_layout Standard
4763 The number of columns specifies how many columns should be spanned.
4764 Distance is a factor for the distance between the dots.
4767 \begin_layout Standard
4768 In the following matrix the command
4774 was inserted in the first box of the second line, to get an ellipsis with
4775 a dot distance twice as long as with the command
4782 \begin_inset Formula \[
4783 \left(\begin{array}{cccc}
4786 q & w & e & r\end{array}\right)\]
4790 Note that the matrix fields that should be spanned must be empty, otherwise
4791 you get LaTeX-errors.
4794 \begin_layout Standard
4795 \begin_inset VSpace bigskip
4798 Furthermore you can fill with the command
4808 \begin_layout Plain Layout
4816 the rest of a line with dots.
4817 The effect of these commands is the same like with
4824 \begin_inset CommandInset ref
4826 reference "sub:Variable-Space"
4833 \begin_layout Standard
4834 For example the command
4842 \begin_layout Plain Layout
4856 \begin_layout Standard
4857 \begin_inset Formula $A\dotfill B$
4863 \begin_layout Standard
4870 there is for a line the command
4880 \begin_layout Plain Layout
4891 \begin_layout Standard
4892 \begin_inset Formula $A\hrulefill B$
4898 \begin_layout Standard
4899 To use the commands for text, they have to be inserted in TeX-mode.
4902 \begin_layout Section
4904 \begin_inset CommandInset label
4914 \begin_layout Plain Layout
4923 \begin_layout Standard
4924 Matrices can be inserted via the math toolbar button
4925 \begin_inset Graphics
4926 filename ../images/dialog-show_mathmatrix.png
4933 Insert\SpecialChar \menuseparator
4934 Math\SpecialChar \menuseparator
4938 You will be asked for the number of matrix columns and rows, and the alignment.
4939 The vertical alignment is hereby only of importance for matrices in inline
4943 \begin_layout Standard
4944 The first matrix is top
4945 \begin_inset Formula $\begin{array}[t]{cccc}
4948 C & F & I & L\end{array}$
4952 \begin_inset Formula $\begin{array}{cccc}
4955 C & F & I & L\end{array}$
4958 , and the third bottom
4959 \begin_inset Formula $\begin{array}[b]{cccc}
4962 C & F & I & L\end{array}$
4968 \begin_layout Standard
4969 The horizontal alignment specifies how the column entries should be aligned.
4970 It is set by entering a letter for every column.
4975 denotes left aligned,
4984 To create for example a 4
4989 \begin_inset space ~
4992 matrix where the first column is left aligned, the second and third are
4993 centered, and the last one is right aligned, one enters for the horizontal
4999 Normally are in a matrix all columns centered, therefore the default is
5000 for every column is a
5007 \begin_layout Standard
5008 Horizontal alignment:
5011 \begin_layout Standard
5017 \begin_inset Formula $\begin{array}{lll}
5020 C & F & 10000\end{array}$
5028 \begin_inset Formula $\begin{array}{ccc}
5031 C & F & 10000\end{array}$
5039 \begin_inset Formula $\begin{array}{rrr}
5042 C & F & 10000\end{array}$
5048 \begin_layout Standard
5049 To add or delete rows and columns subsequently, the math toolbar buttons
5051 \begin_inset Graphics
5052 filename ../images/tabular-feature_append-row.png
5058 \begin_inset Graphics
5059 filename ../images/tabular-feature_delete-row.png
5065 \begin_inset space \thinspace{}
5070 Edit\SpecialChar \menuseparator
5074 New rows can also be created with
5081 \begin_layout Standard
5082 \begin_inset VSpace bigskip
5085 Parentheses around a matrix can can either be created with the commands
5096 \begin_layout Plain Layout
5114 \begin_layout Plain Layout
5125 \begin_inset space ~
5131 \begin_inset CommandInset ref
5133 reference "sub:Automatic-Bracket-Size"
5137 , or by using the following commands:
5138 \begin_inset VSpace medskip
5144 \begin_layout Standard
5145 \begin_inset space \hfill{}
5149 \begin_inset Tabular
5150 <lyxtabular version="3" rows="4" columns="2">
5152 <column alignment="center" valignment="top" width="0">
5153 <column alignment="center" valignment="top" width="0">
5155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5158 \begin_layout Plain Layout
5164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5167 \begin_layout Plain Layout
5169 \begin_inset Note Note
5172 \begin_layout Plain Layout
5179 is only used as spacer.
5191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5194 \begin_layout Plain Layout
5201 \begin_layout Plain Layout
5215 \begin_inset space \thinspace{}
5223 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5226 \begin_layout Plain Layout
5227 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5228 0 & \textrm{-}\mathrm{i}\\
5229 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5242 \begin_layout Plain Layout
5249 \begin_layout Plain Layout
5263 \begin_inset space \thinspace{}
5271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5274 \begin_layout Plain Layout
5275 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5276 0 & \textrm{-}\mathrm{i}\\
5277 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5287 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5290 \begin_layout Plain Layout
5297 \begin_layout Plain Layout
5311 \begin_inset space \thinspace{}
5319 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5322 \begin_layout Plain Layout
5323 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5324 0 & \textrm{-}\mathrm{i}\\
5325 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5339 \begin_inset space \hfill{}
5343 \begin_inset Tabular
5344 <lyxtabular version="3" rows="4" columns="2">
5346 <column alignment="center" valignment="top" width="0">
5347 <column alignment="center" valignment="top" width="0">
5349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5352 \begin_layout Plain Layout
5358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5361 \begin_layout Plain Layout
5369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5372 \begin_layout Plain Layout
5379 \begin_layout Plain Layout
5393 \begin_inset space \thinspace{}
5401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5404 \begin_layout Plain Layout
5405 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5406 0 & \textrm{-}\mathrm{i}\\
5407 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5420 \begin_layout Plain Layout
5427 \begin_layout Plain Layout
5441 \begin_inset space \thinspace{}
5449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5452 \begin_layout Plain Layout
5453 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5454 0 & \textrm{-}\mathrm{i}\\
5455 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5468 \begin_layout Plain Layout
5475 \begin_layout Plain Layout
5489 \begin_inset space \thinspace{}
5497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5500 \begin_layout Plain Layout
5501 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5502 0 & \textrm{-}\mathrm{i}\\
5503 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5517 \begin_inset space \hfill{}
5523 \begin_layout Standard
5524 \begin_inset VSpace medskip
5528 \begin_inset space \thinspace{}
5532 \begin_inset space ~
5541 is inserted, a blue box appears between two vertical lines where the matrix
5545 \begin_layout Standard
5546 \begin_inset VSpace bigskip
5549 As all multiline formulas are matrices, the length
5559 \begin_layout Plain Layout
5567 that is described in
5568 \begin_inset CommandInset ref
5570 reference "sub:Column-Separation"
5574 can also be used to change the column separation of matrices.
5577 \begin_layout Standard
5578 To change the row separation, the command
5588 \begin_layout Plain Layout
5597 It is used as follows:
5600 \begin_layout Standard
5607 arraystretch}{stretch factor}
5611 \begin_layout Plain Layout
5622 \begin_layout Standard
5629 assigns the stretch factor to the predefined command
5637 \begin_inset space \thinspace{}
5641 \begin_inset space ~
5644 the row separation, use the factor 2.
5645 This is then used for all following matrices.
5646 To go back to the original separation, assign the factor 1 to
5655 \begin_layout Standard
5656 To set matrices into a text line, the command
5666 \begin_layout Plain Layout
5675 When it is inserted a blue box with two dashed lines appears.
5676 In this box the matrix is inserted.
5679 \begin_layout Standard
5681 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5682 C & D\end{smallmatrix}\right)$
5688 \begin_layout Section
5689 Brackets and Delimiters
5693 \begin_layout Plain Layout
5703 \begin_layout Plain Layout
5712 \begin_layout Subsection
5713 Vertical Brackets and Delimiters
5717 \begin_layout Plain Layout
5726 \begin_layout Standard
5727 \begin_inset space \hfill{}
5731 \begin_inset Tabular
5732 <lyxtabular version="3" rows="9" columns="2">
5734 <column alignment="center" valignment="top" width="0pt">
5735 <column alignment="center" valignment="top" width="0pt">
5737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5740 \begin_layout Plain Layout
5746 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5749 \begin_layout Plain Layout
5757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5760 \begin_layout Plain Layout
5766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5769 \begin_layout Plain Layout
5770 \begin_inset Formula $($
5780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5783 \begin_layout Plain Layout
5789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5792 \begin_layout Plain Layout
5793 \begin_inset Formula $\{$
5803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5806 \begin_layout Plain Layout
5812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5815 \begin_layout Plain Layout
5816 \begin_inset Formula $[$
5826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5829 \begin_layout Plain Layout
5837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5840 \begin_layout Plain Layout
5841 \begin_inset Formula $\langle$
5851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5854 \begin_layout Plain Layout
5862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5865 \begin_layout Plain Layout
5866 \begin_inset Formula $\lceil$
5876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5879 \begin_layout Plain Layout
5887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5890 \begin_layout Plain Layout
5891 \begin_inset Formula $\lfloor$
5901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5904 \begin_layout Plain Layout
5910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5913 \begin_layout Plain Layout
5914 \begin_inset Formula $/$
5924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5936 \begin_layout Plain Layout
5937 \begin_inset Formula $|$
5951 \begin_inset space \hfill{}
5955 \begin_inset Tabular
5956 <lyxtabular version="3" rows="9" columns="2">
5958 <column alignment="center" valignment="top" width="0pt">
5959 <column alignment="center" valignment="top" width="0pt">
5961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5964 \begin_layout Plain Layout
5970 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5973 \begin_layout Plain Layout
5981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5984 \begin_layout Plain Layout
5990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5993 \begin_layout Plain Layout
5994 \begin_inset Formula $)$
6004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6007 \begin_layout Plain Layout
6013 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6016 \begin_layout Plain Layout
6017 \begin_inset Formula $\}$
6027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6030 \begin_layout Plain Layout
6036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6039 \begin_layout Plain Layout
6040 \begin_inset Formula $]$
6050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6053 \begin_layout Plain Layout
6061 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6064 \begin_layout Plain Layout
6065 \begin_inset Formula $\rangle$
6075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6078 \begin_layout Plain Layout
6086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6089 \begin_layout Plain Layout
6090 \begin_inset Formula $\rceil$
6100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6103 \begin_layout Plain Layout
6111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6114 \begin_layout Plain Layout
6115 \begin_inset Formula $\rfloor$
6125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6128 \begin_layout Plain Layout
6138 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6141 \begin_layout Plain Layout
6142 \begin_inset Formula $\backslash$
6152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6155 \begin_layout Plain Layout
6163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6166 \begin_layout Plain Layout
6167 \begin_inset Formula $\|$
6181 \begin_inset space \hfill{}
6187 \begin_layout Standard
6190 \begin_inset Note Greyedout
6193 \begin_layout Plain Layout
6198 In TeX-mode the command
6208 \begin_layout Plain Layout
6216 must be used for the backslash, because the command
6224 produces there a line break.
6232 \begin_layout Standard
6233 For all characters listed above the size can be adjusted with the commands
6234 described in the following two subsections.
6235 When using these commands, the characters < and > can directly be used
6236 instead of the commands
6251 \begin_layout Subsubsection
6253 \begin_inset CommandInset label
6255 name "sub:Manual-Bracket-Size"
6263 \begin_layout Plain Layout
6264 Bracket size ! manual
6272 \begin_layout Standard
6273 The bracket size can be specified manually by the LaTeX-commands
6283 \begin_layout Plain Layout
6316 denotes the smallest and
6322 the largest bracket size.
6325 \begin_layout Standard
6326 These commands are used to emphasize levels of brackets:
6329 \begin_layout Standard
6331 \begin_inset Tabular
6332 <lyxtabular version="3" rows="2" columns="2">
6334 <column alignment="center" valignment="top" width="0pt">
6335 <column alignment="center" valignment="top" width="0pt">
6337 <cell alignment="center" valignment="top" usebox="none">
6340 \begin_layout Plain Layout
6341 all brackets in the same size:
6346 <cell alignment="center" valignment="top" usebox="none">
6349 \begin_layout Plain Layout
6350 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6360 <cell alignment="center" valignment="top" usebox="none">
6363 \begin_layout Plain Layout
6369 <cell alignment="center" valignment="top" usebox="none">
6372 \begin_layout Plain Layout
6373 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6387 \begin_inset Note Note
6390 \begin_layout Plain Layout
6397 is only used as spacer.
6405 \begin_layout Standard
6406 For the second formula the command
6416 \begin_layout Plain Layout
6430 \begin_layout Standard
6431 Here is an overview about all bracket sizes:
6434 \begin_layout Standard
6454 \begin_layout Plain Layout
6471 \begin_layout Plain Layout
6484 \begin_layout Plain Layout
6500 \begin_layout Standard
6502 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6508 \begin_layout Standard
6509 \begin_inset Newpage newpage
6518 -commands there is the variant
6528 \begin_layout Plain Layout
6536 that adds a bit more space between the bracket and its content, and the
6553 \begin_layout Plain Layout
6563 , that don't add additional space.
6568 at the end of the command
6574 is for a left bracket; for a right bracket this will be replaced by an
6580 A left or right bracket can each be an opening or closing bracket.
6583 \begin_layout Standard
6584 In the following table is a comparison of the variants:
6587 \begin_layout Standard
6589 \begin_inset Tabular
6590 <lyxtabular version="3" rows="5" columns="2">
6592 <column alignment="center" valignment="middle" width="0">
6593 <column alignment="center" valignment="middle" width="0">
6595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6598 \begin_layout Plain Layout
6604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6607 \begin_layout Plain Layout
6609 \begin_inset Note Note
6612 \begin_layout Plain Layout
6619 is only used as spacer.
6631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6634 \begin_layout Plain Layout
6649 \begin_layout Plain Layout
6667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6670 \begin_layout Plain Layout
6671 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6684 \begin_layout Plain Layout
6699 \begin_layout Plain Layout
6717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6720 \begin_layout Plain Layout
6721 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6734 \begin_layout Plain Layout
6749 \begin_layout Plain Layout
6767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6770 \begin_layout Plain Layout
6771 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6784 \begin_layout Plain Layout
6796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6799 \begin_layout Plain Layout
6800 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6816 \begin_layout Subsubsection
6817 Automatic Bracket Size
6818 \begin_inset CommandInset label
6820 name "sub:Automatic-Bracket-Size"
6828 \begin_layout Plain Layout
6829 Bracket size ! automatic
6837 \begin_layout Standard
6838 Brackets with variable size can be inserted with the commands
6848 \begin_layout Plain Layout
6866 \begin_layout Plain Layout
6874 or via the math toolbar button
6875 \begin_inset Graphics
6876 filename ../images/dialog-show_mathdelimiter.png
6894 the wanted bracket must be inserted.
6895 The bracket size will then automatically be calculated for the output.
6898 \begin_layout Standard
6900 normal bracket: The command
6910 \begin_layout Plain Layout
6920 \begin_inset Formula $\downarrow$
6927 \begin_layout Plain Layout
6939 \begin_inset Formula \[
6947 \begin_layout Standard
6949 multiline bracket: The command
6961 \begin_layout Plain Layout
6971 \begin_inset Formula $\downarrow$
6978 \begin_layout Plain Layout
6992 \begin_inset Formula \[
6993 \ln\left(\frac{A}{C}\right)\]
7000 \begin_layout Standard
7016 \begin_inset space ~
7022 This has the advantage that you can see in LyX immediately the real bracket
7023 size and that the matching right bracket will be created too.
7024 \begin_inset Newline newline
7027 The command for the last example would then be:
7041 \begin_layout Plain Layout
7051 \begin_inset Formula $\downarrow$
7057 \begin_layout Standard
7058 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7059 For example the command
7069 \begin_layout Plain Layout
7079 \begin_inset Formula $\downarrow$
7086 \begin_layout Plain Layout
7102 \begin_inset Formula \[
7103 \left.\frac{A}{B}\right\} \]
7121 will be converted by LyX to brackets in the right size when the document
7122 is reloaded and an omitted bracket will appear as dashed line.
7125 \begin_layout Standard
7126 \begin_inset VSpace bigskip
7129 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7140 \begin_layout Plain Layout
7148 is additionally available for all brackets and limits.
7149 With this command the height of the following character is adapted to the
7150 one of the surrounding brackets, what is e.
7151 \begin_inset space \thinspace{}
7155 \begin_inset space ~
7158 needed for physical vectors:
7159 \begin_inset Formula \[
7160 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7164 For physical vectors there is a special LaTeX-package, described in
7165 \begin_inset CommandInset ref
7167 reference "sub:Physical-Vectors"
7174 \begin_layout Subsection
7179 \begin_layout Plain Layout
7180 Brackets ! horizontal
7188 \begin_layout Standard
7190 \begin_inset Tabular
7191 <lyxtabular version="3" rows="4" columns="2">
7193 <column alignment="center" valignment="top" width="0pt">
7194 <column alignment="center" valignment="top" width="0pt">
7196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7199 \begin_layout Plain Layout
7201 \begin_inset Note Note
7204 \begin_layout Plain Layout
7211 is only used as spacer.
7221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7224 \begin_layout Plain Layout
7232 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7235 \begin_layout Plain Layout
7239 \begin_layout Plain Layout
7254 \begin_layout Plain Layout
7267 \begin_layout Plain Layout
7280 \begin_layout Plain Layout
7293 \begin_layout Plain Layout
7304 \begin_layout Plain Layout
7317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7320 \begin_layout Plain Layout
7321 \begin_inset Formula $\overbrace{A+B}^{3}$
7331 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7334 \begin_layout Plain Layout
7338 \begin_layout Plain Layout
7353 \begin_layout Plain Layout
7366 \begin_layout Plain Layout
7379 \begin_layout Plain Layout
7390 \begin_layout Plain Layout
7403 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7406 \begin_layout Plain Layout
7407 \begin_inset Formula $\underbrace{A+B}_{5}$
7417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7420 \begin_layout Plain Layout
7427 \begin_layout Plain Layout
7442 \begin_layout Plain Layout
7455 \begin_layout Plain Layout
7468 \begin_layout Plain Layout
7481 \begin_layout Plain Layout
7494 \begin_layout Plain Layout
7507 \begin_layout Plain Layout
7521 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7524 \begin_layout Plain Layout
7525 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7541 \begin_layout Standard
7542 In the last example it doesn't matter if
7554 is inserted at first.
7557 \begin_layout Standard
7558 \begin_inset VSpace bigskip
7561 When brackets are needed that overlap each other, multiline formulas, as
7563 \begin_inset CommandInset ref
7565 reference "sec:Multiline-Formulas"
7570 \begin_inset Formula \begin{eqnarray*}
7571 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7572 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7576 In the first row the formula is inserted together with the first brace.
7577 It is hereby important that the space command
7581 \begin_layout Plain Layout
7582 Space commands are explained in
7583 \begin_inset CommandInset ref
7585 reference "sub:Predefined-Space"
7600 is inserted before the first
7601 \begin_inset Formula $d$
7604 , because the brace that ends behind the
7605 \begin_inset Formula $q$
7608 prevents that the following
7609 \begin_inset Quotes eld
7613 \begin_inset Quotes erd
7616 is surrounded by space.
7620 \begin_layout Plain Layout
7621 because a bracket is not handled as character, see
7622 \begin_inset CommandInset ref
7624 reference "sub:Binary-Operators"
7633 In the second row the second brace is inserted.
7634 As it should begin before the
7635 \begin_inset Formula $b$
7650 \begin_layout Plain Layout
7658 \begin_inset CommandInset ref
7660 reference "sub:Placeholders"
7669 This space is needed because the
7670 \begin_inset Quotes eld
7674 \begin_inset Quotes erd
7677 is also surrounded by space in the formula.
7678 The brace is placed under the command
7687 \begin_layout Standard
7688 It gets more complicated when brackets overlap each other, like in the following
7693 \begin_layout Plain Layout
7705 \begin_inset Formula \begin{eqnarray*}
7706 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7707 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7715 \begin_layout Plain Layout
7726 The first formula row is the same as the second row of the previous example,
7727 with the difference that the brace is above.
7728 The second row contains the formula together with the second brace.
7729 To avoid that there is space between the upper brace in the first row and
7730 the formula, the row spacing need to be reduced.
7731 This is not easily possible due to a bug in LyX
7735 \begin_layout Plain Layout
7736 \begin_inset CommandInset href
7738 name "LyX-bug #1505"
7739 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7749 As solution for the problem, the global formula row separation
7759 \begin_layout Plain Layout
7767 must be changed to -6
7768 \begin_inset space \thinspace{}
7771 pt before the formula with the command
7786 is set back after the formula to the standard value of 3
7787 \begin_inset space \thinspace{}
7790 pt using the same command.
7791 More about the row separation in formulas is explained in
7792 \begin_inset CommandInset ref
7794 reference "sub:Line-Separation"
7801 \begin_layout Section
7806 \begin_layout Plain Layout
7815 \begin_layout Standard
7816 Arrows can be inserted via the math toolbar button
7817 \begin_inset Graphics
7818 filename ../images/math/leftarrow.png
7823 or the commands listed in the following subsections.
7826 \begin_layout Subsection
7831 \begin_layout Plain Layout
7840 \begin_layout Standard
7841 \begin_inset space \hfill{}
7845 \begin_inset Tabular
7846 <lyxtabular version="3" rows="8" columns="2">
7848 <column alignment="center" valignment="top" width="0pt">
7849 <column alignment="center" valignment="top" width="0pt">
7851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7854 \begin_layout Plain Layout
7860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7863 \begin_layout Plain Layout
7871 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7874 \begin_layout Plain Layout
7882 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7885 \begin_layout Plain Layout
7886 \begin_inset Formula $\gets$
7896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7899 \begin_layout Plain Layout
7907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7910 \begin_layout Plain Layout
7911 \begin_inset Formula $\Leftarrow$
7921 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7924 \begin_layout Plain Layout
7932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7935 \begin_layout Plain Layout
7936 \begin_inset Formula $\longleftarrow$
7946 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7949 \begin_layout Plain Layout
7957 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7960 \begin_layout Plain Layout
7961 \begin_inset Formula $\Longleftarrow$
7971 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7974 \begin_layout Plain Layout
7982 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7985 \begin_layout Plain Layout
7986 \begin_inset Formula $\leftharpoonup$
7996 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7999 \begin_layout Plain Layout
8007 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8010 \begin_layout Plain Layout
8011 \begin_inset Formula $\leftharpoondown$
8021 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8024 \begin_layout Plain Layout
8032 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8035 \begin_layout Plain Layout
8036 \begin_inset Formula $\hookleftarrow$
8050 \begin_inset space \hfill{}
8054 \begin_inset Tabular
8055 <lyxtabular version="3" rows="8" columns="2">
8057 <column alignment="center" valignment="top" width="0pt">
8058 <column alignment="center" valignment="top" width="0pt">
8060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8063 \begin_layout Plain Layout
8069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8072 \begin_layout Plain Layout
8080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8083 \begin_layout Plain Layout
8091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8094 \begin_layout Plain Layout
8095 \begin_inset Formula $\to$
8105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8108 \begin_layout Plain Layout
8116 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8119 \begin_layout Plain Layout
8120 \begin_inset Formula $\Rightarrow$
8130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8133 \begin_layout Plain Layout
8141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8144 \begin_layout Plain Layout
8145 \begin_inset Formula $\longrightarrow$
8155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8158 \begin_layout Plain Layout
8166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8169 \begin_layout Plain Layout
8170 \begin_inset Formula $\Longrightarrow$
8180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8183 \begin_layout Plain Layout
8191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8194 \begin_layout Plain Layout
8195 \begin_inset Formula $\rightharpoonup$
8205 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8208 \begin_layout Plain Layout
8216 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8219 \begin_layout Plain Layout
8220 \begin_inset Formula $\rightharpoondown$
8230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8233 \begin_layout Plain Layout
8241 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8244 \begin_layout Plain Layout
8245 \begin_inset Formula $\hookrightarrow$
8259 \begin_inset space \hfill{}
8265 \begin_layout Standard
8266 \begin_inset space \hfill{}
8270 \begin_inset Tabular
8271 <lyxtabular version="3" rows="6" columns="2">
8273 <column alignment="center" valignment="top" width="0pt">
8274 <column alignment="center" valignment="top" width="0pt">
8276 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8279 \begin_layout Plain Layout
8285 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8288 \begin_layout Plain Layout
8296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8299 \begin_layout Plain Layout
8307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8310 \begin_layout Plain Layout
8311 \begin_inset Formula $\leftrightarrow$
8321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8324 \begin_layout Plain Layout
8332 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8335 \begin_layout Plain Layout
8336 \begin_inset Formula $\Leftrightarrow$
8346 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8349 \begin_layout Plain Layout
8357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8360 \begin_layout Plain Layout
8361 \begin_inset Formula $\longleftrightarrow$
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8374 \begin_layout Plain Layout
8382 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8385 \begin_layout Plain Layout
8386 \begin_inset Formula $\Longleftrightarrow$
8396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8399 \begin_layout Plain Layout
8407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8410 \begin_layout Plain Layout
8411 \begin_inset Formula $\rightleftharpoons$
8425 \begin_inset space \hspace{}
8430 \begin_inset space \hfill{}
8434 \begin_inset Tabular
8435 <lyxtabular version="3" rows="5" columns="2">
8437 <column alignment="center" valignment="top" width="0pt">
8438 <column alignment="center" valignment="top" width="0pt">
8440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8443 \begin_layout Plain Layout
8449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8452 \begin_layout Plain Layout
8460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8463 \begin_layout Plain Layout
8471 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8474 \begin_layout Plain Layout
8475 \begin_inset Formula $\mapsto$
8485 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8488 \begin_layout Plain Layout
8496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8499 \begin_layout Plain Layout
8500 \begin_inset Formula $\longmapsto$
8510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8513 \begin_layout Plain Layout
8521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8524 \begin_layout Plain Layout
8525 \begin_inset Formula $\leadsto$
8535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8538 \begin_layout Plain Layout
8546 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8549 \begin_layout Plain Layout
8550 \begin_inset Formula $\dasharrow$
8564 \begin_inset space \hfill{}
8570 \begin_layout Standard
8571 \begin_inset VSpace medskip
8574 Arrows used as accent like e.
8575 \begin_inset space \thinspace{}
8579 \begin_inset space ~
8582 vector arrows are listed in
8583 \begin_inset CommandInset ref
8585 reference "sec:Accents"
8592 \begin_layout Standard
8593 \begin_inset VSpace bigskip
8596 Furthermore there are the labeled arrows
8600 \begin_layout Plain Layout
8616 \begin_layout Plain Layout
8634 \begin_layout Plain Layout
8641 \begin_layout Plain Layout
8656 When inserting one of these commands in a formula, an arrow with two blue
8657 boxes appear where the label can be inserted.
8658 The length of the arrow adapts to the label width.
8661 \begin_layout Standard
8663 \begin_inset Tabular
8664 <lyxtabular version="3" rows="3" columns="2">
8666 <column alignment="center" valignment="top" width="0pt">
8667 <column alignment="center" valignment="top" width="0pt">
8669 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8672 \begin_layout Plain Layout
8678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8681 \begin_layout Plain Layout
8683 \begin_inset Note Note
8686 \begin_layout Plain Layout
8693 is only used as spacer.
8705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8708 \begin_layout Plain Layout
8715 \begin_layout Plain Layout
8725 \begin_inset Formula $\downarrow$
8729 \begin_inset Formula $\to$
8737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8740 \begin_layout Plain Layout
8741 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8754 \begin_layout Plain Layout
8761 \begin_layout Plain Layout
8771 \begin_inset Formula $\downarrow$
8775 \begin_inset Formula $\to$
8783 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8786 \begin_layout Plain Layout
8787 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8803 \begin_layout Subsection
8804 Vertical and diagonal Arrows
8808 \begin_layout Plain Layout
8818 \begin_layout Plain Layout
8827 \begin_layout Standard
8828 \begin_inset space \hfill{}
8832 \begin_inset Tabular
8833 <lyxtabular version="3" rows="7" columns="2">
8835 <column alignment="center" valignment="top" width="0pt">
8836 <column alignment="center" valignment="top" width="0pt">
8838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8841 \begin_layout Plain Layout
8847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8850 \begin_layout Plain Layout
8858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8861 \begin_layout Plain Layout
8869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8872 \begin_layout Plain Layout
8873 \begin_inset Formula $\uparrow$
8883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8886 \begin_layout Plain Layout
8894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8897 \begin_layout Plain Layout
8898 \begin_inset Formula $\Uparrow$
8908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8911 \begin_layout Plain Layout
8919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8922 \begin_layout Plain Layout
8923 \begin_inset Formula $\updownarrow$
8933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8936 \begin_layout Plain Layout
8944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8947 \begin_layout Plain Layout
8948 \begin_inset Formula $\Updownarrow$
8958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8961 \begin_layout Plain Layout
8969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8972 \begin_layout Plain Layout
8973 \begin_inset Formula $\Downarrow$
8983 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8986 \begin_layout Plain Layout
8994 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8997 \begin_layout Plain Layout
8998 \begin_inset Formula $\downarrow$
9012 \begin_inset space \hfill{}
9016 \begin_inset Tabular
9017 <lyxtabular version="3" rows="5" columns="2">
9019 <column alignment="center" valignment="top" width="0pt">
9020 <column alignment="center" valignment="top" width="0pt">
9022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9025 \begin_layout Plain Layout
9031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9034 \begin_layout Plain Layout
9042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9045 \begin_layout Plain Layout
9053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9056 \begin_layout Plain Layout
9057 \begin_inset Formula $\nearrow$
9067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9070 \begin_layout Plain Layout
9078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9081 \begin_layout Plain Layout
9082 \begin_inset Formula $\searrow$
9092 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9095 \begin_layout Plain Layout
9103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9106 \begin_layout Plain Layout
9107 \begin_inset Formula $\swarrow$
9117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9120 \begin_layout Plain Layout
9128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9131 \begin_layout Plain Layout
9132 \begin_inset Formula $\nwarrow$
9146 \begin_inset space \hfill{}
9152 \begin_layout Standard
9153 \begin_inset VSpace medskip
9156 Vertical arrows can be used also as delimiter together with the commands
9158 \begin_inset CommandInset ref
9160 reference "sub:Manual-Bracket-Size"
9165 \begin_inset CommandInset ref
9167 reference "sub:Automatic-Bracket-Size"
9174 \begin_layout Standard
9175 \begin_inset Newpage newpage
9181 \begin_layout Section
9183 \begin_inset CommandInset label
9193 \begin_layout Plain Layout
9202 \begin_layout Standard
9203 Accents can be inserted via the math toolbar button
9204 \begin_inset Graphics
9205 filename ../images/math/hat.png
9210 or the commands listed in the following subsections.
9213 \begin_layout Subsection
9214 Accents for one Character
9218 \begin_layout Plain Layout
9231 \begin_layout Plain Layout
9233 \begin_inset CommandInset ref
9235 reference "sub:Accents-in-Text"
9248 \begin_layout Plain Layout
9256 \begin_inset Note Note
9259 \begin_layout Plain Layout
9262 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9265 \begin_layout Plain Layout
9268 texorpdfstring is in section
9269 \begin_inset CommandInset ref
9271 reference "sub:Formulas-in-Section"
9281 \begin_inset CommandInset label
9283 name "sub:Accents-for-one"
9291 \begin_layout Plain Layout
9292 Accents ! for one character
9300 \begin_layout Standard
9301 \begin_inset space \hfill{}
9305 \begin_inset Tabular
9306 <lyxtabular version="3" rows="8" columns="2">
9308 <column alignment="center" valignment="top" width="0pt">
9309 <column alignment="center" valignment="top" width="0pt">
9311 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9314 \begin_layout Plain Layout
9320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9323 \begin_layout Plain Layout
9325 \begin_inset Note Note
9328 \begin_layout Plain Layout
9335 is only used as spacer.
9347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9350 \begin_layout Plain Layout
9357 \begin_layout Plain Layout
9371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9374 \begin_layout Plain Layout
9375 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9385 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9388 \begin_layout Plain Layout
9395 \begin_layout Plain Layout
9409 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9412 \begin_layout Plain Layout
9413 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9423 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9426 \begin_layout Plain Layout
9433 \begin_layout Plain Layout
9447 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9450 \begin_layout Plain Layout
9451 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9461 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9464 \begin_layout Plain Layout
9472 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9475 \begin_layout Plain Layout
9476 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9486 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9489 \begin_layout Plain Layout
9496 \begin_layout Plain Layout
9509 \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 $\raisebox{5mm}{}\vec{A}$
9534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9537 \begin_layout Plain Layout
9544 \begin_layout Plain Layout
9558 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9561 \begin_layout Plain Layout
9562 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9575 \begin_layout Plain Layout
9582 \begin_layout Plain Layout
9596 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9599 \begin_layout Plain Layout
9600 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9614 \begin_inset space \hfill{}
9618 \begin_inset Tabular
9619 <lyxtabular version="3" rows="7" columns="2">
9621 <column alignment="center" valignment="top" width="0pt">
9622 <column alignment="center" valignment="top" width="0pt">
9624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9627 \begin_layout Plain Layout
9633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9636 \begin_layout Plain Layout
9644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9647 \begin_layout Plain Layout
9654 \begin_layout Plain Layout
9668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9671 \begin_layout Plain Layout
9672 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9682 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9685 \begin_layout Plain Layout
9692 \begin_layout Plain Layout
9706 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9709 \begin_layout Plain Layout
9710 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9723 \begin_layout Plain Layout
9730 \begin_layout Plain Layout
9744 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9747 \begin_layout Plain Layout
9748 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9761 \begin_layout Plain Layout
9768 \begin_layout Plain Layout
9782 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9785 \begin_layout Plain Layout
9786 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9799 \begin_layout Plain Layout
9806 \begin_layout Plain Layout
9820 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9823 \begin_layout Plain Layout
9824 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9834 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9837 \begin_layout Plain Layout
9844 \begin_layout Plain Layout
9858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9861 \begin_layout Plain Layout
9862 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9876 \begin_inset space \hfill{}
9882 \begin_layout Standard
9883 \begin_inset VSpace bigskip
9890 \begin_layout Plain Layout
9896 in formulas, a quotation mark is inserted before the vowel.
9897 These two characters are then treated by LaTeX as
9901 character when the formula part with the umlaut is marked as German.
9909 \begin_inset Quotes eld
9913 \begin_inset Quotes erd
9916 umlauts are created as demonstrated in the following example:
9919 \begin_layout Standard
9920 \begin_inset VSpace -2mm
9926 \begin_layout Standard
9928 \begin_inset Tabular
9929 <lyxtabular version="3" rows="3" columns="2">
9931 <column alignment="center" valignment="top" width="0">
9932 <column alignment="center" valignment="top" width="0">
9934 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9937 \begin_layout Plain Layout
9943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9946 \begin_layout Plain Layout
9948 \begin_inset Note Note
9951 \begin_layout Plain Layout
9958 is only used as spacer.
9970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9973 \begin_layout Plain Layout
9976 \begin_inset Quotes grd
9984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9987 \begin_layout Plain Layout
9990 \begin_inset Formula $"i$
10000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10003 \begin_layout Plain Layout
10010 \begin_layout Plain Layout
10024 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10027 \begin_layout Plain Layout
10028 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10044 \begin_layout Standard
10045 Another advantage to
10051 is that umlauts can directly be converted to mathematical text because
10052 the accent commands above are
10058 in mathematical text
10061 To convert an accented character to mathematical text, only the character
10062 under the accent may be converted.
10063 This applies also for all other conversions, e.
10064 \begin_inset space \thinspace{}
10068 \begin_inset space ~
10074 \begin_layout Standard
10075 In mathematical text, umlauts and other accented characters can directly
10079 \begin_layout Subsection
10080 Accents for Operators
10084 \begin_layout Plain Layout
10085 Accents ! for operators
10093 \begin_layout Standard
10104 \begin_layout Plain Layout
10122 \begin_layout Plain Layout
10130 characters can be placed above or below an operator, respectively, to accent
10142 \begin_layout Plain Layout
10150 characters can be set before and behind an operator.
10151 The command scheme is:
10154 \begin_layout Standard
10170 \begin_layout Standard
10177 must always be before the operator that should be accented.
10178 You can accent with several characters and even with other operators and
10186 for example only characters behind an operator, write nothing between the
10187 first braces but don't omit the braces.
10190 \begin_layout Standard
10191 For example the command
10196 \begin_inset Formula $\to$
10206 \begin_inset Formula $\to$
10215 \begin_layout Plain Layout
10231 \begin_inset Formula \[
10232 \sideset{}{'}\sum_{k=1}^{n}\]
10239 \begin_layout Standard
10248 \begin_layout Plain Layout
10263 \begin_layout Plain Layout
10275 \begin_inset Formula $\uparrow$
10283 \begin_inset Formula \[
10284 \overset{a}{\maltese}\]
10288 As seen in the last example, with
10300 also symbols and characters can be accented; with
10306 this is not possible.
10309 \begin_layout Subsection
10310 Accents for several Characters
10311 \begin_inset CommandInset label
10313 name "sub:Accents-for-several"
10321 \begin_layout Plain Layout
10322 Accents ! for several characters
10330 \begin_layout Standard
10331 \begin_inset space \hfill{}
10335 \begin_inset Tabular
10336 <lyxtabular version="3" rows="5" columns="2">
10338 <column alignment="center" valignment="top" width="0pt">
10339 <column alignment="center" valignment="top" width="0pt">
10341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10344 \begin_layout Plain Layout
10350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10353 \begin_layout Plain Layout
10355 \begin_inset Note Note
10358 \begin_layout Plain Layout
10365 is only used as spacer.
10377 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10380 \begin_layout Plain Layout
10387 \begin_layout Plain Layout
10401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10404 \begin_layout Plain Layout
10405 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10418 \begin_layout Plain Layout
10425 \begin_layout Plain Layout
10439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10442 \begin_layout Plain Layout
10443 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10456 \begin_layout Plain Layout
10463 \begin_layout Plain Layout
10477 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10480 \begin_layout Plain Layout
10481 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10491 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10494 \begin_layout Plain Layout
10497 underleftrightarrow
10501 \begin_layout Plain Layout
10515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10518 \begin_layout Plain Layout
10519 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10533 \begin_inset space \hfill{}
10537 \begin_inset Tabular
10538 <lyxtabular version="3" rows="5" columns="2">
10540 <column alignment="center" valignment="top" width="0pt">
10541 <column alignment="center" valignment="top" width="0pt">
10543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10546 \begin_layout Plain Layout
10552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10555 \begin_layout Plain Layout
10563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10566 \begin_layout Plain Layout
10573 \begin_layout Plain Layout
10587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10590 \begin_layout Plain Layout
10591 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10601 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10604 \begin_layout Plain Layout
10611 \begin_layout Plain Layout
10625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10628 \begin_layout Plain Layout
10629 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10639 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10642 \begin_layout Plain Layout
10649 \begin_layout Plain Layout
10663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10666 \begin_layout Plain Layout
10667 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10677 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10680 \begin_layout Plain Layout
10687 \begin_layout Plain Layout
10701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10704 \begin_layout Plain Layout
10705 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10719 \begin_inset space \hfill{}
10725 \begin_layout Standard
10726 \begin_inset VSpace medskip
10729 With these commands as many characters as you like can be accented.
10742 will only be set in the output with a length of three characters, as shown
10743 in the following example:
10744 \begin_inset Formula \[
10745 \widetilde{A+B=C-D}\]
10752 \begin_layout Standard
10763 \begin_layout Plain Layout
10781 \begin_layout Plain Layout
10789 described in the previous subsection it is also possible to accent several
10799 \begin_layout Plain Layout
10809 \begin_inset Formula $\downarrow$
10815 \begin_inset Formula \[
10816 \underset{***}{A=B}\]
10823 \begin_layout Section
10825 \begin_inset CommandInset label
10835 \begin_layout Plain Layout
10844 \begin_layout Subsection
10846 \begin_inset CommandInset label
10848 name "sub:Predefined-Space"
10856 \begin_layout Plain Layout
10857 Space ! horizontal ! predefined
10865 \begin_layout Standard
10866 Sometimes it is necessary to insert horizontal space to a formula.
10867 This is done by inserting a protected space (shortcut
10873 \begin_inset Quotes eld
10883 \begin_layout Plain Layout
10896 \begin_inset Quotes erd
10899 appears and by pressing
10903 several times one can select one of eight different space sizes.
10904 The spaces can also be inserted using the math toolbar button
10905 \begin_inset Graphics
10906 filename ../images/math/space.png
10911 or special commands.
10912 Independent from the inserted command, one can select the size again by
10920 \begin_layout Standard
10923 \begin_inset VSpace -5mm
10927 \begin_inset Tabular
10928 <lyxtabular version="3" rows="3" columns="7">
10930 <column alignment="center" valignment="middle" width="6.8cm">
10931 <column alignment="center" valignment="top" width="0">
10932 <column alignment="center" valignment="top" width="0">
10933 <column alignment="center" valignment="top" width="0">
10934 <column alignment="center" valignment="top" width="0">
10935 <column alignment="center" valignment="top" width="0">
10936 <column alignment="center" valignment="top" width="0">
10938 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10941 \begin_layout Plain Layout
10947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10950 \begin_layout Plain Layout
10958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10961 \begin_layout Plain Layout
10969 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10972 \begin_layout Plain Layout
10980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10983 \begin_layout Plain Layout
10991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10994 \begin_layout Plain Layout
11002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11005 \begin_layout Plain Layout
11015 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11018 \begin_layout Plain Layout
11023 keystrokes after inserting the protected space
11028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11031 \begin_layout Plain Layout
11037 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11040 \begin_layout Plain Layout
11046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11049 \begin_layout Plain Layout
11055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11058 \begin_layout Plain Layout
11064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11067 \begin_layout Plain Layout
11073 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11076 \begin_layout Plain Layout
11084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11087 \begin_layout Plain Layout
11093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11096 \begin_layout Plain Layout
11097 \begin_inset Formula $A\, B$
11105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11108 \begin_layout Plain Layout
11109 \begin_inset Formula $A\: B$
11117 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11120 \begin_layout Plain Layout
11121 \begin_inset Formula $A\; B$
11129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11132 \begin_layout Plain Layout
11133 \begin_inset Formula $A\quad B$
11141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11145 \begin_inset Formula $A\qquad B$
11153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11156 \begin_layout Plain Layout
11157 \begin_inset Formula $A\! B$
11173 \begin_layout Standard
11174 The last size seem to produce no space.
11175 It is displayed red in LyX contrary to the other sizes, because it is a
11177 There are two more negative spaces:
11180 \begin_layout Standard
11182 \begin_inset Tabular
11183 <lyxtabular version="3" rows="3" columns="3">
11185 <column alignment="center" valignment="middle" width="6.8cm">
11186 <column alignment="center" valignment="top" width="0pt">
11187 <column alignment="center" valignment="top" width="0pt">
11189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11192 \begin_layout Plain Layout
11198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11212 \begin_layout Plain Layout
11222 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11225 \begin_layout Plain Layout
11230 keystrokes after inserting the protected space
11235 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11238 \begin_layout Plain Layout
11244 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11247 \begin_layout Plain Layout
11255 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11258 \begin_layout Plain Layout
11264 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11267 \begin_layout Plain Layout
11268 \begin_inset Formula $A\negmedspace B$
11276 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11279 \begin_layout Plain Layout
11280 \begin_inset Formula $A\negthickspace B$
11296 \begin_layout Standard
11297 Negative spaces can lead to characters overlapping each other.
11298 Thus they can be used to enforce ligatures, what is e.
11299 \begin_inset space \thinspace{}
11303 \begin_inset space ~
11306 useful for summation operators:
11309 \begin_layout Standard
11311 \begin_inset Tabular
11312 <lyxtabular version="3" rows="3" columns="2">
11314 <column alignment="center" valignment="top" width="0">
11315 <column alignment="center" valignment="top" width="0">
11317 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11320 \begin_layout Plain Layout
11326 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11329 \begin_layout Plain Layout
11331 \begin_inset Note Note
11334 \begin_layout Plain Layout
11341 is only used as spacer.
11353 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11356 \begin_layout Plain Layout
11365 \begin_layout Plain Layout
11379 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11382 \begin_layout Plain Layout
11383 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11396 \begin_layout Plain Layout
11407 \begin_layout Plain Layout
11421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11424 \begin_layout Plain Layout
11425 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11441 \begin_layout Standard
11442 Relations like for example equal signs, are always surrounded by space.
11443 To suppress this, the equal sign is placed into a TeX-brace.
11444 The following example demonstrates this:
11447 \begin_layout Standard
11449 \begin_inset Tabular
11450 <lyxtabular version="3" rows="2" columns="2">
11452 <column alignment="center" valignment="top" width="0pt">
11453 <column alignment="center" valignment="top" width="0pt">
11455 <cell alignment="center" valignment="top" usebox="none">
11458 \begin_layout Plain Layout
11464 <cell alignment="center" valignment="top" usebox="none">
11467 \begin_layout Plain Layout
11468 \begin_inset Formula $A=B$
11478 <cell alignment="center" valignment="top" usebox="none">
11481 \begin_layout Plain Layout
11482 \begin_inset Note Note
11485 \begin_layout Plain Layout
11492 is only used as spacer.
11498 \begin_inset Formula $\raisebox{5mm}{}$
11501 equation without space
11506 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11509 \begin_layout Plain Layout
11510 \begin_inset Formula $A{=}B$
11526 \begin_layout Standard
11528 The command for the last formula is:
11533 \begin_inset Formula $\to$
11539 \begin_layout Standard
11540 \begin_inset VSpace bigskip
11543 Spaces are needed for physical units, because the space between the value
11544 and the unit is the smallest one and not a normal space.
11545 For units in text, the smallest space is inserted via the menu
11547 Insert\SpecialChar \menuseparator
11548 Formatting\SpecialChar \menuseparator
11550 \begin_inset space ~
11562 \begin_layout Standard
11563 An example to visualize the difference:
11566 \begin_layout Standard
11567 \begin_inset Tabular
11568 <lyxtabular version="3" rows="2" columns="2">
11570 <column alignment="left" valignment="top" width="0">
11571 <column alignment="left" valignment="top" width="0">
11573 <cell alignment="center" valignment="top" usebox="none">
11576 \begin_layout Plain Layout
11578 \begin_inset Formula $\cdot$
11586 <cell alignment="center" valignment="top" usebox="none">
11589 \begin_layout Plain Layout
11590 space between value and unit
11597 <cell alignment="center" valignment="top" usebox="none">
11600 \begin_layout Plain Layout
11602 \begin_inset space \thinspace{}
11606 \begin_inset Formula $\cdot$
11614 <cell alignment="center" valignment="top" usebox="none">
11617 \begin_layout Plain Layout
11618 smallest space between value and unit
11631 \begin_layout Subsection
11636 \begin_layout Plain Layout
11649 \begin_layout Plain Layout
11650 for vertical space in formulas see
11651 \begin_inset CommandInset ref
11653 reference "sub:Line-Separation"
11666 \begin_layout Plain Layout
11674 \begin_inset Note Note
11677 \begin_layout Plain Layout
11680 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11683 \begin_layout Plain Layout
11686 texorpdfstring is in section
11687 \begin_inset CommandInset ref
11689 reference "sub:Formulas-in-Section"
11699 \begin_inset CommandInset label
11701 name "sub:Variable-Space"
11709 \begin_layout Plain Layout
11710 Space ! horizontal ! variable
11718 \begin_layout Standard
11719 Space with a defined length can be inserted in LyX with the command
11720 \begin_inset Newline newline
11733 \begin_layout Plain Layout
11742 For the length all units listed in
11743 \begin_inset CommandInset ref
11745 reference "tab:Used-units"
11749 are allowed, except of the unit
11750 \begin_inset Quotes eld
11754 \begin_inset Quotes erd
11758 The length may also be negative.
11759 To insert so many space that the formula uses all available space, the
11770 \begin_layout Plain Layout
11781 \begin_layout Standard
11782 \begin_inset VSpace -1mm
11788 \begin_layout Standard
11790 \begin_inset Tabular
11791 <lyxtabular version="3" rows="4" columns="2">
11793 <column alignment="center" valignment="top" width="0">
11794 <column alignment="center" valignment="top" width="0">
11796 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11799 \begin_layout Plain Layout
11805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11808 \begin_layout Plain Layout
11816 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11819 \begin_layout Plain Layout
11823 \begin_inset Formula $\to$
11833 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11836 \begin_layout Plain Layout
11837 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11850 \begin_layout Plain Layout
11854 \begin_inset Formula $\to$
11864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11867 \begin_layout Plain Layout
11868 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11881 \begin_layout Plain Layout
11888 \begin_layout Plain Layout
11902 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11905 \begin_layout Plain Layout
11906 \begin_inset Formula $A=A\hfill B=B$
11922 \begin_layout Standard
11923 In the last example the available space is given by the longest column entry
11925 In an inline formula the space depends on the length of the line in which
11933 Thus, when the line uses the full width, no space will be created.
11940 only has an effect on displayed formulas when the formula style
11945 (Formula styles are explained in
11946 \begin_inset CommandInset ref
11948 reference "sec:Formula-Styles"
11955 \begin_layout Standard
11956 For text, variable space can be inserted via the menu
11958 Insert\SpecialChar \menuseparator
11959 Formatting\SpecialChar \menuseparator
11961 \begin_inset space ~
11966 , what is not possible in formulas:
11969 \begin_layout Standard
11970 This is a line with
11971 \begin_inset space \hspace{}
11976 \begin_inset space \thinspace{}
11982 \begin_layout Standard
11983 This is a line with
11984 \begin_inset space \hfill{}
11990 \begin_layout Subsection
11991 Space besides inline Formulas
11995 \begin_layout Plain Layout
11996 Space ! besides inline formulas
12004 \begin_layout Standard
12005 The space that surrounds inline formulas can be adjusted with the length
12014 \begin_layout Plain Layout
12025 The value of a length is set with the command
12033 \begin_layout Plain Layout
12043 that has the following scheme:
12046 \begin_layout Standard
12051 setlength{length name}{value}
12054 \begin_layout Standard
12062 \begin_inset space \thinspace{}
12068 \begin_layout Standard
12078 \begin_layout Standard
12079 is inserted in TeX-mode.
12081 \begin_inset space \thinspace{}
12084 mm space will now be set around all inline formulas:
12088 \begin_layout Plain Layout
12102 \begin_layout Standard
12103 This is a line with an inline formula
12104 \begin_inset Formula $A=B$
12108 \begin_inset space \thinspace{}
12111 mm surrounding space.
12115 \begin_layout Plain Layout
12129 \begin_layout Standard
12130 To return to the predefined value,
12136 is set to the value 0
12137 \begin_inset space \thinspace{}
12143 \begin_layout Section
12148 \begin_layout Plain Layout
12158 \begin_layout Plain Layout
12163 \begin_layout Plain Layout
12174 \begin_layout Plain Layout
12189 \begin_layout Standard
12190 Boxes for text are described in chapter
12197 \begin_inset space ~
12205 \begin_layout Subsection
12207 \begin_inset CommandInset label
12209 name "sub:Boxes-with-Frame"
12217 \begin_layout Plain Layout
12226 \begin_layout Standard
12227 It is possible to frame formulas or parts of it with the commands
12237 \begin_layout Plain Layout
12255 \begin_layout Plain Layout
12266 \begin_layout Standard
12267 When one of these commands is inserted to a formula, a blue box appears
12268 within a frame to enter formula parts.
12275 an additional formula has to be created by
12283 \begin_layout Plain Layout
12284 Due to a bug in LyX it is not possible to create a new formula with
12289 \begin_inset CommandInset href
12291 name "LyX-bug #1435"
12292 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12301 , because the box content will otherwise be treated as mathematical text.
12308 is used, a new formula is automatically created inside the frame.
12311 \begin_layout Standard
12318 is not suitable to frame displayed formulas, because the formula will always
12319 be set in the size of the text.
12326 is in contrary not suitable to frame inline formulas, because the formula
12327 will always be set in the size of a displayed formula.
12330 \begin_layout Standard
12337 there is the command
12347 \begin_layout Plain Layout
12355 where additionally the frame width and the alignment can be specified.
12362 is used in the following scheme:
12365 \begin_layout Standard
12370 framebox[frame width][position]{box content}
12373 \begin_layout Standard
12374 The position can either be
12391 right aligns the formula in the box.
12392 When no position is given, the formula will be centered.
12393 \begin_inset Newline newline
12396 Is no width given, also no position can be given.
12397 In this case the frame width is adjusted to the box content like for
12406 \begin_layout Standard
12413 is inserted, a box appears containing three blue boxes.
12414 The first two boxes are surrounded by brackets and denote the two optional
12416 The third box is for formula parts like for
12425 \begin_layout Standard
12427 \begin_inset Note Note
12430 \begin_layout Plain Layout
12431 The table has been set into a minipage to make the footnote appearing.
12432 Otherwise the footnote text would not be displayed.
12438 \begin_inset Box Frameless
12447 height_special "totalheight"
12450 \begin_layout Plain Layout
12452 \begin_inset Tabular
12453 <lyxtabular version="3" rows="5" columns="2">
12455 <column alignment="center" valignment="top" width="0">
12456 <column alignment="center" valignment="top" width="0">
12458 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12461 \begin_layout Plain Layout
12466 \begin_layout Plain Layout
12467 Due to a bug in LyX it is not possible to create a new formula with
12472 \begin_inset CommandInset href
12474 name "LyX-bug #1435"
12475 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12492 \begin_layout Plain Layout
12494 \begin_inset Note Note
12497 \begin_layout Plain Layout
12504 is only used as spacer.
12516 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12519 \begin_layout Plain Layout
12526 \begin_layout Plain Layout
12545 \begin_layout Plain Layout
12559 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12562 \begin_layout Plain Layout
12563 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12577 \begin_layout Plain Layout
12584 \begin_layout Plain Layout
12599 \begin_layout Plain Layout
12613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12616 \begin_layout Plain Layout
12617 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12627 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12630 \begin_layout Plain Layout
12637 \begin_layout Plain Layout
12651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12654 \begin_layout Plain Layout
12655 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12668 \begin_layout Plain Layout
12675 \begin_layout Plain Layout
12685 \begin_inset Formula $\to$
12689 \begin_inset Formula $\to$
12702 \begin_layout Plain Layout
12712 \begin_inset Formula $\downarrow$
12720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12723 \begin_layout Plain Layout
12724 \begin_inset Formula $\raisebox{6mm}{}$
12728 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12732 \begin_inset Formula $\raisebox{-4mm}{}$
12753 \begin_layout Standard
12754 The frame thickness can also be adjusted.
12755 To do this the following commands have to be inserted in TeX-mode before
12759 \begin_layout Standard
12769 \begin_inset Quotes eld
12773 \begin_inset Quotes erd
12787 \begin_inset Quotes eld
12791 \begin_inset Quotes erd
12797 \begin_layout Standard
12798 \begin_inset Quotes eld
12802 \begin_inset Quotes erd
12805 specifies the minimal distance between the frame and the first character
12807 An example for this is the following framed formula:
12811 \begin_layout Plain Layout
12823 \begin_inset Formula \[
12828 Before this formula the commands
12831 \begin_layout Standard
12853 \begin_layout Standard
12854 were inserted in TeX-mode.
12855 The given values are used for all following boxes.
12858 \begin_layout Standard
12859 To return to the standard frame size, the command
12862 \begin_layout Standard
12887 \begin_layout Plain Layout
12901 \begin_layout Standard
12902 is inserted in TeX-mode before the next formula.
12905 \begin_layout Subsection
12906 Boxes without Frame
12907 \begin_inset CommandInset label
12909 name "sub:Boxes-without-Frame"
12917 \begin_layout Plain Layout
12918 Boxes ! without frame
12926 \begin_layout Standard
12927 For boxes without a frame there are the following box commands:
12937 \begin_layout Plain Layout
12955 \begin_layout Plain Layout
12973 \begin_layout Plain Layout
12984 \begin_layout Standard
12991 a box can be super- or subscripted.
12992 But in contrary to normal super- and subscripting, the characters in the
12993 box keep their font size.
13000 is used in the following scheme:
13003 \begin_layout Standard
13008 raisebox{height}{box content}
13011 \begin_layout Standard
13012 When the box should contain a formula, an extra formula is needed like for
13022 \begin_layout Standard
13024 \begin_inset Tabular
13025 <lyxtabular version="3" rows="4" columns="2">
13027 <column alignment="center" valignment="top" width="0">
13028 <column alignment="center" valignment="top" width="0">
13030 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13033 \begin_layout Plain Layout
13039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13042 \begin_layout Plain Layout
13050 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13053 \begin_layout Plain Layout
13057 \begin_inset Formula $\to$
13063 \begin_inset Formula $\to$
13071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13074 \begin_layout Plain Layout
13075 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13088 \begin_layout Plain Layout
13092 \begin_inset Formula $\to$
13098 \begin_inset Formula $\to$
13106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13109 \begin_layout Plain Layout
13110 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13123 \begin_layout Plain Layout
13127 \begin_inset Formula $\to$
13142 \begin_layout Plain Layout
13156 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13159 \begin_layout Plain Layout
13163 \begin_layout Plain Layout
13187 \begin_layout Standard
13188 The last formula can currently only be created using TeX-mode because LyX
13189 inserts a box instead of the needed extra formula.
13193 \begin_layout Plain Layout
13195 \begin_inset CommandInset href
13197 name "LyX-bug #1435"
13198 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13210 \begin_layout Standard
13235 , with the difference that there is no frame.
13238 \begin_layout Subsection
13240 \begin_inset CommandInset label
13242 name "sub:Colored-Boxes"
13250 \begin_layout Plain Layout
13259 \begin_layout Standard
13260 To be able to use all commands explained in this section, the LaTeX-package
13269 \begin_layout Plain Layout
13274 is part of every LaTeX standard installation.
13283 \begin_layout Plain Layout
13289 has to be loaded in the LaTeX-preamble with the line
13293 \begin_layout Plain Layout
13294 When text is colored somewhere in the document with a predefined color,
13295 LyX loads the LaTeX-package
13300 Thus it is possible that the package is loaded twice, but this doesn't
13307 \begin_inset Note Note
13310 \begin_layout Plain Layout
13311 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13320 \begin_layout Standard
13328 \begin_layout Standard
13329 \begin_inset VSpace medskip
13332 To color boxes, the command
13342 \begin_layout Plain Layout
13350 is used in the following scheme:
13353 \begin_layout Standard
13358 colorbox{color}{box content}
13361 \begin_layout Standard
13362 The box content can also be a box and a
13368 can also be part of another box (see the 2nd and 3rd example).
13369 When the box should contain a formula, an extra formula has to be created,
13380 \begin_layout Plain Layout
13381 This also applies for the command
13389 \begin_inset CommandInset href
13391 name "LyX-bug #1435"
13392 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13404 \begin_layout Standard
13405 One of the following predefined colors can be chosen:
13408 \begin_layout Standard
13442 \begin_layout Standard
13444 \begin_inset Tabular
13445 <lyxtabular version="3" rows="4" columns="2">
13447 <column alignment="center" valignment="top" width="0">
13448 <column alignment="center" valignment="top" width="0">
13450 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13453 \begin_layout Plain Layout
13459 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13462 \begin_layout Plain Layout
13464 \begin_inset Note Note
13467 \begin_layout Plain Layout
13474 is only used as spacer.
13486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13489 \begin_layout Plain Layout
13493 \begin_inset Formula $\to$
13503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13506 \begin_layout Plain Layout
13507 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13520 \begin_layout Plain Layout
13524 \begin_inset Formula $\to$
13535 \begin_layout Plain Layout
13549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13552 \begin_layout Plain Layout
13553 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13563 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13566 \begin_layout Plain Layout
13573 \begin_layout Plain Layout
13585 \begin_inset Formula $\to$
13595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13598 \begin_layout Plain Layout
13599 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13615 \begin_layout Standard
13622 only colors the box but not the characters in the box.
13623 To color all characters, the whole formula is highlighted and the wanted
13624 color is chosen in the
13627 \begin_inset space ~
13633 The dialog can be called with the toolbar button
13634 \begin_inset Graphics
13635 filename ../images/dialog-show_character.png
13642 Edit\SpecialChar \menuseparator
13644 \begin_inset space ~
13647 Style\SpecialChar \menuseparator
13651 The formula number has then the same color as the formula.
13652 When the formula number should get another color than the formula characters,
13653 the color must be changed within the formula.
13656 \begin_layout Standard
13660 \begin_layout Standard
13663 \begin_inset Formula \begin{equation}
13664 \int A=B\label{eq:red}\end{equation}
13671 \begin_inset Formula \begin{equation}
13672 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13679 \begin_layout Standard
13681 \begin_inset CommandInset ref
13687 is completely colored red.
13688 \begin_inset Newline newline
13692 \begin_inset CommandInset ref
13694 reference "eq:redgreen"
13698 was first completely colored green to set the color for the formula number.
13699 Subsequently the formula characters were colored red.
13702 \begin_layout Standard
13703 \begin_inset VSpace bigskip
13706 To color the frame different than the rest of the box, the command
13716 \begin_layout Plain Layout
13724 is used in the following scheme:
13727 \begin_layout Standard
13732 fcolorbox{frame color}{color}{box content}
13735 \begin_layout Standard
13742 is an extension of the command
13749 The frame width is set, like for
13772 \begin_layout Plain Layout
13784 \begin_inset Formula \[
13785 \fcolorbox{cyan}{magenta}{A=B}\]
13793 \begin_layout Plain Layout
13807 \begin_layout Standard
13808 This formula was created with the command
13809 \begin_inset Newline newline
13817 \begin_inset Formula $\to$
13823 \begin_inset Formula $\to$
13833 \begin_layout Standard
13834 \begin_inset VSpace bigskip
13837 To use other colors than the predefined ones, they have to be defined first.
13840 \begin_layout Standard
13841 One can for example define the color
13842 \begin_inset Quotes eld
13850 \begin_inset Quotes erd
13853 with the LaTeX-preamble line:
13856 \begin_layout Standard
13861 definecolor{darkgreen}{cmyk}{0.5,
13879 \begin_layout Plain Layout
13890 \begin_layout Standard
13895 is the color space that denotes the colors
13912 The four comma separated numbers are the portion factor for the corresponding
13913 colors of the color space.
13914 The factors can be in the range of 0
13915 \begin_inset space \thinspace{}
13919 \begin_inset space \thinspace{}
13927 also the color space
13931 can be used for definitions.
13948 , so that there are in this case three portion factors for the corresponding
13950 Furthermore there is the color space
13954 with one portion factor for the gray value.
13957 \begin_layout Standard
13958 As example a framed box with the new defined color
13962 where the characters have been colored
13967 \begin_inset Formula \begin{equation}
13968 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13975 \begin_layout Standard
13976 Self-defined colors can also be used for text with the help of the command
13987 \begin_layout Plain Layout
13996 \begin_layout Standard
14000 \begin_layout Plain Layout
14004 textcolor{darkgreen}{
14010 \begin_inset Quotes eld
14014 \begin_inset Quotes erd
14021 \begin_layout Plain Layout
14031 \begin_layout Standard
14042 \begin_layout Plain Layout
14050 is used in the scheme
14054 textcolor{color}{characters to color}
14059 \begin_layout Subsection
14061 \begin_inset CommandInset label
14063 name "sub:Paragraph-Boxes"
14071 \begin_layout Plain Layout
14072 Boxes ! as paragraph
14080 \begin_layout Standard
14081 A box that can contain several lines and paragraphs, a so called paragraph
14082 box (parbox), can be created with the menu
14084 Insert\SpecialChar \menuseparator
14087 or the toolbar button
14088 \begin_inset Graphics
14089 filename ../images/box-insert.png
14097 \begin_layout Standard
14098 The following example shows a framed parbox in a line:
14101 \begin_layout Standard
14102 \begin_inset VSpace medskip
14106 \begin_inset Box Boxed
14115 height_special "totalheight"
14118 \begin_layout Plain Layout
14119 This is a paragraph box.
14121 \begin_inset space \thinspace{}
14124 cm long and can also contain formulas:
14125 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14136 \begin_layout Standard
14137 \begin_inset VSpace medskip
14143 \begin_layout Standard
14144 Such a box is created by right-clicking on the gray box inset.
14145 A dialog pops up showing the box properties.
14159 \begin_inset space \thinspace{}
14164 Vertical Box Alignment
14169 \begin_layout Standard
14170 \begin_inset VSpace medskip
14173 In LaTeX a parbox is created with the command
14183 \begin_layout Plain Layout
14191 that has the following scheme:
14194 \begin_layout Standard
14199 parbox[position]{width}{box content}
14202 \begin_layout Standard
14216 for bottom means that the box is aligned within the surrounding text with
14222 for top this is done with the first line.
14223 When no position is given, the box will be vertically centered, see section
14231 \begin_inset space ~
14236 manual for examples.
14239 \begin_layout Standard
14240 \begin_inset VSpace bigskip
14243 To frame formulas completely, including the formula number, the formula
14244 must be set into a parbox.
14245 To do this, the command
14259 is inserted in TeX-mode before the formula.
14268 \begin_layout Plain Layout
14278 is hereby the line width set for the document.
14279 Because the frame is outside the parbox, 2
14280 \begin_inset space \thinspace{}
14283 times the frame separation and the frame thickness must be subtracted from
14285 As this is not automatically done by LyX due to a bug
14289 \begin_layout Plain Layout
14290 \begin_inset CommandInset href
14292 name "LyX-bug #4483"
14293 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14302 , TeX-mode has to be used.
14303 To be able to multiply and subtract in arguments, the LaTeX-package
14311 \begin_layout Plain Layout
14316 is part of every LaTeX standard installation.
14325 \begin_layout Plain Layout
14331 must be loaded in the LaTeX-preamble with the line
14334 \begin_layout Standard
14342 \begin_layout Standard
14343 Behind the formula both boxes are closed by entering
14348 Here is an example:
14352 \begin_layout Plain Layout
14366 \begin_layout Standard
14370 \begin_layout Plain Layout
14388 \begin_inset Formula \begin{equation}
14389 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14397 \begin_layout Plain Layout
14408 \begin_layout Plain Layout
14422 \begin_layout Standard
14423 \begin_inset VSpace medskip
14426 As a parbox is used as argument of
14432 , there is in this case no difference between
14447 \begin_layout Standard
14448 \begin_inset VSpace bigskip
14451 Paragraph boxes are very useful to comment formulas directly.
14458 is used in combination with the command
14472 \begin_inset CommandInset ref
14474 reference "sub:User-defined-Numbering"
14481 \begin_layout Standard
14482 An example of a formula commented with
14491 \begin_layout Standard
14495 \begin_layout Plain Layout
14508 This is a description.
14509 It is distinctly separated from the formula and multiline.
14513 \begin_layout Plain Layout
14525 \begin_layout Standard
14526 Such a formula must be inserted completely in TeX-mode because LyX does
14527 not yet support the command
14534 The formula is created with the following command sequence:
14537 \begin_layout Standard
14550 is inserted in TeX-mode.
14554 \begin_layout Plain Layout
14555 When the formula style
14567 can also be replaced by
14574 (formula styles see
14575 \begin_inset CommandInset ref
14577 reference "sec:Formula-Styles"
14586 Then the description follows as normal text, and finally
14592 is inserted in TeX-mode.
14605 hereby create a displayed formula.
14608 \begin_layout Standard
14615 can be seen in this example that was
14616 \begin_inset Quotes eld
14620 \begin_inset Quotes erd
14623 using the mathematical textmode:
14624 \begin_inset Formula \[
14625 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14632 \begin_layout Section
14637 \begin_layout Plain Layout
14646 \begin_layout Subsection
14648 \begin_inset CommandInset label
14650 name "sub:Big-Operators"
14658 \begin_layout Plain Layout
14668 \begin_layout Plain Layout
14678 \begin_layout Plain Layout
14687 \begin_layout Standard
14688 To be able to use all integral operators listed here, the option
14690 Use esint package automatically
14692 must be set in the document settings under
14695 \begin_inset space ~
14703 \begin_layout Standard
14704 \begin_inset space \hfill{}
14708 \begin_inset Tabular
14709 <lyxtabular version="3" rows="11" columns="2">
14711 <column alignment="center" valignment="top" width="0pt">
14712 <column alignment="center" valignment="top" width="0pt">
14714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14717 \begin_layout Plain Layout
14723 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14726 \begin_layout Plain Layout
14734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14737 \begin_layout Plain Layout
14744 \begin_layout Plain Layout
14757 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14760 \begin_layout Plain Layout
14761 \begin_inset Formula $\sum$
14771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14774 \begin_layout Plain Layout
14781 \begin_layout Plain Layout
14794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14797 \begin_layout Plain Layout
14798 \begin_inset Formula $\int$
14808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14811 \begin_layout Plain Layout
14819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14822 \begin_layout Plain Layout
14823 \begin_inset Formula $\intop$
14833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14836 \begin_layout Plain Layout
14844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14847 \begin_layout Plain Layout
14848 \begin_inset Formula $\oint$
14858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14861 \begin_layout Plain Layout
14869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14872 \begin_layout Plain Layout
14873 \begin_inset Formula $\ointop$
14883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14886 \begin_layout Plain Layout
14894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14897 \begin_layout Plain Layout
14898 \begin_inset Formula $\ointctrclockwise$
14908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14911 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14922 \begin_layout Plain Layout
14923 \begin_inset Formula $\ointclockwise$
14933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14936 \begin_layout Plain Layout
14944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14947 \begin_layout Plain Layout
14948 \begin_inset Formula $\sqint$
14958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14961 \begin_layout Plain Layout
14969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14972 \begin_layout Plain Layout
14973 \begin_inset Formula $\bigcap$
14983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14986 \begin_layout Plain Layout
14994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14997 \begin_layout Plain Layout
14998 \begin_inset Formula $\bigcup$
15012 \begin_inset space \hfill{}
15016 \begin_inset Tabular
15017 <lyxtabular version="3" rows="10" columns="2">
15019 <column alignment="center" valignment="top" width="0pt">
15020 <column alignment="center" valignment="top" width="0pt">
15022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15025 \begin_layout Plain Layout
15031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15034 \begin_layout Plain Layout
15042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15045 \begin_layout Plain Layout
15052 \begin_layout Plain Layout
15065 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15068 \begin_layout Plain Layout
15069 \begin_inset Formula $\prod$
15079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15082 \begin_layout Plain Layout
15090 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15093 \begin_layout Plain Layout
15094 \begin_inset Formula $\coprod$
15104 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15107 \begin_layout Plain Layout
15115 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15118 \begin_layout Plain Layout
15119 \begin_inset Formula $\bigodot$
15129 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15132 \begin_layout Plain Layout
15140 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15143 \begin_layout Plain Layout
15144 \begin_inset Formula $\bigotimes$
15154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15157 \begin_layout Plain Layout
15165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15168 \begin_layout Plain Layout
15169 \begin_inset Formula $\bigoplus$
15179 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15182 \begin_layout Plain Layout
15190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15193 \begin_layout Plain Layout
15194 \begin_inset Formula $\bigwedge$
15204 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15207 \begin_layout Plain Layout
15215 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15218 \begin_layout Plain Layout
15219 \begin_inset Formula $\bigvee$
15229 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15232 \begin_layout Plain Layout
15240 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15243 \begin_layout Plain Layout
15244 \begin_inset Formula $\bigsqcup$
15254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15257 \begin_layout Plain Layout
15265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15268 \begin_layout Plain Layout
15269 \begin_inset Formula $\biguplus$
15283 \begin_inset space \hfill{}
15289 \begin_layout Standard
15290 All big operators can also be inserted via the math toolbar button
15291 \begin_inset Graphics
15292 filename ../images/math/intop.png
15300 \begin_layout Standard
15301 The operators are called big because they are bigger than the sometimes
15302 equal looking binary operators.
15303 All big operators can have limits as described in the next subsection.
15306 \begin_layout Standard
15332 \begin_inset space ~
15335 in the style the operator limits are displayed, see
15336 \begin_inset CommandInset ref
15338 reference "sub:Operator-Limits"
15346 \begin_layout Subsubsection*
15347 Advices for Integrals
15350 \begin_layout Standard
15355 in an integral is an operator, that therefore has to be set upright.
15356 This is done by highlighting the
15360 and using the keyboard shortcut
15363 \begin_inset space ~
15372 \begin_layout Plain Layout
15378 \begin_inset CommandInset ref
15380 reference "sub:Font-Styles"
15390 Finally the smallest space is inserted before the
15394 , as this is usual for operators.
15398 \begin_layout Standard
15400 \begin_inset Formula $\int A(x)dx$
15404 \begin_inset Newline newline
15411 \begin_layout Plain Layout
15421 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15427 \begin_layout Standard
15428 For multiple integrals there are the following commands:
15429 \begin_inset VSpace medskip
15435 \begin_layout Standard
15436 \begin_inset space \hfill{}
15440 \begin_inset Tabular
15441 <lyxtabular version="3" rows="4" columns="2">
15443 <column alignment="center" valignment="top" width="0">
15444 <column alignment="center" valignment="top" width="0">
15446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15449 \begin_layout Plain Layout
15455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15458 \begin_layout Plain Layout
15460 \begin_inset Note Note
15463 \begin_layout Plain Layout
15470 is only used as spacer.
15482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15485 \begin_layout Plain Layout
15493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15496 \begin_layout Plain Layout
15497 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15510 \begin_layout Plain Layout
15518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15521 \begin_layout Plain Layout
15522 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15532 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15535 \begin_layout Plain Layout
15543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15546 \begin_layout Plain Layout
15547 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15561 \begin_inset space \hfill{}
15565 \begin_inset Tabular
15566 <lyxtabular version="3" rows="4" columns="2">
15568 <column alignment="center" valignment="top" width="0">
15569 <column alignment="center" valignment="top" width="0">
15571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15574 \begin_layout Plain Layout
15580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15583 \begin_layout Plain Layout
15591 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15594 \begin_layout Plain Layout
15602 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15605 \begin_layout Plain Layout
15606 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15616 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15619 \begin_layout Plain Layout
15627 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15630 \begin_layout Plain Layout
15631 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15655 \begin_layout Plain Layout
15656 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15670 \begin_inset space \hfill{}
15676 \begin_layout Subsection
15678 \begin_inset CommandInset label
15680 name "sub:Operator-Limits"
15688 \begin_layout Plain Layout
15697 \begin_layout Standard
15698 Limits are created by super- and subscripts:
15701 \begin_layout Standard
15703 \begin_inset Tabular
15704 <lyxtabular version="3" rows="2" columns="2">
15706 <column alignment="center" valignment="top" width="0pt">
15707 <column alignment="center" valignment="top" width="0pt">
15709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15712 \begin_layout Plain Layout
15718 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15721 \begin_layout Plain Layout
15723 \begin_inset Note Note
15726 \begin_layout Plain Layout
15733 is only used as spacer.
15745 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15748 \begin_layout Plain Layout
15757 \begin_layout Plain Layout
15767 \begin_inset Formula $\to$
15771 \begin_inset Formula $\to$
15779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15782 \begin_layout Plain Layout
15783 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15799 \begin_layout Standard
15800 Limits of inline formulas are set right beside the operator.
15801 Limits in displayed formulas are set above or below the operator, except
15802 of integral limits.
15805 \begin_layout Standard
15806 To force that the limits are set beside the operator, the cursor is set
15807 directly behind the operator and the limits type is changed with the menu
15810 Edit\SpecialChar \menuseparator
15811 Math\SpecialChar \menuseparator
15823 \begin_inset space ~
15832 \begin_layout Standard
15833 The default limits type is this:
15834 \begin_inset Formula \[
15835 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15839 This is how it looks when the limits type was changed to
15846 \begin_inset Formula \[
15847 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15851 For integrals, except of
15863 , the limits are by default set beside the operator.
15864 But for multiple integrals the limits are often set below the operator.
15865 In the following example the limits type was therefore set to
15869 and so set below the integrals:
15870 \begin_inset Formula \begin{equation}
15871 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15878 \begin_layout Standard
15879 \begin_inset VSpace medskip
15882 To specify conditions for limits, the commands
15892 \begin_layout Plain Layout
15910 \begin_layout Plain Layout
15919 To create for example this expression
15920 \begin_inset Formula \begin{equation}
15921 \sum_{\begin{subarray}{c}
15923 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15930 \begin_layout Standard
15931 the following has to be done:
15932 \begin_inset Newline newline
15947 \begin_layout Plain Layout
15959 One is now in a blue box under the summation operator and insert there
15968 \begin_layout Plain Layout
15980 The blue box is now within a purple box and now several lines can be written
15982 A new line is created by inserting a line break (
15988 \begin_inset Newline newline
15993 0<k<1000 Ctrl-Return
15994 \begin_inset Newline newline
15999 is typed in, a new box appears below for the new line.
16002 \begin_layout Standard
16003 The alignment of the lines can be changed to left aligned with the
16013 Edit\SpecialChar \menuseparator
16017 To get right alignment,
16025 \begin_layout Plain Layout
16036 is inserted at the beginning of the line.
16039 \begin_layout Standard
16052 with the difference that the lines are always centered.
16055 \begin_layout Standard
16056 \begin_inset VSpace bigskip
16060 \begin_inset CommandInset ref
16062 reference "eq:substack"
16066 there can be too much space beside an operator, because the characters
16067 following the operator are set beside the limits.
16070 \begin_layout Standard
16071 To avoid this, the following macro can be used in the LaTeX-preamble:
16074 \begin_layout Standard
16088 \begin_inset Newline newline
16100 \begin_inset Newline newline
16107 mathclapinternal #1#2{
16111 mathsurround =0pt #1{#2}$}}
16114 \begin_layout Standard
16115 This defines the command
16125 \begin_layout Plain Layout
16133 that sets the width of the limit to 0
16134 \begin_inset space \thinspace{}
16138 The command scheme is
16141 \begin_layout Standard
16149 \begin_layout Standard
16150 where the limit can consist of several conditions.
16153 \begin_layout Standard
16155 \begin_inset CommandInset ref
16157 reference "eq:substack"
16161 , one uses the command
16164 \begin_layout Standard
16177 \begin_layout Plain Layout
16186 0<k<1000 Ctrl-Enter
16189 \begin_layout Standard
16190 to create the lower limit.
16191 The summand is now directly behind the summation operator:
16192 \begin_inset Formula \[
16193 \sum_{\mathclap{\substack{0<k<1000\\
16194 \\k\,\in\,\mathbb{N}}
16202 \begin_layout Standard
16203 \begin_inset VSpace bigskip
16206 How to use one limit for several operators is described in
16207 \begin_inset CommandInset ref
16209 reference "sub:Self-defined-Operators"
16216 \begin_layout Subsection
16218 \begin_inset CommandInset label
16220 name "sub:Binary-Operators"
16228 \begin_layout Plain Layout
16237 \begin_layout Standard
16238 Binary operators are surrounded by space when there is a character before
16240 \begin_inset VSpace medskip
16246 \begin_layout Standard
16247 \begin_inset space \hfill{}
16251 \begin_inset Tabular
16252 <lyxtabular version="3" rows="13" columns="2">
16254 <column alignment="center" valignment="top" width="0pt">
16255 <column alignment="center" valignment="top" width="0pt">
16257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16260 \begin_layout Plain Layout
16262 \begin_inset Note Note
16265 \begin_layout Plain Layout
16272 is only used as spacer.
16282 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16285 \begin_layout Plain Layout
16293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16296 \begin_layout Plain Layout
16302 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16305 \begin_layout Plain Layout
16306 \begin_inset Formula $+$
16316 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16319 \begin_layout Plain Layout
16325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16328 \begin_layout Plain Layout
16329 \begin_inset Formula $-$
16339 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16342 \begin_layout Plain Layout
16350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16353 \begin_layout Plain Layout
16354 \begin_inset Formula $\pm$
16364 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16367 \begin_layout Plain Layout
16375 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16378 \begin_layout Plain Layout
16379 \begin_inset Formula $\mp$
16389 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16392 \begin_layout Plain Layout
16400 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16403 \begin_layout Plain Layout
16404 \begin_inset Formula $\cdot$
16414 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16417 \begin_layout Plain Layout
16425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16428 \begin_layout Plain Layout
16429 \begin_inset Formula $\times$
16439 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16442 \begin_layout Plain Layout
16450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16453 \begin_layout Plain Layout
16454 \begin_inset Formula $\div$
16464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16467 \begin_layout Plain Layout
16471 \begin_layout Plain Layout
16484 \begin_layout Plain Layout
16496 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16499 \begin_layout Plain Layout
16500 \begin_inset Formula $*$
16510 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16513 \begin_layout Plain Layout
16521 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16524 \begin_layout Plain Layout
16525 \begin_inset Formula $\star$
16535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16538 \begin_layout Plain Layout
16546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16549 \begin_layout Plain Layout
16550 \begin_inset Formula $\circ$
16560 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16563 \begin_layout Plain Layout
16571 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16574 \begin_layout Plain Layout
16575 \begin_inset Formula $\diamond$
16585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16588 \begin_layout Plain Layout
16596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16599 \begin_layout Plain Layout
16600 \begin_inset Formula $\bullet$
16614 \begin_inset space \hfill{}
16618 \begin_inset Tabular
16619 <lyxtabular version="3" rows="13" columns="2">
16621 <column alignment="center" valignment="top" width="0pt">
16622 <column alignment="center" valignment="top" width="0pt">
16624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16627 \begin_layout Plain Layout
16633 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16636 \begin_layout Plain Layout
16644 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16647 \begin_layout Plain Layout
16655 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16658 \begin_layout Plain Layout
16659 \begin_inset Formula $\nabla$
16669 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16672 \begin_layout Plain Layout
16680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16683 \begin_layout Plain Layout
16684 \begin_inset Formula $\bigtriangledown$
16694 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16697 \begin_layout Plain Layout
16705 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16708 \begin_layout Plain Layout
16709 \begin_inset Formula $\bigtriangleup$
16719 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16722 \begin_layout Plain Layout
16730 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16733 \begin_layout Plain Layout
16734 \begin_inset Formula $\Box$
16744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16747 \begin_layout Plain Layout
16755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16758 \begin_layout Plain Layout
16759 \begin_inset Formula $\cap$
16769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16772 \begin_layout Plain Layout
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16783 \begin_layout Plain Layout
16784 \begin_inset Formula $\cup$
16794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16797 \begin_layout Plain Layout
16805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16808 \begin_layout Plain Layout
16809 \begin_inset Formula $\dagger$
16819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16822 \begin_layout Plain Layout
16830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16833 \begin_layout Plain Layout
16834 \begin_inset Formula $\ddagger$
16844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16847 \begin_layout Plain Layout
16855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16858 \begin_layout Plain Layout
16859 \begin_inset Formula $\wr$
16869 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16872 \begin_layout Plain Layout
16880 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16883 \begin_layout Plain Layout
16884 \begin_inset Formula $\bigcirc$
16894 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16897 \begin_layout Plain Layout
16905 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16908 \begin_layout Plain Layout
16909 \begin_inset Formula $\wedge$
16919 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16922 \begin_layout Plain Layout
16930 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16933 \begin_layout Plain Layout
16934 \begin_inset Formula $\vee$
16948 \begin_inset space \hfill{}
16952 \begin_inset Tabular
16953 <lyxtabular version="3" rows="13" columns="2">
16955 <column alignment="center" valignment="top" width="0pt">
16956 <column alignment="center" valignment="top" width="0pt">
16958 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16961 \begin_layout Plain Layout
16967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16970 \begin_layout Plain Layout
16978 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16981 \begin_layout Plain Layout
16989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16992 \begin_layout Plain Layout
16993 \begin_inset Formula $\oplus$
17003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17006 \begin_layout Plain Layout
17014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17017 \begin_layout Plain Layout
17018 \begin_inset Formula $\ominus$
17028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17031 \begin_layout Plain Layout
17039 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17042 \begin_layout Plain Layout
17043 \begin_inset Formula $\otimes$
17053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17056 \begin_layout Plain Layout
17064 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17067 \begin_layout Plain Layout
17068 \begin_inset Formula $\oslash$
17078 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17081 \begin_layout Plain Layout
17089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17092 \begin_layout Plain Layout
17093 \begin_inset Formula $\odot$
17103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17106 \begin_layout Plain Layout
17114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17117 \begin_layout Plain Layout
17118 \begin_inset Formula $\amalg$
17128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17131 \begin_layout Plain Layout
17139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17142 \begin_layout Plain Layout
17143 \begin_inset Formula $\uplus$
17153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17156 \begin_layout Plain Layout
17164 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17167 \begin_layout Plain Layout
17168 \begin_inset Formula $\setminus$
17178 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17181 \begin_layout Plain Layout
17189 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17192 \begin_layout Plain Layout
17193 \begin_inset Formula $\sqcap$
17203 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17206 \begin_layout Plain Layout
17214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17217 \begin_layout Plain Layout
17218 \begin_inset Formula $\sqcup$
17228 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17231 \begin_layout Plain Layout
17239 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17242 \begin_layout Plain Layout
17243 \begin_inset Formula $\triangleleft$
17253 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17256 \begin_layout Plain Layout
17264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17267 \begin_layout Plain Layout
17268 \begin_inset Formula $\triangleright$
17282 \begin_inset space \hfill{}
17288 \begin_layout Standard
17289 All binary operators can also be inserted via the math toolbar button
17290 \begin_inset Graphics
17291 filename ../images/math/pm.png
17299 \begin_layout Standard
17300 To typeset the Laplace operator also
17317 \begin_inset Formula $\nabla^{2}$
17320 ) can be used instead of
17329 \begin_layout Standard
17336 Insert\SpecialChar \menuseparator
17348 \begin_layout Subsection
17349 Self-defined Operators
17350 \begin_inset CommandInset label
17352 name "sub:Self-defined-Operators"
17360 \begin_layout Plain Layout
17361 Operators ! self-defined
17369 \begin_layout Standard
17370 With the help of the command
17374 DeclareMathOperator
17380 \begin_layout Plain Layout
17385 DeclareMathOperator
17390 custom operators can be defined in the LaTeX-preamble.
17391 Its command scheme is:
17394 \begin_layout Standard
17399 DeclareMathOperator{new command}{display}
17402 \begin_layout Standard
17403 Display can be characters or symbols that define how the operator looks
17405 To define a big operator a * is set behind the command.
17406 All self-defined big operators can have limits as described in
17407 \begin_inset CommandInset ref
17409 reference "sub:Operator-Limits"
17416 \begin_layout Standard
17417 For example the LaTeX-preamble line
17420 \begin_layout Standard
17425 DeclareMathOperator*{
17432 \begin_layout Standard
17433 defines the command
17439 , that inserts a big operator consisting of the lozenge symbol from
17440 \begin_inset CommandInset ref
17442 reference "sub:Miscellaneous-Symbols"
17447 \begin_inset Formula \[
17448 \Lozenge_{n=1}^{\infty}\]
17452 The command for this formula is:
17463 \begin_inset Formula $\to$
17469 \begin_layout Standard
17470 \begin_inset VSpace bigskip
17473 When self-defined operators are not used several times in the document,
17474 they can also be defined with the commands
17484 \begin_layout Plain Layout
17502 \begin_layout Plain Layout
17510 , which have the following scheme:
17513 \begin_layout Standard
17527 \begin_layout Standard
17534 defines big operators,
17543 \begin_layout Standard
17551 \begin_inset space \thinspace{}
17555 \begin_inset space ~
17558 be used to use one limit for several operators:
17561 \begin_layout Standard
17562 \begin_inset Formula \[
17563 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17570 \begin_layout Standard
17571 The command for the formula above is:
17572 \begin_inset Newline newline
17591 \begin_layout Plain Layout
17603 \begin_inset Formula $\to$
17612 \begin_layout Plain Layout
17626 \begin_layout Section
17631 \begin_layout Plain Layout
17640 \begin_layout Subsection
17642 \begin_inset CommandInset label
17644 name "sub:Font-Styles"
17652 \begin_layout Plain Layout
17661 \begin_layout Standard
17662 Latin letters in formulas can be set in one of the following font styles:
17663 \begin_inset VSpace -2mm
17669 \begin_layout Standard
17671 \begin_inset Tabular
17672 <lyxtabular version="3" rows="6" columns="3">
17674 <column alignment="center" valignment="top" width="0">
17675 <column alignment="center" valignment="top" width="0">
17676 <column alignment="center" valignment="top" width="0">
17678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17681 \begin_layout Plain Layout
17687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17690 \begin_layout Plain Layout
17696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17699 \begin_layout Plain Layout
17707 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17710 \begin_layout Plain Layout
17719 \begin_layout Plain Layout
17735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17738 \begin_layout Plain Layout
17739 \begin_inset Formula $\mathbb{ABC}$
17747 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17750 \begin_layout Plain Layout
17758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17761 \begin_layout Plain Layout
17770 \begin_layout Plain Layout
17786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17789 \begin_layout Plain Layout
17790 \begin_inset Formula $\mathbf{AbC}$
17798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17801 \begin_layout Plain Layout
17809 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17812 \begin_layout Plain Layout
17821 \begin_layout Plain Layout
17837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17840 \begin_layout Plain Layout
17841 \begin_inset Formula $\boldsymbol{AbC}$
17849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17852 \begin_layout Plain Layout
17860 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17863 \begin_layout Plain Layout
17872 \begin_layout Plain Layout
17888 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17891 \begin_layout Plain Layout
17892 \begin_inset Formula $\mathcal{ABC}$
17900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17903 \begin_layout Plain Layout
17911 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17914 \begin_layout Plain Layout
17923 \begin_layout Plain Layout
17939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17942 \begin_layout Plain Layout
17943 \begin_inset Formula $\mathfrak{AbC}$
17951 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17954 \begin_layout Plain Layout
17968 \begin_layout Standard
17970 \begin_inset Tabular
17971 <lyxtabular version="3" rows="5" columns="3">
17973 <column alignment="center" valignment="top" width="0">
17974 <column alignment="center" valignment="top" width="0">
17975 <column alignment="center" valignment="top" width="0">
17977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17980 \begin_layout Plain Layout
17986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17989 \begin_layout Plain Layout
17995 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17998 \begin_layout Plain Layout
18006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18009 \begin_layout Plain Layout
18018 \begin_layout Plain Layout
18034 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18037 \begin_layout Plain Layout
18038 \begin_inset Formula $\mathit{AbC}$
18046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18049 \begin_layout Plain Layout
18057 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18060 \begin_layout Plain Layout
18069 \begin_layout Plain Layout
18085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18088 \begin_layout Plain Layout
18089 \begin_inset Formula $\mathrm{AbC}$
18097 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18100 \begin_layout Plain Layout
18108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18111 \begin_layout Plain Layout
18120 \begin_layout Plain Layout
18136 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18139 \begin_layout Plain Layout
18140 \begin_inset Formula $\mathsf{AbC}$
18148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18151 \begin_layout Plain Layout
18159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18162 \begin_layout Plain Layout
18171 \begin_layout Plain Layout
18187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18190 \begin_layout Plain Layout
18191 \begin_inset Formula $\mathtt{AbC}$
18199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18202 \begin_layout Plain Layout
18216 \begin_layout Standard
18217 \begin_inset Note Greyedout
18220 \begin_layout Plain Layout
18237 can only be used for big letters.
18245 \begin_layout Standard
18246 Predefined is the style
18255 \begin_layout Standard
18256 The style commands work also for letters in mathematical constructs:
18257 \begin_inset Formula \[
18258 \mathfrak{A=\frac{b}{C}}\]
18265 \begin_layout Standard
18266 Characters in mathematical text don't appear in a math font style but in
18267 the text font style
18274 That their style can't be set correctly via the text style dialog is a
18279 \begin_layout Plain Layout
18280 \begin_inset CommandInset href
18282 name "LyX-bug #4091"
18283 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18295 \begin_layout Standard
18296 Instead of the style commands the dialog
18298 Edit\SpecialChar \menuseparator
18299 Math\SpecialChar \menuseparator
18302 or the toolbar button
18303 \begin_inset Graphics
18304 filename ../images/math/font.png
18312 \begin_layout Subsection
18314 \begin_inset CommandInset label
18316 name "sub:Bold-Formulas"
18324 \begin_layout Plain Layout
18333 \begin_layout Standard
18334 To make a complete formula bold, the command
18340 from the previous subsection cannot be used, because it doesn't work for
18341 small Greek letters.
18342 Furthermore it prints Latin letters always upright, like in the following
18346 \begin_layout Standard
18347 \begin_inset Formula \[
18348 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18355 \begin_layout Standard
18356 To display the formula correctly, the command
18363 \begin_inset Formula \[
18364 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18368 It is also possible to set the formula in a
18370 boldmath environment
18373 This environment is created by inserting the command
18381 \begin_layout Plain Layout
18392 To end the environment, the command
18400 \begin_layout Plain Layout
18410 is inserted in TeX-mode.
18414 \begin_layout Plain Layout
18424 \begin_inset Formula \[
18425 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18433 \begin_layout Plain Layout
18445 \begin_layout Subsection
18447 \begin_inset CommandInset label
18449 name "sub:Font-Sizes"
18457 \begin_layout Plain Layout
18466 \begin_layout Standard
18467 For characters in formulas there are, analog to characters in text, the
18468 following size commands:
18471 \begin_layout Standard
18515 \begin_inset Newline newline
18537 \begin_layout Standard
18538 The size produced by the commands depends on the document font size, that
18539 corresponds with the command
18546 The other commands produce smaller or larger sizes than
18553 The font size can however not exceed a certain value.
18554 Is for example the document font size 12
18555 \begin_inset space \thinspace{}
18564 switches to the same size as
18574 \begin_layout Standard
18575 A size command is inserted in TeX-mode before the formula and sets the size
18576 for all following formula and text characters.
18577 To switch back to the initial size, the command
18583 is inserted behind the formula in TeX-mode.
18586 \begin_layout Standard
18587 Within a formula the size can only be changed for symbols or letters in
18589 To do this, the size command is inserted in mathematical text.
18590 All following characters until the end of the mathematical text or until
18591 another size command will have the selected size.
18593 \begin_inset VSpace -2mm
18599 \begin_layout Standard
18603 \begin_layout Plain Layout
18613 \begin_inset Formula \[
18614 A=\frac{B}{c}\cdot\maltese\]
18619 \begin_inset Formula \[
18620 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18628 \begin_layout Plain Layout
18640 \begin_layout Standard
18641 \begin_inset VSpace medskip
18644 Before both formulas the command
18651 The command for the second formula is:
18652 \begin_inset Newline newline
18663 \begin_layout Plain Layout
18678 \begin_layout Plain Layout
18693 \begin_layout Plain Layout
18708 \begin_layout Plain Layout
18718 \begin_inset Formula $\to$
18722 \begin_inset Formula $\to$
18726 \begin_inset Newline newline
18730 \begin_inset space \hspace*{}
18744 \begin_layout Plain Layout
18759 \begin_layout Plain Layout
18774 \begin_layout Plain Layout
18786 \begin_layout Standard
18787 If a symbol cannot be displayed in different sizes, it will always be displayed
18788 in the default size.
18791 \begin_layout Section
18796 \begin_layout Plain Layout
18805 \begin_layout Standard
18806 All Greek letters can also be inserted via the toolbar button
18807 \begin_inset Graphics
18808 filename ../images/math/alpha.png
18816 \begin_layout Subsection
18818 \begin_inset CommandInset label
18820 name "sub:Small-Letters"
18828 \begin_layout Plain Layout
18829 Greek letters ! small
18837 \begin_layout Standard
18838 \begin_inset space \hfill{}
18842 \begin_inset Tabular
18843 <lyxtabular version="3" rows="11" columns="2">
18845 <column alignment="center" valignment="top" width="0pt">
18846 <column alignment="center" valignment="top" width="0pt">
18848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18851 \begin_layout Plain Layout
18857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18860 \begin_layout Plain Layout
18868 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18871 \begin_layout Plain Layout
18879 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18882 \begin_layout Plain Layout
18883 \begin_inset Formula $\alpha$
18893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18896 \begin_layout Plain Layout
18904 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18907 \begin_layout Plain Layout
18908 \begin_inset Formula $\beta$
18918 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18921 \begin_layout Plain Layout
18929 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18932 \begin_layout Plain Layout
18933 \begin_inset Formula $\gamma$
18943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18946 \begin_layout Plain Layout
18954 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18957 \begin_layout Plain Layout
18958 \begin_inset Formula $\delta$
18968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18971 \begin_layout Plain Layout
18979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18982 \begin_layout Plain Layout
18983 \begin_inset Formula $\epsilon$
18993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18996 \begin_layout Plain Layout
19004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19007 \begin_layout Plain Layout
19008 \begin_inset Formula $\varepsilon$
19018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19021 \begin_layout Plain Layout
19029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19032 \begin_layout Plain Layout
19033 \begin_inset Formula $\zeta$
19043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19046 \begin_layout Plain Layout
19054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19057 \begin_layout Plain Layout
19058 \begin_inset Formula $\eta$
19068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19071 \begin_layout Plain Layout
19079 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19082 \begin_layout Plain Layout
19083 \begin_inset Formula $\theta$
19093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19096 \begin_layout Plain Layout
19104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19107 \begin_layout Plain Layout
19108 \begin_inset Formula $\vartheta$
19122 \begin_inset space \hfill{}
19126 \begin_inset Tabular
19127 <lyxtabular version="3" rows="12" columns="2">
19129 <column alignment="center" valignment="top" width="0pt">
19130 <column alignment="center" valignment="top" width="0pt">
19132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19135 \begin_layout Plain Layout
19141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19144 \begin_layout Plain Layout
19152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19155 \begin_layout Plain Layout
19163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19166 \begin_layout Plain Layout
19167 \begin_inset Formula $\iota$
19177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19180 \begin_layout Plain Layout
19188 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19191 \begin_layout Plain Layout
19192 \begin_inset Formula $\kappa$
19202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19205 \begin_layout Plain Layout
19213 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19216 \begin_layout Plain Layout
19217 \begin_inset Formula $\varkappa$
19227 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19230 \begin_layout Plain Layout
19238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19241 \begin_layout Plain Layout
19242 \begin_inset Formula $\lambda$
19252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19255 \begin_layout Plain Layout
19263 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19266 \begin_layout Plain Layout
19267 \begin_inset Formula $\mu$
19277 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19280 \begin_layout Plain Layout
19288 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19291 \begin_layout Plain Layout
19292 \begin_inset Formula $\nu$
19302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19305 \begin_layout Plain Layout
19313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19316 \begin_layout Plain Layout
19317 \begin_inset Formula $\xi$
19327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19330 \begin_layout Plain Layout
19336 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19339 \begin_layout Plain Layout
19340 \begin_inset Formula $o$
19350 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19353 \begin_layout Plain Layout
19361 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19364 \begin_layout Plain Layout
19365 \begin_inset Formula $\pi$
19375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19378 \begin_layout Plain Layout
19386 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19389 \begin_layout Plain Layout
19390 \begin_inset Formula $\varpi$
19400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19403 \begin_layout Plain Layout
19411 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19414 \begin_layout Plain Layout
19415 \begin_inset Formula $\rho$
19429 \begin_inset space \hfill{}
19433 \begin_inset Tabular
19434 <lyxtabular version="3" rows="11" columns="2">
19436 <column alignment="center" valignment="top" width="0pt">
19437 <column alignment="center" valignment="top" width="0pt">
19439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19442 \begin_layout Plain Layout
19448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19451 \begin_layout Plain Layout
19459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19462 \begin_layout Plain Layout
19470 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19473 \begin_layout Plain Layout
19474 \begin_inset Formula $\varrho$
19484 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19487 \begin_layout Plain Layout
19495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19498 \begin_layout Plain Layout
19499 \begin_inset Formula $\sigma$
19509 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19512 \begin_layout Plain Layout
19520 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19523 \begin_layout Plain Layout
19524 \begin_inset Formula $\varsigma$
19534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19537 \begin_layout Plain Layout
19545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19548 \begin_layout Plain Layout
19549 \begin_inset Formula $\tau$
19559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19562 \begin_layout Plain Layout
19570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19573 \begin_layout Plain Layout
19574 \begin_inset Formula $\upsilon$
19584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19587 \begin_layout Plain Layout
19595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19598 \begin_layout Plain Layout
19599 \begin_inset Formula $\phi$
19609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19612 \begin_layout Plain Layout
19620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19623 \begin_layout Plain Layout
19624 \begin_inset Formula $\varphi$
19634 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19637 \begin_layout Plain Layout
19645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19648 \begin_layout Plain Layout
19649 \begin_inset Formula $\chi$
19659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19662 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19673 \begin_layout Plain Layout
19674 \begin_inset Formula $\psi$
19684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19687 \begin_layout Plain Layout
19695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19698 \begin_layout Plain Layout
19699 \begin_inset Formula $\omega$
19713 \begin_inset space \hfill{}
19719 \begin_layout Standard
19720 \begin_inset VSpace medskip
19726 \begin_layout Standard
19727 How to create upright Greek letters is explained in
19728 \begin_inset CommandInset ref
19730 reference "sub:Upright-small-Greek"
19737 \begin_layout Subsection
19742 \begin_layout Plain Layout
19743 Greek letters ! big
19751 \begin_layout Standard
19752 \begin_inset space \hfill{}
19756 \begin_inset Tabular
19757 <lyxtabular version="3" rows="7" columns="2">
19759 <column alignment="center" valignment="top" width="0pt">
19760 <column alignment="center" valignment="top" width="0pt">
19762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19765 \begin_layout Plain Layout
19771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19774 \begin_layout Plain Layout
19782 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19785 \begin_layout Plain Layout
19793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19796 \begin_layout Plain Layout
19797 \begin_inset Formula $\Gamma$
19807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19810 \begin_layout Plain Layout
19818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19821 \begin_layout Plain Layout
19822 \begin_inset Formula $\Delta$
19832 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19835 \begin_layout Plain Layout
19843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19846 \begin_layout Plain Layout
19847 \begin_inset Formula $\Theta$
19857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19860 \begin_layout Plain Layout
19868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19871 \begin_layout Plain Layout
19872 \begin_inset Formula $\Lambda$
19882 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19885 \begin_layout Plain Layout
19893 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19896 \begin_layout Plain Layout
19897 \begin_inset Formula $\Xi$
19907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19910 \begin_layout Plain Layout
19918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19921 \begin_layout Plain Layout
19922 \begin_inset Formula $\Pi$
19936 \begin_inset space \hfill{}
19940 \begin_inset Tabular
19941 <lyxtabular version="3" rows="6" columns="2">
19943 <column alignment="center" valignment="top" width="0pt">
19944 <column alignment="center" valignment="top" width="0pt">
19946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19949 \begin_layout Plain Layout
19955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19958 \begin_layout Plain Layout
19966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19969 \begin_layout Plain Layout
19977 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19980 \begin_layout Plain Layout
19981 \begin_inset Formula $\Sigma$
19991 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19994 \begin_layout Plain Layout
20002 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20005 \begin_layout Plain Layout
20006 \begin_inset Formula $\Upsilon$
20016 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20019 \begin_layout Plain Layout
20027 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20030 \begin_layout Plain Layout
20031 \begin_inset Formula $\Phi$
20041 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20044 \begin_layout Plain Layout
20052 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20055 \begin_layout Plain Layout
20056 \begin_inset Formula $\Psi$
20066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20069 \begin_layout Plain Layout
20077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20080 \begin_layout Plain Layout
20081 \begin_inset Formula $\Omega$
20095 \begin_inset space \hfill{}
20101 \begin_layout Standard
20102 \begin_inset VSpace medskip
20105 That the big Greek letters appear upright is caused by a design bug when
20107 To get correct italic big letters, begin every command with
20112 For example the command
20119 \begin_inset Formula $\varGamma$
20125 \begin_layout Subsection
20130 \begin_layout Plain Layout
20131 Greek letters ! bold
20139 \begin_layout Standard
20140 Greek letters cannot be set with different font styles like Latin letters.
20141 They can only be made bold with the command
20151 \begin_layout Plain Layout
20162 \begin_layout Standard
20164 \begin_inset Tabular
20165 <lyxtabular version="3" rows="3" columns="2">
20167 <column alignment="center" valignment="top" width="0">
20168 <column alignment="center" valignment="top" width="0">
20170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20173 \begin_layout Plain Layout
20179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20182 \begin_layout Plain Layout
20190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20193 \begin_layout Plain Layout
20205 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20208 \begin_layout Plain Layout
20209 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20222 \begin_layout Plain Layout
20234 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20237 \begin_layout Plain Layout
20238 \begin_inset Formula $\theta\boldsymbol{\theta}$
20254 \begin_layout Section
20259 \begin_layout Plain Layout
20272 \begin_layout Plain Layout
20273 A list with all symbols of most of the LaTeX-packages can be found in
20274 \begin_inset CommandInset citation
20289 \begin_layout Plain Layout
20297 \begin_inset Note Note
20300 \begin_layout Plain Layout
20303 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20306 \begin_layout Plain Layout
20309 texorpdfstring is in section
20310 \begin_inset CommandInset ref
20312 reference "sub:Formulas-in-Section"
20325 \begin_layout Plain Layout
20334 \begin_layout Standard
20335 Many of the symbols listed in this section can also be inserted via the
20337 \begin_inset Graphics
20338 filename ../images/math/nabla.png
20344 \begin_inset Graphics
20345 filename ../images/math/digamma.png
20353 \begin_layout Subsection
20354 Mathematical Symbols
20355 \begin_inset CommandInset label
20357 name "sub:Mathematical-Symbols"
20365 \begin_layout Plain Layout
20366 Symbols ! mathematical
20374 \begin_layout Standard
20375 \begin_inset space \hfill{}
20379 \begin_inset Tabular
20380 <lyxtabular version="3" rows="10" columns="2">
20382 <column alignment="center" valignment="top" width="0pt">
20383 <column alignment="center" valignment="top" width="0pt">
20385 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20388 \begin_layout Plain Layout
20394 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20397 \begin_layout Plain Layout
20405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20408 \begin_layout Plain Layout
20416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20419 \begin_layout Plain Layout
20420 \begin_inset Formula $\neg$
20430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20433 \begin_layout Plain Layout
20441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20444 \begin_layout Plain Layout
20445 \begin_inset Formula $\Im$
20455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20458 \begin_layout Plain Layout
20466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20469 \begin_layout Plain Layout
20470 \begin_inset Formula $\Re$
20480 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20483 \begin_layout Plain Layout
20491 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20494 \begin_layout Plain Layout
20495 \begin_inset Formula $\aleph$
20505 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20508 \begin_layout Plain Layout
20516 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20519 \begin_layout Plain Layout
20520 \begin_inset Formula $\partial$
20530 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20533 \begin_layout Plain Layout
20541 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20544 \begin_layout Plain Layout
20545 \begin_inset Formula $\infty$
20555 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20558 \begin_layout Plain Layout
20566 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20569 \begin_layout Plain Layout
20570 \begin_inset Formula $\wp$
20580 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20583 \begin_layout Plain Layout
20591 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20594 \begin_layout Plain Layout
20595 \begin_inset Formula $\imath$
20605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20608 \begin_layout Plain Layout
20616 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20619 \begin_layout Plain Layout
20620 \begin_inset Formula $\jmath$
20634 \begin_inset space \hfill{}
20638 \begin_inset Tabular
20639 <lyxtabular version="3" rows="10" columns="2">
20641 <column alignment="center" valignment="top" width="0pt">
20642 <column alignment="center" valignment="top" width="0pt">
20644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20647 \begin_layout Plain Layout
20653 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20656 \begin_layout Plain Layout
20658 \begin_inset Note Note
20661 \begin_layout Plain Layout
20668 is only used as spacer.
20680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20683 \begin_layout Plain Layout
20691 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20694 \begin_layout Plain Layout
20695 \begin_inset Formula $\forall$
20705 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20708 \begin_layout Plain Layout
20716 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20719 \begin_layout Plain Layout
20720 \begin_inset Formula $\exists$
20730 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20733 \begin_layout Plain Layout
20741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20744 \begin_layout Plain Layout
20745 \begin_inset Formula $\nexists$
20755 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20758 \begin_layout Plain Layout
20766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20769 \begin_layout Plain Layout
20770 \begin_inset Formula $\emptyset$
20780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20783 \begin_layout Plain Layout
20791 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20794 \begin_layout Plain Layout
20795 \begin_inset Formula $\varnothing$
20805 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20808 \begin_layout Plain Layout
20816 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20819 \begin_layout Plain Layout
20820 \begin_inset Formula $\dag$
20830 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20833 \begin_layout Plain Layout
20841 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20844 \begin_layout Plain Layout
20845 \begin_inset Formula $\ddag$
20855 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20858 \begin_layout Plain Layout
20866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20869 \begin_layout Plain Layout
20873 \begin_layout Plain Layout
20883 \begin_inset Formula $\complement$
20890 \begin_layout Plain Layout
20904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20907 \begin_layout Plain Layout
20915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20918 \begin_layout Plain Layout
20919 \begin_inset Formula $\Bbbk$
20933 \begin_inset space \hfill{}
20937 \begin_inset Tabular
20938 <lyxtabular version="3" rows="10" columns="2">
20940 <column alignment="center" valignment="top" width="0pt">
20941 <column alignment="center" valignment="top" width="0pt">
20943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20946 \begin_layout Plain Layout
20952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20955 \begin_layout Plain Layout
20963 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20966 \begin_layout Plain Layout
20974 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20977 \begin_layout Plain Layout
20978 \begin_inset Formula $\prime$
20988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20991 \begin_layout Plain Layout
20999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21002 \begin_layout Plain Layout
21003 \begin_inset Formula $\backprime$
21013 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21016 \begin_layout Plain Layout
21024 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21027 \begin_layout Plain Layout
21028 \begin_inset Formula $\mho$
21038 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21041 \begin_layout Plain Layout
21049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21052 \begin_layout Plain Layout
21053 \begin_inset Formula $\triangle$
21063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21066 \begin_layout Plain Layout
21074 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21077 \begin_layout Plain Layout
21078 \begin_inset Formula $\angle$
21088 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21091 \begin_layout Plain Layout
21099 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21102 \begin_layout Plain Layout
21103 \begin_inset Formula $\measuredangle$
21113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21116 \begin_layout Plain Layout
21124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21127 \begin_layout Plain Layout
21128 \begin_inset Formula $\sphericalangle$
21138 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21141 \begin_layout Plain Layout
21149 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21152 \begin_layout Plain Layout
21153 \begin_inset Formula $\top$
21163 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21166 \begin_layout Plain Layout
21174 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21177 \begin_layout Plain Layout
21178 \begin_inset Formula $\bot$
21192 \begin_inset space \hfill{}
21198 \begin_layout Standard
21199 \begin_inset Newpage newpage
21205 \begin_layout Subsection
21206 Miscellaneous Symbols
21207 \begin_inset CommandInset label
21209 name "sub:Miscellaneous-Symbols"
21217 \begin_layout Plain Layout
21218 Symbols ! miscellaneous
21226 \begin_layout Standard
21229 \begin_inset Tabular
21230 <lyxtabular version="3" rows="10" columns="2">
21232 <column alignment="center" valignment="top" width="0pt">
21233 <column alignment="center" valignment="top" width="0pt">
21235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21238 \begin_layout Plain Layout
21244 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21247 \begin_layout Plain Layout
21255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21258 \begin_layout Plain Layout
21266 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21269 \begin_layout Plain Layout
21270 \begin_inset Formula $\flat$
21280 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21283 \begin_layout Plain Layout
21291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21294 \begin_layout Plain Layout
21295 \begin_inset Formula $\natural$
21305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21308 \begin_layout Plain Layout
21316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21319 \begin_layout Plain Layout
21320 \begin_inset Formula $\sharp$
21330 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21333 \begin_layout Plain Layout
21341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21344 \begin_layout Plain Layout
21345 \begin_inset Formula $\surd$
21355 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21358 \begin_layout Plain Layout
21366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21369 \begin_layout Plain Layout
21370 \begin_inset Formula $\checkmark$
21380 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21383 \begin_layout Plain Layout
21391 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21394 \begin_layout Plain Layout
21395 \begin_inset Formula $\yen$
21405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21408 \begin_layout Plain Layout
21416 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21419 \begin_layout Plain Layout
21420 \begin_inset Formula $\pounds$
21430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21433 \begin_layout Plain Layout
21439 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21442 \begin_layout Plain Layout
21443 \begin_inset Formula $\$$
21453 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21456 \begin_layout Plain Layout
21462 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21465 \begin_layout Plain Layout
21466 \begin_inset Formula $§$
21480 \begin_inset Tabular
21481 <lyxtabular version="3" rows="10" columns="2">
21483 <column alignment="center" valignment="top" width="0">
21484 <column alignment="center" valignment="top" width="0">
21486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21489 \begin_layout Plain Layout
21495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21498 \begin_layout Plain Layout
21506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21509 \begin_layout Plain Layout
21517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21520 \begin_layout Plain Layout
21521 \begin_inset Formula $\hbar$
21531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21534 \begin_layout Plain Layout
21542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21545 \begin_layout Plain Layout
21546 \begin_inset Formula $\hslash$
21556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21559 \begin_layout Plain Layout
21567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21570 \begin_layout Plain Layout
21571 \begin_inset Formula $\clubsuit$
21581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21584 \begin_layout Plain Layout
21592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21595 \begin_layout Plain Layout
21596 \begin_inset Formula $\spadesuit$
21606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21609 \begin_layout Plain Layout
21617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21620 \begin_layout Plain Layout
21621 \begin_inset Formula $\bigstar$
21631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21634 \begin_layout Plain Layout
21642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21645 \begin_layout Plain Layout
21646 \begin_inset Formula $\blacklozenge$
21656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21659 \begin_layout Plain Layout
21667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21670 \begin_layout Plain Layout
21671 \begin_inset Formula $\blacktriangle$
21681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21684 \begin_layout Plain Layout
21692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21695 \begin_layout Plain Layout
21696 \begin_inset Formula $\blacktriangledown$
21706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21709 \begin_layout Plain Layout
21717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21720 \begin_layout Plain Layout
21721 \begin_inset Formula $\bullet$
21735 \begin_inset Tabular
21736 <lyxtabular version="3" rows="10" columns="2">
21738 <column alignment="center" valignment="top" width="0pt">
21739 <column alignment="center" valignment="top" width="0pt">
21741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21744 \begin_layout Plain Layout
21750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21753 \begin_layout Plain Layout
21761 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21764 \begin_layout Plain Layout
21772 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21775 \begin_layout Plain Layout
21776 \begin_inset Formula $\diamondsuit$
21786 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21789 \begin_layout Plain Layout
21797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21800 \begin_layout Plain Layout
21801 \begin_inset Formula $\Diamond$
21811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21814 \begin_layout Plain Layout
21822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21825 \begin_layout Plain Layout
21826 \begin_inset Formula $\heartsuit$
21836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21839 \begin_layout Plain Layout
21847 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21850 \begin_layout Plain Layout
21851 \begin_inset Formula $\P$
21861 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21864 \begin_layout Plain Layout
21872 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21875 \begin_layout Plain Layout
21876 \begin_inset Formula $\copyright$
21886 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21889 \begin_layout Plain Layout
21897 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21900 \begin_layout Plain Layout
21901 \begin_inset Formula $\circledR$
21911 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21914 \begin_layout Plain Layout
21922 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21925 \begin_layout Plain Layout
21926 \begin_inset Formula $\maltese$
21936 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21939 \begin_layout Plain Layout
21947 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21950 \begin_layout Plain Layout
21951 \begin_inset Formula $\diagup$
21961 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21964 \begin_layout Plain Layout
21972 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21975 \begin_layout Plain Layout
21976 \begin_inset Formula $\diagdown$
21992 \begin_layout Standard
21993 \begin_inset VSpace medskip
21996 More symbols are listed in
21997 \begin_inset CommandInset ref
21999 reference "sub:Miscellaneous-Special-Characters"
22006 \begin_layout Standard
22007 Some symbols can be displayed in different sizes, see
22008 \begin_inset CommandInset ref
22010 reference "sub:Font-Sizes"
22017 \begin_layout Subsection
22022 \begin_layout Plain Layout
22023 Symbols ! Euro-symbol
22032 \begin_layout Plain Layout
22036 \begin_layout Plain Layout
22053 \begin_layout Standard
22054 To use the Euro symbol in formulas, the LaTeX-package
22062 \begin_layout Plain Layout
22068 must be installed and loaded with the LaTeX-preamble line
22071 \begin_layout Standard
22076 usepackage[gennarrow]{eurosym}
22079 \begin_layout Standard
22080 The Euro symbol can now be inserted with the command
22090 \begin_layout Plain Layout
22101 \begin_layout Standard
22102 The Euro symbol can directly be inserted with the € key in mathematical
22103 text, without having
22118 can also be inserted in TeX-mode.
22119 The official currency symbol can then be inserted with the command
22129 \begin_layout Plain Layout
22137 , that is only available in TeX-mode.
22140 \begin_layout Standard
22144 \begin_layout Plain Layout
22154 \begin_inset Note Note
22157 \begin_layout Plain Layout
22158 The following table will only be displayed when the LaTeX-package
22170 \begin_layout Standard
22171 An overview about the different Euro symbols:
22174 \begin_layout Standard
22176 \begin_inset Tabular
22177 <lyxtabular version="3" rows="4" columns="3">
22179 <column alignment="center" valignment="top" width="0pt">
22180 <column alignment="center" valignment="top" width="0pt">
22181 <column alignment="center" valignment="top" width="0pt">
22183 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22186 \begin_layout Plain Layout
22192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22195 \begin_layout Plain Layout
22201 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22204 \begin_layout Plain Layout
22212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22215 \begin_layout Plain Layout
22221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22224 \begin_layout Plain Layout
22232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22235 \begin_layout Plain Layout
22236 \begin_inset Formula $\euro$
22246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22249 \begin_layout Plain Layout
22255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22258 \begin_layout Plain Layout
22264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22267 \begin_layout Plain Layout
22268 \begin_inset Formula $\mbox{€}$
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" usebox="none">
22290 \begin_layout Plain Layout
22298 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22301 \begin_layout Plain Layout
22305 \begin_layout Plain Layout
22327 \begin_layout Standard
22331 \begin_layout Plain Layout
22341 \begin_inset Note Note
22344 \begin_layout Plain Layout
22345 The following will be displayed when the LaTeX-package
22357 \begin_layout Standard
22358 You need to install the LaTeX-package
22362 to see the rest of this subsection in the output.
22365 \begin_layout Standard
22369 \begin_layout Plain Layout
22381 \begin_layout Section
22383 \begin_inset CommandInset label
22385 name "sec:Relations"
22393 \begin_layout Plain Layout
22403 \begin_layout Plain Layout
22408 \begin_layout Plain Layout
22419 \begin_layout Plain Layout
22434 \begin_layout Standard
22435 All relations can also be inserted via the toolbar button
22436 \begin_inset Graphics
22437 filename ../images/math/leq.png
22445 \begin_layout Standard
22446 \begin_inset space \hfill{}
22450 \begin_inset Tabular
22451 <lyxtabular version="3" rows="17" columns="2">
22453 <column alignment="center" valignment="top" width="0pt">
22454 <column alignment="center" valignment="top" width="0pt">
22456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22459 \begin_layout Plain Layout
22465 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22468 \begin_layout Plain Layout
22476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22479 \begin_layout Plain Layout
22485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22488 \begin_layout Plain Layout
22489 \begin_inset Formula $<$
22499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22502 \begin_layout Plain Layout
22510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22513 \begin_layout Plain Layout
22514 \begin_inset Formula $\le$
22524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22527 \begin_layout Plain Layout
22535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22538 \begin_layout Plain Layout
22539 \begin_inset Formula $\ll$
22549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22552 \begin_layout Plain Layout
22560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22563 \begin_layout Plain Layout
22564 \begin_inset Formula $\prec$
22574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22577 \begin_layout Plain Layout
22585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22588 \begin_layout Plain Layout
22589 \begin_inset Formula $\preceq$
22599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22602 \begin_layout Plain Layout
22610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22613 \begin_layout Plain Layout
22614 \begin_inset Formula $\subset$
22624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22627 \begin_layout Plain Layout
22635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22638 \begin_layout Plain Layout
22639 \begin_inset Formula $\subseteq$
22649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22652 \begin_layout Plain Layout
22660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22663 \begin_layout Plain Layout
22664 \begin_inset Formula $\sqsubseteq$
22674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22677 \begin_layout Plain Layout
22685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22688 \begin_layout Plain Layout
22689 \begin_inset Formula $\in$
22699 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22702 \begin_layout Plain Layout
22710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22713 \begin_layout Plain Layout
22714 \begin_inset Formula $\vdash$
22724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22727 \begin_layout Plain Layout
22735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22738 \begin_layout Plain Layout
22739 \begin_inset Formula $\smile$
22749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22752 \begin_layout Plain Layout
22760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22763 \begin_layout Plain Layout
22764 \begin_inset Formula $\lhd$
22774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22777 \begin_layout Plain Layout
22785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22788 \begin_layout Plain Layout
22789 \begin_inset Formula $\unlhd$
22799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22802 \begin_layout Plain Layout
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22813 \begin_layout Plain Layout
22814 \begin_inset Formula $\gtrless$
22824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22827 \begin_layout Plain Layout
22835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22838 \begin_layout Plain Layout
22839 \begin_inset Formula $\mid$
22849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22852 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22864 \begin_inset Formula $\nmid$
22878 \begin_inset space \hfill{}
22882 \begin_inset Tabular
22883 <lyxtabular version="3" rows="17" columns="2">
22885 <column alignment="center" valignment="top" width="0pt">
22886 <column alignment="center" valignment="top" width="0pt">
22888 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22891 \begin_layout Plain Layout
22897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22900 \begin_layout Plain Layout
22908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22920 \begin_layout Plain Layout
22921 \begin_inset Formula $=$
22931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22934 \begin_layout Plain Layout
22942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22945 \begin_layout Plain Layout
22946 \begin_inset Formula $\not=$
22956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22959 \begin_layout Plain Layout
22967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22970 \begin_layout Plain Layout
22971 \begin_inset Formula $\equiv$
22981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22984 \begin_layout Plain Layout
22992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22995 \begin_layout Plain Layout
22996 \begin_inset Formula $\sim$
23006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23009 \begin_layout Plain Layout
23017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23020 \begin_layout Plain Layout
23021 \begin_inset Formula $\simeq$
23031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23034 \begin_layout Plain Layout
23042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23045 \begin_layout Plain Layout
23046 \begin_inset Formula $\approx$
23056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23059 \begin_layout Plain Layout
23067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23070 \begin_layout Plain Layout
23071 \begin_inset Formula $\cong$
23081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23084 \begin_layout Plain Layout
23092 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23095 \begin_layout Plain Layout
23096 \begin_inset Formula $\bowtie$
23106 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23109 \begin_layout Plain Layout
23117 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23120 \begin_layout Plain Layout
23121 \begin_inset Formula $\notin$
23131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23134 \begin_layout Plain Layout
23142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23145 \begin_layout Plain Layout
23146 \begin_inset Formula $\perp$
23156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23159 \begin_layout Plain Layout
23167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23170 \begin_layout Plain Layout
23171 \begin_inset Formula $\propto$
23181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23184 \begin_layout Plain Layout
23192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23195 \begin_layout Plain Layout
23196 \begin_inset Formula $\asymp$
23206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23209 \begin_layout Plain Layout
23217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23220 \begin_layout Plain Layout
23221 \begin_inset Formula $\doteq$
23231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23234 \begin_layout Plain Layout
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23245 \begin_layout Plain Layout
23246 \begin_inset Formula $\circeq$
23256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23259 \begin_layout Plain Layout
23267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23270 \begin_layout Plain Layout
23271 \begin_inset Formula $\models$
23281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23284 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $\widehat{=}$
23310 \begin_inset space \hfill{}
23314 \begin_inset Tabular
23315 <lyxtabular version="3" rows="17" columns="2">
23317 <column alignment="center" valignment="top" width="0pt">
23318 <column alignment="center" valignment="top" width="0pt">
23320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23323 \begin_layout Plain Layout
23329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23332 \begin_layout Plain Layout
23340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23343 \begin_layout Plain Layout
23349 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23352 \begin_layout Plain Layout
23353 \begin_inset Formula $>$
23363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23366 \begin_layout Plain Layout
23374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23377 \begin_layout Plain Layout
23378 \begin_inset Formula $\ge$
23388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23391 \begin_layout Plain Layout
23399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23402 \begin_layout Plain Layout
23403 \begin_inset Formula $\gg$
23413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23416 \begin_layout Plain Layout
23424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23427 \begin_layout Plain Layout
23428 \begin_inset Formula $\succ$
23438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23441 \begin_layout Plain Layout
23449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23452 \begin_layout Plain Layout
23453 \begin_inset Formula $\succeq$
23463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23466 \begin_layout Plain Layout
23474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23477 \begin_layout Plain Layout
23478 \begin_inset Formula $\supset$
23488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23491 \begin_layout Plain Layout
23499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23502 \begin_layout Plain Layout
23503 \begin_inset Formula $\supseteq$
23513 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23516 \begin_layout Plain Layout
23524 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23527 \begin_layout Plain Layout
23528 \begin_inset Formula $\sqsupseteq$
23538 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23541 \begin_layout Plain Layout
23549 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23552 \begin_layout Plain Layout
23553 \begin_inset Formula $\ni$
23563 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23566 \begin_layout Plain Layout
23574 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23577 \begin_layout Plain Layout
23578 \begin_inset Formula $\dashv$
23588 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23591 \begin_layout Plain Layout
23599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23602 \begin_layout Plain Layout
23603 \begin_inset Formula $\frown$
23613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23616 \begin_layout Plain Layout
23624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23627 \begin_layout Plain Layout
23628 \begin_inset Formula $\rhd$
23638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23641 \begin_layout Plain Layout
23649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23652 \begin_layout Plain Layout
23653 \begin_inset Formula $\unrhd$
23663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23666 \begin_layout Plain Layout
23674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23677 \begin_layout Plain Layout
23678 \begin_inset Formula $\lessgtr$
23688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23691 \begin_layout Plain Layout
23699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23702 \begin_layout Plain Layout
23703 \begin_inset Formula $\parallel$
23713 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23716 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23728 \begin_inset Formula $\nparallel$
23742 \begin_inset space \hfill{}
23748 \begin_layout Standard
23749 \begin_inset VSpace medskip
23764 are bigger than the equal looking operators
23779 \begin_layout Standard
23780 Relations are, in contrary to symbols, always surrounded by space.
23783 \begin_layout Standard
23784 Relations with labels can be created with the command
23794 \begin_layout Plain Layout
23805 \begin_layout Standard
23807 \begin_inset Tabular
23808 <lyxtabular version="3" rows="2" columns="2">
23810 <column alignment="center" valignment="top" width="0">
23811 <column alignment="center" valignment="top" width="0">
23813 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23816 \begin_layout Plain Layout
23822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23825 \begin_layout Plain Layout
23827 \begin_inset Note Note
23830 \begin_layout Plain Layout
23837 is only used as spacer.
23849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23852 \begin_layout Plain Layout
23859 \begin_layout Plain Layout
23876 \begin_layout Plain Layout
23886 \begin_inset Formula $\downarrow$
23895 \begin_layout Plain Layout
23908 \begin_layout Plain Layout
23922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23925 \begin_layout Plain Layout
23926 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23942 \begin_layout Section
23946 \begin_layout Subsection
23947 Predefined Functions
23948 \begin_inset CommandInset label
23950 name "sub:Predefined-Functions"
23958 \begin_layout Plain Layout
23959 Functions ! predefined
23967 \begin_layout Standard
23968 In general, variables are set
23972 in mathematical expressions, but not function names, because
23973 \begin_inset Formula $sin$
23976 could be misunderstood as
23977 \begin_inset Formula $s\cdot i\cdot n$
23981 Therefore there are predefined functions, that are additionally a bit separated
23983 They are inserted as commands starting with a backslash before their name.
23986 \begin_layout Standard
23988 \begin_inset Tabular
23989 <lyxtabular version="3" rows="2" columns="4">
23991 <column alignment="center" valignment="top" width="0pt">
23992 <column alignment="center" valignment="top" width="0pt">
23993 <column alignment="center" valignment="top" width="0pt">
23994 <column alignment="center" valignment="top" width="0pt">
23996 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23999 \begin_layout Plain Layout
24005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24008 \begin_layout Plain Layout
24014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24017 \begin_layout Plain Layout
24023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24026 \begin_layout Plain Layout
24034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24037 \begin_layout Plain Layout
24043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24046 \begin_layout Plain Layout
24047 \begin_inset Formula $Asin(x)+B$
24055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24058 \begin_layout Plain Layout
24066 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24069 \begin_layout Plain Layout
24070 \begin_inset Formula $A\sin(x)+B$
24084 \begin_inset Newpage pagebreak
24090 \begin_layout Standard
24091 The following functions are predefined:
24094 \begin_layout Standard
24095 \begin_inset VSpace -2mm
24101 \begin_layout Standard
24103 \begin_inset Tabular
24104 <lyxtabular version="3" rows="9" columns="4">
24106 <column alignment="center" valignment="top" width="0pt">
24107 <column alignment="center" valignment="top" width="0pt">
24108 <column alignment="center" valignment="top" width="0pt">
24109 <column alignment="center" valignment="top" width="0pt">
24111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24114 \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" usebox="none">
24132 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24141 \begin_layout Plain Layout
24149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24152 \begin_layout Plain Layout
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24174 \begin_layout Plain Layout
24182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24185 \begin_layout Plain Layout
24195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24198 \begin_layout Plain Layout
24206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24209 \begin_layout Plain Layout
24217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24220 \begin_layout Plain Layout
24228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24231 \begin_layout Plain Layout
24241 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24244 \begin_layout Plain Layout
24252 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24255 \begin_layout Plain Layout
24263 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24266 \begin_layout Plain Layout
24274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24277 \begin_layout Plain Layout
24287 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24290 \begin_layout Plain Layout
24298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24301 \begin_layout Plain Layout
24309 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24312 \begin_layout Plain Layout
24320 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24323 \begin_layout Plain Layout
24333 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24336 \begin_layout Plain Layout
24344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24347 \begin_layout Plain Layout
24355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24358 \begin_layout Plain Layout
24366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24369 \begin_layout Plain Layout
24379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24382 \begin_layout Plain Layout
24390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24393 \begin_layout Plain Layout
24401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24404 \begin_layout Plain Layout
24412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24415 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24450 \begin_layout Plain Layout
24458 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24461 \begin_layout Plain Layout
24471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24474 \begin_layout Plain Layout
24482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24485 \begin_layout Plain Layout
24493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24496 \begin_layout Plain Layout
24504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24507 \begin_layout Plain Layout
24523 \begin_layout Standard
24524 They can also be inserted with the math toolbar button
24525 \begin_inset Graphics
24526 filename ../images/math/functions.png
24534 \begin_layout Subsection
24535 Self-defined Functions
24539 \begin_layout Plain Layout
24540 Functions ! self-defined
24548 \begin_layout Standard
24549 To use a function that is not predefined, like for example the sign function
24550 sgn(x), there are two possibilities:
24553 \begin_layout Itemize
24554 Define the function by inserting the following line to the LaTeX-preamble
24558 \begin_layout Plain Layout
24563 DeclareMathOperator
24566 \begin_inset CommandInset ref
24568 reference "sub:Self-defined-Operators"
24578 \begin_inset Newline newline
24582 \begin_inset VSpace -3mm
24586 \begin_inset Newline newline
24593 DeclareMathOperator{
24601 \begin_layout Plain Layout
24606 DeclareMathOperator
24612 \begin_inset Newline newline
24616 \begin_inset VSpace -2mm
24620 \begin_inset Newline newline
24623 Now the new defined function can be called with the command
24632 \begin_layout Itemize
24633 Write the the formula as usual, mark the formula name, in our example the
24638 , and change it to mathematical text.
24639 At last a space is inserted between prefactor and function.
24642 \begin_layout Standard
24643 The result is the same with both methods as with a predefined function
24647 \begin_layout Plain Layout
24648 In LyX self-defined functions are displayed red, predefined ones black.
24656 \begin_layout Standard
24658 \begin_inset Tabular
24659 <lyxtabular version="3" rows="3" columns="2">
24661 <column alignment="center" valignment="top" width="0pt">
24662 <column alignment="center" valignment="top" width="0pt">
24664 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24667 \begin_layout Plain Layout
24673 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24676 \begin_layout Plain Layout
24684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24687 \begin_layout Plain Layout
24695 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24698 \begin_layout Plain Layout
24699 \begin_inset Formula $A\sgn(x)+B$
24709 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24712 \begin_layout Plain Layout
24716 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24727 \begin_layout Plain Layout
24728 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24744 \begin_layout Standard
24745 The first method is more suitable when the self-defined function should
24746 be used several times.
24749 \begin_layout Subsection
24754 \begin_layout Plain Layout
24763 \begin_layout Standard
24764 For limits there are defined besides
24774 \begin_layout Plain Layout
24794 furthermore the following functions:
24797 \begin_layout Standard
24799 \begin_inset Tabular
24800 <lyxtabular version="3" rows="5" columns="2">
24802 <column alignment="center" valignment="top" width="0">
24803 <column alignment="center" valignment="top" width="0">
24805 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24808 \begin_layout Plain Layout
24814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24817 \begin_layout Plain Layout
24819 \begin_inset Note Note
24822 \begin_layout Plain Layout
24829 is only used as spacer.
24841 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24844 \begin_layout Plain Layout
24852 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24855 \begin_layout Plain Layout
24856 \begin_inset Formula $\varliminf$
24866 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24869 \begin_layout Plain Layout
24877 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24880 \begin_layout Plain Layout
24881 \begin_inset Formula $\varlimsup$
24891 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24894 \begin_layout Plain Layout
24902 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24905 \begin_layout Plain Layout
24906 \begin_inset Formula $\varprojlim$
24916 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24919 \begin_layout Plain Layout
24927 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24930 \begin_layout Plain Layout
24931 \begin_inset Formula $\varinjlim$
24935 \begin_inset Formula $\raisebox{-2.5mm}{}$
24951 \begin_layout Standard
24952 \begin_inset VSpace medskip
24955 The limit is created by inserting a subscript.
24956 It is set right beside the function in an inline formula:
24959 \begin_layout Standard
24961 \begin_inset Tabular
24962 <lyxtabular version="3" rows="2" columns="2">
24964 <column alignment="center" valignment="top" width="0pt">
24965 <column alignment="center" valignment="top" width="0pt">
24967 <cell alignment="center" valignment="top" usebox="none">
24970 \begin_layout Plain Layout
24976 <cell alignment="center" valignment="top" usebox="none">
24979 \begin_layout Plain Layout
24980 \begin_inset space \hspace{}
24985 \begin_inset Note Note
24988 \begin_layout Plain Layout
25001 are used here as spacer.
25013 <cell alignment="center" valignment="top" usebox="none">
25016 \begin_layout Plain Layout
25025 \begin_layout Plain Layout
25038 \begin_layout Plain Layout
25052 <cell alignment="center" valignment="top" usebox="none">
25055 \begin_layout Plain Layout
25056 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25072 \begin_layout Standard
25073 In a displayed formula the limit is set below the formula, as usual:
25074 \begin_inset Formula \[
25082 \begin_layout Subsection
25087 \begin_layout Plain Layout
25088 Functions ! modulo-
25096 \begin_layout Standard
25097 The modulo-function is special, because it exists in four variants.
25100 \begin_layout Standard
25101 The variants in a displayed formula:
25102 \begin_inset Formula \begin{align*}
25103 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25104 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25105 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25106 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25107 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25114 \begin_layout Standard
25115 In an inline formula less space is set before the function names for all
25119 \begin_layout Section
25124 \begin_layout Plain Layout
25133 \begin_layout Subsection
25134 Special Characters in Mathematical Text
25137 \begin_layout Standard
25138 The following commands can only be used in mathematical text or in TeX-mode:
25141 \begin_layout Standard
25142 \begin_inset space \hfill{}
25146 \begin_inset Tabular
25147 <lyxtabular version="3" rows="8" columns="2">
25149 <column alignment="block" valignment="top" width="0">
25150 <column alignment="block" valignment="top" width="0">
25152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25155 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25164 \begin_layout Plain Layout
25172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25175 \begin_layout Plain Layout
25183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25186 \begin_layout Plain Layout
25187 \begin_inset Formula $\textrm{œ}$
25197 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25200 \begin_layout Plain Layout
25208 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25211 \begin_layout Plain Layout
25212 \begin_inset Formula $\textrm{Œ}$
25222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25225 \begin_layout Plain Layout
25233 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25236 \begin_layout Plain Layout
25237 \begin_inset Formula $\textrm{æ}$
25247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25250 \begin_layout Plain Layout
25258 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25261 \begin_layout Plain Layout
25262 \begin_inset Formula $\textrm{Æ}$
25272 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25275 \begin_layout Plain Layout
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25286 \begin_layout Plain Layout
25287 \begin_inset Formula $\textrm{\aa}$
25297 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25300 \begin_layout Plain Layout
25307 \begin_layout Plain Layout
25311 \begin_layout Plain Layout
25319 \begin_layout Plain Layout
25330 \begin_layout Plain Layout
25346 \begin_layout Plain Layout
25354 \begin_layout Plain Layout
25365 \begin_layout Plain Layout
25381 \begin_layout Plain Layout
25392 \begin_layout Plain Layout
25400 \begin_layout Plain Layout
25411 \begin_layout Plain Layout
25427 \begin_layout Plain Layout
25444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25447 \begin_layout Plain Layout
25448 \begin_inset Formula $\textrm{Å}$
25458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25461 \begin_layout Plain Layout
25469 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25472 \begin_layout Plain Layout
25473 \begin_inset Formula $\textrm{ı}$
25487 \begin_inset space \hfill{}
25491 \begin_inset Tabular
25492 <lyxtabular version="3" rows="8" columns="2">
25494 <column alignment="block" valignment="top" width="0">
25495 <column alignment="center" valignment="top" width="0">
25497 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25500 \begin_layout Plain Layout
25502 \begin_inset Note Note
25505 \begin_layout Plain Layout
25512 is used for separation, because otherwise the output will be ¡ and ¿ respective
25523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25537 \begin_layout Plain Layout
25545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25548 \begin_layout Plain Layout
25549 \begin_inset Formula $\textrm{ø}$
25559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25562 \begin_layout Plain Layout
25570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25573 \begin_layout Plain Layout
25574 \begin_inset Formula $\textrm{Ø}$
25584 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25587 \begin_layout Plain Layout
25595 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25598 \begin_layout Plain Layout
25599 \begin_inset Formula $\textrm{ł}$
25609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25612 \begin_layout Plain Layout
25620 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25623 \begin_layout Plain Layout
25624 \begin_inset Formula $\textrm{Ł}$
25634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25637 \begin_layout Plain Layout
25639 \begin_inset space \hspace{}
25647 \begin_layout Plain Layout
25661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25664 \begin_layout Plain Layout
25665 \begin_inset Formula $\textrm{!`}$
25675 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25678 \begin_layout Plain Layout
25680 \begin_inset space \hspace{}
25688 \begin_layout Plain Layout
25702 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25705 \begin_layout Plain Layout
25706 \begin_inset Formula $\textrm{?`}$
25716 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25719 \begin_layout Plain Layout
25727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25730 \begin_layout Plain Layout
25731 \begin_inset Formula $\textrm{ȷ}$
25745 \begin_inset space \hfill{}
25751 \begin_layout Standard
25753 \begin_inset Formula $\textrm{\textrm{Å}}$
25757 \begin_inset Formula $\textrm{\textrm{Ø}}$
25760 can also be inserted via the math toolbar button
25761 \begin_inset Graphics
25762 filename ../images/math/digamma.png
25770 \begin_layout Standard
25771 An exception are the commands
25774 \begin_inset space \hspace{}
25783 \begin_inset space \hspace{}
25789 , because they can be inserted in LyX directly to text.
25792 \begin_layout Subsection
25794 \begin_inset CommandInset label
25796 name "sub:Accents-in-Text"
25804 \begin_layout Plain Layout
25813 \begin_layout Standard
25814 With the following commands all letters can be accented.
25815 The commands must be inserted in TeX-mode.
25818 \begin_layout Standard
25819 \begin_inset space \hfill{}
25823 \begin_inset Tabular
25824 <lyxtabular version="3" rows="8" columns="2">
25826 <column alignment="block" valignment="top" width="0">
25827 <column alignment="block" valignment="top" width="0">
25829 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25832 \begin_layout Plain Layout
25838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25841 \begin_layout Plain Layout
25849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25852 \begin_layout Plain Layout
25856 \begin_inset Quotes grd
25864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25867 \begin_layout Plain Layout
25871 \begin_layout Plain Layout
25887 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25890 \begin_layout Plain Layout
25898 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25901 \begin_layout Plain Layout
25905 \begin_layout Plain Layout
25921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25924 \begin_layout Plain Layout
25931 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25948 \begin_layout Plain Layout
25952 \begin_layout Plain Layout
25968 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25971 \begin_layout Plain Layout
25979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25982 \begin_layout Plain Layout
25986 \begin_layout Plain Layout
26002 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26005 \begin_layout Plain Layout
26012 \begin_layout Plain Layout
26026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26029 \begin_layout Plain Layout
26033 \begin_layout Plain Layout
26049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26052 \begin_layout Plain Layout
26059 \begin_layout Plain Layout
26073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26076 \begin_layout Plain Layout
26080 \begin_layout Plain Layout
26096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26099 \begin_layout Plain Layout
26106 \begin_layout Plain Layout
26120 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26123 \begin_layout Plain Layout
26127 \begin_layout Plain Layout
26147 \begin_inset space \hfill{}
26151 \begin_inset Tabular
26152 <lyxtabular version="3" rows="8" columns="2">
26154 <column alignment="block" valignment="top" width="0">
26155 <column alignment="center" valignment="top" width="0">
26157 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26160 \begin_layout Plain Layout
26166 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26169 \begin_layout Plain Layout
26177 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26180 \begin_layout Plain Layout
26187 \begin_layout Plain Layout
26201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26204 \begin_layout Plain Layout
26208 \begin_layout Plain Layout
26224 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26227 \begin_layout Plain Layout
26235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26238 \begin_layout Plain Layout
26242 \begin_layout Plain Layout
26258 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26261 \begin_layout Plain Layout
26268 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26282 \begin_layout Plain Layout
26286 \begin_layout Plain Layout
26302 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26305 \begin_layout Plain Layout
26313 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26316 \begin_layout Plain Layout
26320 \begin_layout Plain Layout
26336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26339 \begin_layout Plain Layout
26346 \begin_layout Plain Layout
26360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26363 \begin_layout Plain Layout
26367 \begin_layout Plain Layout
26383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26386 \begin_layout Plain Layout
26393 \begin_layout Plain Layout
26407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26410 \begin_layout Plain Layout
26414 \begin_layout Plain Layout
26430 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26433 \begin_layout Plain Layout
26440 \begin_layout Plain Layout
26454 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26457 \begin_layout Plain Layout
26461 \begin_layout Plain Layout
26481 \begin_inset space \hfill{}
26487 \begin_layout Standard
26488 \begin_inset VSpace medskip
26497 also two different characters can be accented.
26506 \begin_layout Plain Layout
26521 \begin_layout Plain Layout
26533 \begin_layout Standard
26546 can in combination with vowels directly be inserted with the keyboard without
26548 The same applies for the tilde
26552 \begin_layout Plain Layout
26553 This only applies for keyboards where the tilde is defined as accent.
26562 in combination with
26577 \begin_layout Standard
26620 , and accents inserted directly with the keyboard are also available in
26622 For the other accents there are special math commands to be used in formulas,
26624 \begin_inset CommandInset ref
26626 reference "sub:Accents-for-one"
26633 \begin_layout Standard
26634 \begin_inset VSpace bigskip
26637 Furthermore, with the command
26647 \begin_layout Plain Layout
26655 all numbers and letters can be set into a circle, quasi accented with a
26656 circle, similar to the the copyright symbol.
26659 \begin_layout Standard
26661 \begin_inset Tabular
26662 <lyxtabular version="3" rows="3" columns="2">
26664 <column alignment="center" valignment="top" width="0">
26665 <column alignment="center" valignment="top" width="0">
26667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26670 \begin_layout Plain Layout
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26679 \begin_layout Plain Layout
26681 \begin_inset Note Note
26684 \begin_layout Plain Layout
26691 is only used as spacer.
26703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26706 \begin_layout Plain Layout
26714 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26717 \begin_layout Plain Layout
26721 \begin_layout Plain Layout
26737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26740 \begin_layout Plain Layout
26751 raisebox{-1.5pt}{W}}
26756 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26759 \begin_layout Plain Layout
26760 \begin_inset Formula $\raisebox{4.5mm}{}$
26767 \begin_layout Plain Layout
26785 \begin_inset Formula $\raisebox{-2mm}{}$
26801 \begin_layout Standard
26802 One has to take care that the character fits in the circle.
26813 \begin_layout Plain Layout
26815 \begin_inset CommandInset ref
26817 reference "sub:Font-Sizes"
26826 specifies thereby the size of the circle.
26837 \begin_layout Plain Layout
26839 \begin_inset CommandInset ref
26841 reference "sub:Boxes-without-Frame"
26850 the character can be centered.
26853 \begin_layout Subsection
26858 \begin_layout Plain Layout
26867 \begin_layout Standard
26868 Minuscule numbers are created with the command
26878 \begin_layout Plain Layout
26887 The command can be used in formulas and in TeX-mode.
26888 The command scheme is:
26891 \begin_layout Standard
26896 oldstylenums{number}
26899 \begin_layout Standard
26904 oldstylenums{0123456789
26907 \begin_inset Formula $\oldstylenums{0123456789}$
26913 \begin_layout Subsection
26914 Miscellaneous Special Characters
26915 \begin_inset CommandInset label
26917 name "sub:Miscellaneous-Special-Characters"
26925 \begin_layout Plain Layout
26926 Special characters ! miscellaneous
26934 \begin_layout Standard
26935 The following characters can only be inserted to formulas by using commands:
26938 \begin_layout Standard
26940 \begin_inset Tabular
26941 <lyxtabular version="3" rows="4" columns="2">
26943 <column alignment="center" valignment="top" width="0">
26944 <column alignment="center" valignment="top" width="0">
26946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26949 \begin_layout Plain Layout
26955 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26958 \begin_layout Plain Layout
26966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26969 \begin_layout Plain Layout
26976 \begin_layout Plain Layout
26990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26993 \begin_layout Plain Layout
26994 \begin_inset Formula $\mathcircumflex$
27004 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27007 \begin_layout Plain Layout
27015 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27018 \begin_layout Plain Layout
27019 \begin_inset Formula $\_$
27029 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27032 \begin_layout Plain Layout
27037 \begin_layout Plain Layout
27052 \begin_layout Plain Layout
27063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27066 \begin_layout Plain Layout
27067 \begin_inset Formula $^{\circ}$
27083 \begin_layout Standard
27084 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27085 contains the following line
27089 \begin_layout Plain Layout
27090 More about this is described in
27091 \begin_inset CommandInset ref
27093 reference "sub:Text-Characters-in"
27105 \begin_layout Standard
27110 DeclareInputtext{176}{
27123 \begin_layout Section
27125 \begin_inset CommandInset label
27127 name "sec:Formula-Styles"
27135 \begin_layout Plain Layout
27144 \begin_layout Itemize
27145 There are two different alignment styles:
27149 \begin_layout Description
27150 Centered is the predefined standard
27153 \begin_layout Description
27154 Indented for this the option
27158 must be inserted in the menu
27160 Document\SpecialChar \menuseparator
27166 \begin_inset space ~
27172 \begin_layout Standard
27177 is used, the indentation can be adjusted with the length
27187 \begin_layout Plain Layout
27196 Should the distance be 15
27197 \begin_inset space \thinspace{}
27200 mm, the following command line is inserted in the LaTeX-preamble
27203 \begin_layout Standard
27213 \begin_layout Standard
27214 When no length is specified, the predefined value of 30
27215 \begin_inset space \thinspace{}
27222 \begin_layout Itemize
27223 And two different numbering styles:
27227 \begin_layout Description
27228 Right is the predefined standard
27231 \begin_layout Description
27232 Left for this the option
27236 must be inserted in the menu
27238 Document\SpecialChar \menuseparator
27244 \begin_inset space ~
27251 \begin_layout Standard
27260 can also be used together.
27261 In this case both options are inserted, separated by a comma.
27264 \begin_layout Standard
27265 The chosen styles are used for all displayed formulas of the document.
27266 When both, centered and indented formulas should be created in a document,
27272 The indented formulas are then set in a flalign environment, see
27273 \begin_inset CommandInset ref
27275 reference "sub:Flalign-Environment"
27282 \begin_layout Section
27284 \begin_inset CommandInset label
27286 name "sec:Multiline-Formulas"
27294 \begin_layout Plain Layout
27295 Formula ! multiline
27303 \begin_layout Subsection
27307 \begin_layout Standard
27308 In LyX multiline formulas are created by pressing
27319 that is described in
27320 \begin_inset CommandInset ref
27322 reference "sub:Standard-align-Environment"
27329 \begin_layout Standard
27330 There are other multiline formula environments that can be created via the
27333 Insert\SpecialChar \menuseparator
27337 These environments are described in the following sections.
27340 \begin_layout Standard
27341 In all multiline formula environments a new line is created by pressing
27347 To add or delete lines, the math toolbar buttons
27348 \begin_inset Graphics
27349 filename ../images/tabular-feature_append-row.png
27355 \begin_inset Graphics
27356 filename ../images/tabular-feature_delete-row.png
27361 , respectively, or the menu
27363 Edit\SpecialChar \menuseparator
27369 \begin_layout Subsubsection
27371 \begin_inset CommandInset label
27373 name "sub:Line-Separation"
27381 \begin_layout Plain Layout
27382 Formula ! multiline ! Line separation
27390 \begin_layout Standard
27391 There is sometimes not enough space in multiline formulas between the lines:
27392 \begin_inset Formula \begin{eqnarray*}
27393 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}\\
27394 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*}
27401 \begin_layout Standard
27402 In LaTeX additional line space is specified as optional argument of the
27404 This is not yet possible in LyX
27408 \begin_layout Plain Layout
27410 \begin_inset CommandInset href
27412 name "LyX-bug #1505"
27413 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27422 , therefore the whole formula must be inserted in TeX-mode.
27423 To add in our example space, the command
27431 is inserted at the end of the first line.
27436 \begin_layout Plain Layout
27443 \begin_layout Plain Layout
27445 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27448 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27455 \begin_layout Plain Layout
27459 left(B^{2}+x_{0}^{2}
27467 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27472 \begin_layout Plain Layout
27484 \begin_layout Standard
27485 \begin_inset VSpace bigskip
27488 To set the the line separation for all lines in a formula, the length
27498 \begin_layout Plain Layout
27508 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27519 \begin_inset space \thinspace{}
27524 \begin_inset space \thinspace{}
27527 mm additional line separation as in the previous example, the command
27530 \begin_layout Standard
27540 \begin_layout Standard
27541 is inserted in TeX-mode before the formula.
27542 This requires that the LaTeX-package
27550 \begin_layout Plain Layout
27555 is part of every LaTeX standard installation.
27564 \begin_layout Plain Layout
27570 was loaded in LaTeX-preamble with the line
27573 \begin_layout Standard
27581 \begin_layout Standard
27586 \begin_layout Plain Layout
27598 \begin_inset Formula \begin{eqnarray*}
27599 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}\\
27600 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*}
27607 \begin_layout Standard
27611 \begin_layout Plain Layout
27622 To get back to the predefined distance,
27628 is set to the value 3
27629 \begin_inset space \thinspace{}
27635 \begin_layout Subsubsection
27637 \begin_inset CommandInset label
27639 name "sub:Column-Separation"
27647 \begin_layout Plain Layout
27648 Formula ! multiline ! Column separation
27656 \begin_layout Standard
27657 Multiline formulas form a matrix.
27658 A formula in the eqnarray environment is for example a matrix with three
27660 By changing the column separation in this environment, the space beside
27661 the relation sign can be changed.
27664 \begin_layout Standard
27665 The column separation is specified with the length
27675 \begin_layout Plain Layout
27684 \begin_inset Newline newline
27687 column separation = 2
27688 \begin_inset space \thinspace{}
27698 \begin_inset Newline newline
27704 \begin_layout Standard
27714 \begin_layout Standard
27715 inserted in TeX-mode, sets for all following formulas a column separation
27717 \begin_inset space \thinspace{}
27721 To get back to the predefined distance,
27728 \begin_inset space \thinspace{}
27734 \begin_layout Standard
27736 \begin_inset space \thinspace{}
27739 cm column separation:
27743 \begin_layout Plain Layout
27755 \begin_inset Formula \begin{eqnarray*}
27757 C & \ne & A\end{eqnarray*}
27761 A formula with the predefined column separation for matrices of 10
27762 \begin_inset space \thinspace{}
27769 \begin_layout Plain Layout
27781 \begin_inset Formula \begin{eqnarray*}
27783 C & \ne & A\end{eqnarray*}
27790 \begin_layout Subsubsection
27795 \begin_layout Plain Layout
27804 \begin_layout Standard
27805 Long formulas can be typeset using these methods:
27808 \begin_layout Itemize
27809 When one side of the equation is much shorther than the line width, this
27810 one is chosen for the left side and the right side is typeset over two
27815 \begin_layout Plain Layout
27825 \begin_inset Formula \begin{eqnarray}
27826 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 \\
27827 & & -\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}
27835 \begin_layout Plain Layout
27845 \begin_inset Newline newline
27848 The minus sign at the beginning of the second line does normally not appear
27849 as operator because it is the first character of the line.
27850 Thus it would not be surrounded by space and could not be distinguished
27851 from the fraction bar.
27852 To avoid this, space was inserted behind the minus sign with the command
27863 \begin_layout Plain Layout
27871 \begin_inset CommandInset ref
27873 reference "sub:Variable-Space"
27886 \begin_layout Plain Layout
27897 \begin_layout Itemize
27898 When both sides of the equation are too long, the command
27908 \begin_layout Plain Layout
27917 It is inserted to the first column of the first line and effects that all
27918 further insertions overwrite the following columns:
27922 \begin_layout Plain Layout
27932 \begin_inset Formula \begin{eqnarray}
27933 \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 \\
27934 & & -\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 \\
27935 & & =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}
27943 \begin_layout Plain Layout
27953 \begin_inset Newline newline
27956 After the insertion of
27962 , the cursor is in a purple box that is a bit shifted to the left from the
27964 In this the formula is inserted.
27968 \begin_layout Plain Layout
27978 \begin_inset Newline newline
27981 The content of the further lines is inserted to the second or another formula
27983 The greater the column number where it was inserted, the larger the indentation.
27987 \begin_layout Plain Layout
27997 \begin_inset Newline newline
28001 \begin_inset Note Greyedout
28004 \begin_layout Plain Layout
28005 Note the following when using
28014 \begin_layout Itemize
28015 The formula doesn't use the full page width.
28017 \begin_inset space \thinspace{}
28021 \begin_inset space ~
28025 \begin_inset Formula $-B^{2}$
28028 is added to the first line in the above example, it would have been outside
28030 To better use the width, negative space can be inserted at the beginning
28034 \begin_layout Itemize
28035 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28040 \begin_layout Plain Layout
28041 \begin_inset CommandInset href
28043 name "LyX-bug #1429"
28044 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
28053 One can only set the cursor at the beginning of the line and move it with
28062 \begin_layout Itemize
28063 Other methods to set long formulas are offered by the environments described
28065 \begin_inset CommandInset ref
28067 reference "sub:Multline-Environment"
28072 \begin_inset CommandInset ref
28074 reference "sub:Multiline-Formula-Parts"
28081 \begin_layout Subsubsection
28083 \begin_inset CommandInset label
28085 name "sub:Multiline-Brackets"
28093 \begin_layout Plain Layout
28094 Brackets ! for multiline expressions
28102 \begin_layout Standard
28103 For brackets spanning multiple lines the following problem occurs:
28104 \begin_inset Formula \begin{eqnarray*}
28105 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28106 & & \left.\cdots+B-D\right]\end{eqnarray*}
28113 \begin_layout Standard
28114 The closing bracket is smaller than the opening bracket because brackets
28115 with variable size may not span multiple lines.
28118 \begin_layout Standard
28119 To set the bracket size for the second line correctly, the first line is
28130 \begin_layout Plain Layout
28138 and the second line with
28146 \begin_layout Plain Layout
28160 \begin_inset CommandInset ref
28162 reference "sub:Automatic-Bracket-Size"
28177 \begin_layout Plain Layout
28203 \begin_layout Plain Layout
28222 \begin_layout Plain Layout
28241 \begin_layout Plain Layout
28253 \begin_inset Formula $\downarrow$
28262 \begin_layout Plain Layout
28270 is inserted, because the multiplication operator with its limits is the
28271 largest symbol in the first line and this should be the size for the bracket
28272 in the second line.
28275 \begin_layout Standard
28276 The result is this:
28277 \begin_inset Formula \begin{eqnarray*}
28278 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28279 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28286 \begin_layout Subsection
28290 \begin_layout Standard
28291 Align environments can be used for every kind of multiline formulas.
28292 They are specially useful to set several formulas side by side.
28295 \begin_layout Standard
28296 Align environments consist of columns.
28297 The odd columns are right aligned, the even ones left aligned.
28298 Every line in an Align environment can be numbered.
28301 \begin_layout Standard
28302 Align environments are created via the menu
28304 Insert\SpecialChar \menuseparator
28310 Edit\SpecialChar \menuseparator
28311 Math\SpecialChar \menuseparator
28312 Change Formula Type
28314 already existing formulas can be converted to Align environments.
28317 \begin_layout Standard
28318 To add or delete columns, the math toolbar buttons
28319 \begin_inset Graphics
28320 filename ../images/tabular-feature_append-column.png
28326 \begin_inset Graphics
28327 filename ../images/tabular-feature_delete-column.png
28332 , respectively, or the menu
28334 Edit\SpecialChar \menuseparator
28340 \begin_layout Subsubsection
28341 Standard align Environment
28342 \begin_inset CommandInset label
28344 name "sub:Standard-align-Environment"
28352 \begin_layout Plain Layout
28353 Formula ! multiline ! align environment
28361 \begin_layout Standard
28362 This Align environment is created by presssing
28366 in a formula or by the menu
28368 Insert\SpecialChar \menuseparator
28369 Math\SpecialChar \menuseparator
28370 AMS align Environment
28375 \begin_layout Standard
28376 An example for two formulas set side by side, that are created with a four
28377 column align environment:
28378 \begin_inset Formula \begin{align*}
28379 A & =\sin(B) & C & =D\\
28380 C & \ne A & B & \ne D\end{align*}
28384 As it can be seen, the formulas in this environment are placed so as if
28393 \begin_layout Plain Layout
28401 \begin_inset CommandInset ref
28403 reference "sub:Variable-Space"
28414 before the first and after every even column.
28415 When the formula style
28421 \begin_layout Plain Layout
28423 \begin_inset CommandInset ref
28425 reference "sec:Formula-Styles"
28436 is used, the formula is set without the
28442 before the first column.
28445 \begin_layout Subsubsection
28446 Alignat Environment
28450 \begin_layout Plain Layout
28451 Formula ! multiline ! alignat environment
28459 \begin_layout Standard
28460 The alignat environment has no predefined column separation.
28461 It can be inserted manually with the spaces that are described
28462 \begin_inset CommandInset ref
28464 reference "sub:Space"
28471 \begin_layout Standard
28472 The above example in the alignat environment where 1
28473 \begin_inset space \thinspace{}
28476 cm space was inserted at the beginning of the second formula:
28477 \begin_inset Formula \begin{alignat*}{2}
28478 A & =\sin(B) & \hspace{1cm}C & =D\\
28479 C & \ne A & B & \ne D\end{alignat*}
28483 Because the column separation can be set separately for every column, this
28484 environment is especially suitable to set three and more formulas side
28488 \begin_layout Subsubsection
28489 Flalign Environment
28490 \begin_inset CommandInset label
28492 name "sub:Flalign-Environment"
28500 \begin_layout Plain Layout
28501 Formula ! multiline ! flalign environment
28509 \begin_layout Standard
28510 In this environment the first two columns are always set as much as possible
28511 to the left and the last two ones to the right.
28513 \begin_inset Formula \begin{flalign*}
28514 A & =1 & B & =2 & C & =3\\
28515 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28522 \begin_layout Standard
28523 By creating a flalign environment with an odd number of columns where an
28524 empty TeX-brace is inserted to the last column, several formulas in a document
28525 can be set to the left, although the formula style
28530 As example the indented formula
28531 \begin_inset CommandInset ref
28533 reference "eq:VolInt"
28538 \begin_inset Formula \begin{flalign}
28539 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28543 The first two columns contain the formula.
28544 To indent it as with the formula style
28549 \begin_inset space \thinspace{}
28552 pt space was inserted at the beginning of the first column.
28555 \begin_layout Subsection
28556 Eqnarray Environment
28560 \begin_layout Plain Layout
28561 Formula ! multiline ! eqnarray environment
28569 \begin_layout Standard
28570 When this environment has been created, three blue boxes appear.
28571 The content of the first box is right aligned, the content of the last
28573 The content of the middle box appears centered and a bit smaller, because
28574 it is designed to insert there only relation characters.
28575 \begin_inset Formula \begin{eqnarray*}
28576 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28578 A & = & A\end{eqnarray*}
28585 \begin_layout Subsection
28590 \begin_layout Plain Layout
28591 Formula ! multiline ! gather environment
28599 \begin_layout Standard
28600 This environment consists of only one centered column.
28601 Every line can be numbered.
28602 \begin_inset Formula \begin{gather}
28604 X=\textrm{-}1\end{gather}
28611 \begin_layout Subsection
28612 Multline Environment
28613 \begin_inset CommandInset label
28615 name "sub:Multline-Environment"
28623 \begin_layout Plain Layout
28624 Formula ! multiline ! multline environment
28632 \begin_layout Standard
28633 The multline environment consists, like the gather environment, of only
28635 But the first line is left aligned, the last one right aligned.
28636 All other lines are centered.
28637 Therefore this environment is suitable for long formulas.
28639 \begin_inset CommandInset ref
28641 reference "eq:lefteqn"
28645 in the multline environment:
28646 \begin_inset Formula \begin{multline}
28647 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}\\
28648 -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}\\
28649 =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}
28656 \begin_layout Standard
28657 In the output only the last (first) line of a multline environment appears
28658 numbered when the document numbering is right (left).
28662 \begin_layout Plain Layout
28663 numbering styles see
28664 \begin_inset CommandInset ref
28666 reference "sec:Formula-Styles"
28678 \begin_layout Standard
28687 \begin_layout Plain Layout
28705 \begin_layout Plain Layout
28715 a centered line can be right or left aligned, respectively.
28716 The commands are used as follows:
28719 \begin_layout Standard
28724 shoveright{line content}
28730 shoveleft{line content}
28733 \begin_layout Standard
28734 \begin_inset VSpace medskip
28745 \begin_layout Plain Layout
28755 specifies the distance of the first line from the left page margin.
28756 Predefined is the length 0
28757 \begin_inset space \thinspace{}
28763 \begin_layout Standard
28764 As example the above formula where the command
28767 \begin_layout Standard
28777 \begin_layout Standard
28778 was inserted in TeX-mode before:
28782 \begin_layout Plain Layout
28794 \begin_inset Formula \begin{multline}
28795 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}\\
28796 \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}}\\
28797 =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}
28805 \begin_layout Plain Layout
28816 The second line was left aligned using
28825 \begin_layout Subsection
28826 Multiline Formula Parts
28827 \begin_inset CommandInset label
28829 name "sub:Multiline-Formula-Parts"
28837 \begin_layout Plain Layout
28838 Formula ! multiline ! formula parts
28846 \begin_layout Standard
28847 To display only parts of a formula with multiple lines, one of the following
28848 environments are used:
28865 They can be inserted via the menu
28867 Insert\SpecialChar \menuseparator
28870 or by using the commands described in this section.
28873 \begin_layout Standard
28874 The first three have the same properties as the corresponding multiline
28875 formula environments, but it is possible to set further formula parts beside
28878 \begin_inset Formula \[
28879 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28880 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28881 \right\} \textrm{Uncertainty relations}\]
28888 \begin_layout Standard
28889 To get this formula, a displayed formula is created where the command
28897 \begin_layout Plain Layout
28908 A purple box appears around the blue formula box where now columns and
28909 lines can be added.
28910 Outside the multiline environment other formula parts can be set, like
28914 \begin_layout Standard
28915 The aligned environment is also suitable for long formulas whose lines are
28916 horizontally aligned.
28917 Using aligned in a displayed formula has the advantage that the formula
28918 number is vertically centered behind the lines.
28920 \begin_inset CommandInset ref
28922 reference "eq:kurzlang"
28926 in the aligned environment:
28927 \begin_inset Formula \begin{equation}
28928 \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}|}\\
28929 & -\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}
28937 \begin_layout Standard
28938 To use the environments
28960 \begin_layout Plain Layout
28978 \begin_layout Plain Layout
28996 \begin_layout Plain Layout
29004 are inserted, respectively.
29005 The split environment has the same properties as the aligned environment
29006 but it can only have two columns.
29009 \begin_layout Subsection
29010 Text in multiline Formulas
29011 \begin_inset CommandInset label
29013 name "sub:Text-in-multiline"
29021 \begin_layout Plain Layout
29031 \begin_layout Plain Layout
29032 Formula ! multiline ! text
29040 \begin_layout Standard
29041 In the Align environments, and the multline and gather environment, text
29042 can be inserted that will appear in a separate line and doesn't affect
29043 the column alignment.
29044 To do this, the command
29052 \begin_layout Plain Layout
29062 is used in the following scheme:
29065 \begin_layout Standard
29073 \begin_layout Standard
29074 The text should not be longer than a line because it cannot be hyphenated.
29075 As LyX doesn't yet support
29081 directly, the text is written as mathematical text.
29088 must hereby be at the beginning of a line and appears in the output above
29090 An example where the text was inserted at the beginning of the second line:
29091 \begin_inset Formula \begin{align}
29092 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29093 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29100 \begin_layout Section
29105 \begin_layout Plain Layout
29115 \begin_layout Plain Layout
29116 Formula ! numbering|see
29120 \begin_layout Plain Layout
29131 \begin_layout Plain Layout
29146 \begin_layout Subsection
29150 \begin_layout Standard
29151 Numbered formulas can be created with the menu
29153 Insert\SpecialChar \menuseparator
29154 Math\SpecialChar \menuseparator
29156 \begin_inset space ~
29164 \begin_inset space ~
29170 Existing formulas can be numbered with the menu
29172 Edit\SpecialChar \menuseparator
29173 Math\SpecialChar \menuseparator
29175 \begin_inset space ~
29183 \begin_inset space ~
29189 The formula number is displayed in LyX behind the formula as number sign
29191 The number sign is replaced in the output by the formula number.
29194 \begin_layout Standard
29195 When numbering is turned on in multiline formulas, all lines will be numbered.
29196 But the numbering can be controlled with the menu
29198 Edit\SpecialChar \menuseparator
29199 Math\SpecialChar \menuseparator
29201 \begin_inset space ~
29205 \begin_inset space ~
29209 \begin_inset space ~
29217 \begin_inset space ~
29225 \begin_layout Standard
29226 Except of inline formulas, all formulas can be numbered with two different
29228 \begin_inset CommandInset ref
29230 reference "sec:Formula-Styles"
29237 \begin_layout Subsection
29239 \begin_inset CommandInset label
29241 name "sub:Cross-References"
29249 \begin_layout Plain Layout
29250 Cross-references ! to formulas
29258 \begin_layout Standard
29259 All labeled formulas can be cross-referenced.
29260 A label is added by the menu
29262 Insert\SpecialChar \menuseparator
29265 or the toolbar button
29266 \begin_inset Graphics
29267 filename ../images/label-insert.png
29273 The cursor must hereby be inside a displayed formula.
29274 A dialog pops up displaying the prefix
29279 The label is inserted there behind the prefix.
29280 The predefined prefix means
29281 \begin_inset Quotes eld
29285 \begin_inset Quotes erd
29288 and makes it easier to find labels in large documents because it marks
29289 it as formula label to divide it from e.
29290 \begin_inset space \thinspace{}
29294 \begin_inset space ~
29298 To change a label, the menu
29300 Insert\SpecialChar \menuseparator
29306 \begin_layout Standard
29307 The name of the label is displayed in LyX within two parentheses behind
29309 A formula with a label is always numbered.
29312 \begin_layout Standard
29313 Cross-references are inserted via the menu
29315 Insert\SpecialChar \menuseparator
29318 or with the toolbar button
29319 \begin_inset Graphics
29320 filename ../images/dialog-show-new-inset_ref.png
29326 A formula cross-reference appears in the output as formula number.
29327 When in the cross-reference dialog window the format
29331 is chosen, the cross-reference appears in the output as formula number
29333 \begin_inset Newline newline
29336 By right-clicking on a cross-reference in LyX, one jumps to the formula
29337 that is referenced.
29340 \begin_layout Standard
29341 Here are as examples cross-references to formulas of the following subsections:
29342 \begin_inset Note Note
29345 \begin_layout Plain Layout
29346 Note the different cross-reference types.
29354 \begin_layout Standard
29356 \begin_inset CommandInset ref
29363 \begin_inset CommandInset ref
29371 \begin_inset CommandInset ref
29377 ) big Latin letters are used for the numbering in contrary to (
29378 \begin_inset CommandInset ref
29387 \begin_layout Standard
29388 \begin_inset VSpace medskip
29391 When the argument of
29399 \begin_layout Plain Layout
29407 \begin_inset CommandInset ref
29409 reference "sub:User-defined-Numbering"
29420 contains a box like in
29421 \begin_inset CommandInset ref
29423 reference "sub:Paragraph-Boxes"
29427 , the formula cannot be referenced.
29430 \begin_layout Subsection
29435 \begin_layout Plain Layout
29436 Formula numbering ! subnumbering
29444 \begin_layout Standard
29445 With the help of the commands
29449 begin{subequations}
29457 formulas can be subnumbered.
29458 Both commands are inserted in TeX-mode.
29461 \begin_layout Standard
29463 \begin_inset Formula \begin{equation}
29464 A=C-B\label{eq:a}\end{equation}
29472 \begin_layout Plain Layout
29476 addtocounter{equation}{-1}
29485 \begin_layout Plain Layout
29489 begin{subequations}
29495 \begin_inset VSpace -5mm
29499 \begin_inset Formula \begin{equation}
29500 B=C-A\label{eq:b}\end{equation}
29505 \begin_inset Formula \begin{equation}
29506 C=A+B\label{eq:c}\end{equation}
29513 \begin_layout Standard
29517 \begin_layout Plain Layout
29529 \begin_layout Standard
29530 To create the example, the following is done:
29533 \begin_layout Enumerate
29534 first formula is inserted
29537 \begin_layout Enumerate
29542 addtocounter{equation}{-1}
29544 begin{subequations}
29548 \begin_layout Plain Layout
29557 \begin_inset Newline newline
29562 is inserted after the first formula
29565 \begin_layout Enumerate
29566 second formula is inserted
29569 \begin_layout Enumerate
29570 third formula is inserted
29573 \begin_layout Enumerate
29580 is inserted after the third formula
29583 \begin_layout Standard
29584 Every formula between the commands
29596 is subnumbered as a, b,
29597 \begin_inset Newline linebreak
29600 c, \SpecialChar \ldots{}
29601 For multiline formulas every line will be subnumbered.
29602 All subnumbered formulas are treated as
29607 But as every numbered formula increases the counter
29611 by one, the command
29617 is needed to decrease it.
29618 Otherwise the formulas
29619 \begin_inset CommandInset ref
29626 \begin_inset CommandInset ref
29633 \begin_inset CommandInset ref
29639 would be numbered as
29640 \begin_inset CommandInset ref
29647 \begin_inset CommandInset ref
29654 \begin_inset CommandInset ref
29663 \begin_layout Standard
29664 By inserting the commands in TeX-mode, a space is created between the first
29667 \begin_inset space \thinspace{}
29670 mm vertical space is inserted after the command
29674 begin{subequations}
29677 When the formula style
29683 \begin_layout Plain Layout
29685 \begin_inset CommandInset ref
29687 reference "sec:Formula-Styles"
29699 \begin_inset space \thinspace{}
29702 mm space is inserted instead.
29705 \begin_layout Standard
29706 Here is an example for a multiline formula where the numbering was turned
29707 off for the second line:
29711 \begin_layout Plain Layout
29715 begin{subequations}
29721 \begin_inset Formula \begin{eqnarray}
29722 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29723 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29724 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29732 \begin_layout Plain Layout
29744 \begin_layout Subsection
29745 User-defined Numbering
29746 \begin_inset CommandInset label
29748 name "sub:User-defined-Numbering"
29756 \begin_layout Plain Layout
29757 Formula numbering ! user-defined
29765 \begin_layout Standard
29769 \begin_layout Plain Layout
29770 Formula numbering ! self-defined delimiters
29775 With the standard numbering parentheses are set around the formula number.
29776 To replace the parentheses for example by vertical bars, the following
29777 line is added to the LaTeX-preamble:
29780 \begin_layout Standard
29792 \begin_inset Note Note
29795 \begin_layout Plain Layout
29796 This macro is already declared in the LaTeX-preamble for testing.
29797 To activate it, remove the percent sign at the beginning.
29805 \begin_layout Standard
29806 To use other characters, the vertical bars besides the
29810 are replaced by one ore more characters.
29811 To get only the formula number the vertical bars are omitted.
29814 \begin_layout Standard
29815 \begin_inset VSpace bigskip
29818 When there should be an expression of your choice instead of the consecutive
29819 formula number in parentheses behind the formula, the command
29829 \begin_layout Plain Layout
29838 \begin_inset Formula \begin{equation}
29839 A+B=C\tag{something}\label{eq:tag}\end{equation}
29843 In this example the command
29851 \begin_layout Plain Layout
29862 was inserted to the formula.
29865 \begin_layout Standard
29874 \begin_layout Plain Layout
29885 is inserted instead, the star prevents the parentheses around the expression:
29886 \begin_inset Formula \[
29887 A+B=C\tag*{something}\]
29894 \begin_layout Standard
29895 \begin_inset VSpace bigskip
29898 To restart the formula numbering with new document parts or sections, the
29899 following command is used:
29902 \begin_layout Standard
29907 @addtoreset{equation}{part}
29913 \begin_layout Plain Layout
29918 \begin_layout Plain Layout
29929 \begin_layout Plain Layout
29942 \begin_layout Plain Layout
29953 \begin_layout Plain Layout
29966 \begin_inset Newline newline
29970 \begin_inset Newline newline
29977 @addtoreset{equation}{section}
29980 \begin_layout Standard
29981 To be able to use these commands in TeX-mode, the
29982 \begin_inset Quotes eld
29986 \begin_inset Quotes erd
29989 character has to be made
29990 \begin_inset Quotes eld
29994 \begin_inset Quotes erd
29997 for LaTeX using the command
30011 So the command sequence in TeX-mode is:
30014 \begin_layout Standard
30020 \begin_inset Newline newline
30025 @addtoreset{equation}{section}
30026 \begin_inset Newline newline
30034 \begin_layout Standard
30035 In the LaTeX-preamble
30047 can be omitted as they are automatically internally inserted by LyX.
30050 \begin_layout Standard
30065 \begin_layout Plain Layout
30070 is part of the LaTeX-package
30078 \begin_layout Plain Layout
30079 Packages ! carlisle
30084 that is part of every LaTeX standard installation.
30093 \begin_layout Plain Layout
30094 Packages ! remreset
30099 has to be loaded in the LaTeX-preamble with the line
30102 \begin_layout Standard
30107 usepackage{remreset}
30110 \begin_layout Standard
30121 \begin_layout Plain Layout
30126 \begin_layout Plain Layout
30137 \begin_layout Plain Layout
30150 \begin_layout Plain Layout
30161 \begin_layout Plain Layout
30173 can be used with the same scheme as
30182 \begin_layout Standard
30183 \begin_inset VSpace bigskip
30186 Sometimes formulas should be numbered in the following form:
30189 \begin_layout Standard
30192 (section number.formula number)
30195 \begin_layout Standard
30196 The formula number should start with every section with
30197 \begin_inset Quotes eld
30201 \begin_inset Quotes erd
30207 \begin_layout Standard
30208 For this case there is the command
30218 \begin_layout Plain Layout
30226 , which is used with the following scheme:
30229 \begin_layout Standard
30234 numberwithin{counter}{sectioning}
30237 \begin_layout Standard
30238 Counter denotes what kind of numbering is affected, sectioning denotes what
30239 number is before the dot.
30242 \begin_layout Standard
30243 Thus in our case the following LaTeX-preamble or ERT line is used:
30246 \begin_layout Standard
30251 numberwithin{equation}{section}
30254 \begin_layout Standard
30255 This is the result:
30259 \begin_layout Plain Layout
30263 numberwithin{equation}{section}
30269 \begin_inset Formula \begin{equation}
30270 A+B=C\end{equation}
30277 \begin_layout Standard
30279 \begin_inset space \thinspace{}
30283 \begin_inset space ~
30286 tables so that the number of the part is the sectioning,
30287 \begin_inset Newline newline
30294 numberwithin{table}{part}
30299 \begin_layout Standard
30300 To go back to the standard numbering or to prevent this kind of numbering
30301 when it is defined by the document class, the following command is inserted
30302 as ERT or to the LaTeX-preamble:
30305 \begin_layout Standard
30318 \begin_layout Plain Layout
30332 \begin_layout Plain Layout
30348 \begin_inset Newline newline
30356 \begin_inset Newline newline
30368 \begin_layout Standard
30375 uses internally the command
30381 , described above, that also needs to be reverted.
30385 \begin_layout Plain Layout
30392 \begin_layout Plain Layout
30396 @removefromreset{equation}{section}
30399 \begin_layout Plain Layout
30411 \begin_layout Subsection
30412 Numbering with Roman Numbers and Letters
30413 \begin_inset CommandInset label
30415 name "sub:Numbering-with-Roman"
30423 \begin_layout Plain Layout
30424 Formula numbering ! with letters
30433 \begin_layout Plain Layout
30434 Formula numbering ! with Roman numbers
30442 \begin_layout Standard
30443 Formulas can also be numbered with Roman numbers and Latin letters.
30444 To number for example with small Roman numbers, the command
30447 \begin_layout Standard
30459 \begin_layout Standard
30460 is inserted before the formula in TeX-mode.
30471 \begin_layout Plain Layout
30479 redefines the predefined command
30495 \begin_layout Plain Layout
30502 has the same scheme like the command
30508 that is described in
30509 \begin_inset CommandInset ref
30511 reference "sec:User-defined-commands"
30525 is the formula counter.
30532 is used as prefix for a counter, the value of the counter is output as
30534 When a formula is numbered, LaTeX sets internally the command
30540 behind the formula.
30549 \begin_layout Plain Layout
30559 outputs the counter as small Roman number.
30562 \begin_layout Standard
30563 All formulas behind the command
30573 are now numbered Roman.
30574 To switch to numbering with big Roman numbers, the command is inserted
30591 \begin_layout Plain Layout
30603 \begin_inset Quotes eld
30607 \begin_inset Quotes erd
30610 with small Latin letters there is the command
30620 \begin_layout Plain Layout
30628 , for big ones there is the command
30638 \begin_layout Plain Layout
30651 \begin_layout Standard
30652 \begin_inset Note Greyedout
30655 \begin_layout Plain Layout
30660 Only maximal 26 formulas can be numbered with Latin letters in one document.
30668 \begin_layout Standard
30672 \begin_layout Plain Layout
30688 \begin_layout Standard
30689 \begin_inset Formula \begin{equation}
30690 A=\textrm{small roman}\label{eq:rom}\end{equation}
30698 \begin_layout Plain Layout
30712 \begin_inset Formula \begin{equation}
30713 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30721 \begin_layout Plain Layout
30735 \begin_inset Formula \begin{equation}
30736 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30744 \begin_layout Plain Layout
30758 \begin_inset Formula \begin{equation}
30759 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30766 \begin_layout Standard
30767 To switch back to the default numbering, insert the command:
30770 \begin_layout Standard
30783 \begin_layout Plain Layout
30794 \begin_layout Standard
30798 \begin_layout Plain Layout
30812 \begin_inset Formula \begin{equation}
30813 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30820 \begin_layout Standard
30821 \begin_inset VSpace medskip
30824 As you see, formulas are numbered serially independent from the numbering
30826 When then numbering should start with
30827 \begin_inset Quotes eld
30831 \begin_inset Quotes erd
30834 when the style is changed, new equation counters have to be defined.
30835 A description about this can be found in the file
30836 \begin_inset CommandInset href
30838 target "Formula-numbering.lyx"
30845 \begin_layout Section
30846 User-defined commands
30847 \begin_inset CommandInset label
30849 name "sec:User-defined-commands"
30857 \begin_layout Plain Layout
30858 User-defined commands
30866 \begin_layout Standard
30867 Many LaTeX-commands are too long to be used frequently.
30868 But it is possible to define with the command
30878 \begin_layout Plain Layout
30886 new shorter commands.
30889 \begin_layout Standard
30890 The command scheme of
30899 \begin_layout Standard
30904 newcommand{new command name}[number of arguments][optional
30909 \begin_inset Newline newline
30916 \begin_layout Plain Layout
30931 \begin_layout Plain Layout
30938 {command definition}
30941 \begin_layout Standard
30942 \begin_inset Note Greyedout
30945 \begin_layout Plain Layout
30950 Assure that the name of the new command is not already used in your document
30951 or by LaTeX-packages that you use.
30952 When you for example define the command
30964 , you get an error message because
30970 is already defined as command for
30971 \begin_inset Quotes eld
30975 \begin_inset Formula $\le$
30979 \begin_inset Quotes erd
30990 \begin_layout Standard
30991 \begin_inset Note Greyedout
30994 \begin_layout Plain Layout
30999 The names of user-defined commands may only consist of Latin letters.
31007 \begin_layout Standard
31008 The number of arguments is an integer in the range 0
31009 \begin_inset space \thinspace{}
31013 \begin_inset space \thinspace{}
31016 9 and specifies how many arguments the new command should have.
31017 With the optional value a value for an optional argument can be predefined.
31018 When this is done, the
31026 rgument of the new command is automatically an optional one.
31029 \begin_layout Standard
31030 Here are some examples:
31033 \begin_layout Itemize
31034 To define the command
31046 , the LaTeX-preamble line is:
31050 \begin_layout Plain Layout
31062 \begin_inset Newline newline
31074 \begin_layout Itemize
31075 To define the command
31087 , the argument (that should be underlined) must be taken into account.
31088 For this the preamble line is:
31092 \begin_layout Plain Layout
31104 \begin_inset Newline newline
31119 \begin_layout Plain Layout
31131 \begin_inset Newline newline
31140 acts as argument placeholder, the
31144 behind it denotes that it is the placeholder for the first argument.
31147 \begin_layout Itemize
31155 \begin_inset space \thinspace{}
31159 \begin_inset space ~
31172 \begin_layout Plain Layout
31184 \begin_inset Newline newline
31193 framebox#1#2{$#3$}}
31199 \begin_layout Plain Layout
31211 \begin_inset Newline newline
31216 The two Dollar signs creates the extra formula needed for
31223 \begin_inset CommandInset ref
31225 reference "sub:Boxes-with-Frame"
31232 \begin_layout Itemize
31233 To create a new command for
31239 where the color for the box needn't to be specified, the argument for the
31240 color is defined optional:
31244 \begin_layout Plain Layout
31256 \begin_inset Newline newline
31265 fcolorbox{#2}{#1}{$#3$}}
31271 \begin_layout Plain Layout
31281 \begin_inset Newline newline
31284 When the color is not specified when using
31290 , the predefined color
31297 \begin_layout Standard
31298 A test of the new defined commands:
31301 \begin_layout Standard
31303 \begin_inset Tabular
31304 <lyxtabular version="3" rows="6" columns="2">
31306 <column alignment="center" valignment="top" width="0">
31307 <column alignment="center" valignment="top" width="0">
31309 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31312 \begin_layout Plain Layout
31318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31321 \begin_layout Plain Layout
31323 \begin_inset Note Note
31326 \begin_layout Plain Layout
31333 is only used as spacer.
31345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31348 \begin_layout Plain Layout
31355 \begin_layout Plain Layout
31369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31372 \begin_layout Plain Layout
31373 \begin_inset Formula $A\gr B$
31383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31386 \begin_layout Plain Layout
31394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31397 \begin_layout Plain Layout
31398 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31411 \begin_layout Plain Layout
31415 \begin_inset Formula $\to$
31421 \begin_inset Formula $\to$
31432 \begin_layout Plain Layout
31446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31449 \begin_layout Plain Layout
31450 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31463 \begin_layout Plain Layout
31467 \begin_inset Formula $\to$
31478 \begin_layout Plain Layout
31492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31495 \begin_layout Plain Layout
31496 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31509 \begin_layout Plain Layout
31515 \begin_inset Formula $\to$
31526 \begin_layout Plain Layout
31540 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31543 \begin_layout Plain Layout
31544 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31560 \begin_layout Section
31565 \begin_layout Plain Layout
31574 \begin_layout Standard
31575 To create diagrams, the LaTeX-package
31581 \begin_layout Plain Layout
31586 is part of every LaTeX standard installation.
31597 \begin_layout Plain Layout
31604 It is loaded in the LaTeX-preamble with the line
31607 \begin_layout Standard
31615 \begin_layout Standard
31616 Diagrams visualize relations and look like this:
31617 \begin_inset Formula \[
31618 \begin{CD}A@>>>B@>>>C\\
31620 F@<<<E@<<<D\end{CD}\]
31627 \begin_layout Standard
31628 To get them, the command
31636 \begin_layout Plain Layout
31646 is inserted to a formula.
31647 A blue box appears with two dashed lines where further commands can be
31653 a new line is created.
31654 Horizontal relations are inserted in odd, vertical in even formula lines.
31657 \begin_layout Standard
31658 To create the relations there are the following commands:
31661 \begin_layout Itemize
31666 creates a left arrow,
31677 \begin_layout Itemize
31682 creates an up arrow,
31690 a vertical equal sign
31693 \begin_layout Itemize
31699 is a placeholder for non-existent relations
31702 \begin_layout Standard
31703 All arrows can be labeled as follows:
31706 \begin_layout Itemize
31707 Is text inserted between the first and second < or >, resp., it is placed
31709 When it is inserted between the second and third one, it appears under
31713 \begin_layout Itemize
31714 When text for vertical arrows is inserted between the first and second A
31715 or V, resp., it is placed left beside the arrow.
31716 When it is inserted between the second and third one, it appears right
31718 If the text contains an A or V, these letters must be set into a TeX-brace.
31721 \begin_layout Standard
31722 As example a diagram with all possible relations:
31725 \begin_layout Standard
31726 \begin_inset Formula \[
31727 \begin{CD}A@>j>>B@>>k>C@=F\\
31729 D@<<j<E@>k>>F@=C\end{CD}\]
31736 \begin_layout Standard
31737 The command for this is:
31738 \begin_inset Newline newline
31749 \begin_layout Plain Layout
31758 A@>j>>B@>>k>C@=F Ctrl-Enter
31759 \begin_inset Newline newline
31766 \begin_layout Plain Layout
31781 \begin_layout Plain Layout
31794 \begin_layout Plain Layout
31806 \begin_inset Formula $\to$
31812 \begin_inset Newline newline
31819 \begin_layout Plain Layout
31834 \begin_layout Plain Layout
31847 \begin_layout Plain Layout
31857 \begin_layout Standard
31858 \begin_inset Newpage newpage
31864 \begin_layout Section
31869 \begin_layout Plain Layout
31882 \begin_layout Plain Layout
31883 Other useful math tips can be found in
31884 \begin_inset CommandInset citation
31899 \begin_layout Plain Layout
31907 \begin_inset Note Note
31910 \begin_layout Plain Layout
31913 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31916 \begin_layout Plain Layout
31919 texorpdfstring is in section
31920 \begin_inset CommandInset ref
31922 reference "sub:Formulas-in-Section"
31935 \begin_layout Plain Layout
31945 \begin_layout Plain Layout
31950 \begin_layout Plain Layout
31957 Chemical characters
31961 \begin_layout Plain Layout
31976 \begin_layout Subsection
31977 Chemical Symbols and Equations
31978 \begin_inset CommandInset label
31980 name "sub:Chemical-Symbols-and"
31988 \begin_layout Plain Layout
31989 Chemical characters ! Symbols
31998 \begin_layout Plain Layout
32008 \begin_layout Plain Layout
32017 \begin_layout Standard
32018 An example text from chemistry:
32021 \begin_layout Quote
32023 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
32026 -ion reacts with two
32027 \begin_inset Formula $\mathrm{Na^{+}}$
32030 -ions to sodium sulfate
32031 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
32035 The chemical equation for this is:
32036 \begin_inset Formula \[
32037 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
32044 \begin_layout Standard
32045 This chemical equation can directly be created as formula.
32046 To avoid that the symbols appear italic, everything is highlighted and
32047 changed by the shortcut
32050 \begin_inset space ~
32055 to the upright font style.
32059 \begin_layout Plain Layout
32065 \begin_inset CommandInset ref
32067 reference "sub:Font-Styles"
32079 \begin_layout Subsection
32084 \begin_layout Plain Layout
32093 \begin_layout Standard
32094 Negative numbers often look ugly in formulas because the minus sign before
32095 the number is set with the same length as the minus operator sign.
32096 When writing the negative number in normal text, the minus sign appears
32100 \begin_layout Standard
32101 Thus, the problem disappears when converting the minus sign to mathematical
32105 \begin_layout Standard
32106 An example to visualize the problem:
32109 \begin_layout Standard
32111 \begin_inset Tabular
32112 <lyxtabular version="3" rows="3" columns="2">
32114 <column alignment="right" valignment="top" width="0">
32115 <column alignment="left" valignment="top" width="0">
32117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32120 \begin_layout Plain Layout
32126 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32129 \begin_layout Plain Layout
32137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32140 \begin_layout Plain Layout
32146 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32149 \begin_layout Plain Layout
32150 \begin_inset Formula $x=-2$
32160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32163 \begin_layout Plain Layout
32169 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32172 \begin_layout Plain Layout
32173 \begin_inset Formula $x=\textrm{-}2$
32189 \begin_layout Subsection
32190 Comma as Decimal Separator
32194 \begin_layout Plain Layout
32203 \begin_layout Standard
32204 In LaTeX a comma inside a formula is used, according to the English convention,
32205 as number group separator.
32206 So there will be space added behind all commas in formulas.
32209 \begin_layout Standard
32210 To avoid this, the comma is highlighted and changed to mathematical text
32214 \begin_inset space ~
32222 \begin_layout Standard
32223 To use all formula commas in the document as decimal separator, the file
32232 \begin_layout Plain Layout
32237 is part of the LaTeX-package
32245 \begin_layout Plain Layout
32250 \begin_layout Plain Layout
32273 \begin_layout Plain Layout
32279 is loaded with the LaTeX-preamble line
32282 \begin_layout Standard
32290 \begin_layout Subsection
32292 \begin_inset CommandInset label
32294 name "sub:Physical-Vectors"
32302 \begin_layout Plain Layout
32311 \begin_layout Standard
32312 Predefined vectors are offered by the LaTeX-package
32320 \begin_layout Plain Layout
32325 should be part of every LaTeX standard installation.
32334 \begin_layout Plain Layout
32340 that is loaded with the LaTeX-preamble line
32343 \begin_layout Standard
32351 \begin_layout Standard
32355 \begin_layout Plain Layout
32365 \begin_inset Note Note
32368 \begin_layout Plain Layout
32369 The following table will only be displayed when the LaTeX-package
32378 The following commands are defined:
32381 \begin_layout Standard
32383 \begin_inset Tabular
32384 <lyxtabular version="3" rows="4" columns="2">
32386 <column alignment="center" valignment="top" width="0">
32387 <column alignment="center" valignment="top" width="0">
32389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32392 \begin_layout Plain Layout
32398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32401 \begin_layout Plain Layout
32409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32412 \begin_layout Plain Layout
32422 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32425 \begin_layout Plain Layout
32426 \begin_inset Formula $\Bra{\psi}$
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 $\Ket{\psi}$
32463 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32466 \begin_layout Plain Layout
32478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32481 \begin_layout Plain Layout
32482 \begin_inset Formula $\Braket{\psi|\phi}$
32498 \begin_layout Standard
32505 assures that all vertical bars are set in the size of the surrounding brackets:
32506 \begin_inset Formula \[
32507 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32515 \begin_layout Plain Layout
32525 \begin_inset Note Note
32528 \begin_layout Plain Layout
32529 The following will be displayed when the LaTeX-package
32541 \begin_layout Standard
32542 You need to install the LaTeX-package
32546 to see the rest of this subsection in the output.
32549 \begin_layout Standard
32553 \begin_layout Plain Layout
32565 \begin_layout Standard
32572 can also be achieved using the command
32578 , that is described in
32579 \begin_inset CommandInset ref
32581 reference "sub:Automatic-Bracket-Size"
32588 \begin_layout Subsection
32589 Self-defined Fractions
32590 \begin_inset CommandInset label
32592 name "sub:Self-defined-Fractions"
32600 \begin_layout Plain Layout
32601 Fractions ! self-defined
32609 \begin_layout Standard
32610 To define custom commands for fractions, the command
32620 \begin_layout Plain Layout
32628 is used in the following scheme:
32631 \begin_layout Standard
32644 bracket}{fraction bar thickness}{style}
32645 \begin_inset Newline newline
32652 \begin_layout Plain Layout
32667 \begin_layout Plain Layout
32674 {numerator}{denominator}
32677 \begin_layout Standard
32678 The style is a number in the range of 0
32679 \begin_inset space \thinspace{}
32683 \begin_inset space \thinspace{}
32689 \begin_layout Standard
32691 \begin_inset Tabular
32692 <lyxtabular version="3" rows="5" columns="2">
32694 <column alignment="center" valignment="top" width="0">
32695 <column alignment="center" valignment="top" width="0">
32697 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32700 \begin_layout Plain Layout
32706 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32709 \begin_layout Plain Layout
32717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32720 \begin_layout Plain Layout
32726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32729 \begin_layout Plain Layout
32730 display style formula
32737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32740 \begin_layout Plain Layout
32746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32749 \begin_layout Plain Layout
32757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32760 \begin_layout Plain Layout
32766 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32769 \begin_layout Plain Layout
32777 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32780 \begin_layout Plain Layout
32786 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32789 \begin_layout Plain Layout
32803 \begin_layout Standard
32804 When no style is given, the size is adjusted to the surrounding environment
32805 like for the command
32814 \begin_layout Standard
32815 When no fraction bar thickness is given, the predefined value of 0.4
32816 \begin_inset space \thinspace{}
32822 \begin_layout Standard
32823 \begin_inset VSpace medskip
32826 For example, the commands
32839 \begin_inset CommandInset ref
32841 reference "sub:Fractions"
32845 are defined with the commands
32848 \begin_layout Standard
32857 genfrac{}{}{}{0}{#1}{#2}}
32860 \begin_layout Standard
32864 \begin_layout Standard
32873 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32876 \begin_layout Standard
32877 \begin_inset VSpace medskip
32880 To define a fraction where the fraction bar thickness can be given as optional
32881 argument, the following line is inserted to the LaTeX-preamble:
32884 \begin_layout Standard
32893 genfrac{}{}{#1}{}{#2}{#3}}
32896 \begin_layout Standard
32898 \begin_inset Formula \begin{align*}
32899 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32900 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32904 As one can see, the distance of the numerator and the denominator to the
32905 fraction bar is round about three times the bar thickness.
32908 \begin_layout Subsection
32910 \begin_inset CommandInset label
32912 name "sub:Canceled-Formulas"
32920 \begin_layout Plain Layout
32929 \begin_layout Standard
32930 To cancel formulas or formula parts, the LaTeX-package
32938 \begin_layout Plain Layout
32943 is part of every LaTeX standard installation.
32952 \begin_layout Plain Layout
32958 has to be loaded with the LaTeX-preamble line
32961 \begin_layout Standard
32966 usepackage[samesize]{cancel}
32969 \begin_layout Standard
32970 There are four ways to cancel formulas:
32973 \begin_layout Standard
32975 \begin_inset Tabular
32976 <lyxtabular version="3" rows="5" columns="2">
32978 <column alignment="center" valignment="top" width="0">
32979 <column alignment="center" valignment="top" width="0">
32981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32984 \begin_layout Plain Layout
32990 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32993 \begin_layout Plain Layout
32995 \begin_inset Note Note
32998 \begin_layout Plain Layout
33011 are used here as spacer.
33023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33026 \begin_layout Plain Layout
33035 \begin_layout Plain Layout
33049 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33052 \begin_layout Plain Layout
33053 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33063 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33066 \begin_layout Plain Layout
33075 \begin_layout Plain Layout
33089 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33092 \begin_layout Plain Layout
33093 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33106 \begin_layout Plain Layout
33115 \begin_layout Plain Layout
33129 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33132 \begin_layout Plain Layout
33133 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33146 \begin_layout Plain Layout
33150 \begin_inset Formula $\to$
33161 \begin_layout Plain Layout
33175 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33178 \begin_layout Plain Layout
33179 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33195 \begin_layout Standard
33202 is especially suitable to visualize the reduction of fractions within formulas:
33203 \begin_inset Formula \[
33204 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33211 \begin_layout Subsection
33212 Formulas in Section Headings
33213 \begin_inset CommandInset label
33215 name "sub:Formulas-in-Section"
33223 \begin_layout Plain Layout
33224 Formula ! in section headings
33232 \begin_layout Standard
33233 When formulas are used in section headings, the following has to be taken
33237 \begin_layout Standard
33238 \begin_inset Note Greyedout
33241 \begin_layout Plain Layout
33250 \begin_layout Plain Layout
33251 Packages ! hyperref
33256 support is enabled in the document settings dialog under
33259 \begin_inset space ~
33264 , PDF-bookmarks are created for every section heading in the table of contents.
33265 If a section heading contains formulas, they are incorrectly displayed
33266 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33275 \begin_layout Standard
33276 Both problems can be solved by inserting at the end of the section heading
33277 a short title with the menu
33279 Insert\SpecialChar \menuseparator
33281 \begin_inset space ~
33287 Short titles are used as alternative for multiline section headings to
33288 keep the table of contents clearly arranged.
33289 Only the short title appears in the table of contents and therefore also
33290 in the PDF-bookmark.
33293 \begin_layout Standard
33294 When formulas should be used in the table of contents but
33298 is used, one can use the following command in TeX-mode:
33301 \begin_layout Standard
33306 texorpdfstring{part}{alternative}
33310 \begin_layout Plain Layout
33321 \begin_layout Standard
33322 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33323 This can be characters, formulas, footnotes, but also cross-references.
33324 The alternative is used instead of the part for the bookmark.
33327 \begin_layout Standard
33328 Here are two example headings:
33329 \begin_inset VSpace -3mm
33336 \begin_layout Plain Layout
33348 \begin_layout Subsubsection
33349 Heading without formula in table of contents
33350 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33354 \begin_inset OptArg
33357 \begin_layout Plain Layout
33358 Heading without formula in table of contents
33366 \begin_layout Subsubsection
33367 Heading with formula in table of contents
33371 \begin_layout Plain Layout
33381 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33388 \begin_layout Plain Layout
33398 \begin_layout Standard
33402 \begin_layout Plain Layout
33411 In the first heading a short title was used, in the second one
33420 \begin_layout Standard
33421 To get the same formatting as for the other headings, the complete heading
33424 boldmath environment
33430 \begin_layout Plain Layout
33432 \begin_inset CommandInset ref
33434 reference "sub:Bold-Formulas"
33446 \begin_layout Subsection
33447 Formulas in multi-column Text
33451 \begin_layout Plain Layout
33452 Formula ! in multi-column text
33460 \begin_layout Standard
33461 Formulas in multi-column text are often too wide to fit into a column and
33462 thus need to be set over the whole page width.
33463 This is done by using the LaTeX-package
33471 \begin_layout Plain Layout
33476 is part of every LaTeX standard installation.
33485 \begin_layout Plain Layout
33486 Packages ! multicol
33491 , that is loaded with the LaTeX-preamble line
33494 \begin_layout Standard
33499 usepackage{multicol}
33502 \begin_layout Standard
33503 \begin_inset Note Greyedout
33506 \begin_layout Plain Layout
33507 Note herby that the setting
33510 \begin_inset space ~
33517 Document\SpecialChar \menuseparator
33523 \begin_inset space ~
33543 \begin_layout Standard
33544 Before the multi-column text the command
33547 \begin_layout Standard
33552 begin{multicols}{column number}
33555 \begin_layout Standard
33556 is written in TeX-mode.
33557 The column number is a number in the range of 2
33558 \begin_inset space \thinspace{}
33562 \begin_inset space \thinspace{}
33566 Before the formula the multi-column text is ended by inserting the command
33569 \begin_layout Standard
33577 \begin_layout Standard
33581 \begin_layout Standard
33582 Due to the command some space is automatically added before the formula.
33584 \begin_inset space \thinspace{}
33587 mm vertical space is inserted before the formula.
33588 When the formula style
33594 \begin_layout Plain Layout
33596 \begin_inset CommandInset ref
33598 reference "sec:Formula-Styles"
33610 \begin_inset space \thinspace{}
33613 mm space is inserted instead.
33616 \begin_layout Standard
33617 As example a multi-column text with a displayed formula:
33620 \begin_layout Standard
33624 \begin_layout Plain Layout
33628 begin{multicols}{2}
33633 Das Spektrum wird fouriertransformiert.
33634 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33635 , Lösungsmittel) zu trennen.
33636 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33637 nun das Aussehen des Ausgangssignals.
33638 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33639 über alle Phasen integrieren muss.
33641 \begin_inset Formula $S$
33644 unser normiertes Ausgangssignal and
33645 \begin_inset Formula $P$
33648 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33652 \begin_layout Plain Layout
33662 \begin_inset VSpace -6mm
33666 \begin_inset Formula \begin{equation}
33667 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33675 \begin_layout Plain Layout
33679 begin{multicols}{2}
33685 \begin_inset Formula $S_{0}$
33688 das Signal ohne Gradient ist and the Normierungsbedingung
33689 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33693 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33695 \begin_inset Formula $\nicefrac{\pi}{2}$
33699 \begin_inset space \thinspace{}
33702 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33703 das Signal zusätzlich abschwächt.
33704 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33706 \begin_inset Formula $T_{2}$
33712 \begin_layout Standard
33716 \begin_layout Plain Layout
33728 \begin_layout Subsection
33729 Formulas with Description of Variables
33733 \begin_layout Plain Layout
33734 Formula ! with description of variables
33742 \begin_layout Standard
33743 To describe variables within a formula, like in formula
33744 \begin_inset CommandInset ref
33746 reference "eq:within"
33755 \begin_inset Formula $n$
33759 \begin_inset space ~
33762 matrix is used with left aligned columns for the
33763 \begin_inset Formula $n$
33770 \begin_layout Plain Layout
33772 \begin_inset CommandInset ref
33774 reference "sec:Matrices"
33783 To set the description in a smaller size, before the matrix e.
33784 \begin_inset space \thinspace{}
33788 \begin_inset space ~
33801 \begin_layout Plain Layout
33803 \begin_inset CommandInset ref
33805 reference "sub:Font-Sizes"
33817 \begin_layout Standard
33818 When the formula style
33824 \begin_layout Plain Layout
33826 \begin_inset CommandInset ref
33828 reference "sec:Formula-Styles"
33849 \begin_layout Plain Layout
33856 only works in formulas with the style
33861 \begin_inset CommandInset ref
33863 reference "sub:Variable-Space"
33872 is inserted before and after the matrix to have the same separation of
33873 the matrix from the equation and the side margin.
33876 \begin_layout Standard
33877 When the formula style
33881 is used, the method described in
33882 \begin_inset CommandInset ref
33884 reference "sub:Flalign-Environment"
33888 is used to indent formulas.
33890 \begin_inset CommandInset ref
33892 reference "eq:within"
33896 consists of five columns whereas in the first two columns contain the equation,
33897 the third the matrix, and the last one an empty TeX-brace.
33898 \begin_inset Formula \begin{flalign}
33899 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33900 \rho & \textrm{density}\\
33901 V & \textrm{volume}\\
33902 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33909 \begin_layout Subsection
33910 Upright small Greek Letters
33911 \begin_inset CommandInset label
33913 name "sub:Upright-small-Greek"
33921 \begin_layout Plain Layout
33922 Greek letters ! upright
33930 \begin_layout Standard
33931 Most of the math fonts only provide italic small Greek letters.
33932 But for symbols of elementary particles like pions and neutrinos, upright
33933 Greek letters are needed.
33942 \begin_layout Plain Layout
33947 is part of the LaTeX-package
33955 \begin_layout Plain Layout
33960 \begin_layout Plain Layout
33983 \begin_layout Plain Layout
33989 that is loaded with the LaTeX-preamble line
33992 \begin_layout Standard
33997 usepackage{upgreek}
34000 \begin_layout Standard
34006 \begin_layout Plain Layout
34016 \begin_inset Note Note
34019 \begin_layout Plain Layout
34020 The following table will only be displayed when the LaTeX-package
34029 They are created when the command for a small Greek letters is started
34035 For example the command
34042 \begin_inset Formula $\uptau$
34048 \begin_layout Standard
34049 With these commands reactions of elementary particles can be typeset:
34050 \begin_inset Formula \[
34051 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34058 \begin_layout Standard
34059 The upright letters are more bold and wider than the italic ones.
34060 They should therefore not be used for units like
34061 \begin_inset Quotes eld
34065 \begin_inset Quotes erd
34071 \begin_layout Standard
34075 \begin_layout Plain Layout
34085 \begin_inset Note Note
34088 \begin_layout Plain Layout
34089 The following will be displayed when the LaTeX-package
34101 \begin_layout Standard
34102 You need to install the LaTeX-package
34106 to see the rest of this subsection in the output.
34109 \begin_layout Standard
34113 \begin_layout Plain Layout
34125 \begin_layout Subsection
34126 Text Characters in Formulas
34127 \begin_inset CommandInset label
34129 name "sub:Text-Characters-in"
34137 \begin_layout Plain Layout
34146 \begin_layout Standard
34147 In some cases you might want to insert text characters directly into formulas.
34148 When for example the centered dot · is often used in formulas like
34149 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34152 , one would have to insert the command
34162 \begin_layout Plain Layout
34164 \begin_inset CommandInset ref
34166 reference "sub:Binary-Operators"
34175 all the time, because this character is defined in all encodings as text
34177 But the encoding can be changed by this LaTeX-preamble line:
34180 \begin_layout Standard
34185 Declare Inputtext{183}{
34195 f\SpecialChar \textcompwordmark{}
34199 \begin_layout Standard
34200 The character encoding (menu
34202 Document\SpecialChar \menuseparator
34203 Settings\SpecialChar \menuseparator
34206 ) specifies what character appears when a keyboard key is pressed.
34207 When the key for the character '·' is pressed, internally the command
34214 But this command is not available in a formula so that you would get LaTeX-erro
34216 With the changed encoding the right command is chosen automatically, depending
34217 on if the character was inserted into a formula or not.
34220 \begin_layout Standard
34221 The encoding of several characters is saved in definition files.
34222 Fore example the encoding
34226 is defined in the file
34230 that is in the installation folder of LaTeX.
34231 Encodings should only be changed via the LaTeX-preamble and not in the
34233 Otherwise own documents could not be edited by other LyX users working
34234 on other computers.
34237 \begin_layout Standard
34238 \begin_inset VSpace medskip
34241 Besides the centered dot, in this document the degree sign ° is defined
34242 with the following LaTeX-preamble line so that it can directly be inserted
34246 \begin_layout Standard
34251 DeclareInputtext{176}{
34261 f\SpecialChar \textcompwordmark{}
34265 \begin_layout Standard
34266 \begin_inset Newpage newpage
34272 \begin_layout Section
34274 Typographic Advises
34278 \begin_layout Plain Layout
34279 Typographic Advises
34287 \begin_layout Standard
34288 This section is a summary of the most important typographic rules, listed
34293 \begin_layout Plain Layout
34294 This collection was partly taken from the German semi-official dictionary
34296 \begin_inset Quotes eld
34300 \begin_inset Quotes erd
34304 \begin_inset CommandInset citation
34310 that lists some of the ISO rules.
34318 \begin_layout Itemize
34327 \begin_layout Plain Layout
34328 done with font styles, see
34329 \begin_inset CommandInset ref
34331 reference "sub:Font-Styles"
34341 \begin_inset space \thinspace{}
34345 \begin_inset Newline newline
34348 Between the value and the unit is the smallest space, see
34349 \begin_inset CommandInset ref
34351 reference "sub:Predefined-Space"
34358 \begin_layout Itemize
34359 Percent and perthousand signs are set like physical units:
34360 \begin_inset Newline newline
34364 \begin_inset space \thinspace{}
34370 \begin_layout Itemize
34371 The degree sign follows directly on the value: 15°, but not when it is used
34373 \begin_inset space \thinspace{}
34379 \begin_layout Itemize
34380 In numbers with more than four digits the smallest space is inserted before
34381 every third digit to group them:
34391 \begin_inset space \thinspace{}
34395 \begin_inset space \thinspace{}
34401 \begin_layout Itemize
34402 For dimensionings like 120×90×40
34403 \begin_inset space \thinspace{}
34406 cm the multiplication sign
34407 \begin_inset Quotes eld
34411 \begin_inset Quotes erd
34415 It is available with the LaTeX-command
34421 , but can also directly be inserted with some keyboard definitions.
34424 \begin_layout Itemize
34425 Functions with names consisting of several letters are set upright to avoid
34427 \begin_inset CommandInset ref
34429 reference "sub:Predefined-Functions"
34436 \begin_layout Itemize
34437 Indices consisting of several letters, are set upright:
34438 \begin_inset Formula $E_{\mathrm{kin}}$
34442 \begin_inset Newline newline
34445 Components of matrices are set italic:
34446 \begin_inset Formula $\hat{H}_{kl}$
34452 \begin_layout Itemize
34453 The differentiation/integration operator 'd', the Euler's number 'e', and
34454 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34458 \begin_layout Standard
34459 \begin_inset Newpage newpage
34465 \begin_layout Section
34470 \begin_layout Plain Layout
34479 \begin_layout Standard
34480 Some characters and symbols can be created with several commands.
34481 Here is a list of the synonym commands:
34484 \begin_layout Standard
34485 \begin_inset VSpace bigskip
34489 \begin_inset space \hfill{}
34493 \begin_inset Tabular
34494 <lyxtabular version="3" rows="12" columns="2">
34496 <column alignment="center" valignment="top" width="0pt">
34497 <column alignment="center" valignment="top" width="0pt">
34499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34502 \begin_layout Plain Layout
34508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34511 \begin_layout Plain Layout
34513 \begin_inset Note Note
34516 \begin_layout Plain Layout
34523 is only used as spacer.
34535 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34538 \begin_layout Plain Layout
34546 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34549 \begin_layout Plain Layout
34553 \begin_layout Plain Layout
34566 \begin_layout Plain Layout
34580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34583 \begin_layout Plain Layout
34591 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34594 \begin_layout Plain Layout
34604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34607 \begin_layout Plain Layout
34615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34618 \begin_layout Plain Layout
34628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34631 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34642 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34653 \begin_layout Plain Layout
34661 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34664 \begin_layout Plain Layout
34672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34675 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34686 \begin_layout Plain Layout
34696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34699 \begin_layout Plain Layout
34707 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34710 \begin_layout Plain Layout
34720 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34723 \begin_layout Plain Layout
34731 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34734 \begin_layout Plain Layout
34744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34747 \begin_layout Plain Layout
34755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34758 \begin_layout Plain Layout
34768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34771 \begin_layout Plain Layout
34779 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34782 \begin_layout Plain Layout
34790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34793 \begin_layout Plain Layout
34801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34804 \begin_layout Plain Layout
34816 \begin_inset space \hfill{}
34820 \begin_inset Tabular
34821 <lyxtabular version="3" rows="12" columns="2">
34823 <column alignment="center" valignment="top" width="0pt">
34824 <column alignment="center" valignment="top" width="0pt">
34826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34829 \begin_layout Plain Layout
34835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34838 \begin_layout Plain Layout
34846 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34849 \begin_layout Plain Layout
34857 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34860 \begin_layout Plain Layout
34872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34875 \begin_layout Plain Layout
34883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34886 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34910 \begin_layout Plain Layout
34920 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34923 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34934 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34945 \begin_layout Plain Layout
34953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34956 \begin_layout Plain Layout
34964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34967 \begin_layout Plain Layout
34975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34978 \begin_layout Plain Layout
34988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34991 \begin_layout Plain Layout
34999 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35002 \begin_layout Plain Layout
35012 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35015 \begin_layout Plain Layout
35023 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35026 \begin_layout Plain Layout
35036 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35039 \begin_layout Plain Layout
35047 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35050 \begin_layout Plain Layout
35060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35063 \begin_layout Plain Layout
35071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35074 \begin_layout Plain Layout
35084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35087 \begin_layout Plain Layout
35095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35098 \begin_layout Plain Layout
35112 \begin_inset space \hfill{}
35118 \begin_layout Standard
35119 \begin_inset Newpage newpage
35125 \begin_layout Bibliography
35126 \begin_inset CommandInset bibitem
35127 LatexCommand bibitem
35139 The LaTeX Companion
35142 Addison Wesley, 2004
35145 \begin_layout Bibliography
35146 \begin_inset CommandInset bibitem
35147 LatexCommand bibitem
35153 \begin_inset CommandInset href
35156 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35160 of LaTeX's math abilities
35163 \begin_layout Bibliography
35164 \begin_inset CommandInset bibitem
35165 LatexCommand bibitem
35170 LaTeX tips and tricks-
35171 \begin_inset CommandInset href
35174 target "http://tug.org/TeXnik/"
35181 \begin_layout Bibliography
35182 \begin_inset CommandInset bibitem
35183 LatexCommand bibitem
35189 \begin_inset CommandInset href
35192 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35200 \begin_layout Plain Layout
35212 \begin_layout Bibliography
35213 \begin_inset CommandInset bibitem
35214 LatexCommand bibitem
35220 \begin_inset CommandInset href
35223 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35227 of all symbols available with LaTeX-packages
35230 \begin_layout Bibliography
35231 \begin_inset CommandInset bibitem
35232 LatexCommand bibitem
35238 \begin_inset CommandInset href
35240 name "Documentation"
35241 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35245 of the LaTeX-package
35253 \begin_layout Plain Layout
35254 Packages ! hyperref
35262 \begin_layout Bibliography
35263 \begin_inset CommandInset bibitem
35264 LatexCommand bibitem
35270 \begin_inset CommandInset href
35273 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35284 \begin_inset CommandInset ref
35286 reference "sub:Operator-Limits"
35294 \begin_layout Plain Layout
35305 \begin_layout Bibliography
35306 \begin_inset CommandInset bibitem
35307 LatexCommand bibitem
35318 Auflage, Duden 2001
35321 \begin_layout Subsubsection*
35322 \begin_inset CommandInset index_print
35323 LatexCommand printindex