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]{\contentsname}{}
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
698 \begin_inset Note Note
701 \begin_layout Plain Layout
702 In LyX there are three
703 \begin_inset Quotes eld
707 \begin_inset Quotes erd
710 that appear in the output with sub- and superscript letters: TeX, LaTeX,
714 \begin_layout Plain Layout
715 To avoid that these names are recognized as proper names, a TeX-brace pair
724 \begin_layout Standard
725 To change the LaTeX-preamble
729 \begin_layout Plain Layout
737 Document\SpecialChar \menuseparator
738 Settings\SpecialChar \menuseparator
743 \begin_layout Plain Layout
759 \begin_layout Standard
760 To edit matrices, case differentiations, and multiline formulas subsequently,
763 Edit\SpecialChar \menuseparator
768 Edit\SpecialChar \menuseparator
770 \begin_inset space \thinspace{}
774 \begin_inset space \thinspace{}
784 When lines and columns are swapped via the menu, the column or line where
785 the cursor is in is exchanged with the column to the right or the line
787 Is the cursor in the last column or row, the exchange is done with the
788 column to the left or the line above.
791 \begin_layout Standard
792 To write text in formulas
796 \begin_layout Plain Layout
797 For multiline formulas the command
804 \begin_inset CommandInset ref
806 reference "sub:Text-in-multiline"
823 \begin_layout Plain Layout
833 \begin_layout Plain Layout
840 This mode is invoked with the the shortcut
848 or by the insertion of the command
856 \begin_layout Plain Layout
867 The text appears black in LyX and can therefore be distinguished from the
868 other formula parts that appear blue.
869 In the output mathematical text is set upright, in contrary to other formula
873 \begin_layout Subsection*
877 \begin_layout Standard
878 Most of the LaTeX-commands for math constructs have the following scheme:
881 \begin_layout Standard
897 \begin_layout Standard
898 A command starts always with a backslash
899 \begin_inset Quotes gld
909 \begin_inset Quotes grd
913 To omit optional arguments, also omit the associated brackets.
914 The braces around the required arguments are named in this document as
919 \begin_layout Plain Layout
926 If you add in a formula a left brace to a command name, LyX creates automatical
928 In all other cases TeX-braces are created in formulas with the command
936 TeX-braces appear red in LyX, in contrary to normal braces that appear
938 In TeX-mode no command is needed to get TeX-braces.
939 TeX-braces don't appear in the output.
942 \begin_layout Standard
943 When commands without arguments, like commands for symbols are entered in
944 TeX-mode, a space character must
948 be behind the command to end it.
949 This space doesn't appear in the output.
950 When the space should appear in the output, the space must be followed
951 by a protected space in normal text.
954 \begin_layout Standard
955 A protected space is inserted with
962 \begin_layout Subsection*
963 \begin_inset Newpage newpage
969 \begin_layout Itemize
974 \begin_layout Plain Layout
975 This visible space character can be created with the command
985 \begin_layout Plain Layout
993 , inserted in TeX-mode.
1002 \begin_layout Plain Layout
1012 \begin_inset space ~
1015 denotes a space character to be input.
1018 \begin_layout Itemize
1020 \begin_inset Formula $\to$
1023 denotes the usage of the corresponding arrow key on the keyboard.
1026 \begin_layout Subsection*
1030 \begin_layout Standard
1032 \begin_inset Float table
1038 \begin_layout Plain Layout
1040 \begin_inset Caption
1042 \begin_layout Plain Layout
1043 \begin_inset CommandInset label
1045 name "tab:Used-units"
1057 \begin_layout Plain Layout
1059 \begin_inset Tabular
1060 <lyxtabular version="3" rows="13" columns="2">
1062 <column alignment="center" valignment="top" width="0">
1063 <column alignment="center" valignment="top" width="0">
1065 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1068 \begin_layout Plain Layout
1074 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1077 \begin_layout Plain Layout
1085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1088 \begin_layout Plain Layout
1094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1097 \begin_layout Plain Layout
1105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1108 \begin_layout Plain Layout
1114 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1117 \begin_layout Plain Layout
1125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1128 \begin_layout Plain Layout
1134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1137 \begin_layout Plain Layout
1139 \begin_inset space \thinspace{}
1143 \begin_inset space \thinspace{}
1153 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1156 \begin_layout Plain Layout
1162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1165 \begin_layout Plain Layout
1167 \begin_inset space \thinspace{}
1171 \begin_inset space \thinspace{}
1181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1184 \begin_layout Plain Layout
1190 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1193 \begin_layout Plain Layout
1195 \begin_inset space \thinspace{}
1199 \begin_inset space \thinspace{}
1209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1212 \begin_layout Plain Layout
1218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1221 \begin_layout Plain Layout
1223 \begin_inset space \thinspace{}
1227 \begin_inset space \thinspace{}
1237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1240 \begin_layout Plain Layout
1246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1249 \begin_layout Plain Layout
1251 \begin_inset space \thinspace{}
1255 \begin_inset space \thinspace{}
1265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1268 \begin_layout Plain Layout
1274 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1277 \begin_layout Plain Layout
1279 \begin_inset space \thinspace{}
1283 \begin_inset Formula $\approx$
1287 \begin_inset space \thinspace{}
1297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1300 \begin_layout Plain Layout
1306 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1309 \begin_layout Plain Layout
1311 \begin_inset space \thinspace{}
1315 \begin_inset space \thinspace{}
1325 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1328 \begin_layout Plain Layout
1334 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1337 \begin_layout Plain Layout
1341 \begin_inset Quotes eld
1347 \begin_inset Quotes erd
1357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1360 \begin_layout Plain Layout
1366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1369 \begin_layout Plain Layout
1371 \begin_inset Quotes eld
1379 \begin_inset Quotes erd
1389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1392 \begin_layout Plain Layout
1398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1401 \begin_layout Plain Layout
1403 \begin_inset space \thinspace{}
1407 \begin_inset Formula $\nicefrac{1}{18}$
1411 \begin_inset space \thinspace{}
1432 \begin_layout Standard
1433 \begin_inset Newpage newpage
1439 \begin_layout Section
1443 \begin_layout Subsection
1448 \begin_layout Plain Layout
1458 \begin_layout Plain Layout
1468 \begin_layout Plain Layout
1473 \begin_layout Plain Layout
1484 \begin_layout Plain Layout
1500 \begin_layout Plain Layout
1505 \begin_layout Plain Layout
1516 \begin_layout Plain Layout
1531 \begin_layout Standard
1532 Indices are created with an underscore
1533 \begin_inset Quotes eld
1537 \begin_inset Quotes erd
1540 or via the math toolbar button
1541 \begin_inset Graphics
1542 filename ../images/math-subscript.png
1547 , exponents with a caret
1548 \begin_inset Quotes eld
1552 \begin_inset Quotes erd
1555 or via the math toolbar button
1556 \begin_inset Graphics
1557 filename ../images/math-superscript.png
1565 \begin_layout Standard
1567 \begin_inset Tabular
1568 <lyxtabular version="3" rows="4" columns="2">
1570 <column alignment="center" valignment="top" width="0pt">
1571 <column alignment="center" valignment="top" width="0pt">
1573 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1576 \begin_layout Plain Layout
1582 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1585 \begin_layout Plain Layout
1587 \begin_inset Note Note
1590 \begin_layout Plain Layout
1597 is only used as spacer.
1609 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1612 \begin_layout Plain Layout
1618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1621 \begin_layout Plain Layout
1622 \begin_inset Formula $B_{V}$
1632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1635 \begin_layout Plain Layout
1641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1644 \begin_layout Plain Layout
1645 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1655 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1658 \begin_layout Plain Layout
1663 \begin_layout Plain Layout
1677 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1680 \begin_layout Plain Layout
1681 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1697 \begin_layout Standard
1698 As the caret is in some languages an accent, vowels will be accentuated
1699 in this case and not set as exponents
1703 \begin_layout Plain Layout
1704 Depending on the used keyboard settings this can also happen for other character
1711 To get in this case exponents, press
1715 after the caret as in the last example.
1718 \begin_layout Subsection
1720 \begin_inset CommandInset label
1722 name "sub:Fractions"
1730 \begin_layout Plain Layout
1739 \begin_layout Standard
1740 Fractions are generated with the command
1750 \begin_layout Plain Layout
1758 or via the math toolbar button
1759 \begin_inset Graphics
1760 filename ../images/math/frac.png
1766 The font size is adjusted automatically, depending on whether the fraction
1767 is in an inline or display style formula.
1768 With the math toolbar button
1769 \begin_inset Graphics
1770 filename ../images/math/frac-square.png
1775 you can select different fraction types.
1778 \begin_layout Standard
1787 \begin_layout Plain Layout
1797 a fraction can be created that has in any case the size of a display style
1807 \begin_layout Plain Layout
1817 the fraction appears always with the size of an inline formula.
1821 \begin_layout Standard
1822 A line with the fraction
1823 \begin_inset Formula $\frac{1}{2}$
1826 that was created with the command
1835 \begin_layout Standard
1836 A line with the fraction
1837 \begin_inset Formula $\dfrac{1}{2}$
1840 that was created with the command
1849 \begin_layout Standard
1851 \begin_inset Tabular
1852 <lyxtabular version="3" rows="4" columns="2">
1854 <column alignment="center" valignment="top" width="0pt">
1855 <column alignment="center" valignment="top" width="0pt">
1857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1860 \begin_layout Plain Layout
1866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1869 \begin_layout Plain Layout
1871 \begin_inset Note Note
1874 \begin_layout Plain Layout
1881 is only used as spacer.
1893 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1896 \begin_layout Plain Layout
1903 \begin_layout Plain Layout
1913 \begin_inset Formula $\downarrow$
1921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1924 \begin_layout Plain Layout
1925 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1938 \begin_layout Plain Layout
1945 \begin_layout Plain Layout
1955 \begin_inset Formula $\downarrow$
1963 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1966 \begin_layout Plain Layout
1967 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1980 \begin_layout Plain Layout
1987 \begin_layout Plain Layout
2000 \begin_layout Plain Layout
2015 \begin_layout Plain Layout
2025 \begin_inset Formula $\downarrow$
2029 \begin_inset Formula $\downarrow\downarrow$
2037 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2040 \begin_layout Plain Layout
2041 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2057 \begin_layout Standard
2058 \begin_inset VSpace bigskip
2062 \begin_inset Newpage newpage
2065 For nested fractions the command
2075 \begin_layout Plain Layout
2085 \begin_inset VSpace -3mm
2091 \begin_layout Standard
2092 \begin_inset Formula \begin{align*}
2093 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2094 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
2101 \begin_layout Standard
2102 The command for the example above is:
2105 \begin_layout Standard
2111 \begin_inset Formula $\to$
2121 \begin_inset Formula $\to$
2127 \begin_inset Formula $\to\to$
2135 \begin_layout Standard
2136 \begin_inset VSpace medskip
2142 \begin_layout Standard
2149 sets the fraction always in the size of a displayed formula, also when
2150 it is part of another fraction.
2157 has the following command scheme:
2160 \begin_layout Standard
2165 cfrac[numerator position]{numerator}{denominator}
2168 \begin_layout Standard
2169 The numerator position can be
2182 l or r aligns the numerator to the left or right, resp.
2183 \begin_inset space ~
2186 with the fraction stroke.
2191 or no position is given, the numerator appears centered.
2192 These fractions demonstrate the different alignments:
2193 \begin_inset Newline newline
2199 \begin_inset Formula $\cfrac[l]{A}{B+C}$
2203 \begin_inset Formula $\cfrac{A}{B+C}$
2207 \begin_inset Formula $\cfrac[r]{A}{B+C}$
2213 \begin_layout Standard
2214 \begin_inset VSpace medskip
2217 It is often advantageous to combine
2230 \begin_inset Formula \[
2231 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
2238 \begin_layout Standard
2239 For inline fractions with a sloped fraction stroke you can use the command
2248 \begin_layout Plain Layout
2259 \begin_inset Formula $\nicefrac{5}{31}$
2265 \begin_layout Standard
2266 How to define own fractions where the fraction stroke can be changed, is
2268 \begin_inset CommandInset ref
2270 reference "sub:Self-defined-Fractions"
2277 \begin_layout Subsection
2282 \begin_layout Plain Layout
2291 \begin_layout Standard
2292 Square roots are created with
2302 \begin_layout Plain Layout
2310 or the math toolbar button
2311 \begin_inset Graphics
2312 filename ../images/math/sqrt.png
2317 , all other roots with the command
2327 \begin_layout Plain Layout
2335 or with the math toolbar button
2336 \begin_inset Graphics
2337 filename ../images/math/root.png
2345 \begin_layout Standard
2347 \begin_inset Tabular
2348 <lyxtabular version="3" rows="3" columns="2">
2350 <column alignment="center" valignment="top" width="0pt">
2351 <column alignment="center" valignment="top" width="0pt">
2353 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2356 \begin_layout Plain Layout
2362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2365 \begin_layout Plain Layout
2367 \begin_inset Note Note
2370 \begin_layout Plain Layout
2377 is only used as spacer.
2389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2392 \begin_layout Plain Layout
2399 \begin_layout Plain Layout
2413 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2416 \begin_layout Plain Layout
2417 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2427 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2430 \begin_layout Plain Layout
2437 \begin_layout Plain Layout
2447 \begin_inset Formula $\downarrow$
2455 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2458 \begin_layout Plain Layout
2459 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2475 \begin_layout Standard
2476 A square root can also be created with
2482 when the root index field is left empty.
2485 \begin_layout Standard
2486 With certain indices the distance to the root is too small, like in this
2488 \begin_inset Formula $\sqrt[\beta]{B}$
2492 \begin_inset Newline newline
2496 \begin_inset Formula $\beta$
2500 To avoid this, the commands
2510 \begin_layout Plain Layout
2528 \begin_layout Plain Layout
2536 are used with the following scheme:
2539 \begin_layout Standard
2553 \begin_layout Standard
2554 Distance is the number of Big Points (unit bp;
2555 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2558 ), that the index should be moved to the left or top, resp..
2559 The commands are written to the index.
2560 This way the command
2561 \begin_inset Newline newline
2571 \begin_inset Formula $\to$
2577 \begin_inset Formula $\to$
2586 \begin_layout Plain Layout
2596 \begin_inset Formula $\to$
2600 \begin_inset Newline newline
2605 produces a correct typeset formula:
2606 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2612 \begin_layout Subsection
2613 Binomial coefficients
2617 \begin_layout Plain Layout
2618 Binomial coefficient s
2626 \begin_layout Standard
2627 Binomial coefficients are inserted with the command
2637 \begin_layout Plain Layout
2645 or with the submenu of the math toolbar button
2646 \begin_inset Graphics
2647 filename ../images/math/frac-square.png
2653 Analog to fractions (
2673 \begin_layout Plain Layout
2693 \begin_layout Plain Layout
2702 For other brackets around binomial coeficients there are the commands
2712 \begin_layout Plain Layout
2730 \begin_layout Plain Layout
2741 \begin_layout Standard
2743 \begin_inset Tabular
2744 <lyxtabular version="3" rows="6" columns="2">
2746 <column alignment="center" valignment="top" width="0pt">
2747 <column alignment="center" valignment="top" width="0pt">
2749 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2752 \begin_layout Plain Layout
2758 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2761 \begin_layout Plain Layout
2763 \begin_inset Note Note
2766 \begin_layout Plain Layout
2773 is only used as spacer.
2785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2788 \begin_layout Plain Layout
2795 \begin_layout Plain Layout
2805 \begin_inset Formula $\downarrow$
2813 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2816 \begin_layout Plain Layout
2817 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2827 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2830 \begin_layout Plain Layout
2837 \begin_layout Plain Layout
2847 \begin_inset Formula $\downarrow$
2855 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2858 \begin_layout Plain Layout
2859 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2872 \begin_layout Plain Layout
2879 \begin_layout Plain Layout
2889 \begin_inset Formula $\downarrow$
2897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2900 \begin_layout Plain Layout
2901 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
2911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2914 \begin_layout Plain Layout
2921 \begin_layout Plain Layout
2931 \begin_inset Formula $\downarrow$
2939 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2942 \begin_layout Plain Layout
2943 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
2953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2956 \begin_layout Plain Layout
2963 \begin_layout Plain Layout
2973 \begin_inset Formula $\downarrow$
2981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2984 \begin_layout Plain Layout
2985 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3001 \begin_layout Subsection
3002 Case differentiations
3006 \begin_layout Plain Layout
3007 Case differentiations
3015 \begin_layout Standard
3017 \begin_inset Tabular
3018 <lyxtabular version="3" rows="3" columns="2">
3020 <column alignment="center" valignment="top" width="0pt">
3021 <column alignment="center" valignment="top" width="0pt">
3023 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3026 \begin_layout Plain Layout
3032 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3035 \begin_layout Plain Layout
3043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3053 \begin_layout Plain Layout
3063 \begin_inset Formula $\to$
3070 \begin_layout Plain Layout
3083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3086 \begin_layout Plain Layout
3087 \begin_inset Formula $\begin{cases}
3098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3101 \begin_layout Plain Layout
3108 \begin_layout Plain Layout
3122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3125 \begin_layout Plain Layout
3126 \begin_inset Formula $\begin{cases}
3127 A & \textrm{for }x>0\\
3128 B & \textrm{for }x=0\end{cases}$
3144 \begin_layout Standard
3151 or the usage of the math toolbar button
3152 \begin_inset Graphics
3153 filename ../images/math/cases.png
3158 you can create new lines with the shortcut
3162 or the table toolbar button
3163 \begin_inset Graphics
3164 filename ../images/tabular-feature_append-row.png
3172 \begin_layout Standard
3179 is also available via the menu
3181 Insert\SpecialChar \menuseparator
3182 Math\SpecialChar \menuseparator
3188 \begin_layout Subsection
3193 \begin_layout Plain Layout
3202 \begin_layout Standard
3213 \begin_layout Plain Layout
3221 every character can be displayed canceled.
3222 The characters are quasi accentuated by a slash.
3225 \begin_layout Standard
3227 \begin_inset Tabular
3228 <lyxtabular version="3" rows="4" columns="2">
3230 <column alignment="center" valignment="top" width="0pt">
3231 <column alignment="center" valignment="top" width="0pt">
3233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3236 \begin_layout Plain Layout
3242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3245 \begin_layout Plain Layout
3253 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3256 \begin_layout Plain Layout
3264 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3267 \begin_layout Plain Layout
3268 \begin_inset Formula $\not=$
3278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3281 \begin_layout Plain Layout
3291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3294 \begin_layout Plain Layout
3295 \begin_inset Formula $\not\le$
3305 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3308 \begin_layout Plain Layout
3318 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3321 \begin_layout Plain Layout
3322 \begin_inset Formula $\not\parallel$
3338 \begin_layout Standard
3339 The last example shows, that not all negations look good.
3340 Therefore there are for some negations special commands (see
3341 \begin_inset CommandInset ref
3343 reference "sub:Mathematical-Symbols"
3348 \begin_inset CommandInset ref
3350 reference "sec:Relations"
3357 \begin_layout Subsection
3359 \begin_inset CommandInset label
3361 name "sub:Placeholders"
3369 \begin_layout Plain Layout
3379 \begin_layout Plain Layout
3380 Chemical characters ! Isotopes
3389 \begin_layout Plain Layout
3394 \begin_layout Plain Layout
3405 \begin_layout Plain Layout
3420 \begin_layout Standard
3422 \begin_inset space \thinspace{}
3426 \begin_inset space ~
3433 \begin_layout Plain Layout
3434 More about chemical symbols is written in
3435 \begin_inset CommandInset ref
3437 reference "sub:Chemical-Symbols-and"
3446 the following problem occurs:
3449 \begin_layout Standard
3451 \begin_inset Tabular
3452 <lyxtabular version="3" rows="2" columns="2">
3454 <column alignment="center" valignment="top" width="0pt">
3455 <column alignment="center" valignment="top" width="0pt">
3457 <cell alignment="center" valignment="top" usebox="none">
3460 \begin_layout Plain Layout
3461 Indices created with sub- and superscripts:
3466 <cell alignment="center" valignment="top" usebox="none">
3469 \begin_layout Plain Layout
3470 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3480 <cell alignment="center" valignment="top" usebox="none">
3483 \begin_layout Plain Layout
3489 <cell alignment="center" valignment="top" usebox="none">
3492 \begin_layout Plain Layout
3493 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3507 \begin_inset Note Note
3510 \begin_layout Plain Layout
3517 is only used as spacer.
3525 \begin_layout Standard
3526 The shorter index is by default placed below or above the first character
3527 of the longer index.
3528 To avoid this there is the command
3538 \begin_layout Plain Layout
3546 or the math toolbar button
3547 \begin_inset space \thinspace{}
3554 \begin_layout Plain Layout
3555 can be found in the submenu of the toolbar button
3556 \begin_inset Graphics
3557 filename ../images/math/space.png
3568 \begin_inset Graphics
3569 filename ../images/math/phantom.png
3574 that creates one or more phantom characters.
3581 a small blue box appears that is superposed with two red arrows.
3582 The arrows indicate that the complete width and height of the box content
3583 will be created as placeholder.
3584 Phantom characters are accordingly placeholders with the size of the characters.
3587 \begin_layout Standard
3589 \begin_inset Tabular
3590 <lyxtabular version="3" rows="4" columns="2">
3592 <column alignment="center" valignment="top" width="0">
3593 <column alignment="center" valignment="top" width="0">
3595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3598 \begin_layout Plain Layout
3604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3607 \begin_layout Plain Layout
3609 \begin_inset Note Note
3612 \begin_layout Plain Layout
3619 is only used as spacer.
3631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3634 \begin_layout Plain Layout
3639 \begin_layout Plain Layout
3654 \begin_layout Plain Layout
3664 \begin_inset Formula $\to$
3671 \begin_layout Plain Layout
3685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3688 \begin_layout Plain Layout
3689 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3702 \begin_layout Plain Layout
3707 \begin_layout Plain Layout
3722 \begin_layout Plain Layout
3732 \begin_inset Formula $\to$
3739 \begin_layout Plain Layout
3753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3756 \begin_layout Plain Layout
3757 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3770 \begin_layout Plain Layout
3777 \begin_layout Plain Layout
3792 \begin_layout Plain Layout
3802 \begin_inset Formula $\to$
3809 \begin_layout Plain Layout
3823 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3826 \begin_layout Plain Layout
3827 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3843 \begin_layout Standard
3844 Furthermore there are the commands
3854 \begin_layout Plain Layout
3863 \begin_inset space ~
3867 \begin_inset Graphics
3868 filename ../images/math/vphantom.png
3883 \begin_layout Plain Layout
3892 \begin_inset space ~
3896 \begin_inset Graphics
3897 filename ../images/math/hphantom.png
3909 creates only space for the maximal height of the characters in the box
3910 but not for its width.
3917 creates only space for the width of the box content.
3918 Therefore the boxes of both commands have only one red arrow.
3921 \begin_layout Standard
3932 \begin_layout Plain Layout
3947 space for the height of the integral sign,
3951 \begin_layout Plain Layout
3958 creates an integral sign, see
3959 \begin_inset CommandInset ref
3961 reference "sub:Big-Operators"
3970 because this is the larger character.
3971 An example application is in
3972 \begin_inset CommandInset ref
3974 reference "sub:Multiline-Brackets"
3981 \begin_layout Subsection
3986 \begin_layout Plain Layout
3996 \begin_layout Plain Layout
3997 Formula ! underlined
4005 \begin_layout Standard
4007 \begin_inset Tabular
4008 <lyxtabular version="3" rows="4" columns="2">
4010 <column alignment="center" valignment="top" width="0pt">
4011 <column alignment="center" valignment="top" width="0pt">
4013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4016 \begin_layout Plain Layout
4022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4025 \begin_layout Plain Layout
4027 \begin_inset Note Note
4030 \begin_layout Plain Layout
4037 is only used as spacer.
4049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4052 \begin_layout Plain Layout
4059 \begin_layout Plain Layout
4072 \begin_layout Plain Layout
4085 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4088 \begin_layout Plain Layout
4089 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4102 \begin_layout Plain Layout
4109 \begin_layout Plain Layout
4122 \begin_layout Plain Layout
4135 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4138 \begin_layout Plain Layout
4139 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4152 \begin_layout Plain Layout
4159 \begin_layout Plain Layout
4174 \begin_layout Plain Layout
4188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4191 \begin_layout Plain Layout
4192 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4208 \begin_layout Standard
4209 In the last example it doesn't matter if first
4224 \begin_layout Standard
4225 To double underline e.
4226 \begin_inset space \thinspace{}
4239 \begin_layout Standard
4240 It is possible to place up to 6 lines above or below characters.
4243 \begin_layout Subsection
4248 \begin_layout Plain Layout
4257 \begin_layout Standard
4258 There are different types of ellipses available.
4262 \begin_layout Plain Layout
4263 In the math toolbar in the submenu of the button
4264 \begin_inset Graphics
4265 filename ../images/math/ldots.png
4275 For listings dots at the baseline are used (
4285 \begin_layout Plain Layout
4293 ), while for operations dots are needed that are on the same height as the
4304 \begin_layout Plain Layout
4313 When using the command
4323 \begin_layout Plain Layout
4331 , LaTeX decides on the basis of the next character what type is used.
4334 \begin_layout Standard
4336 \begin_inset Tabular
4337 <lyxtabular version="3" rows="8" columns="2">
4339 <column alignment="center" valignment="top" width="0pt">
4340 <column alignment="center" valignment="top" width="0pt">
4342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4345 \begin_layout Plain Layout
4351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4354 \begin_layout Plain Layout
4362 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4365 \begin_layout Plain Layout
4370 \begin_layout Plain Layout
4385 \begin_layout Plain Layout
4399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4402 \begin_layout Plain Layout
4403 \begin_inset Formula $A_{1},\dots,A_{n}$
4413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4416 \begin_layout Plain Layout
4421 \begin_layout Plain Layout
4436 \begin_layout Plain Layout
4450 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4453 \begin_layout Plain Layout
4454 \begin_inset Formula $A_{1}+\dots+A_{n}$
4464 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4467 \begin_layout Plain Layout
4472 \begin_layout Plain Layout
4487 \begin_layout Plain Layout
4501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4504 \begin_layout Plain Layout
4505 \begin_inset Formula $A_{1},\ldots,A_{n}$
4515 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4518 \begin_layout Plain Layout
4523 \begin_layout Plain Layout
4538 \begin_layout Plain Layout
4552 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4555 \begin_layout Plain Layout
4556 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4566 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4569 \begin_layout Plain Layout
4577 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4580 \begin_layout Plain Layout
4581 \begin_inset Formula $\vdots$
4591 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4594 \begin_layout Plain Layout
4602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4605 \begin_layout Plain Layout
4606 \begin_inset Formula $\ddots$
4616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4619 \begin_layout Plain Layout
4621 \begin_inset space \thinspace{}
4624 matrix with the different dots
4629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4632 \begin_layout Plain Layout
4633 \begin_inset Formula $\begin{array}{ccc}
4634 A_{11} & \cdots & A_{1m}\\
4635 \vdots & \ddots & \vdots\\
4636 A_{n1} & \cdots & A_{nm}\end{array}$
4652 \begin_layout Standard
4653 The ellipses available in menu
4655 Insert\SpecialChar \menuseparator
4657 \begin_inset space ~
4671 \begin_layout Standard
4672 \begin_inset VSpace medskip
4675 Specially for matrices there are ellipses that span over several columns.
4676 They are created with the command
4686 \begin_layout Plain Layout
4694 , that has the following scheme:
4697 \begin_layout Standard
4702 hdotsfor[distance]{number of columns}
4705 \begin_layout Standard
4706 The number of columns specifies how many columns should be spanned.
4707 Distance is a factor for the distance between the dots.
4710 \begin_layout Standard
4711 In the following matrix the command
4717 was inserted in the first box of the second line, to get an ellipsis with
4718 a dot distance twice as long as with the command
4725 \begin_inset Formula \[
4726 \left(\begin{array}{cccc}
4729 q & w & e & r\end{array}\right)\]
4733 Note that the matrix fields that should be spanned must be empty, otherwise
4734 you get LaTeX-errors.
4737 \begin_layout Standard
4738 \begin_inset VSpace bigskip
4741 Furthermore you can fill with the command
4751 \begin_layout Plain Layout
4759 the rest of a line with dots.
4760 The effect of these commands is the same like with
4767 \begin_inset CommandInset ref
4769 reference "sub:Variable-Space"
4776 \begin_layout Standard
4777 For example the command
4785 \begin_layout Plain Layout
4799 \begin_layout Standard
4800 \begin_inset Formula $A\dotfill B$
4806 \begin_layout Standard
4813 there is for a line the command
4823 \begin_layout Plain Layout
4834 \begin_layout Standard
4835 \begin_inset Formula $A\hrulefill B$
4841 \begin_layout Standard
4842 To use the commands for text, they have to be inserted in TeX-mode.
4845 \begin_layout Section
4847 \begin_inset CommandInset label
4857 \begin_layout Plain Layout
4866 \begin_layout Standard
4867 Matrices can be inserted via the math toolbar button
4868 \begin_inset Graphics
4869 filename ../images/dialog-show_mathmatrix.png
4876 Insert\SpecialChar \menuseparator
4877 Math\SpecialChar \menuseparator
4881 You will be asked for the number of matrix columns and rows, and the alignment.
4882 The vertical alignment is hereby only of importance for matrices in inline
4886 \begin_layout Standard
4887 The first matrix is top
4888 \begin_inset Formula $\begin{array}[t]{cccc}
4891 C & F & I & L\end{array}$
4895 \begin_inset Formula $\begin{array}{cccc}
4898 C & F & I & L\end{array}$
4901 , and the third bottom
4902 \begin_inset Formula $\begin{array}[b]{cccc}
4905 C & F & I & L\end{array}$
4911 \begin_layout Standard
4912 The horizontal alignment specifies how the column entries should be aligned.
4913 It is set by entering a letter for every column.
4918 denotes left aligned,
4927 To create for example a 4
4932 \begin_inset space ~
4935 matrix where the first column is left aligned, the second and third are
4936 centered, and the last one is right aligned, one enters for the horizontal
4942 Normally are in a matrix all columns centered, therefore the default is
4943 for every column is a
4950 \begin_layout Standard
4951 Horizontal alignment:
4954 \begin_layout Standard
4960 \begin_inset Formula $\begin{array}{lll}
4963 C & F & 10000\end{array}$
4971 \begin_inset Formula $\begin{array}{ccc}
4974 C & F & 10000\end{array}$
4982 \begin_inset Formula $\begin{array}{rrr}
4985 C & F & 10000\end{array}$
4991 \begin_layout Standard
4992 To add or delete rows and columns subsequently, the math toolbar buttons
4994 \begin_inset Graphics
4995 filename ../images/tabular-feature_append-row.png
5001 \begin_inset Graphics
5002 filename ../images/tabular-feature_delete-row.png
5008 \begin_inset space \thinspace{}
5013 Edit\SpecialChar \menuseparator
5017 New rows can also be created with
5024 \begin_layout Standard
5025 \begin_inset VSpace bigskip
5028 Parentheses around a matrix can can either be created with the commands
5039 \begin_layout Plain Layout
5057 \begin_layout Plain Layout
5068 \begin_inset space ~
5074 \begin_inset CommandInset ref
5076 reference "sub:Automatic-Bracket-Size"
5080 , or by using the following commands:
5081 \begin_inset VSpace medskip
5087 \begin_layout Standard
5088 \begin_inset space \hfill{}
5092 \begin_inset Tabular
5093 <lyxtabular version="3" rows="4" columns="2">
5095 <column alignment="center" valignment="top" width="0">
5096 <column alignment="center" valignment="top" width="0">
5098 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5101 \begin_layout Plain Layout
5107 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5110 \begin_layout Plain Layout
5112 \begin_inset Note Note
5115 \begin_layout Plain Layout
5122 is only used as spacer.
5134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5137 \begin_layout Plain Layout
5144 \begin_layout Plain Layout
5158 \begin_inset space \thinspace{}
5166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5169 \begin_layout Plain Layout
5170 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5171 0 & \textrm{-}\mathrm{i}\\
5172 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5185 \begin_layout Plain Layout
5192 \begin_layout Plain Layout
5206 \begin_inset space \thinspace{}
5214 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5217 \begin_layout Plain Layout
5218 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5219 0 & \textrm{-}\mathrm{i}\\
5220 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5233 \begin_layout Plain Layout
5240 \begin_layout Plain Layout
5254 \begin_inset space \thinspace{}
5262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5265 \begin_layout Plain Layout
5266 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5267 0 & \textrm{-}\mathrm{i}\\
5268 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5282 \begin_inset space \hfill{}
5286 \begin_inset Tabular
5287 <lyxtabular version="3" rows="4" columns="2">
5289 <column alignment="center" valignment="top" width="0">
5290 <column alignment="center" valignment="top" width="0">
5292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5295 \begin_layout Plain Layout
5301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5304 \begin_layout Plain Layout
5312 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5315 \begin_layout Plain Layout
5322 \begin_layout Plain Layout
5336 \begin_inset space \thinspace{}
5344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5347 \begin_layout Plain Layout
5348 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5349 0 & \textrm{-}\mathrm{i}\\
5350 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5363 \begin_layout Plain Layout
5370 \begin_layout Plain Layout
5384 \begin_inset space \thinspace{}
5392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5395 \begin_layout Plain Layout
5396 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5397 0 & \textrm{-}\mathrm{i}\\
5398 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5411 \begin_layout Plain Layout
5418 \begin_layout Plain Layout
5432 \begin_inset space \thinspace{}
5440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5443 \begin_layout Plain Layout
5444 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5445 0 & \textrm{-}\mathrm{i}\\
5446 \mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
5460 \begin_inset space \hfill{}
5466 \begin_layout Standard
5467 \begin_inset VSpace medskip
5471 \begin_inset space \thinspace{}
5475 \begin_inset space ~
5484 is inserted, a blue box appears between two vertical lines where the matrix
5488 \begin_layout Standard
5489 \begin_inset VSpace bigskip
5492 As all multiline formulas are matrices, the length
5502 \begin_layout Plain Layout
5510 that is described in
5511 \begin_inset CommandInset ref
5513 reference "sub:Column-Separation"
5517 can also be used to change the column separation of matrices.
5520 \begin_layout Standard
5521 To change the row separation, the command
5531 \begin_layout Plain Layout
5540 It is used as follows:
5543 \begin_layout Standard
5550 arraystretch}{stretch factor}
5554 \begin_layout Plain Layout
5565 \begin_layout Standard
5572 assigns the stretch factor to the predefined command
5580 \begin_inset space \thinspace{}
5584 \begin_inset space ~
5587 the row separation, use the factor 2.
5588 This is then used for all following matrices.
5589 To go back to the original separation, assign the factor 1 to
5598 \begin_layout Standard
5599 To set matrices into a text line, the command
5609 \begin_layout Plain Layout
5618 When it is inserted a blue box with two dashed lines appears.
5619 In this box the matrix is inserted.
5622 \begin_layout Standard
5624 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5625 C & D\end{smallmatrix}\right)$
5631 \begin_layout Section
5632 Brackets and Delimiters
5636 \begin_layout Plain Layout
5646 \begin_layout Plain Layout
5655 \begin_layout Subsection
5656 Vertical Brackets and Delimiters
5660 \begin_layout Plain Layout
5669 \begin_layout Standard
5670 \begin_inset space \hfill{}
5674 \begin_inset Tabular
5675 <lyxtabular version="3" rows="9" columns="2">
5677 <column alignment="center" valignment="top" width="0pt">
5678 <column alignment="center" valignment="top" width="0pt">
5680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5683 \begin_layout Plain Layout
5689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5692 \begin_layout Plain Layout
5700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5703 \begin_layout Plain Layout
5709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5712 \begin_layout Plain Layout
5713 \begin_inset Formula $($
5723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5726 \begin_layout Plain Layout
5732 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5735 \begin_layout Plain Layout
5736 \begin_inset Formula $\{$
5746 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5749 \begin_layout Plain Layout
5755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5758 \begin_layout Plain Layout
5759 \begin_inset Formula $[$
5769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5772 \begin_layout Plain Layout
5780 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5783 \begin_layout Plain Layout
5784 \begin_inset Formula $\langle$
5794 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5797 \begin_layout Plain Layout
5805 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5808 \begin_layout Plain Layout
5809 \begin_inset Formula $\lceil$
5819 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5822 \begin_layout Plain Layout
5830 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5833 \begin_layout Plain Layout
5834 \begin_inset Formula $\lfloor$
5844 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5847 \begin_layout Plain Layout
5853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5856 \begin_layout Plain Layout
5857 \begin_inset Formula $/$
5867 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5870 \begin_layout Plain Layout
5876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5879 \begin_layout Plain Layout
5880 \begin_inset Formula $|$
5894 \begin_inset space \hfill{}
5898 \begin_inset Tabular
5899 <lyxtabular version="3" rows="9" columns="2">
5901 <column alignment="center" valignment="top" width="0pt">
5902 <column alignment="center" valignment="top" width="0pt">
5904 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5907 \begin_layout Plain Layout
5913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5916 \begin_layout Plain Layout
5924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5927 \begin_layout Plain Layout
5933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5936 \begin_layout Plain Layout
5937 \begin_inset Formula $)$
5947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5950 \begin_layout Plain Layout
5956 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5959 \begin_layout Plain Layout
5960 \begin_inset Formula $\}$
5970 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5973 \begin_layout Plain Layout
5979 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5982 \begin_layout Plain Layout
5983 \begin_inset Formula $]$
5993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5996 \begin_layout Plain Layout
6004 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6007 \begin_layout Plain Layout
6008 \begin_inset Formula $\rangle$
6018 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6021 \begin_layout Plain Layout
6029 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6032 \begin_layout Plain Layout
6033 \begin_inset Formula $\rceil$
6043 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6046 \begin_layout Plain Layout
6054 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6057 \begin_layout Plain Layout
6058 \begin_inset Formula $\rfloor$
6068 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6071 \begin_layout Plain Layout
6081 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6084 \begin_layout Plain Layout
6085 \begin_inset Formula $\backslash$
6095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6098 \begin_layout Plain Layout
6106 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6109 \begin_layout Plain Layout
6110 \begin_inset Formula $\|$
6124 \begin_inset space \hfill{}
6130 \begin_layout Standard
6133 \begin_inset Note Greyedout
6136 \begin_layout Plain Layout
6141 In TeX-mode the command
6151 \begin_layout Plain Layout
6159 must be used for the backslash, because the command
6167 produces there a line break.
6175 \begin_layout Standard
6176 For all characters listed above the size can be adjusted with the commands
6177 described in the following two subsections.
6178 When using these commands, the characters < and > can directly be used
6179 instead of the commands
6194 \begin_layout Subsubsection
6196 \begin_inset CommandInset label
6198 name "sub:Manual-Bracket-Size"
6206 \begin_layout Plain Layout
6207 Bracket size ! manual
6215 \begin_layout Standard
6216 The bracket size can be specified manually by the LaTeX-commands
6226 \begin_layout Plain Layout
6259 denotes the smallest and
6265 the largest bracket size.
6268 \begin_layout Standard
6269 These commands are used to emphasize levels of brackets:
6272 \begin_layout Standard
6274 \begin_inset Tabular
6275 <lyxtabular version="3" rows="2" columns="2">
6277 <column alignment="center" valignment="top" width="0pt">
6278 <column alignment="center" valignment="top" width="0pt">
6280 <cell alignment="center" valignment="top" usebox="none">
6283 \begin_layout Plain Layout
6284 all brackets in the same size:
6289 <cell alignment="center" valignment="top" usebox="none">
6292 \begin_layout Plain Layout
6293 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6303 <cell alignment="center" valignment="top" usebox="none">
6306 \begin_layout Plain Layout
6312 <cell alignment="center" valignment="top" usebox="none">
6315 \begin_layout Plain Layout
6316 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6330 \begin_inset Note Note
6333 \begin_layout Plain Layout
6340 is only used as spacer.
6348 \begin_layout Standard
6349 For the second formula the command
6359 \begin_layout Plain Layout
6373 \begin_layout Standard
6374 Here is an overview about all bracket sizes:
6377 \begin_layout Standard
6397 \begin_layout Plain Layout
6414 \begin_layout Plain Layout
6427 \begin_layout Plain Layout
6443 \begin_layout Standard
6445 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6451 \begin_layout Standard
6452 \begin_inset Newpage newpage
6461 -commands there is the variant
6471 \begin_layout Plain Layout
6479 that adds a bit more space between the bracket and its content, and the
6496 \begin_layout Plain Layout
6506 , that don't add additional space.
6511 at the end of the command
6517 is for a left bracket; for a right bracket this will be replaced by an
6523 A left or right bracket can each be an opening or closing bracket.
6526 \begin_layout Standard
6527 In the following table is a comparison of the variants:
6530 \begin_layout Standard
6532 \begin_inset Tabular
6533 <lyxtabular version="3" rows="5" columns="2">
6535 <column alignment="center" valignment="middle" width="0">
6536 <column alignment="center" valignment="middle" width="0">
6538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6541 \begin_layout Plain Layout
6547 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6550 \begin_layout Plain Layout
6552 \begin_inset Note Note
6555 \begin_layout Plain Layout
6562 is only used as spacer.
6574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6577 \begin_layout Plain Layout
6592 \begin_layout Plain Layout
6610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6613 \begin_layout Plain Layout
6614 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6627 \begin_layout Plain Layout
6642 \begin_layout Plain Layout
6660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6663 \begin_layout Plain Layout
6664 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
6674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6677 \begin_layout Plain Layout
6692 \begin_layout Plain Layout
6710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6713 \begin_layout Plain Layout
6714 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
6724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6727 \begin_layout Plain Layout
6739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6742 \begin_layout Plain Layout
6743 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
6759 \begin_layout Subsubsection
6760 Automatic Bracket Size
6761 \begin_inset CommandInset label
6763 name "sub:Automatic-Bracket-Size"
6771 \begin_layout Plain Layout
6772 Bracket size ! automatic
6780 \begin_layout Standard
6781 Brackets with variable size can be inserted with the commands
6791 \begin_layout Plain Layout
6809 \begin_layout Plain Layout
6817 or via the math toolbar button
6818 \begin_inset Graphics
6819 filename ../images/dialog-show_mathdelimiter.png
6837 the wanted bracket must be inserted.
6838 The bracket size will then automatically be calculated for the output.
6841 \begin_layout Standard
6843 normal bracket: The command
6853 \begin_layout Plain Layout
6863 \begin_inset Formula $\downarrow$
6870 \begin_layout Plain Layout
6882 \begin_inset Formula \[
6890 \begin_layout Standard
6892 multiline bracket: The command
6904 \begin_layout Plain Layout
6914 \begin_inset Formula $\downarrow$
6921 \begin_layout Plain Layout
6935 \begin_inset Formula \[
6936 \ln\left(\frac{A}{C}\right)\]
6943 \begin_layout Standard
6959 \begin_inset space ~
6965 This has the advantage that you can see in LyX immediately the real bracket
6966 size and that the matching right bracket will be created too.
6967 \begin_inset Newline newline
6970 The command for the last example would then be:
6984 \begin_layout Plain Layout
6994 \begin_inset Formula $\downarrow$
7000 \begin_layout Standard
7001 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7002 For example the command
7012 \begin_layout Plain Layout
7022 \begin_inset Formula $\downarrow$
7029 \begin_layout Plain Layout
7045 \begin_inset Formula \[
7046 \left.\frac{A}{B}\right\} \]
7064 will be converted by LyX to brackets in the right size when the document
7065 is reloaded and an omitted bracket will appear as dashed line.
7068 \begin_layout Standard
7069 \begin_inset VSpace bigskip
7072 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7083 \begin_layout Plain Layout
7091 is additionally available for all brackets and limits.
7092 With this command the height of the following character is adapted to the
7093 one of the surrounding brackets, what is e.
7094 \begin_inset space \thinspace{}
7098 \begin_inset space ~
7101 needed for physical vectors:
7102 \begin_inset Formula \[
7103 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7107 For physical vectors there is a special LaTeX-package, described in
7108 \begin_inset CommandInset ref
7110 reference "sub:Physical-Vectors"
7117 \begin_layout Subsection
7122 \begin_layout Plain Layout
7123 Brackets ! horizontal
7131 \begin_layout Standard
7133 \begin_inset Tabular
7134 <lyxtabular version="3" rows="4" columns="2">
7136 <column alignment="center" valignment="top" width="0pt">
7137 <column alignment="center" valignment="top" width="0pt">
7139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7142 \begin_layout Plain Layout
7144 \begin_inset Note Note
7147 \begin_layout Plain Layout
7154 is only used as spacer.
7164 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7167 \begin_layout Plain Layout
7175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7178 \begin_layout Plain Layout
7182 \begin_layout Plain Layout
7197 \begin_layout Plain Layout
7210 \begin_layout Plain Layout
7223 \begin_layout Plain Layout
7236 \begin_layout Plain Layout
7247 \begin_layout Plain Layout
7260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7263 \begin_layout Plain Layout
7264 \begin_inset Formula $\overbrace{A+B}^{3}$
7274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7277 \begin_layout Plain Layout
7281 \begin_layout Plain Layout
7296 \begin_layout Plain Layout
7309 \begin_layout Plain Layout
7322 \begin_layout Plain Layout
7333 \begin_layout Plain Layout
7346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7349 \begin_layout Plain Layout
7350 \begin_inset Formula $\underbrace{A+B}_{5}$
7360 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7363 \begin_layout Plain Layout
7370 \begin_layout Plain Layout
7385 \begin_layout Plain Layout
7398 \begin_layout Plain Layout
7411 \begin_layout Plain Layout
7424 \begin_layout Plain Layout
7437 \begin_layout Plain Layout
7450 \begin_layout Plain Layout
7464 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7467 \begin_layout Plain Layout
7468 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7484 \begin_layout Standard
7485 In the last example it doesn't matter if
7497 is inserted at first.
7500 \begin_layout Standard
7501 \begin_inset VSpace bigskip
7504 When brackets are needed that overlap each other, multiline formulas, as
7506 \begin_inset CommandInset ref
7508 reference "sec:Multiline-Formulas"
7513 \begin_inset Formula \begin{eqnarray*}
7514 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7515 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7519 In the first row the formula is inserted together with the first brace.
7520 It is hereby important that the space command
7524 \begin_layout Plain Layout
7525 Space commands are explained in
7526 \begin_inset CommandInset ref
7528 reference "sub:Predefined-Space"
7543 is inserted before the first
7544 \begin_inset Formula $d$
7547 , because the brace that ends behind the
7548 \begin_inset Formula $q$
7551 prevents that the following
7552 \begin_inset Quotes eld
7556 \begin_inset Quotes erd
7559 is surrounded by space.
7563 \begin_layout Plain Layout
7564 because a bracket is not handled as character, see
7565 \begin_inset CommandInset ref
7567 reference "sub:Binary-Operators"
7576 In the second row the second brace is inserted.
7577 As it should begin before the
7578 \begin_inset Formula $b$
7593 \begin_layout Plain Layout
7601 \begin_inset CommandInset ref
7603 reference "sub:Placeholders"
7612 This space is needed because the
7613 \begin_inset Quotes eld
7617 \begin_inset Quotes erd
7620 is also surrounded by space in the formula.
7621 The brace is placed under the command
7630 \begin_layout Standard
7631 It gets more complicated when brackets overlap each other, like in the following
7636 \begin_layout Plain Layout
7648 \begin_inset Formula \begin{eqnarray*}
7649 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7650 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7658 \begin_layout Plain Layout
7669 The first formula row is the same as the second row of the previous example,
7670 with the difference that the brace is above.
7671 The second row contains the formula together with the second brace.
7672 To avoid that there is space between the upper brace in the first row and
7673 the formula, the row spacing need to be reduced.
7674 This is not easily possible due to a bug in LyX
7678 \begin_layout Plain Layout
7679 \begin_inset CommandInset href
7681 name "LyX-bug #1505"
7682 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7692 As solution for the problem, the global formula row separation
7702 \begin_layout Plain Layout
7710 must be changed to -6
7711 \begin_inset space \thinspace{}
7714 pt before the formula with the command
7729 is set back after the formula to the standard value of 3
7730 \begin_inset space \thinspace{}
7733 pt using the same command.
7734 More about the row separation in formulas is explained in
7735 \begin_inset CommandInset ref
7737 reference "sub:Line-Separation"
7744 \begin_layout Section
7749 \begin_layout Plain Layout
7758 \begin_layout Standard
7759 Arrows can be inserted via the math toolbar button
7760 \begin_inset Graphics
7761 filename ../images/math/leftarrow.png
7766 or the commands listed in the following subsections.
7769 \begin_layout Subsection
7774 \begin_layout Plain Layout
7783 \begin_layout Standard
7784 \begin_inset space \hfill{}
7788 \begin_inset Tabular
7789 <lyxtabular version="3" rows="8" columns="2">
7791 <column alignment="center" valignment="top" width="0pt">
7792 <column alignment="center" valignment="top" width="0pt">
7794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7797 \begin_layout Plain Layout
7803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7806 \begin_layout Plain Layout
7814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7817 \begin_layout Plain Layout
7825 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7828 \begin_layout Plain Layout
7829 \begin_inset Formula $\gets$
7839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7842 \begin_layout Plain Layout
7850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7853 \begin_layout Plain Layout
7854 \begin_inset Formula $\Leftarrow$
7864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7867 \begin_layout Plain Layout
7875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7878 \begin_layout Plain Layout
7879 \begin_inset Formula $\longleftarrow$
7889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7892 \begin_layout Plain Layout
7900 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7903 \begin_layout Plain Layout
7904 \begin_inset Formula $\Longleftarrow$
7914 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7917 \begin_layout Plain Layout
7925 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7928 \begin_layout Plain Layout
7929 \begin_inset Formula $\leftharpoonup$
7939 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7942 \begin_layout Plain Layout
7950 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7953 \begin_layout Plain Layout
7954 \begin_inset Formula $\leftharpoondown$
7964 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7967 \begin_layout Plain Layout
7975 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7978 \begin_layout Plain Layout
7979 \begin_inset Formula $\hookleftarrow$
7993 \begin_inset space \hfill{}
7997 \begin_inset Tabular
7998 <lyxtabular version="3" rows="8" columns="2">
8000 <column alignment="center" valignment="top" width="0pt">
8001 <column alignment="center" valignment="top" width="0pt">
8003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8006 \begin_layout Plain Layout
8012 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8015 \begin_layout Plain Layout
8023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8026 \begin_layout Plain Layout
8034 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8037 \begin_layout Plain Layout
8038 \begin_inset Formula $\to$
8048 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8051 \begin_layout Plain Layout
8059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8062 \begin_layout Plain Layout
8063 \begin_inset Formula $\Rightarrow$
8073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8076 \begin_layout Plain Layout
8084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8087 \begin_layout Plain Layout
8088 \begin_inset Formula $\longrightarrow$
8098 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8101 \begin_layout Plain Layout
8109 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8112 \begin_layout Plain Layout
8113 \begin_inset Formula $\Longrightarrow$
8123 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8126 \begin_layout Plain Layout
8134 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8137 \begin_layout Plain Layout
8138 \begin_inset Formula $\rightharpoonup$
8148 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8151 \begin_layout Plain Layout
8159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8162 \begin_layout Plain Layout
8163 \begin_inset Formula $\rightharpoondown$
8173 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8176 \begin_layout Plain Layout
8184 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8187 \begin_layout Plain Layout
8188 \begin_inset Formula $\hookrightarrow$
8202 \begin_inset space \hfill{}
8208 \begin_layout Standard
8209 \begin_inset space \hfill{}
8213 \begin_inset Tabular
8214 <lyxtabular version="3" rows="6" columns="2">
8216 <column alignment="center" valignment="top" width="0pt">
8217 <column alignment="center" valignment="top" width="0pt">
8219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8222 \begin_layout Plain Layout
8228 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8231 \begin_layout Plain Layout
8239 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8242 \begin_layout Plain Layout
8250 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8253 \begin_layout Plain Layout
8254 \begin_inset Formula $\leftrightarrow$
8264 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8267 \begin_layout Plain Layout
8275 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8278 \begin_layout Plain Layout
8279 \begin_inset Formula $\Leftrightarrow$
8289 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8292 \begin_layout Plain Layout
8300 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8303 \begin_layout Plain Layout
8304 \begin_inset Formula $\longleftrightarrow$
8314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8317 \begin_layout Plain Layout
8325 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8328 \begin_layout Plain Layout
8329 \begin_inset Formula $\Longleftrightarrow$
8339 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8342 \begin_layout Plain Layout
8350 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8353 \begin_layout Plain Layout
8354 \begin_inset Formula $\rightleftharpoons$
8368 \begin_inset space \hspace{}
8373 \begin_inset space \hfill{}
8377 \begin_inset Tabular
8378 <lyxtabular version="3" rows="5" columns="2">
8380 <column alignment="center" valignment="top" width="0pt">
8381 <column alignment="center" valignment="top" width="0pt">
8383 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8386 \begin_layout Plain Layout
8392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8395 \begin_layout Plain Layout
8403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8406 \begin_layout Plain Layout
8414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8417 \begin_layout Plain Layout
8418 \begin_inset Formula $\mapsto$
8428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8431 \begin_layout Plain Layout
8439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8442 \begin_layout Plain Layout
8443 \begin_inset Formula $\longmapsto$
8453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8456 \begin_layout Plain Layout
8464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8467 \begin_layout Plain Layout
8468 \begin_inset Formula $\leadsto$
8478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8481 \begin_layout Plain Layout
8489 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8492 \begin_layout Plain Layout
8493 \begin_inset Formula $\dasharrow$
8507 \begin_inset space \hfill{}
8513 \begin_layout Standard
8514 \begin_inset VSpace medskip
8517 Arrows used as accent like e.
8518 \begin_inset space \thinspace{}
8522 \begin_inset space ~
8525 vector arrows are listed in
8526 \begin_inset CommandInset ref
8528 reference "sec:Accents"
8535 \begin_layout Standard
8536 \begin_inset VSpace bigskip
8539 Furthermore there are the labeled arrows
8543 \begin_layout Plain Layout
8559 \begin_layout Plain Layout
8577 \begin_layout Plain Layout
8584 \begin_layout Plain Layout
8599 When inserting one of these commands in a formula, an arrow with two blue
8600 boxes appear where the label can be inserted.
8601 The length of the arrow adapts to the label width.
8604 \begin_layout Standard
8606 \begin_inset Tabular
8607 <lyxtabular version="3" rows="3" columns="2">
8609 <column alignment="center" valignment="top" width="0pt">
8610 <column alignment="center" valignment="top" width="0pt">
8612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8615 \begin_layout Plain Layout
8621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8624 \begin_layout Plain Layout
8626 \begin_inset Note Note
8629 \begin_layout Plain Layout
8636 is only used as spacer.
8648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8651 \begin_layout Plain Layout
8658 \begin_layout Plain Layout
8668 \begin_inset Formula $\downarrow$
8672 \begin_inset Formula $\to$
8680 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8683 \begin_layout Plain Layout
8684 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
8694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8697 \begin_layout Plain Layout
8704 \begin_layout Plain Layout
8714 \begin_inset Formula $\downarrow$
8718 \begin_inset Formula $\to$
8726 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8729 \begin_layout Plain Layout
8730 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
8746 \begin_layout Subsection
8747 Vertical and diagonal Arrows
8751 \begin_layout Plain Layout
8761 \begin_layout Plain Layout
8770 \begin_layout Standard
8771 \begin_inset space \hfill{}
8775 \begin_inset Tabular
8776 <lyxtabular version="3" rows="7" columns="2">
8778 <column alignment="center" valignment="top" width="0pt">
8779 <column alignment="center" valignment="top" width="0pt">
8781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8784 \begin_layout Plain Layout
8790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8793 \begin_layout Plain Layout
8801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8804 \begin_layout Plain Layout
8812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8815 \begin_layout Plain Layout
8816 \begin_inset Formula $\uparrow$
8826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8829 \begin_layout Plain Layout
8837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8840 \begin_layout Plain Layout
8841 \begin_inset Formula $\Uparrow$
8851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8854 \begin_layout Plain Layout
8862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8865 \begin_layout Plain Layout
8866 \begin_inset Formula $\updownarrow$
8876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8879 \begin_layout Plain Layout
8887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8890 \begin_layout Plain Layout
8891 \begin_inset Formula $\Updownarrow$
8901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8904 \begin_layout Plain Layout
8912 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8915 \begin_layout Plain Layout
8916 \begin_inset Formula $\Downarrow$
8926 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8929 \begin_layout Plain Layout
8937 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8940 \begin_layout Plain Layout
8941 \begin_inset Formula $\downarrow$
8955 \begin_inset space \hfill{}
8959 \begin_inset Tabular
8960 <lyxtabular version="3" rows="5" columns="2">
8962 <column alignment="center" valignment="top" width="0pt">
8963 <column alignment="center" valignment="top" width="0pt">
8965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8968 \begin_layout Plain Layout
8974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8977 \begin_layout Plain Layout
8985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8988 \begin_layout Plain Layout
8996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8999 \begin_layout Plain Layout
9000 \begin_inset Formula $\nearrow$
9010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9013 \begin_layout Plain Layout
9021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9024 \begin_layout Plain Layout
9025 \begin_inset Formula $\searrow$
9035 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9038 \begin_layout Plain Layout
9046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9049 \begin_layout Plain Layout
9050 \begin_inset Formula $\swarrow$
9060 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9063 \begin_layout Plain Layout
9071 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9074 \begin_layout Plain Layout
9075 \begin_inset Formula $\nwarrow$
9089 \begin_inset space \hfill{}
9095 \begin_layout Standard
9096 \begin_inset VSpace medskip
9099 Vertical arrows can be used also as delimiter together with the commands
9101 \begin_inset CommandInset ref
9103 reference "sub:Manual-Bracket-Size"
9108 \begin_inset CommandInset ref
9110 reference "sub:Automatic-Bracket-Size"
9117 \begin_layout Standard
9118 \begin_inset Newpage newpage
9124 \begin_layout Section
9126 \begin_inset CommandInset label
9136 \begin_layout Plain Layout
9145 \begin_layout Standard
9146 Accents can be inserted via the math toolbar button
9147 \begin_inset Graphics
9148 filename ../images/math/hat.png
9153 or the commands listed in the following subsections.
9156 \begin_layout Subsection
9157 Accents for one Character
9161 \begin_layout Plain Layout
9174 \begin_layout Plain Layout
9176 \begin_inset CommandInset ref
9178 reference "sub:Accents-in-Text"
9191 \begin_layout Plain Layout
9199 \begin_inset Note Note
9202 \begin_layout Plain Layout
9205 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9208 \begin_layout Plain Layout
9211 texorpdfstring is in section
9212 \begin_inset CommandInset ref
9214 reference "sub:Formulas-in-Section"
9224 \begin_inset CommandInset label
9226 name "sub:Accents-for-one"
9234 \begin_layout Plain Layout
9235 Accents ! for one character
9243 \begin_layout Standard
9244 \begin_inset space \hfill{}
9248 \begin_inset Tabular
9249 <lyxtabular version="3" rows="8" columns="2">
9251 <column alignment="center" valignment="top" width="0pt">
9252 <column alignment="center" valignment="top" width="0pt">
9254 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9257 \begin_layout Plain Layout
9263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9266 \begin_layout Plain Layout
9268 \begin_inset Note Note
9271 \begin_layout Plain Layout
9278 is only used as spacer.
9290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9293 \begin_layout Plain Layout
9300 \begin_layout Plain Layout
9314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9317 \begin_layout Plain Layout
9318 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9331 \begin_layout Plain Layout
9338 \begin_layout Plain Layout
9352 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9355 \begin_layout Plain Layout
9356 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9366 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9369 \begin_layout Plain Layout
9376 \begin_layout Plain Layout
9390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9393 \begin_layout Plain Layout
9394 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9407 \begin_layout Plain Layout
9415 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9418 \begin_layout Plain Layout
9419 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9429 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9432 \begin_layout Plain Layout
9439 \begin_layout Plain Layout
9452 \begin_layout Plain Layout
9463 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9466 \begin_layout Plain Layout
9467 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9477 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9480 \begin_layout Plain Layout
9487 \begin_layout Plain Layout
9501 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9504 \begin_layout Plain Layout
9505 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9515 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9518 \begin_layout Plain Layout
9525 \begin_layout Plain Layout
9539 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9542 \begin_layout Plain Layout
9543 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9557 \begin_inset space \hfill{}
9561 \begin_inset Tabular
9562 <lyxtabular version="3" rows="7" columns="2">
9564 <column alignment="center" valignment="top" width="0pt">
9565 <column alignment="center" valignment="top" width="0pt">
9567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9570 \begin_layout Plain Layout
9576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9579 \begin_layout Plain Layout
9587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9590 \begin_layout Plain Layout
9597 \begin_layout Plain Layout
9611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9614 \begin_layout Plain Layout
9615 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9625 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9628 \begin_layout Plain Layout
9635 \begin_layout Plain Layout
9649 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9652 \begin_layout Plain Layout
9653 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
9663 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9666 \begin_layout Plain Layout
9673 \begin_layout Plain Layout
9687 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9690 \begin_layout Plain Layout
9691 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
9701 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9704 \begin_layout Plain Layout
9711 \begin_layout Plain Layout
9725 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9728 \begin_layout Plain Layout
9729 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
9739 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9742 \begin_layout Plain Layout
9749 \begin_layout Plain Layout
9763 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9766 \begin_layout Plain Layout
9767 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
9777 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9780 \begin_layout Plain Layout
9787 \begin_layout Plain Layout
9801 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9804 \begin_layout Plain Layout
9805 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
9819 \begin_inset space \hfill{}
9825 \begin_layout Standard
9826 \begin_inset VSpace bigskip
9833 \begin_layout Plain Layout
9839 in formulas, a quotation mark is inserted before the vowel.
9840 These two characters are then treated by LaTeX as
9844 character when the formula part with the umlaut is marked as German.
9852 \begin_inset Quotes eld
9856 \begin_inset Quotes erd
9859 umlauts are created as demonstrated in the following example:
9862 \begin_layout Standard
9863 \begin_inset VSpace -2mm
9869 \begin_layout Standard
9871 \begin_inset Tabular
9872 <lyxtabular version="3" rows="3" columns="2">
9874 <column alignment="center" valignment="top" width="0">
9875 <column alignment="center" valignment="top" width="0">
9877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9880 \begin_layout Plain Layout
9886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9889 \begin_layout Plain Layout
9891 \begin_inset Note Note
9894 \begin_layout Plain Layout
9901 is only used as spacer.
9913 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9916 \begin_layout Plain Layout
9919 \begin_inset Quotes grd
9927 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9930 \begin_layout Plain Layout
9933 \begin_inset Formula $"i$
9943 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9946 \begin_layout Plain Layout
9953 \begin_layout Plain Layout
9967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9970 \begin_layout Plain Layout
9971 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
9987 \begin_layout Standard
9988 Another advantage to
9994 is that umlauts can directly be converted to mathematical text because
9995 the accent commands above are
10001 in mathematical text
10004 To convert an accented character to mathematical text, only the character
10005 under the accent may be converted.
10006 This applies also for all other conversions, e.
10007 \begin_inset space \thinspace{}
10011 \begin_inset space ~
10017 \begin_layout Standard
10018 In mathematical text, umlauts and other accented characters can directly
10022 \begin_layout Subsection
10023 Accents for Operators
10027 \begin_layout Plain Layout
10028 Accents ! for operators
10036 \begin_layout Standard
10047 \begin_layout Plain Layout
10065 \begin_layout Plain Layout
10073 characters can be placed above or below an operator, respectively, to accent
10085 \begin_layout Plain Layout
10093 characters can be set before and behind an operator.
10094 The command scheme is:
10097 \begin_layout Standard
10113 \begin_layout Standard
10120 must always be before the operator that should be accented.
10121 You can accent with several characters and even with other operators and
10129 for example only characters behind an operator, write nothing between the
10130 first braces but don't omit the braces.
10133 \begin_layout Standard
10134 For example the command
10139 \begin_inset Formula $\to$
10149 \begin_inset Formula $\to$
10158 \begin_layout Plain Layout
10174 \begin_inset Formula \[
10175 \sideset{}{'}\sum_{k=1}^{n}\]
10182 \begin_layout Standard
10191 \begin_layout Plain Layout
10206 \begin_layout Plain Layout
10218 \begin_inset Formula $\uparrow$
10226 \begin_inset Formula \[
10227 \overset{a}{\maltese}\]
10231 As seen in the last example, with
10243 also symbols and characters can be accented; with
10249 this is not possible.
10252 \begin_layout Subsection
10253 Accents for several Characters
10254 \begin_inset CommandInset label
10256 name "sub:Accents-for-several"
10264 \begin_layout Plain Layout
10265 Accents ! for several characters
10273 \begin_layout Standard
10274 \begin_inset space \hfill{}
10278 \begin_inset Tabular
10279 <lyxtabular version="3" rows="5" columns="2">
10281 <column alignment="center" valignment="top" width="0pt">
10282 <column alignment="center" valignment="top" width="0pt">
10284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10287 \begin_layout Plain Layout
10293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10296 \begin_layout Plain Layout
10298 \begin_inset Note Note
10301 \begin_layout Plain Layout
10308 is only used as spacer.
10320 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10323 \begin_layout Plain Layout
10330 \begin_layout Plain Layout
10344 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10347 \begin_layout Plain Layout
10348 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10361 \begin_layout Plain Layout
10368 \begin_layout Plain Layout
10382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10385 \begin_layout Plain Layout
10386 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10399 \begin_layout Plain Layout
10406 \begin_layout Plain Layout
10420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10423 \begin_layout Plain Layout
10424 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10434 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10437 \begin_layout Plain Layout
10440 underleftrightarrow
10444 \begin_layout Plain Layout
10458 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10461 \begin_layout Plain Layout
10462 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10476 \begin_inset space \hfill{}
10480 \begin_inset Tabular
10481 <lyxtabular version="3" rows="5" columns="2">
10483 <column alignment="center" valignment="top" width="0pt">
10484 <column alignment="center" valignment="top" width="0pt">
10486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10489 \begin_layout Plain Layout
10495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10498 \begin_layout Plain Layout
10506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10509 \begin_layout Plain Layout
10516 \begin_layout Plain Layout
10530 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10533 \begin_layout Plain Layout
10534 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10547 \begin_layout Plain Layout
10554 \begin_layout Plain Layout
10568 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10571 \begin_layout Plain Layout
10572 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10582 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10585 \begin_layout Plain Layout
10592 \begin_layout Plain Layout
10606 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10609 \begin_layout Plain Layout
10610 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10620 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10623 \begin_layout Plain Layout
10630 \begin_layout Plain Layout
10644 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10647 \begin_layout Plain Layout
10648 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10662 \begin_inset space \hfill{}
10668 \begin_layout Standard
10669 \begin_inset VSpace medskip
10672 With these commands as many characters as you like can be accented.
10685 will only be set in the output with a length of three characters, as shown
10686 in the following example:
10687 \begin_inset Formula \[
10688 \widetilde{A+B=C-D}\]
10695 \begin_layout Standard
10706 \begin_layout Plain Layout
10724 \begin_layout Plain Layout
10732 described in the previous subsection it is also possible to accent several
10742 \begin_layout Plain Layout
10752 \begin_inset Formula $\downarrow$
10758 \begin_inset Formula \[
10759 \underset{***}{A=B}\]
10766 \begin_layout Section
10768 \begin_inset CommandInset label
10778 \begin_layout Plain Layout
10787 \begin_layout Subsection
10789 \begin_inset CommandInset label
10791 name "sub:Predefined-Space"
10799 \begin_layout Plain Layout
10800 Space ! horizontal ! predefined
10808 \begin_layout Standard
10809 Sometimes it is necessary to insert horizontal space to a formula.
10810 This is done by inserting a protected space (shortcut
10816 \begin_inset Quotes eld
10826 \begin_layout Plain Layout
10839 \begin_inset Quotes erd
10842 appears and by pressing
10846 several times one can select one of eight different space sizes.
10847 The spaces can also be inserted using the math toolbar button
10848 \begin_inset Graphics
10849 filename ../images/math/space.png
10854 or special commands.
10855 Independent from the inserted command, one can select the size again by
10863 \begin_layout Standard
10866 \begin_inset VSpace -5mm
10870 \begin_inset Tabular
10871 <lyxtabular version="3" rows="3" columns="7">
10873 <column alignment="center" valignment="middle" width="6.8cm">
10874 <column alignment="center" valignment="top" width="0">
10875 <column alignment="center" valignment="top" width="0">
10876 <column alignment="center" valignment="top" width="0">
10877 <column alignment="center" valignment="top" width="0">
10878 <column alignment="center" valignment="top" width="0">
10879 <column alignment="center" valignment="top" width="0">
10881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10884 \begin_layout Plain Layout
10890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10893 \begin_layout Plain Layout
10901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10904 \begin_layout Plain Layout
10912 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10915 \begin_layout Plain Layout
10923 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10926 \begin_layout Plain Layout
10934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10937 \begin_layout Plain Layout
10945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10948 \begin_layout Plain Layout
10958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10961 \begin_layout Plain Layout
10966 keystrokes after inserting the protected space
10971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10974 \begin_layout Plain Layout
10980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10983 \begin_layout Plain Layout
10989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10992 \begin_layout Plain Layout
10998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11007 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11010 \begin_layout Plain Layout
11016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11019 \begin_layout Plain Layout
11027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11030 \begin_layout Plain Layout
11036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11039 \begin_layout Plain Layout
11040 \begin_inset Formula $A\, B$
11048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11051 \begin_layout Plain Layout
11052 \begin_inset Formula $A\: B$
11060 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11063 \begin_layout Plain Layout
11064 \begin_inset Formula $A\; B$
11072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11075 \begin_layout Plain Layout
11076 \begin_inset Formula $A\quad B$
11084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11087 \begin_layout Plain Layout
11088 \begin_inset Formula $A\qquad B$
11096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11099 \begin_layout Plain Layout
11100 \begin_inset Formula $A\! B$
11116 \begin_layout Standard
11117 The last size seem to produce no space.
11118 It is displayed red in LyX contrary to the other sizes, because it is a
11120 There are two more negative spaces:
11123 \begin_layout Standard
11125 \begin_inset Tabular
11126 <lyxtabular version="3" rows="3" columns="3">
11128 <column alignment="center" valignment="middle" width="6.8cm">
11129 <column alignment="center" valignment="top" width="0pt">
11130 <column alignment="center" valignment="top" width="0pt">
11132 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11135 \begin_layout Plain Layout
11141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11144 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11155 \begin_layout Plain Layout
11165 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11168 \begin_layout Plain Layout
11173 keystrokes after inserting the protected space
11178 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11181 \begin_layout Plain Layout
11187 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11190 \begin_layout Plain Layout
11198 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11201 \begin_layout Plain Layout
11207 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11210 \begin_layout Plain Layout
11211 \begin_inset Formula $A\negmedspace B$
11219 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11223 \begin_inset Formula $A\negthickspace B$
11239 \begin_layout Standard
11240 Negative spaces can lead to characters overlapping each other.
11241 Thus they can be used to enforce ligatures, what is e.
11242 \begin_inset space \thinspace{}
11246 \begin_inset space ~
11249 useful for summation operators:
11252 \begin_layout Standard
11254 \begin_inset Tabular
11255 <lyxtabular version="3" rows="3" columns="2">
11257 <column alignment="center" valignment="top" width="0">
11258 <column alignment="center" valignment="top" width="0">
11260 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11263 \begin_layout Plain Layout
11269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11272 \begin_layout Plain Layout
11274 \begin_inset Note Note
11277 \begin_layout Plain Layout
11284 is only used as spacer.
11296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11299 \begin_layout Plain Layout
11308 \begin_layout Plain Layout
11322 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11325 \begin_layout Plain Layout
11326 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11336 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11339 \begin_layout Plain Layout
11350 \begin_layout Plain Layout
11364 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11367 \begin_layout Plain Layout
11368 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11384 \begin_layout Standard
11385 Relations like for example equal signs, are always surrounded by space.
11386 To suppress this, the equal sign is placed into a TeX-brace.
11387 The following example demonstrates this:
11390 \begin_layout Standard
11392 \begin_inset Tabular
11393 <lyxtabular version="3" rows="2" columns="2">
11395 <column alignment="center" valignment="top" width="0pt">
11396 <column alignment="center" valignment="top" width="0pt">
11398 <cell alignment="center" valignment="top" usebox="none">
11401 \begin_layout Plain Layout
11407 <cell alignment="center" valignment="top" usebox="none">
11410 \begin_layout Plain Layout
11411 \begin_inset Formula $A=B$
11421 <cell alignment="center" valignment="top" usebox="none">
11424 \begin_layout Plain Layout
11425 \begin_inset Note Note
11428 \begin_layout Plain Layout
11435 is only used as spacer.
11441 \begin_inset Formula $\raisebox{5mm}{}$
11444 equation without space
11449 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11452 \begin_layout Plain Layout
11453 \begin_inset Formula $A{=}B$
11469 \begin_layout Standard
11471 The command for the last formula is:
11476 \begin_inset Formula $\to$
11482 \begin_layout Standard
11483 \begin_inset VSpace bigskip
11486 Spaces are needed for physical units, because the space between the value
11487 and the unit is the smallest one and not a normal space.
11488 For units in text, the smallest space is inserted via the menu
11490 Insert\SpecialChar \menuseparator
11491 Formatting\SpecialChar \menuseparator
11493 \begin_inset space ~
11505 \begin_layout Standard
11506 An example to visualize the difference:
11509 \begin_layout Standard
11510 \begin_inset Tabular
11511 <lyxtabular version="3" rows="2" columns="2">
11513 <column alignment="left" valignment="top" width="0">
11514 <column alignment="left" valignment="top" width="0">
11516 <cell alignment="center" valignment="top" usebox="none">
11519 \begin_layout Plain Layout
11521 \begin_inset Formula $\cdot$
11529 <cell alignment="center" valignment="top" usebox="none">
11532 \begin_layout Plain Layout
11533 space between value and unit
11540 <cell alignment="center" valignment="top" usebox="none">
11543 \begin_layout Plain Layout
11545 \begin_inset space \thinspace{}
11549 \begin_inset Formula $\cdot$
11557 <cell alignment="center" valignment="top" usebox="none">
11560 \begin_layout Plain Layout
11561 smallest space between value and unit
11574 \begin_layout Subsection
11579 \begin_layout Plain Layout
11592 \begin_layout Plain Layout
11593 for vertical space in formulas see
11594 \begin_inset CommandInset ref
11596 reference "sub:Line-Separation"
11609 \begin_layout Plain Layout
11617 \begin_inset Note Note
11620 \begin_layout Plain Layout
11623 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11626 \begin_layout Plain Layout
11629 texorpdfstring is in section
11630 \begin_inset CommandInset ref
11632 reference "sub:Formulas-in-Section"
11642 \begin_inset CommandInset label
11644 name "sub:Variable-Space"
11652 \begin_layout Plain Layout
11653 Space ! horizontal ! variable
11661 \begin_layout Standard
11662 Space with a defined length can be inserted in LyX with the command
11663 \begin_inset Newline newline
11676 \begin_layout Plain Layout
11685 For the length all units listed in
11686 \begin_inset CommandInset ref
11688 reference "tab:Used-units"
11692 are allowed, except of the unit
11693 \begin_inset Quotes eld
11697 \begin_inset Quotes erd
11701 The length may also be negative.
11702 To insert so many space that the formula uses all available space, the
11713 \begin_layout Plain Layout
11724 \begin_layout Standard
11725 \begin_inset VSpace -1mm
11731 \begin_layout Standard
11733 \begin_inset Tabular
11734 <lyxtabular version="3" rows="4" columns="2">
11736 <column alignment="center" valignment="top" width="0">
11737 <column alignment="center" valignment="top" width="0">
11739 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11742 \begin_layout Plain Layout
11748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11751 \begin_layout Plain Layout
11759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11762 \begin_layout Plain Layout
11766 \begin_inset Formula $\to$
11776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11779 \begin_layout Plain Layout
11780 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
11790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11793 \begin_layout Plain Layout
11797 \begin_inset Formula $\to$
11807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11810 \begin_layout Plain Layout
11811 \begin_inset Formula $A\hspace{-1mm}A\not=A$
11821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11824 \begin_layout Plain Layout
11831 \begin_layout Plain Layout
11845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11848 \begin_layout Plain Layout
11849 \begin_inset Formula $A=A\hfill B=B$
11865 \begin_layout Standard
11866 In the last example the available space is given by the longest column entry
11868 In an inline formula the space depends on the length of the line in which
11876 Thus, when the line uses the full width, no space will be created.
11883 only has an effect on displayed formulas when the formula style
11888 (Formula styles are explained in
11889 \begin_inset CommandInset ref
11891 reference "sec:Formula-Styles"
11898 \begin_layout Standard
11899 For text, variable space can be inserted via the menu
11901 Insert\SpecialChar \menuseparator
11902 Formatting\SpecialChar \menuseparator
11904 \begin_inset space ~
11909 , what is not possible in formulas:
11912 \begin_layout Standard
11913 This is a line with
11914 \begin_inset space \hspace{}
11919 \begin_inset space \thinspace{}
11925 \begin_layout Standard
11926 This is a line with
11927 \begin_inset space \hfill{}
11933 \begin_layout Subsection
11934 Space besides inline Formulas
11938 \begin_layout Plain Layout
11939 Space ! besides inline formulas
11947 \begin_layout Standard
11948 The space that surrounds inline formulas can be adjusted with the length
11957 \begin_layout Plain Layout
11968 The value of a length is set with the command
11976 \begin_layout Plain Layout
11986 that has the following scheme:
11989 \begin_layout Standard
11994 setlength{length name}{value}
11997 \begin_layout Standard
12005 \begin_inset space \thinspace{}
12011 \begin_layout Standard
12021 \begin_layout Standard
12022 is inserted in TeX-mode.
12024 \begin_inset space \thinspace{}
12027 mm space will now be set around all inline formulas:
12031 \begin_layout Plain Layout
12045 \begin_layout Standard
12046 This is a line with an inline formula
12047 \begin_inset Formula $A=B$
12051 \begin_inset space \thinspace{}
12054 mm surrounding space.
12058 \begin_layout Plain Layout
12072 \begin_layout Standard
12073 To return to the predefined value,
12079 is set to the value 0
12080 \begin_inset space \thinspace{}
12086 \begin_layout Section
12091 \begin_layout Plain Layout
12101 \begin_layout Plain Layout
12106 \begin_layout Plain Layout
12117 \begin_layout Plain Layout
12132 \begin_layout Standard
12133 Boxes for text are described in chapter
12140 \begin_inset space ~
12148 \begin_layout Subsection
12150 \begin_inset CommandInset label
12152 name "sub:Boxes-with-Frame"
12160 \begin_layout Plain Layout
12169 \begin_layout Standard
12170 It is possible to frame formulas or parts of it with the commands
12180 \begin_layout Plain Layout
12198 \begin_layout Plain Layout
12209 \begin_layout Standard
12210 When one of these commands is inserted to a formula, a blue box appears
12211 within a frame to enter formula parts.
12218 an additional formula has to be created by
12226 \begin_layout Plain Layout
12227 Due to a bug in LyX it is not possible to create a new formula with
12232 \begin_inset CommandInset href
12234 name "LyX-bug #1435"
12235 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12244 , because the box content will otherwise be treated as mathematical text.
12251 is used, a new formula is automatically created inside the frame.
12254 \begin_layout Standard
12261 is not suitable to frame displayed formulas, because the formula will always
12262 be set in the size of the text.
12269 is in contrary not suitable to frame inline formulas, because the formula
12270 will always be set in the size of a displayed formula.
12273 \begin_layout Standard
12280 there is the command
12290 \begin_layout Plain Layout
12298 where additionally the frame width and the alignment can be specified.
12305 is used in the following scheme:
12308 \begin_layout Standard
12313 framebox[frame width][position]{box content}
12316 \begin_layout Standard
12317 The position can either be
12334 right aligns the formula in the box.
12335 When no position is given, the formula will be centered.
12336 \begin_inset Newline newline
12339 Is no width given, also no position can be given.
12340 In this case the frame width is adjusted to the box content like for
12349 \begin_layout Standard
12356 is inserted, a box appears containing three blue boxes.
12357 The first two boxes are surrounded by brackets and denote the two optional
12359 The third box is for formula parts like for
12368 \begin_layout Standard
12370 \begin_inset Note Note
12373 \begin_layout Plain Layout
12374 The table has been set into a minipage to make the footnote appearing.
12375 Otherwise the footnote text would not be displayed.
12381 \begin_inset Box Frameless
12390 height_special "totalheight"
12393 \begin_layout Plain Layout
12395 \begin_inset Tabular
12396 <lyxtabular version="3" rows="5" columns="2">
12398 <column alignment="center" valignment="top" width="0">
12399 <column alignment="center" valignment="top" width="0">
12401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12404 \begin_layout Plain Layout
12409 \begin_layout Plain Layout
12410 Due to a bug in LyX it is not possible to create a new formula with
12415 \begin_inset CommandInset href
12417 name "LyX-bug #1435"
12418 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12435 \begin_layout Plain Layout
12437 \begin_inset Note Note
12440 \begin_layout Plain Layout
12447 is only used as spacer.
12459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12462 \begin_layout Plain Layout
12469 \begin_layout Plain Layout
12488 \begin_layout Plain Layout
12502 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12505 \begin_layout Plain Layout
12506 \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
12517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12520 \begin_layout Plain Layout
12527 \begin_layout Plain Layout
12542 \begin_layout Plain Layout
12556 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12559 \begin_layout Plain Layout
12560 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12570 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12573 \begin_layout Plain Layout
12580 \begin_layout Plain Layout
12594 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12597 \begin_layout Plain Layout
12598 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12611 \begin_layout Plain Layout
12618 \begin_layout Plain Layout
12628 \begin_inset Formula $\to$
12632 \begin_inset Formula $\to$
12645 \begin_layout Plain Layout
12655 \begin_inset Formula $\downarrow$
12663 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12666 \begin_layout Plain Layout
12667 \begin_inset Formula $\raisebox{6mm}{}$
12671 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12675 \begin_inset Formula $\raisebox{-4mm}{}$
12696 \begin_layout Standard
12697 The frame thickness can also be adjusted.
12698 To do this the following commands have to be inserted in TeX-mode before
12702 \begin_layout Standard
12712 \begin_inset Quotes eld
12716 \begin_inset Quotes erd
12730 \begin_inset Quotes eld
12734 \begin_inset Quotes erd
12740 \begin_layout Standard
12741 \begin_inset Quotes eld
12745 \begin_inset Quotes erd
12748 specifies the minimal distance between the frame and the first character
12750 An example for this is the following framed formula:
12754 \begin_layout Plain Layout
12766 \begin_inset Formula \[
12771 Before this formula the commands
12774 \begin_layout Standard
12796 \begin_layout Standard
12797 were inserted in TeX-mode.
12798 The given values are used for all following boxes.
12801 \begin_layout Standard
12802 To return to the standard frame size, the command
12805 \begin_layout Standard
12830 \begin_layout Plain Layout
12844 \begin_layout Standard
12845 is inserted in TeX-mode before the next formula.
12848 \begin_layout Subsection
12849 Boxes without Frame
12850 \begin_inset CommandInset label
12852 name "sub:Boxes-without-Frame"
12860 \begin_layout Plain Layout
12861 Boxes ! without frame
12869 \begin_layout Standard
12870 For boxes without a frame there are the following box commands:
12880 \begin_layout Plain Layout
12898 \begin_layout Plain Layout
12916 \begin_layout Plain Layout
12927 \begin_layout Standard
12934 a box can be super- or subscripted.
12935 But in contrary to normal super- and subscripting, the characters in the
12936 box keep their font size.
12943 is used in the following scheme:
12946 \begin_layout Standard
12951 raisebox{height}{box content}
12954 \begin_layout Standard
12955 When the box should contain a formula, an extra formula is needed like for
12965 \begin_layout Standard
12967 \begin_inset Tabular
12968 <lyxtabular version="3" rows="4" columns="2">
12970 <column alignment="center" valignment="top" width="0">
12971 <column alignment="center" valignment="top" width="0">
12973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12976 \begin_layout Plain Layout
12982 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12985 \begin_layout Plain Layout
12993 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12996 \begin_layout Plain Layout
13000 \begin_inset Formula $\to$
13006 \begin_inset Formula $\to$
13014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13017 \begin_layout Plain Layout
13018 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13028 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13031 \begin_layout Plain Layout
13035 \begin_inset Formula $\to$
13041 \begin_inset Formula $\to$
13049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13052 \begin_layout Plain Layout
13053 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13066 \begin_layout Plain Layout
13070 \begin_inset Formula $\to$
13085 \begin_layout Plain Layout
13099 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13102 \begin_layout Plain Layout
13106 \begin_layout Plain Layout
13130 \begin_layout Standard
13131 The last formula can currently only be created using TeX-mode because LyX
13132 inserts a box instead of the needed extra formula.
13136 \begin_layout Plain Layout
13138 \begin_inset CommandInset href
13140 name "LyX-bug #1435"
13141 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13153 \begin_layout Standard
13178 , with the difference that there is no frame.
13181 \begin_layout Subsection
13183 \begin_inset CommandInset label
13185 name "sub:Colored-Boxes"
13193 \begin_layout Plain Layout
13202 \begin_layout Standard
13203 To be able to use all commands explained in this section, the LaTeX-package
13212 \begin_layout Plain Layout
13217 is part of every LaTeX standard installation.
13226 \begin_layout Plain Layout
13232 has to be loaded in the LaTeX-preamble with the line
13236 \begin_layout Plain Layout
13237 When text is colored somewhere in the document with a predefined color,
13238 LyX loads the LaTeX-package
13243 Thus it is possible that the package is loaded twice, but this doesn't
13250 \begin_inset Note Note
13253 \begin_layout Plain Layout
13254 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13263 \begin_layout Standard
13271 \begin_layout Standard
13272 \begin_inset VSpace medskip
13275 To color boxes, the command
13285 \begin_layout Plain Layout
13293 is used in the following scheme:
13296 \begin_layout Standard
13301 colorbox{color}{box content}
13304 \begin_layout Standard
13305 The box content can also be a box and a
13311 can also be part of another box (see the 2nd and 3rd example).
13312 When the box should contain a formula, an extra formula has to be created,
13323 \begin_layout Plain Layout
13324 This also applies for the command
13332 \begin_inset CommandInset href
13334 name "LyX-bug #1435"
13335 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13347 \begin_layout Standard
13348 One of the following predefined colors can be chosen:
13351 \begin_layout Standard
13385 \begin_layout Standard
13387 \begin_inset Tabular
13388 <lyxtabular version="3" rows="4" columns="2">
13390 <column alignment="center" valignment="top" width="0">
13391 <column alignment="center" valignment="top" width="0">
13393 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13396 \begin_layout Plain Layout
13402 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13405 \begin_layout Plain Layout
13407 \begin_inset Note Note
13410 \begin_layout Plain Layout
13417 is only used as spacer.
13429 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13432 \begin_layout Plain Layout
13436 \begin_inset Formula $\to$
13446 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13449 \begin_layout Plain Layout
13450 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13460 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13463 \begin_layout Plain Layout
13467 \begin_inset Formula $\to$
13478 \begin_layout Plain Layout
13492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13495 \begin_layout Plain Layout
13496 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13506 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13509 \begin_layout Plain Layout
13516 \begin_layout Plain Layout
13528 \begin_inset Formula $\to$
13538 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13541 \begin_layout Plain Layout
13542 \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
13558 \begin_layout Standard
13565 only colors the box but not the characters in the box.
13566 To color all characters, the whole formula is highlighted and the wanted
13567 color is chosen in the
13570 \begin_inset space ~
13576 The dialog can be called with the toolbar button
13577 \begin_inset Graphics
13578 filename ../images/dialog-show_character.png
13585 Edit\SpecialChar \menuseparator
13587 \begin_inset space ~
13590 Style\SpecialChar \menuseparator
13594 The formula number has then the same color as the formula.
13595 When the formula number should get another color than the formula characters,
13596 the color must be changed within the formula.
13599 \begin_layout Standard
13603 \begin_layout Standard
13606 \begin_inset Formula \begin{equation}
13607 \int A=B\label{eq:red}\end{equation}
13614 \begin_inset Formula \begin{equation}
13615 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13622 \begin_layout Standard
13624 \begin_inset CommandInset ref
13630 is completely colored red.
13631 \begin_inset Newline newline
13635 \begin_inset CommandInset ref
13637 reference "eq:redgreen"
13641 was first completely colored green to set the color for the formula number.
13642 Subsequently the formula characters were colored red.
13645 \begin_layout Standard
13646 \begin_inset VSpace bigskip
13649 To color the frame different than the rest of the box, the command
13659 \begin_layout Plain Layout
13667 is used in the following scheme:
13670 \begin_layout Standard
13675 fcolorbox{frame color}{color}{box content}
13678 \begin_layout Standard
13685 is an extension of the command
13692 The frame width is set, like for
13715 \begin_layout Plain Layout
13727 \begin_inset Formula \[
13728 \fcolorbox{cyan}{magenta}{A=B}\]
13736 \begin_layout Plain Layout
13750 \begin_layout Standard
13751 This formula was created with the command
13752 \begin_inset Newline newline
13760 \begin_inset Formula $\to$
13766 \begin_inset Formula $\to$
13776 \begin_layout Standard
13777 \begin_inset VSpace bigskip
13780 To use other colors than the predefined ones, they have to be defined first.
13783 \begin_layout Standard
13784 One can for example define the color
13785 \begin_inset Quotes eld
13793 \begin_inset Quotes erd
13796 with the LaTeX-preamble line:
13799 \begin_layout Standard
13804 definecolor{darkgreen}{cmyk}{0.5,
13822 \begin_layout Plain Layout
13833 \begin_layout Standard
13838 is the color space that denotes the colors
13855 The four comma separated numbers are the portion factor for the corresponding
13856 colors of the color space.
13857 The factors can be in the range of 0
13858 \begin_inset space \thinspace{}
13862 \begin_inset space \thinspace{}
13870 also the color space
13874 can be used for definitions.
13891 , so that there are in this case three portion factors for the corresponding
13893 Furthermore there is the color space
13897 with one portion factor for the gray value.
13900 \begin_layout Standard
13901 As example a framed box with the new defined color
13905 where the characters have been colored
13910 \begin_inset Formula \begin{equation}
13911 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13918 \begin_layout Standard
13919 Self-defined colors can also be used for text with the help of the command
13930 \begin_layout Plain Layout
13939 \begin_layout Standard
13943 \begin_layout Plain Layout
13947 textcolor{darkgreen}{
13953 \begin_inset Quotes eld
13957 \begin_inset Quotes erd
13964 \begin_layout Plain Layout
13974 \begin_layout Standard
13985 \begin_layout Plain Layout
13993 is used in the scheme
13997 textcolor{color}{characters to color}
14002 \begin_layout Subsection
14004 \begin_inset CommandInset label
14006 name "sub:Paragraph-Boxes"
14014 \begin_layout Plain Layout
14015 Boxes ! as paragraph
14023 \begin_layout Standard
14024 A box that can contain several lines and paragraphs, a so called paragraph
14025 box (parbox), can be created with the menu
14027 Insert\SpecialChar \menuseparator
14030 or the toolbar button
14031 \begin_inset Graphics
14032 filename ../images/box-insert.png
14040 \begin_layout Standard
14041 The following example shows a framed parbox in a line:
14044 \begin_layout Standard
14045 \begin_inset VSpace medskip
14049 \begin_inset Box Boxed
14058 height_special "totalheight"
14061 \begin_layout Plain Layout
14062 This is a paragraph box.
14064 \begin_inset space \thinspace{}
14067 cm long and can also contain formulas:
14068 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14079 \begin_layout Standard
14080 \begin_inset VSpace medskip
14086 \begin_layout Standard
14087 Such a box is created by right-clicking on the gray box inset.
14088 A dialog pops up showing the box properties.
14102 \begin_inset space \thinspace{}
14107 Vertical Box Alignment
14112 \begin_layout Standard
14113 \begin_inset VSpace medskip
14116 In LaTeX a parbox is created with the command
14126 \begin_layout Plain Layout
14134 that has the following scheme:
14137 \begin_layout Standard
14142 parbox[position]{width}{box content}
14145 \begin_layout Standard
14159 for bottom means that the box is aligned within the surrounding text with
14165 for top this is done with the first line.
14166 When no position is given, the box will be vertically centered, see section
14174 \begin_inset space ~
14179 manual for examples.
14182 \begin_layout Standard
14183 \begin_inset VSpace bigskip
14186 To frame formulas completely, including the formula number, the formula
14187 must be set into a parbox.
14188 To do this, the command
14202 is inserted in TeX-mode before the formula.
14211 \begin_layout Plain Layout
14221 is hereby the line width set for the document.
14222 Because the frame is outside the parbox, 2
14223 \begin_inset space \thinspace{}
14226 times the frame separation and the frame thickness must be subtracted from
14228 As this is not automatically done by LyX due to a bug
14232 \begin_layout Plain Layout
14233 \begin_inset CommandInset href
14235 name "LyX-bug #4483"
14236 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14245 , TeX-mode has to be used.
14246 To be able to multiply and subtract in arguments, the LaTeX-package
14254 \begin_layout Plain Layout
14259 is part of every LaTeX standard installation.
14268 \begin_layout Plain Layout
14274 must be loaded in the LaTeX-preamble with the line
14277 \begin_layout Standard
14285 \begin_layout Standard
14286 Behind the formula both boxes are closed by entering
14291 Here is an example:
14295 \begin_layout Plain Layout
14309 \begin_layout Standard
14313 \begin_layout Plain Layout
14331 \begin_inset Formula \begin{equation}
14332 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14340 \begin_layout Plain Layout
14351 \begin_layout Plain Layout
14365 \begin_layout Standard
14366 \begin_inset VSpace medskip
14369 As a parbox is used as argument of
14375 , there is in this case no difference between
14390 \begin_layout Standard
14391 \begin_inset VSpace bigskip
14394 Paragraph boxes are very useful to comment formulas directly.
14401 is used in combination with the command
14415 \begin_inset CommandInset ref
14417 reference "sub:User-defined-Numbering"
14424 \begin_layout Standard
14425 An example of a formula commented with
14434 \begin_layout Standard
14438 \begin_layout Plain Layout
14451 This is a description.
14452 It is distinctly separated from the formula and multiline.
14456 \begin_layout Plain Layout
14468 \begin_layout Standard
14469 Such a formula must be inserted completely in TeX-mode because LyX does
14470 not yet support the command
14477 The formula is created with the following command sequence:
14480 \begin_layout Standard
14493 is inserted in TeX-mode.
14497 \begin_layout Plain Layout
14498 When the formula style
14510 can also be replaced by
14517 (formula styles see
14518 \begin_inset CommandInset ref
14520 reference "sec:Formula-Styles"
14529 Then the description follows as normal text, and finally
14535 is inserted in TeX-mode.
14548 hereby create a displayed formula.
14551 \begin_layout Standard
14558 can be seen in this example that was
14559 \begin_inset Quotes eld
14563 \begin_inset Quotes erd
14566 using the mathematical textmode:
14567 \begin_inset Formula \[
14568 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14575 \begin_layout Section
14580 \begin_layout Plain Layout
14589 \begin_layout Subsection
14591 \begin_inset CommandInset label
14593 name "sub:Big-Operators"
14601 \begin_layout Plain Layout
14611 \begin_layout Plain Layout
14621 \begin_layout Plain Layout
14630 \begin_layout Standard
14631 To be able to use all integral operators listed here, the option
14633 Use esint package automatically
14635 must be set in the document settings under
14638 \begin_inset space ~
14646 \begin_layout Standard
14647 \begin_inset space \hfill{}
14651 \begin_inset Tabular
14652 <lyxtabular version="3" rows="11" columns="2">
14654 <column alignment="center" valignment="top" width="0pt">
14655 <column alignment="center" valignment="top" width="0pt">
14657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14660 \begin_layout Plain Layout
14666 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14669 \begin_layout Plain Layout
14677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14680 \begin_layout Plain Layout
14687 \begin_layout Plain Layout
14700 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14703 \begin_layout Plain Layout
14704 \begin_inset Formula $\sum$
14714 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14717 \begin_layout Plain Layout
14724 \begin_layout Plain Layout
14737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14740 \begin_layout Plain Layout
14741 \begin_inset Formula $\int$
14751 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14754 \begin_layout Plain Layout
14762 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14765 \begin_layout Plain Layout
14766 \begin_inset Formula $\intop$
14776 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14779 \begin_layout Plain Layout
14787 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14790 \begin_layout Plain Layout
14791 \begin_inset Formula $\oint$
14801 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14804 \begin_layout Plain Layout
14812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14815 \begin_layout Plain Layout
14816 \begin_inset Formula $\ointop$
14826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14829 \begin_layout Plain Layout
14837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14840 \begin_layout Plain Layout
14841 \begin_inset Formula $\ointctrclockwise$
14851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14854 \begin_layout Plain Layout
14862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14865 \begin_layout Plain Layout
14866 \begin_inset Formula $\ointclockwise$
14876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14879 \begin_layout Plain Layout
14887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14890 \begin_layout Plain Layout
14891 \begin_inset Formula $\sqint$
14901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14904 \begin_layout Plain Layout
14912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14915 \begin_layout Plain Layout
14916 \begin_inset Formula $\bigcap$
14926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14929 \begin_layout Plain Layout
14937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14940 \begin_layout Plain Layout
14941 \begin_inset Formula $\bigcup$
14955 \begin_inset space \hfill{}
14959 \begin_inset Tabular
14960 <lyxtabular version="3" rows="10" columns="2">
14962 <column alignment="center" valignment="top" width="0pt">
14963 <column alignment="center" valignment="top" width="0pt">
14965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14968 \begin_layout Plain Layout
14974 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14977 \begin_layout Plain Layout
14985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14988 \begin_layout Plain Layout
14995 \begin_layout Plain Layout
15008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15011 \begin_layout Plain Layout
15012 \begin_inset Formula $\prod$
15022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15025 \begin_layout Plain Layout
15033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15036 \begin_layout Plain Layout
15037 \begin_inset Formula $\coprod$
15047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15050 \begin_layout Plain Layout
15058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15061 \begin_layout Plain Layout
15062 \begin_inset Formula $\bigodot$
15072 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15075 \begin_layout Plain Layout
15083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15086 \begin_layout Plain Layout
15087 \begin_inset Formula $\bigotimes$
15097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15100 \begin_layout Plain Layout
15108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15111 \begin_layout Plain Layout
15112 \begin_inset Formula $\bigoplus$
15122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15125 \begin_layout Plain Layout
15133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15136 \begin_layout Plain Layout
15137 \begin_inset Formula $\bigwedge$
15147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15150 \begin_layout Plain Layout
15158 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15161 \begin_layout Plain Layout
15162 \begin_inset Formula $\bigvee$
15172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15175 \begin_layout Plain Layout
15183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15186 \begin_layout Plain Layout
15187 \begin_inset Formula $\bigsqcup$
15197 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15200 \begin_layout Plain Layout
15208 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15211 \begin_layout Plain Layout
15212 \begin_inset Formula $\biguplus$
15226 \begin_inset space \hfill{}
15232 \begin_layout Standard
15233 All big operators can also be inserted via the math toolbar button
15234 \begin_inset Graphics
15235 filename ../images/math/intop.png
15243 \begin_layout Standard
15244 The operators are called big because they are bigger than the sometimes
15245 equal looking binary operators.
15246 All big operators can have limits as described in the next subsection.
15249 \begin_layout Standard
15275 \begin_inset space ~
15278 in the style the operator limits are displayed, see
15279 \begin_inset CommandInset ref
15281 reference "sub:Operator-Limits"
15289 \begin_layout Subsubsection*
15290 Advices for Integrals
15293 \begin_layout Standard
15298 in an integral is an operator, that therefore has to be set upright.
15299 This is done by highlighting the
15303 and using the keyboard shortcut
15306 \begin_inset space ~
15315 \begin_layout Plain Layout
15321 \begin_inset CommandInset ref
15323 reference "sub:Font-Styles"
15333 Finally the smallest space is inserted before the
15337 , as this is usual for operators.
15341 \begin_layout Standard
15343 \begin_inset Formula $\int A(x)dx$
15347 \begin_inset Newline newline
15354 \begin_layout Plain Layout
15364 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15370 \begin_layout Standard
15371 For multiple integrals there are the following commands:
15372 \begin_inset VSpace medskip
15378 \begin_layout Standard
15379 \begin_inset space \hfill{}
15383 \begin_inset Tabular
15384 <lyxtabular version="3" rows="4" columns="2">
15386 <column alignment="center" valignment="top" width="0">
15387 <column alignment="center" valignment="top" width="0">
15389 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15392 \begin_layout Plain Layout
15398 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15401 \begin_layout Plain Layout
15403 \begin_inset Note Note
15406 \begin_layout Plain Layout
15413 is only used as spacer.
15425 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15428 \begin_layout Plain Layout
15436 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15439 \begin_layout Plain Layout
15440 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15453 \begin_layout Plain Layout
15461 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15464 \begin_layout Plain Layout
15465 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15475 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15478 \begin_layout Plain Layout
15486 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15489 \begin_layout Plain Layout
15490 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15504 \begin_inset space \hfill{}
15508 \begin_inset Tabular
15509 <lyxtabular version="3" rows="4" columns="2">
15511 <column alignment="center" valignment="top" width="0">
15512 <column alignment="center" valignment="top" width="0">
15514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15517 \begin_layout Plain Layout
15523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15526 \begin_layout Plain Layout
15534 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15537 \begin_layout Plain Layout
15545 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15548 \begin_layout Plain Layout
15549 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15559 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15562 \begin_layout Plain Layout
15570 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15573 \begin_layout Plain Layout
15574 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15587 \begin_layout Plain Layout
15595 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15598 \begin_layout Plain Layout
15599 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15613 \begin_inset space \hfill{}
15619 \begin_layout Subsection
15621 \begin_inset CommandInset label
15623 name "sub:Operator-Limits"
15631 \begin_layout Plain Layout
15640 \begin_layout Standard
15641 Limits are created by super- and subscripts:
15644 \begin_layout Standard
15646 \begin_inset Tabular
15647 <lyxtabular version="3" rows="2" columns="2">
15649 <column alignment="center" valignment="top" width="0pt">
15650 <column alignment="center" valignment="top" width="0pt">
15652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15655 \begin_layout Plain Layout
15661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15664 \begin_layout Plain Layout
15666 \begin_inset Note Note
15669 \begin_layout Plain Layout
15676 is only used as spacer.
15688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15691 \begin_layout Plain Layout
15700 \begin_layout Plain Layout
15710 \begin_inset Formula $\to$
15714 \begin_inset Formula $\to$
15722 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15725 \begin_layout Plain Layout
15726 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
15742 \begin_layout Standard
15743 Limits of inline formulas are set right beside the operator.
15744 Limits in displayed formulas are set above or below the operator, except
15745 of integral limits.
15748 \begin_layout Standard
15749 To force that the limits are set beside the operator, the cursor is set
15750 directly behind the operator and the limits type is changed with the menu
15753 Edit\SpecialChar \menuseparator
15754 Math\SpecialChar \menuseparator
15766 \begin_inset space ~
15775 \begin_layout Standard
15776 The default limits type is this:
15777 \begin_inset Formula \[
15778 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15782 This is how it looks when the limits type was changed to
15789 \begin_inset Formula \[
15790 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15794 For integrals, except of
15806 , the limits are by default set beside the operator.
15807 But for multiple integrals the limits are often set below the operator.
15808 In the following example the limits type was therefore set to
15812 and so set below the integrals:
15813 \begin_inset Formula \begin{equation}
15814 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15821 \begin_layout Standard
15822 \begin_inset VSpace medskip
15825 To specify conditions for limits, the commands
15835 \begin_layout Plain Layout
15853 \begin_layout Plain Layout
15862 To create for example this expression
15863 \begin_inset Formula \begin{equation}
15864 \sum_{\begin{subarray}{c}
15866 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15873 \begin_layout Standard
15874 the following has to be done:
15875 \begin_inset Newline newline
15890 \begin_layout Plain Layout
15902 One is now in a blue box under the summation operator and insert there
15911 \begin_layout Plain Layout
15923 The blue box is now within a purple box and now several lines can be written
15925 A new line is created by inserting a line break (
15931 \begin_inset Newline newline
15936 0<k<1000 Ctrl-Return
15937 \begin_inset Newline newline
15942 is typed in, a new box appears below for the new line.
15945 \begin_layout Standard
15946 The alignment of the lines can be changed to left aligned with the
15956 Edit\SpecialChar \menuseparator
15960 To get right alignment,
15968 \begin_layout Plain Layout
15979 is inserted at the beginning of the line.
15982 \begin_layout Standard
15995 with the difference that the lines are always centered.
15998 \begin_layout Standard
15999 \begin_inset VSpace bigskip
16003 \begin_inset CommandInset ref
16005 reference "eq:substack"
16009 there can be too much space beside an operator, because the characters
16010 following the operator are set beside the limits.
16013 \begin_layout Standard
16014 To avoid this, the following macro can be used in the LaTeX-preamble:
16017 \begin_layout Standard
16031 \begin_inset Newline newline
16043 \begin_inset Newline newline
16050 mathclapinternal #1#2{
16054 mathsurround =0pt #1{#2}$}}
16057 \begin_layout Standard
16058 This defines the command
16068 \begin_layout Plain Layout
16076 that sets the width of the limit to 0
16077 \begin_inset space \thinspace{}
16081 The command scheme is
16084 \begin_layout Standard
16092 \begin_layout Standard
16093 where the limit can consist of several conditions.
16096 \begin_layout Standard
16098 \begin_inset CommandInset ref
16100 reference "eq:substack"
16104 , one uses the command
16107 \begin_layout Standard
16120 \begin_layout Plain Layout
16129 0<k<1000 Ctrl-Enter
16132 \begin_layout Standard
16133 to create the lower limit.
16134 The summand is now directly behind the summation operator:
16135 \begin_inset Formula \[
16136 \sum_{\mathclap{\substack{0<k<1000\\
16137 \\k\,\in\,\mathbb{N}}
16145 \begin_layout Standard
16146 \begin_inset VSpace bigskip
16149 How to use one limit for several operators is described in
16150 \begin_inset CommandInset ref
16152 reference "sub:Self-defined-Operators"
16159 \begin_layout Subsection
16161 \begin_inset CommandInset label
16163 name "sub:Binary-Operators"
16171 \begin_layout Plain Layout
16180 \begin_layout Standard
16181 Binary operators are surrounded by space when there is a character before
16183 \begin_inset VSpace medskip
16189 \begin_layout Standard
16190 \begin_inset space \hfill{}
16194 \begin_inset Tabular
16195 <lyxtabular version="3" rows="13" columns="2">
16197 <column alignment="center" valignment="top" width="0pt">
16198 <column alignment="center" valignment="top" width="0pt">
16200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16203 \begin_layout Plain Layout
16205 \begin_inset Note Note
16208 \begin_layout Plain Layout
16215 is only used as spacer.
16225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16228 \begin_layout Plain Layout
16236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16239 \begin_layout Plain Layout
16245 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16248 \begin_layout Plain Layout
16249 \begin_inset Formula $+$
16259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16262 \begin_layout Plain Layout
16268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16271 \begin_layout Plain Layout
16272 \begin_inset Formula $-$
16282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16285 \begin_layout Plain Layout
16293 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16296 \begin_layout Plain Layout
16297 \begin_inset Formula $\pm$
16307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16310 \begin_layout Plain Layout
16318 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16321 \begin_layout Plain Layout
16322 \begin_inset Formula $\mp$
16332 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16335 \begin_layout Plain Layout
16343 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16346 \begin_layout Plain Layout
16347 \begin_inset Formula $\cdot$
16357 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16360 \begin_layout Plain Layout
16368 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16371 \begin_layout Plain Layout
16372 \begin_inset Formula $\times$
16382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16385 \begin_layout Plain Layout
16393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16396 \begin_layout Plain Layout
16397 \begin_inset Formula $\div$
16407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16410 \begin_layout Plain Layout
16414 \begin_layout Plain Layout
16427 \begin_layout Plain Layout
16439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16442 \begin_layout Plain Layout
16443 \begin_inset Formula $*$
16453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16456 \begin_layout Plain Layout
16464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16467 \begin_layout Plain Layout
16468 \begin_inset Formula $\star$
16478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16481 \begin_layout Plain Layout
16489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16492 \begin_layout Plain Layout
16493 \begin_inset Formula $\circ$
16503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16506 \begin_layout Plain Layout
16514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16517 \begin_layout Plain Layout
16518 \begin_inset Formula $\diamond$
16528 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16531 \begin_layout Plain Layout
16539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16542 \begin_layout Plain Layout
16543 \begin_inset Formula $\bullet$
16557 \begin_inset space \hfill{}
16561 \begin_inset Tabular
16562 <lyxtabular version="3" rows="13" columns="2">
16564 <column alignment="center" valignment="top" width="0pt">
16565 <column alignment="center" valignment="top" width="0pt">
16567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16570 \begin_layout Plain Layout
16576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16579 \begin_layout Plain Layout
16587 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16590 \begin_layout Plain Layout
16598 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16601 \begin_layout Plain Layout
16602 \begin_inset Formula $\nabla$
16612 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16615 \begin_layout Plain Layout
16623 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16626 \begin_layout Plain Layout
16627 \begin_inset Formula $\bigtriangledown$
16637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16640 \begin_layout Plain Layout
16648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16651 \begin_layout Plain Layout
16652 \begin_inset Formula $\bigtriangleup$
16662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16665 \begin_layout Plain Layout
16673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16676 \begin_layout Plain Layout
16677 \begin_inset Formula $\Box$
16687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16690 \begin_layout Plain Layout
16698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16701 \begin_layout Plain Layout
16702 \begin_inset Formula $\cap$
16712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16715 \begin_layout Plain Layout
16723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16726 \begin_layout Plain Layout
16727 \begin_inset Formula $\cup$
16737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16740 \begin_layout Plain Layout
16748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16751 \begin_layout Plain Layout
16752 \begin_inset Formula $\dagger$
16762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16765 \begin_layout Plain Layout
16773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16776 \begin_layout Plain Layout
16777 \begin_inset Formula $\ddagger$
16787 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16790 \begin_layout Plain Layout
16798 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16801 \begin_layout Plain Layout
16802 \begin_inset Formula $\wr$
16812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16815 \begin_layout Plain Layout
16823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16826 \begin_layout Plain Layout
16827 \begin_inset Formula $\bigcirc$
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16840 \begin_layout Plain Layout
16848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16851 \begin_layout Plain Layout
16852 \begin_inset Formula $\wedge$
16862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16865 \begin_layout Plain Layout
16873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16876 \begin_layout Plain Layout
16877 \begin_inset Formula $\vee$
16891 \begin_inset space \hfill{}
16895 \begin_inset Tabular
16896 <lyxtabular version="3" rows="13" columns="2">
16898 <column alignment="center" valignment="top" width="0pt">
16899 <column alignment="center" valignment="top" width="0pt">
16901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16904 \begin_layout Plain Layout
16910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16913 \begin_layout Plain Layout
16921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16924 \begin_layout Plain Layout
16932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16935 \begin_layout Plain Layout
16936 \begin_inset Formula $\oplus$
16946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16949 \begin_layout Plain Layout
16957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16960 \begin_layout Plain Layout
16961 \begin_inset Formula $\ominus$
16971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16974 \begin_layout Plain Layout
16982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16985 \begin_layout Plain Layout
16986 \begin_inset Formula $\otimes$
16996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16999 \begin_layout Plain Layout
17007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17010 \begin_layout Plain Layout
17011 \begin_inset Formula $\oslash$
17021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17024 \begin_layout Plain Layout
17032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17035 \begin_layout Plain Layout
17036 \begin_inset Formula $\odot$
17046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17049 \begin_layout Plain Layout
17057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17060 \begin_layout Plain Layout
17061 \begin_inset Formula $\amalg$
17071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17074 \begin_layout Plain Layout
17082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17085 \begin_layout Plain Layout
17086 \begin_inset Formula $\uplus$
17096 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17099 \begin_layout Plain Layout
17107 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17110 \begin_layout Plain Layout
17111 \begin_inset Formula $\setminus$
17121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17124 \begin_layout Plain Layout
17132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17135 \begin_layout Plain Layout
17136 \begin_inset Formula $\sqcap$
17146 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17149 \begin_layout Plain Layout
17157 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17160 \begin_layout Plain Layout
17161 \begin_inset Formula $\sqcup$
17171 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17174 \begin_layout Plain Layout
17182 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17185 \begin_layout Plain Layout
17186 \begin_inset Formula $\triangleleft$
17196 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17199 \begin_layout Plain Layout
17207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17210 \begin_layout Plain Layout
17211 \begin_inset Formula $\triangleright$
17225 \begin_inset space \hfill{}
17231 \begin_layout Standard
17232 All binary operators can also be inserted via the math toolbar button
17233 \begin_inset Graphics
17234 filename ../images/math/pm.png
17242 \begin_layout Standard
17243 To typeset the Laplace operator also
17260 \begin_inset Formula $\nabla^{2}$
17263 ) can be used instead of
17272 \begin_layout Standard
17279 Insert\SpecialChar \menuseparator
17291 \begin_layout Subsection
17292 Self-defined Operators
17293 \begin_inset CommandInset label
17295 name "sub:Self-defined-Operators"
17303 \begin_layout Plain Layout
17304 Operators ! self-defined
17312 \begin_layout Standard
17313 With the help of the command
17317 DeclareMathOperator
17323 \begin_layout Plain Layout
17328 DeclareMathOperator
17333 custom operators can be defined in the LaTeX-preamble.
17334 Its command scheme is:
17337 \begin_layout Standard
17342 DeclareMathOperator{new command}{display}
17345 \begin_layout Standard
17346 Display can be characters or symbols that define how the operator looks
17348 To define a big operator a * is set behind the command.
17349 All self-defined big operators can have limits as described in
17350 \begin_inset CommandInset ref
17352 reference "sub:Operator-Limits"
17359 \begin_layout Standard
17360 For example the LaTeX-preamble line
17363 \begin_layout Standard
17368 DeclareMathOperator*{
17375 \begin_layout Standard
17376 defines the command
17382 , that inserts a big operator consisting of the lozenge symbol from
17383 \begin_inset CommandInset ref
17385 reference "sub:Miscellaneous-Symbols"
17390 \begin_inset Formula \[
17391 \Lozenge_{n=1}^{\infty}\]
17395 The command for this formula is:
17406 \begin_inset Formula $\to$
17412 \begin_layout Standard
17413 \begin_inset VSpace bigskip
17416 When self-defined operators are not used several times in the document,
17417 they can also be defined with the commands
17427 \begin_layout Plain Layout
17445 \begin_layout Plain Layout
17453 , which have the following scheme:
17456 \begin_layout Standard
17470 \begin_layout Standard
17477 defines big operators,
17486 \begin_layout Standard
17494 \begin_inset space \thinspace{}
17498 \begin_inset space ~
17501 be used to use one limit for several operators:
17504 \begin_layout Standard
17505 \begin_inset Formula \[
17506 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
17513 \begin_layout Standard
17514 The command for the formula above is:
17515 \begin_inset Newline newline
17534 \begin_layout Plain Layout
17546 \begin_inset Formula $\to$
17555 \begin_layout Plain Layout
17569 \begin_layout Section
17574 \begin_layout Plain Layout
17583 \begin_layout Subsection
17585 \begin_inset CommandInset label
17587 name "sub:Font-Styles"
17595 \begin_layout Plain Layout
17604 \begin_layout Standard
17605 Latin letters in formulas can be set in one of the following font styles:
17606 \begin_inset VSpace -2mm
17612 \begin_layout Standard
17614 \begin_inset Tabular
17615 <lyxtabular version="3" rows="6" columns="3">
17617 <column alignment="center" valignment="top" width="0">
17618 <column alignment="center" valignment="top" width="0">
17619 <column alignment="center" valignment="top" width="0">
17621 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17624 \begin_layout Plain Layout
17630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17633 \begin_layout Plain Layout
17639 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17642 \begin_layout Plain Layout
17650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17653 \begin_layout Plain Layout
17662 \begin_layout Plain Layout
17678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17681 \begin_layout Plain Layout
17682 \begin_inset Formula $\mathbb{ABC}$
17690 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17693 \begin_layout Plain Layout
17701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17704 \begin_layout Plain Layout
17713 \begin_layout Plain Layout
17729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17732 \begin_layout Plain Layout
17733 \begin_inset Formula $\mathbf{AbC}$
17741 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17744 \begin_layout Plain Layout
17752 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17755 \begin_layout Plain Layout
17764 \begin_layout Plain Layout
17780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17783 \begin_layout Plain Layout
17784 \begin_inset Formula $\boldsymbol{AbC}$
17792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17795 \begin_layout Plain Layout
17803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17806 \begin_layout Plain Layout
17815 \begin_layout Plain Layout
17831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17834 \begin_layout Plain Layout
17835 \begin_inset Formula $\mathcal{ABC}$
17843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17846 \begin_layout Plain Layout
17854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17857 \begin_layout Plain Layout
17866 \begin_layout Plain Layout
17882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17885 \begin_layout Plain Layout
17886 \begin_inset Formula $\mathfrak{AbC}$
17894 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17897 \begin_layout Plain Layout
17911 \begin_layout Standard
17913 \begin_inset Tabular
17914 <lyxtabular version="3" rows="5" columns="3">
17916 <column alignment="center" valignment="top" width="0">
17917 <column alignment="center" valignment="top" width="0">
17918 <column alignment="center" valignment="top" width="0">
17920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17923 \begin_layout Plain Layout
17929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17932 \begin_layout Plain Layout
17938 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17941 \begin_layout Plain Layout
17949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17952 \begin_layout Plain Layout
17961 \begin_layout Plain Layout
17977 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17980 \begin_layout Plain Layout
17981 \begin_inset Formula $\mathit{AbC}$
17989 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17992 \begin_layout Plain Layout
18000 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18003 \begin_layout Plain Layout
18012 \begin_layout Plain Layout
18028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18031 \begin_layout Plain Layout
18032 \begin_inset Formula $\mathrm{AbC}$
18040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18043 \begin_layout Plain Layout
18051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18054 \begin_layout Plain Layout
18063 \begin_layout Plain Layout
18079 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18082 \begin_layout Plain Layout
18083 \begin_inset Formula $\mathsf{AbC}$
18091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18094 \begin_layout Plain Layout
18102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18105 \begin_layout Plain Layout
18114 \begin_layout Plain Layout
18130 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18133 \begin_layout Plain Layout
18134 \begin_inset Formula $\mathtt{AbC}$
18142 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18145 \begin_layout Plain Layout
18159 \begin_layout Standard
18160 \begin_inset Note Greyedout
18163 \begin_layout Plain Layout
18180 can only be used for big letters.
18188 \begin_layout Standard
18189 Predefined is the style
18198 \begin_layout Standard
18199 The style commands work also for letters in mathematical constructs:
18200 \begin_inset Formula \[
18201 \mathfrak{A=\frac{b}{C}}\]
18208 \begin_layout Standard
18209 Characters in mathematical text don't appear in a math font style but in
18210 the text font style
18217 That their style can't be set correctly via the text style dialog is a
18222 \begin_layout Plain Layout
18223 \begin_inset CommandInset href
18225 name "LyX-bug #4091"
18226 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18238 \begin_layout Standard
18239 Instead of the style commands the dialog
18241 Edit\SpecialChar \menuseparator
18242 Math\SpecialChar \menuseparator
18245 or the toolbar button
18246 \begin_inset Graphics
18247 filename ../images/math/font.png
18255 \begin_layout Subsection
18257 \begin_inset CommandInset label
18259 name "sub:Bold-Formulas"
18267 \begin_layout Plain Layout
18276 \begin_layout Standard
18277 To make a complete formula bold, the command
18283 from the previous subsection cannot be used, because it doesn't work for
18284 small Greek letters.
18285 Furthermore it prints Latin letters always upright, like in the following
18289 \begin_layout Standard
18290 \begin_inset Formula \[
18291 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18298 \begin_layout Standard
18299 To display the formula correctly, the command
18306 \begin_inset Formula \[
18307 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18311 It is also possible to set the formula in a
18313 boldmath environment
18316 This environment is created by inserting the command
18324 \begin_layout Plain Layout
18335 To end the environment, the command
18343 \begin_layout Plain Layout
18353 is inserted in TeX-mode.
18357 \begin_layout Plain Layout
18367 \begin_inset Formula \[
18368 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18376 \begin_layout Plain Layout
18388 \begin_layout Subsection
18390 \begin_inset CommandInset label
18392 name "sub:Font-Sizes"
18400 \begin_layout Plain Layout
18409 \begin_layout Standard
18410 For characters in formulas there are, analog to characters in text, the
18411 following size commands:
18414 \begin_layout Standard
18458 \begin_inset Newline newline
18480 \begin_layout Standard
18481 The size produced by the commands depends on the document font size, that
18482 corresponds with the command
18489 The other commands produce smaller or larger sizes than
18496 The font size can however not exceed a certain value.
18497 Is for example the document font size 12
18498 \begin_inset space \thinspace{}
18507 switches to the same size as
18517 \begin_layout Standard
18518 A size command is inserted in TeX-mode before the formula and sets the size
18519 for all following formula and text characters.
18520 To switch back to the initial size, the command
18526 is inserted behind the formula in TeX-mode.
18529 \begin_layout Standard
18530 Within a formula the size can only be changed for symbols or letters in
18532 To do this, the size command is inserted in mathematical text.
18533 All following characters until the end of the mathematical text or until
18534 another size command will have the selected size.
18536 \begin_inset VSpace -2mm
18542 \begin_layout Standard
18546 \begin_layout Plain Layout
18556 \begin_inset Formula \[
18557 A=\frac{B}{c}\cdot\maltese\]
18562 \begin_inset Formula \[
18563 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
18571 \begin_layout Plain Layout
18583 \begin_layout Standard
18584 \begin_inset VSpace medskip
18587 Before both formulas the command
18594 The command for the second formula is:
18595 \begin_inset Newline newline
18606 \begin_layout Plain Layout
18621 \begin_layout Plain Layout
18636 \begin_layout Plain Layout
18651 \begin_layout Plain Layout
18661 \begin_inset Formula $\to$
18665 \begin_inset Formula $\to$
18669 \begin_inset Newline newline
18673 \begin_inset space \hspace*{}
18687 \begin_layout Plain Layout
18702 \begin_layout Plain Layout
18717 \begin_layout Plain Layout
18729 \begin_layout Standard
18730 If a symbol cannot be displayed in different sizes, it will always be displayed
18731 in the default size.
18734 \begin_layout Section
18739 \begin_layout Plain Layout
18748 \begin_layout Standard
18749 All Greek letters can also be inserted via the toolbar button
18750 \begin_inset Graphics
18751 filename ../images/math/alpha.png
18759 \begin_layout Subsection
18761 \begin_inset CommandInset label
18763 name "sub:Small-Letters"
18771 \begin_layout Plain Layout
18772 Greek letters ! small
18780 \begin_layout Standard
18781 \begin_inset space \hfill{}
18785 \begin_inset Tabular
18786 <lyxtabular version="3" rows="11" columns="2">
18788 <column alignment="center" valignment="top" width="0pt">
18789 <column alignment="center" valignment="top" width="0pt">
18791 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18794 \begin_layout Plain Layout
18800 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18803 \begin_layout Plain Layout
18811 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18814 \begin_layout Plain Layout
18822 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18825 \begin_layout Plain Layout
18826 \begin_inset Formula $\alpha$
18836 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18839 \begin_layout Plain Layout
18847 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18850 \begin_layout Plain Layout
18851 \begin_inset Formula $\beta$
18861 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18864 \begin_layout Plain Layout
18872 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18875 \begin_layout Plain Layout
18876 \begin_inset Formula $\gamma$
18886 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18889 \begin_layout Plain Layout
18897 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18900 \begin_layout Plain Layout
18901 \begin_inset Formula $\delta$
18911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18914 \begin_layout Plain Layout
18922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18925 \begin_layout Plain Layout
18926 \begin_inset Formula $\epsilon$
18936 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18939 \begin_layout Plain Layout
18947 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18950 \begin_layout Plain Layout
18951 \begin_inset Formula $\varepsilon$
18961 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18964 \begin_layout Plain Layout
18972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18975 \begin_layout Plain Layout
18976 \begin_inset Formula $\zeta$
18986 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18989 \begin_layout Plain Layout
18997 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19000 \begin_layout Plain Layout
19001 \begin_inset Formula $\eta$
19011 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19014 \begin_layout Plain Layout
19022 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19025 \begin_layout Plain Layout
19026 \begin_inset Formula $\theta$
19036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19039 \begin_layout Plain Layout
19047 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19050 \begin_layout Plain Layout
19051 \begin_inset Formula $\vartheta$
19065 \begin_inset space \hfill{}
19069 \begin_inset Tabular
19070 <lyxtabular version="3" rows="12" columns="2">
19072 <column alignment="center" valignment="top" width="0pt">
19073 <column alignment="center" valignment="top" width="0pt">
19075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19078 \begin_layout Plain Layout
19084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19087 \begin_layout Plain Layout
19095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19098 \begin_layout Plain Layout
19106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19109 \begin_layout Plain Layout
19110 \begin_inset Formula $\iota$
19120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19123 \begin_layout Plain Layout
19131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19134 \begin_layout Plain Layout
19135 \begin_inset Formula $\kappa$
19145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19148 \begin_layout Plain Layout
19156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19159 \begin_layout Plain Layout
19160 \begin_inset Formula $\varkappa$
19170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19173 \begin_layout Plain Layout
19181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19184 \begin_layout Plain Layout
19185 \begin_inset Formula $\lambda$
19195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19198 \begin_layout Plain Layout
19206 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19209 \begin_layout Plain Layout
19210 \begin_inset Formula $\mu$
19220 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19223 \begin_layout Plain Layout
19231 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19234 \begin_layout Plain Layout
19235 \begin_inset Formula $\nu$
19245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19248 \begin_layout Plain Layout
19256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19259 \begin_layout Plain Layout
19260 \begin_inset Formula $\xi$
19270 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19273 \begin_layout Plain Layout
19279 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19282 \begin_layout Plain Layout
19283 \begin_inset Formula $o$
19293 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19296 \begin_layout Plain Layout
19304 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19307 \begin_layout Plain Layout
19308 \begin_inset Formula $\pi$
19318 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19321 \begin_layout Plain Layout
19329 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19332 \begin_layout Plain Layout
19333 \begin_inset Formula $\varpi$
19343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19346 \begin_layout Plain Layout
19354 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19357 \begin_layout Plain Layout
19358 \begin_inset Formula $\rho$
19372 \begin_inset space \hfill{}
19376 \begin_inset Tabular
19377 <lyxtabular version="3" rows="11" columns="2">
19379 <column alignment="center" valignment="top" width="0pt">
19380 <column alignment="center" valignment="top" width="0pt">
19382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19385 \begin_layout Plain Layout
19391 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19394 \begin_layout Plain Layout
19402 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19405 \begin_layout Plain Layout
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19416 \begin_layout Plain Layout
19417 \begin_inset Formula $\varrho$
19427 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19430 \begin_layout Plain Layout
19438 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19441 \begin_layout Plain Layout
19442 \begin_inset Formula $\sigma$
19452 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19455 \begin_layout Plain Layout
19463 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19466 \begin_layout Plain Layout
19467 \begin_inset Formula $\varsigma$
19477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19480 \begin_layout Plain Layout
19488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19491 \begin_layout Plain Layout
19492 \begin_inset Formula $\tau$
19502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19505 \begin_layout Plain Layout
19513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19516 \begin_layout Plain Layout
19517 \begin_inset Formula $\upsilon$
19527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19530 \begin_layout Plain Layout
19538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19541 \begin_layout Plain Layout
19542 \begin_inset Formula $\phi$
19552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19555 \begin_layout Plain Layout
19563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19566 \begin_layout Plain Layout
19567 \begin_inset Formula $\varphi$
19577 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19580 \begin_layout Plain Layout
19588 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19591 \begin_layout Plain Layout
19592 \begin_inset Formula $\chi$
19602 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19605 \begin_layout Plain Layout
19613 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19616 \begin_layout Plain Layout
19617 \begin_inset Formula $\psi$
19627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19630 \begin_layout Plain Layout
19638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19641 \begin_layout Plain Layout
19642 \begin_inset Formula $\omega$
19656 \begin_inset space \hfill{}
19662 \begin_layout Standard
19663 \begin_inset VSpace medskip
19669 \begin_layout Standard
19670 How to create upright Greek letters is explained in
19671 \begin_inset CommandInset ref
19673 reference "sub:Upright-small-Greek"
19680 \begin_layout Subsection
19685 \begin_layout Plain Layout
19686 Greek letters ! big
19694 \begin_layout Standard
19695 \begin_inset space \hfill{}
19699 \begin_inset Tabular
19700 <lyxtabular version="3" rows="7" columns="2">
19702 <column alignment="center" valignment="top" width="0pt">
19703 <column alignment="center" valignment="top" width="0pt">
19705 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19708 \begin_layout Plain Layout
19714 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19717 \begin_layout Plain Layout
19725 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19728 \begin_layout Plain Layout
19736 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19739 \begin_layout Plain Layout
19740 \begin_inset Formula $\Gamma$
19750 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19753 \begin_layout Plain Layout
19761 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19764 \begin_layout Plain Layout
19765 \begin_inset Formula $\Delta$
19775 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19778 \begin_layout Plain Layout
19786 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19789 \begin_layout Plain Layout
19790 \begin_inset Formula $\Theta$
19800 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19803 \begin_layout Plain Layout
19811 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19814 \begin_layout Plain Layout
19815 \begin_inset Formula $\Lambda$
19825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19828 \begin_layout Plain Layout
19836 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19839 \begin_layout Plain Layout
19840 \begin_inset Formula $\Xi$
19850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19853 \begin_layout Plain Layout
19861 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19864 \begin_layout Plain Layout
19865 \begin_inset Formula $\Pi$
19879 \begin_inset space \hfill{}
19883 \begin_inset Tabular
19884 <lyxtabular version="3" rows="6" columns="2">
19886 <column alignment="center" valignment="top" width="0pt">
19887 <column alignment="center" valignment="top" width="0pt">
19889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19892 \begin_layout Plain Layout
19898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19901 \begin_layout Plain Layout
19909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19912 \begin_layout Plain Layout
19920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19923 \begin_layout Plain Layout
19924 \begin_inset Formula $\Sigma$
19934 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19937 \begin_layout Plain Layout
19945 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19948 \begin_layout Plain Layout
19949 \begin_inset Formula $\Upsilon$
19959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19962 \begin_layout Plain Layout
19970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19973 \begin_layout Plain Layout
19974 \begin_inset Formula $\Phi$
19984 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19987 \begin_layout Plain Layout
19995 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19998 \begin_layout Plain Layout
19999 \begin_inset Formula $\Psi$
20009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20012 \begin_layout Plain Layout
20020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20023 \begin_layout Plain Layout
20024 \begin_inset Formula $\Omega$
20038 \begin_inset space \hfill{}
20044 \begin_layout Standard
20045 \begin_inset VSpace medskip
20048 That the big Greek letters appear upright is caused by a design bug when
20050 To get correct italic big letters, begin every command with
20055 For example the command
20062 \begin_inset Formula $\varGamma$
20068 \begin_layout Subsection
20073 \begin_layout Plain Layout
20074 Greek letters ! bold
20082 \begin_layout Standard
20083 Greek letters cannot be set with different font styles like Latin letters.
20084 They can only be made bold with the command
20094 \begin_layout Plain Layout
20105 \begin_layout Standard
20107 \begin_inset Tabular
20108 <lyxtabular version="3" rows="3" columns="2">
20110 <column alignment="center" valignment="top" width="0">
20111 <column alignment="center" valignment="top" width="0">
20113 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20116 \begin_layout Plain Layout
20122 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20125 \begin_layout Plain Layout
20133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20136 \begin_layout Plain Layout
20148 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20151 \begin_layout Plain Layout
20152 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20162 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20165 \begin_layout Plain Layout
20177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20180 \begin_layout Plain Layout
20181 \begin_inset Formula $\theta\boldsymbol{\theta}$
20197 \begin_layout Section
20202 \begin_layout Plain Layout
20215 \begin_layout Plain Layout
20216 A list with all symbols of most of the LaTeX-packages can be found in
20217 \begin_inset CommandInset citation
20232 \begin_layout Plain Layout
20240 \begin_inset Note Note
20243 \begin_layout Plain Layout
20246 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20249 \begin_layout Plain Layout
20252 texorpdfstring is in section
20253 \begin_inset CommandInset ref
20255 reference "sub:Formulas-in-Section"
20268 \begin_layout Plain Layout
20277 \begin_layout Standard
20278 Many of the symbols listed in this section can also be inserted via the
20280 \begin_inset Graphics
20281 filename ../images/math/nabla.png
20287 \begin_inset Graphics
20288 filename ../images/math/digamma.png
20296 \begin_layout Subsection
20297 Mathematical Symbols
20298 \begin_inset CommandInset label
20300 name "sub:Mathematical-Symbols"
20308 \begin_layout Plain Layout
20309 Symbols ! mathematical
20317 \begin_layout Standard
20318 \begin_inset space \hfill{}
20322 \begin_inset Tabular
20323 <lyxtabular version="3" rows="10" columns="2">
20325 <column alignment="center" valignment="top" width="0pt">
20326 <column alignment="center" valignment="top" width="0pt">
20328 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20331 \begin_layout Plain Layout
20337 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20340 \begin_layout Plain Layout
20348 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20351 \begin_layout Plain Layout
20359 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20362 \begin_layout Plain Layout
20363 \begin_inset Formula $\neg$
20373 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20376 \begin_layout Plain Layout
20384 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20387 \begin_layout Plain Layout
20388 \begin_inset Formula $\Im$
20398 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20401 \begin_layout Plain Layout
20409 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20412 \begin_layout Plain Layout
20413 \begin_inset Formula $\Re$
20423 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20426 \begin_layout Plain Layout
20434 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20437 \begin_layout Plain Layout
20438 \begin_inset Formula $\aleph$
20448 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20451 \begin_layout Plain Layout
20459 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20462 \begin_layout Plain Layout
20463 \begin_inset Formula $\partial$
20473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20476 \begin_layout Plain Layout
20484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20487 \begin_layout Plain Layout
20488 \begin_inset Formula $\infty$
20498 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20501 \begin_layout Plain Layout
20509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20512 \begin_layout Plain Layout
20513 \begin_inset Formula $\wp$
20523 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20526 \begin_layout Plain Layout
20534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20537 \begin_layout Plain Layout
20538 \begin_inset Formula $\imath$
20548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20551 \begin_layout Plain Layout
20559 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20562 \begin_layout Plain Layout
20563 \begin_inset Formula $\jmath$
20577 \begin_inset space \hfill{}
20581 \begin_inset Tabular
20582 <lyxtabular version="3" rows="10" columns="2">
20584 <column alignment="center" valignment="top" width="0pt">
20585 <column alignment="center" valignment="top" width="0pt">
20587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20590 \begin_layout Plain Layout
20596 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20599 \begin_layout Plain Layout
20601 \begin_inset Note Note
20604 \begin_layout Plain Layout
20611 is only used as spacer.
20623 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20626 \begin_layout Plain Layout
20634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20637 \begin_layout Plain Layout
20638 \begin_inset Formula $\forall$
20648 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20651 \begin_layout Plain Layout
20659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20662 \begin_layout Plain Layout
20663 \begin_inset Formula $\exists$
20673 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20676 \begin_layout Plain Layout
20684 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20687 \begin_layout Plain Layout
20688 \begin_inset Formula $\nexists$
20698 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20701 \begin_layout Plain Layout
20709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20712 \begin_layout Plain Layout
20713 \begin_inset Formula $\emptyset$
20723 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20726 \begin_layout Plain Layout
20734 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20737 \begin_layout Plain Layout
20738 \begin_inset Formula $\varnothing$
20748 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20751 \begin_layout Plain Layout
20759 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20762 \begin_layout Plain Layout
20763 \begin_inset Formula $\dag$
20773 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20776 \begin_layout Plain Layout
20784 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20787 \begin_layout Plain Layout
20788 \begin_inset Formula $\ddag$
20798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20801 \begin_layout Plain Layout
20809 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20812 \begin_layout Plain Layout
20816 \begin_layout Plain Layout
20826 \begin_inset Formula $\complement$
20833 \begin_layout Plain Layout
20847 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20850 \begin_layout Plain Layout
20858 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20861 \begin_layout Plain Layout
20862 \begin_inset Formula $\Bbbk$
20876 \begin_inset space \hfill{}
20880 \begin_inset Tabular
20881 <lyxtabular version="3" rows="10" columns="2">
20883 <column alignment="center" valignment="top" width="0pt">
20884 <column alignment="center" valignment="top" width="0pt">
20886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20889 \begin_layout Plain Layout
20895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20898 \begin_layout Plain Layout
20906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20909 \begin_layout Plain Layout
20917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20920 \begin_layout Plain Layout
20921 \begin_inset Formula $\prime$
20931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20934 \begin_layout Plain Layout
20942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20945 \begin_layout Plain Layout
20946 \begin_inset Formula $\backprime$
20956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20959 \begin_layout Plain Layout
20967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20970 \begin_layout Plain Layout
20971 \begin_inset Formula $\mho$
20981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20984 \begin_layout Plain Layout
20992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20995 \begin_layout Plain Layout
20996 \begin_inset Formula $\triangle$
21006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21009 \begin_layout Plain Layout
21017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21020 \begin_layout Plain Layout
21021 \begin_inset Formula $\angle$
21031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21034 \begin_layout Plain Layout
21042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21045 \begin_layout Plain Layout
21046 \begin_inset Formula $\measuredangle$
21056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21059 \begin_layout Plain Layout
21067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21070 \begin_layout Plain Layout
21071 \begin_inset Formula $\sphericalangle$
21081 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21084 \begin_layout Plain Layout
21092 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21095 \begin_layout Plain Layout
21096 \begin_inset Formula $\top$
21106 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21109 \begin_layout Plain Layout
21117 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21120 \begin_layout Plain Layout
21121 \begin_inset Formula $\bot$
21135 \begin_inset space \hfill{}
21141 \begin_layout Standard
21142 \begin_inset Newpage newpage
21148 \begin_layout Subsection
21149 Miscellaneous Symbols
21150 \begin_inset CommandInset label
21152 name "sub:Miscellaneous-Symbols"
21160 \begin_layout Plain Layout
21161 Symbols ! miscellaneous
21169 \begin_layout Standard
21172 \begin_inset Tabular
21173 <lyxtabular version="3" rows="10" columns="2">
21175 <column alignment="center" valignment="top" width="0pt">
21176 <column alignment="center" valignment="top" width="0pt">
21178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21181 \begin_layout Plain Layout
21187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21190 \begin_layout Plain Layout
21198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21201 \begin_layout Plain Layout
21209 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21212 \begin_layout Plain Layout
21213 \begin_inset Formula $\flat$
21223 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21226 \begin_layout Plain Layout
21234 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21237 \begin_layout Plain Layout
21238 \begin_inset Formula $\natural$
21248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21251 \begin_layout Plain Layout
21259 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21262 \begin_layout Plain Layout
21263 \begin_inset Formula $\sharp$
21273 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21276 \begin_layout Plain Layout
21284 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21287 \begin_layout Plain Layout
21288 \begin_inset Formula $\surd$
21298 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21301 \begin_layout Plain Layout
21309 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21312 \begin_layout Plain Layout
21313 \begin_inset Formula $\checkmark$
21323 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21326 \begin_layout Plain Layout
21334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21337 \begin_layout Plain Layout
21338 \begin_inset Formula $\yen$
21348 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21351 \begin_layout Plain Layout
21359 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21362 \begin_layout Plain Layout
21363 \begin_inset Formula $\pounds$
21373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21376 \begin_layout Plain Layout
21382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21385 \begin_layout Plain Layout
21386 \begin_inset Formula $\$$
21396 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21399 \begin_layout Plain Layout
21405 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21408 \begin_layout Plain Layout
21409 \begin_inset Formula $§$
21423 \begin_inset Tabular
21424 <lyxtabular version="3" rows="10" columns="2">
21426 <column alignment="center" valignment="top" width="0">
21427 <column alignment="center" valignment="top" width="0">
21429 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21432 \begin_layout Plain Layout
21438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21452 \begin_layout Plain Layout
21460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21463 \begin_layout Plain Layout
21464 \begin_inset Formula $\hbar$
21474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21477 \begin_layout Plain Layout
21485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21488 \begin_layout Plain Layout
21489 \begin_inset Formula $\hslash$
21499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21502 \begin_layout Plain Layout
21510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21513 \begin_layout Plain Layout
21514 \begin_inset Formula $\clubsuit$
21524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21527 \begin_layout Plain Layout
21535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21538 \begin_layout Plain Layout
21539 \begin_inset Formula $\spadesuit$
21549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21552 \begin_layout Plain Layout
21560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21563 \begin_layout Plain Layout
21564 \begin_inset Formula $\bigstar$
21574 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21577 \begin_layout Plain Layout
21585 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21588 \begin_layout Plain Layout
21589 \begin_inset Formula $\blacklozenge$
21599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21602 \begin_layout Plain Layout
21610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21613 \begin_layout Plain Layout
21614 \begin_inset Formula $\blacktriangle$
21624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21627 \begin_layout Plain Layout
21635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21638 \begin_layout Plain Layout
21639 \begin_inset Formula $\blacktriangledown$
21649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21652 \begin_layout Plain Layout
21660 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21663 \begin_layout Plain Layout
21664 \begin_inset Formula $\bullet$
21678 \begin_inset Tabular
21679 <lyxtabular version="3" rows="10" columns="2">
21681 <column alignment="center" valignment="top" width="0pt">
21682 <column alignment="center" valignment="top" width="0pt">
21684 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21687 \begin_layout Plain Layout
21693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21696 \begin_layout Plain Layout
21704 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21707 \begin_layout Plain Layout
21715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21718 \begin_layout Plain Layout
21719 \begin_inset Formula $\diamondsuit$
21729 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21732 \begin_layout Plain Layout
21740 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21743 \begin_layout Plain Layout
21744 \begin_inset Formula $\Diamond$
21754 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21757 \begin_layout Plain Layout
21765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21768 \begin_layout Plain Layout
21769 \begin_inset Formula $\heartsuit$
21779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21782 \begin_layout Plain Layout
21790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21793 \begin_layout Plain Layout
21794 \begin_inset Formula $\P$
21804 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21807 \begin_layout Plain Layout
21815 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21818 \begin_layout Plain Layout
21819 \begin_inset Formula $\copyright$
21829 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21832 \begin_layout Plain Layout
21840 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21843 \begin_layout Plain Layout
21844 \begin_inset Formula $\circledR$
21854 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21857 \begin_layout Plain Layout
21865 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21868 \begin_layout Plain Layout
21869 \begin_inset Formula $\maltese$
21879 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21882 \begin_layout Plain Layout
21890 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21893 \begin_layout Plain Layout
21894 \begin_inset Formula $\diagup$
21904 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21907 \begin_layout Plain Layout
21915 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21918 \begin_layout Plain Layout
21919 \begin_inset Formula $\diagdown$
21935 \begin_layout Standard
21936 \begin_inset VSpace medskip
21939 More symbols are listed in
21940 \begin_inset CommandInset ref
21942 reference "sub:Miscellaneous-Special-Characters"
21949 \begin_layout Standard
21950 Some symbols can be displayed in different sizes, see
21951 \begin_inset CommandInset ref
21953 reference "sub:Font-Sizes"
21960 \begin_layout Subsection
21965 \begin_layout Plain Layout
21966 Symbols ! Euro-symbol
21975 \begin_layout Plain Layout
21979 \begin_layout Plain Layout
21996 \begin_layout Standard
21997 To use the Euro symbol in formulas, the LaTeX-package
22005 \begin_layout Plain Layout
22011 must be installed and loaded with the LaTeX-preamble line
22014 \begin_layout Standard
22019 usepackage[gennarrow]{eurosym}
22022 \begin_layout Standard
22023 The Euro symbol can now be inserted with the command
22033 \begin_layout Plain Layout
22044 \begin_layout Standard
22045 The Euro symbol can directly be inserted with the € key in mathematical
22046 text, without having
22061 can also be inserted in TeX-mode.
22062 The official currency symbol can then be inserted with the command
22072 \begin_layout Plain Layout
22080 , that is only available in TeX-mode.
22083 \begin_layout Standard
22087 \begin_layout Plain Layout
22097 \begin_inset Note Note
22100 \begin_layout Plain Layout
22101 The following table will only be displayed when the LaTeX-package
22113 \begin_layout Standard
22114 An overview about the different Euro symbols:
22117 \begin_layout Standard
22119 \begin_inset Tabular
22120 <lyxtabular version="3" rows="4" columns="3">
22122 <column alignment="center" valignment="top" width="0pt">
22123 <column alignment="center" valignment="top" width="0pt">
22124 <column alignment="center" valignment="top" width="0pt">
22126 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22129 \begin_layout Plain Layout
22135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22138 \begin_layout Plain Layout
22144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22147 \begin_layout Plain Layout
22155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22158 \begin_layout Plain Layout
22164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22167 \begin_layout Plain Layout
22175 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22178 \begin_layout Plain Layout
22179 \begin_inset Formula $\euro$
22189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22192 \begin_layout Plain Layout
22198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22201 \begin_layout Plain Layout
22207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22210 \begin_layout Plain Layout
22211 \begin_inset Formula $\mbox{€}$
22221 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22224 \begin_layout Plain Layout
22230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22233 \begin_layout Plain Layout
22241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22244 \begin_layout Plain Layout
22248 \begin_layout Plain Layout
22270 \begin_layout Standard
22274 \begin_layout Plain Layout
22284 \begin_inset Note Note
22287 \begin_layout Plain Layout
22288 The following will be displayed when the LaTeX-package
22300 \begin_layout Standard
22301 You need to install the LaTeX-package
22305 to see the rest of this subsection in the output.
22308 \begin_layout Standard
22312 \begin_layout Plain Layout
22324 \begin_layout Section
22326 \begin_inset CommandInset label
22328 name "sec:Relations"
22336 \begin_layout Plain Layout
22346 \begin_layout Plain Layout
22351 \begin_layout Plain Layout
22362 \begin_layout Plain Layout
22377 \begin_layout Standard
22378 All relations can also be inserted via the toolbar button
22379 \begin_inset Graphics
22380 filename ../images/math/leq.png
22388 \begin_layout Standard
22389 \begin_inset space \hfill{}
22393 \begin_inset Tabular
22394 <lyxtabular version="3" rows="17" columns="2">
22396 <column alignment="center" valignment="top" width="0pt">
22397 <column alignment="center" valignment="top" width="0pt">
22399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22402 \begin_layout Plain Layout
22408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22411 \begin_layout Plain Layout
22419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22422 \begin_layout Plain Layout
22428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22431 \begin_layout Plain Layout
22432 \begin_inset Formula $<$
22442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22445 \begin_layout Plain Layout
22453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22456 \begin_layout Plain Layout
22457 \begin_inset Formula $\le$
22467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22470 \begin_layout Plain Layout
22478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22481 \begin_layout Plain Layout
22482 \begin_inset Formula $\ll$
22492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22495 \begin_layout Plain Layout
22503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22506 \begin_layout Plain Layout
22507 \begin_inset Formula $\prec$
22517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22520 \begin_layout Plain Layout
22528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22531 \begin_layout Plain Layout
22532 \begin_inset Formula $\preceq$
22542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22545 \begin_layout Plain Layout
22553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22556 \begin_layout Plain Layout
22557 \begin_inset Formula $\subset$
22567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22570 \begin_layout Plain Layout
22578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22581 \begin_layout Plain Layout
22582 \begin_inset Formula $\subseteq$
22592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22595 \begin_layout Plain Layout
22603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22606 \begin_layout Plain Layout
22607 \begin_inset Formula $\sqsubseteq$
22617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22620 \begin_layout Plain Layout
22628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22631 \begin_layout Plain Layout
22632 \begin_inset Formula $\in$
22642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22645 \begin_layout Plain Layout
22653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22656 \begin_layout Plain Layout
22657 \begin_inset Formula $\vdash$
22667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22670 \begin_layout Plain Layout
22678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22681 \begin_layout Plain Layout
22682 \begin_inset Formula $\smile$
22692 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22695 \begin_layout Plain Layout
22703 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22706 \begin_layout Plain Layout
22707 \begin_inset Formula $\lhd$
22717 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22720 \begin_layout Plain Layout
22728 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22731 \begin_layout Plain Layout
22732 \begin_inset Formula $\unlhd$
22742 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22745 \begin_layout Plain Layout
22753 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22756 \begin_layout Plain Layout
22757 \begin_inset Formula $\gtrless$
22767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22770 \begin_layout Plain Layout
22778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22781 \begin_layout Plain Layout
22782 \begin_inset Formula $\mid$
22792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22795 \begin_layout Plain Layout
22803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22806 \begin_layout Plain Layout
22807 \begin_inset Formula $\nmid$
22821 \begin_inset space \hfill{}
22825 \begin_inset Tabular
22826 <lyxtabular version="3" rows="17" columns="2">
22828 <column alignment="center" valignment="top" width="0pt">
22829 <column alignment="center" valignment="top" width="0pt">
22831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22834 \begin_layout Plain Layout
22840 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22843 \begin_layout Plain Layout
22851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22854 \begin_layout Plain Layout
22860 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22863 \begin_layout Plain Layout
22864 \begin_inset Formula $=$
22874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22877 \begin_layout Plain Layout
22885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22888 \begin_layout Plain Layout
22889 \begin_inset Formula $\not=$
22899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22902 \begin_layout Plain Layout
22910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22913 \begin_layout Plain Layout
22914 \begin_inset Formula $\equiv$
22924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22927 \begin_layout Plain Layout
22935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22938 \begin_layout Plain Layout
22939 \begin_inset Formula $\sim$
22949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22952 \begin_layout Plain Layout
22960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22963 \begin_layout Plain Layout
22964 \begin_inset Formula $\simeq$
22974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22977 \begin_layout Plain Layout
22985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22988 \begin_layout Plain Layout
22989 \begin_inset Formula $\approx$
22999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23002 \begin_layout Plain Layout
23010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23013 \begin_layout Plain Layout
23014 \begin_inset Formula $\cong$
23024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23027 \begin_layout Plain Layout
23035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23038 \begin_layout Plain Layout
23039 \begin_inset Formula $\bowtie$
23049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23052 \begin_layout Plain Layout
23060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23063 \begin_layout Plain Layout
23064 \begin_inset Formula $\notin$
23074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23077 \begin_layout Plain Layout
23085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23088 \begin_layout Plain Layout
23089 \begin_inset Formula $\perp$
23099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23102 \begin_layout Plain Layout
23110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23113 \begin_layout Plain Layout
23114 \begin_inset Formula $\propto$
23124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23127 \begin_layout Plain Layout
23135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23138 \begin_layout Plain Layout
23139 \begin_inset Formula $\asymp$
23149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23152 \begin_layout Plain Layout
23160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23163 \begin_layout Plain Layout
23164 \begin_inset Formula $\doteq$
23174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23177 \begin_layout Plain Layout
23185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23188 \begin_layout Plain Layout
23189 \begin_inset Formula $\circeq$
23199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23202 \begin_layout Plain Layout
23210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23213 \begin_layout Plain Layout
23214 \begin_inset Formula $\models$
23224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23227 \begin_layout Plain Layout
23235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23238 \begin_layout Plain Layout
23239 \begin_inset Formula $\widehat{=}$
23253 \begin_inset space \hfill{}
23257 \begin_inset Tabular
23258 <lyxtabular version="3" rows="17" columns="2">
23260 <column alignment="center" valignment="top" width="0pt">
23261 <column alignment="center" valignment="top" width="0pt">
23263 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23266 \begin_layout Plain Layout
23272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23275 \begin_layout Plain Layout
23283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23286 \begin_layout Plain Layout
23292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23295 \begin_layout Plain Layout
23296 \begin_inset Formula $>$
23306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23309 \begin_layout Plain Layout
23317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23320 \begin_layout Plain Layout
23321 \begin_inset Formula $\ge$
23331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23334 \begin_layout Plain Layout
23342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23345 \begin_layout Plain Layout
23346 \begin_inset Formula $\gg$
23356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23359 \begin_layout Plain Layout
23367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23370 \begin_layout Plain Layout
23371 \begin_inset Formula $\succ$
23381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23384 \begin_layout Plain Layout
23392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23395 \begin_layout Plain Layout
23396 \begin_inset Formula $\succeq$
23406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23409 \begin_layout Plain Layout
23417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23420 \begin_layout Plain Layout
23421 \begin_inset Formula $\supset$
23431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23434 \begin_layout Plain Layout
23442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23445 \begin_layout Plain Layout
23446 \begin_inset Formula $\supseteq$
23456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23459 \begin_layout Plain Layout
23467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23470 \begin_layout Plain Layout
23471 \begin_inset Formula $\sqsupseteq$
23481 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23484 \begin_layout Plain Layout
23492 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23495 \begin_layout Plain Layout
23496 \begin_inset Formula $\ni$
23506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23509 \begin_layout Plain Layout
23517 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23520 \begin_layout Plain Layout
23521 \begin_inset Formula $\dashv$
23531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23534 \begin_layout Plain Layout
23542 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23545 \begin_layout Plain Layout
23546 \begin_inset Formula $\frown$
23556 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23559 \begin_layout Plain Layout
23567 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23570 \begin_layout Plain Layout
23571 \begin_inset Formula $\rhd$
23581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23584 \begin_layout Plain Layout
23592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23595 \begin_layout Plain Layout
23596 \begin_inset Formula $\unrhd$
23606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23609 \begin_layout Plain Layout
23617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23620 \begin_layout Plain Layout
23621 \begin_inset Formula $\lessgtr$
23631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23634 \begin_layout Plain Layout
23642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23645 \begin_layout Plain Layout
23646 \begin_inset Formula $\parallel$
23656 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23659 \begin_layout Plain Layout
23667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23670 \begin_layout Plain Layout
23671 \begin_inset Formula $\nparallel$
23685 \begin_inset space \hfill{}
23691 \begin_layout Standard
23692 \begin_inset VSpace medskip
23707 are bigger than the equal looking operators
23722 \begin_layout Standard
23723 Relations are, in contrary to symbols, always surrounded by space.
23726 \begin_layout Standard
23727 Relations with labels can be created with the command
23737 \begin_layout Plain Layout
23748 \begin_layout Standard
23750 \begin_inset Tabular
23751 <lyxtabular version="3" rows="2" columns="2">
23753 <column alignment="center" valignment="top" width="0">
23754 <column alignment="center" valignment="top" width="0">
23756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23759 \begin_layout Plain Layout
23765 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23768 \begin_layout Plain Layout
23770 \begin_inset Note Note
23773 \begin_layout Plain Layout
23780 is only used as spacer.
23792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23795 \begin_layout Plain Layout
23802 \begin_layout Plain Layout
23819 \begin_layout Plain Layout
23829 \begin_inset Formula $\downarrow$
23838 \begin_layout Plain Layout
23851 \begin_layout Plain Layout
23865 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23868 \begin_layout Plain Layout
23869 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23885 \begin_layout Section
23889 \begin_layout Subsection
23890 Predefined Functions
23891 \begin_inset CommandInset label
23893 name "sub:Predefined-Functions"
23901 \begin_layout Plain Layout
23902 Functions ! predefined
23910 \begin_layout Standard
23911 In general, variables are set
23915 in mathematical expressions, but not function names, because
23916 \begin_inset Formula $sin$
23919 could be misunderstood as
23920 \begin_inset Formula $s\cdot i\cdot n$
23924 Therefore there are predefined functions, that are additionally a bit separated
23926 They are inserted as commands starting with a backslash before their name.
23929 \begin_layout Standard
23931 \begin_inset Tabular
23932 <lyxtabular version="3" rows="2" columns="4">
23934 <column alignment="center" valignment="top" width="0pt">
23935 <column alignment="center" valignment="top" width="0pt">
23936 <column alignment="center" valignment="top" width="0pt">
23937 <column alignment="center" valignment="top" width="0pt">
23939 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23942 \begin_layout Plain Layout
23948 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23951 \begin_layout Plain Layout
23957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23960 \begin_layout Plain Layout
23966 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23969 \begin_layout Plain Layout
23977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23980 \begin_layout Plain Layout
23986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23989 \begin_layout Plain Layout
23990 \begin_inset Formula $Asin(x)+B$
23998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24001 \begin_layout Plain Layout
24009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24012 \begin_layout Plain Layout
24013 \begin_inset Formula $A\sin(x)+B$
24027 \begin_inset Newpage pagebreak
24033 \begin_layout Standard
24034 The following functions are predefined:
24037 \begin_layout Standard
24038 \begin_inset VSpace -2mm
24044 \begin_layout Standard
24046 \begin_inset Tabular
24047 <lyxtabular version="3" rows="9" columns="4">
24049 <column alignment="center" valignment="top" width="0pt">
24050 <column alignment="center" valignment="top" width="0pt">
24051 <column alignment="center" valignment="top" width="0pt">
24052 <column alignment="center" valignment="top" width="0pt">
24054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24057 \begin_layout Plain Layout
24063 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24066 \begin_layout Plain Layout
24072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24075 \begin_layout Plain Layout
24081 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24084 \begin_layout Plain Layout
24092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24095 \begin_layout Plain Layout
24103 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24106 \begin_layout Plain Layout
24114 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24117 \begin_layout Plain Layout
24125 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24128 \begin_layout Plain Layout
24138 <cell alignment="center" valignment="top" topline="true" leftline="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" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24187 \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" rightline="true" usebox="none">
24220 \begin_layout Plain Layout
24230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24233 \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" rightline="true" usebox="none">
24266 \begin_layout Plain Layout
24276 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24279 \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" rightline="true" usebox="none">
24312 \begin_layout Plain Layout
24322 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24325 \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" rightline="true" usebox="none">
24358 \begin_layout Plain Layout
24368 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24371 \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" rightline="true" usebox="none">
24404 \begin_layout Plain Layout
24414 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24417 \begin_layout Plain Layout
24425 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24428 \begin_layout Plain Layout
24436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24439 \begin_layout Plain Layout
24447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24450 \begin_layout Plain Layout
24466 \begin_layout Standard
24467 They can also be inserted with the math toolbar button
24468 \begin_inset Graphics
24469 filename ../images/math/functions.png
24477 \begin_layout Subsection
24478 Self-defined Functions
24482 \begin_layout Plain Layout
24483 Functions ! self-defined
24491 \begin_layout Standard
24492 To use a function that is not predefined, like for example the sign function
24493 sgn(x), there are two possibilities:
24496 \begin_layout Itemize
24497 Define the function by inserting the following line to the LaTeX-preamble
24501 \begin_layout Plain Layout
24506 DeclareMathOperator
24509 \begin_inset CommandInset ref
24511 reference "sub:Self-defined-Operators"
24521 \begin_inset Newline newline
24525 \begin_inset VSpace -3mm
24529 \begin_inset Newline newline
24536 DeclareMathOperator{
24544 \begin_layout Plain Layout
24549 DeclareMathOperator
24555 \begin_inset Newline newline
24559 \begin_inset VSpace -2mm
24563 \begin_inset Newline newline
24566 Now the new defined function can be called with the command
24575 \begin_layout Itemize
24576 Write the the formula as usual, mark the formula name, in our example the
24581 , and change it to mathematical text.
24582 At last a space is inserted between prefactor and function.
24585 \begin_layout Standard
24586 The result is the same with both methods as with a predefined function
24590 \begin_layout Plain Layout
24591 In LyX self-defined functions are displayed red, predefined ones black.
24599 \begin_layout Standard
24601 \begin_inset Tabular
24602 <lyxtabular version="3" rows="3" columns="2">
24604 <column alignment="center" valignment="top" width="0pt">
24605 <column alignment="center" valignment="top" width="0pt">
24607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24610 \begin_layout Plain Layout
24616 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24619 \begin_layout Plain Layout
24627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24630 \begin_layout Plain Layout
24638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24641 \begin_layout Plain Layout
24642 \begin_inset Formula $A\sgn(x)+B$
24652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24655 \begin_layout Plain Layout
24659 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24670 \begin_layout Plain Layout
24671 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24687 \begin_layout Standard
24688 The first method is more suitable when the self-defined function should
24689 be used several times.
24692 \begin_layout Subsection
24697 \begin_layout Plain Layout
24706 \begin_layout Standard
24707 For limits there are defined besides
24717 \begin_layout Plain Layout
24737 furthermore the following functions:
24740 \begin_layout Standard
24742 \begin_inset Tabular
24743 <lyxtabular version="3" rows="5" columns="2">
24745 <column alignment="center" valignment="top" width="0">
24746 <column alignment="center" valignment="top" width="0">
24748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24751 \begin_layout Plain Layout
24757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24760 \begin_layout Plain Layout
24762 \begin_inset Note Note
24765 \begin_layout Plain Layout
24772 is only used as spacer.
24784 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24787 \begin_layout Plain Layout
24795 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24798 \begin_layout Plain Layout
24799 \begin_inset Formula $\varliminf$
24809 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24812 \begin_layout Plain Layout
24820 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24823 \begin_layout Plain Layout
24824 \begin_inset Formula $\varlimsup$
24834 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24837 \begin_layout Plain Layout
24845 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24848 \begin_layout Plain Layout
24849 \begin_inset Formula $\varprojlim$
24859 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24862 \begin_layout Plain Layout
24870 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24873 \begin_layout Plain Layout
24874 \begin_inset Formula $\varinjlim$
24878 \begin_inset Formula $\raisebox{-2.5mm}{}$
24894 \begin_layout Standard
24895 \begin_inset VSpace medskip
24898 The limit is created by inserting a subscript.
24899 It is set right beside the function in an inline formula:
24902 \begin_layout Standard
24904 \begin_inset Tabular
24905 <lyxtabular version="3" rows="2" columns="2">
24907 <column alignment="center" valignment="top" width="0pt">
24908 <column alignment="center" valignment="top" width="0pt">
24910 <cell alignment="center" valignment="top" usebox="none">
24913 \begin_layout Plain Layout
24919 <cell alignment="center" valignment="top" usebox="none">
24922 \begin_layout Plain Layout
24923 \begin_inset space \hspace{}
24928 \begin_inset Note Note
24931 \begin_layout Plain Layout
24944 are used here as spacer.
24956 <cell alignment="center" valignment="top" usebox="none">
24959 \begin_layout Plain Layout
24968 \begin_layout Plain Layout
24981 \begin_layout Plain Layout
24995 <cell alignment="center" valignment="top" usebox="none">
24998 \begin_layout Plain Layout
24999 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
25015 \begin_layout Standard
25016 In a displayed formula the limit is set below the formula, as usual:
25017 \begin_inset Formula \[
25025 \begin_layout Subsection
25030 \begin_layout Plain Layout
25031 Functions ! modulo-
25039 \begin_layout Standard
25040 The modulo-function is special, because it exists in four variants.
25043 \begin_layout Standard
25044 The variants in a displayed formula:
25045 \begin_inset Formula \begin{align*}
25046 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
25047 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
25048 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
25049 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
25050 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
25057 \begin_layout Standard
25058 In an inline formula less space is set before the function names for all
25062 \begin_layout Section
25067 \begin_layout Plain Layout
25076 \begin_layout Subsection
25077 Special Characters in Mathematical Text
25080 \begin_layout Standard
25081 The following commands can only be used in mathematical text or in TeX-mode:
25084 \begin_layout Standard
25085 \begin_inset space \hfill{}
25089 \begin_inset Tabular
25090 <lyxtabular version="3" rows="8" columns="2">
25092 <column alignment="block" valignment="top" width="0">
25093 <column alignment="block" valignment="top" width="0">
25095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25098 \begin_layout Plain Layout
25104 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25107 \begin_layout Plain Layout
25115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25118 \begin_layout Plain Layout
25126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25129 \begin_layout Plain Layout
25130 \begin_inset Formula $\textrm{œ}$
25140 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25143 \begin_layout Plain Layout
25151 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25154 \begin_layout Plain Layout
25155 \begin_inset Formula $\textrm{Œ}$
25165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25168 \begin_layout Plain Layout
25176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25179 \begin_layout Plain Layout
25180 \begin_inset Formula $\textrm{æ}$
25190 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25193 \begin_layout Plain Layout
25201 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25204 \begin_layout Plain Layout
25205 \begin_inset Formula $\textrm{Æ}$
25215 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25218 \begin_layout Plain Layout
25226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25229 \begin_layout Plain Layout
25230 \begin_inset Formula $\textrm{\aa}$
25240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25243 \begin_layout Plain Layout
25250 \begin_layout Plain Layout
25254 \begin_layout Plain Layout
25262 \begin_layout Plain Layout
25273 \begin_layout Plain Layout
25289 \begin_layout Plain Layout
25297 \begin_layout Plain Layout
25308 \begin_layout Plain Layout
25324 \begin_layout Plain Layout
25335 \begin_layout Plain Layout
25343 \begin_layout Plain Layout
25354 \begin_layout Plain Layout
25370 \begin_layout Plain Layout
25387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25390 \begin_layout Plain Layout
25391 \begin_inset Formula $\textrm{Å}$
25401 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25404 \begin_layout Plain Layout
25412 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25415 \begin_layout Plain Layout
25416 \begin_inset Formula $\textrm{ı}$
25430 \begin_inset space \hfill{}
25434 \begin_inset Tabular
25435 <lyxtabular version="3" rows="8" columns="2">
25437 <column alignment="block" valignment="top" width="0">
25438 <column alignment="center" valignment="top" width="0">
25440 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25443 \begin_layout Plain Layout
25445 \begin_inset Note Note
25448 \begin_layout Plain Layout
25455 is used for separation, because otherwise the output will be ¡ and ¿ respective
25466 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25469 \begin_layout Plain Layout
25477 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25480 \begin_layout Plain Layout
25488 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25491 \begin_layout Plain Layout
25492 \begin_inset Formula $\textrm{ø}$
25502 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25505 \begin_layout Plain Layout
25513 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25516 \begin_layout Plain Layout
25517 \begin_inset Formula $\textrm{Ø}$
25527 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25530 \begin_layout Plain Layout
25538 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25541 \begin_layout Plain Layout
25542 \begin_inset Formula $\textrm{ł}$
25552 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25555 \begin_layout Plain Layout
25563 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25566 \begin_layout Plain Layout
25567 \begin_inset Formula $\textrm{Ł}$
25577 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25580 \begin_layout Plain Layout
25582 \begin_inset space \hspace{}
25590 \begin_layout Plain Layout
25604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25607 \begin_layout Plain Layout
25608 \begin_inset Formula $\textrm{!`}$
25618 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25621 \begin_layout Plain Layout
25623 \begin_inset space \hspace{}
25631 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25648 \begin_layout Plain Layout
25649 \begin_inset Formula $\textrm{?`}$
25659 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25662 \begin_layout Plain Layout
25670 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25673 \begin_layout Plain Layout
25674 \begin_inset Formula $\textrm{ȷ}$
25688 \begin_inset space \hfill{}
25694 \begin_layout Standard
25696 \begin_inset Formula $\textrm{\textrm{Å}}$
25700 \begin_inset Formula $\textrm{\textrm{Ø}}$
25703 can also be inserted via the math toolbar button
25704 \begin_inset Graphics
25705 filename ../images/math/digamma.png
25713 \begin_layout Standard
25714 An exception are the commands
25717 \begin_inset space \hspace{}
25726 \begin_inset space \hspace{}
25732 , because they can be inserted in LyX directly to text.
25735 \begin_layout Subsection
25737 \begin_inset CommandInset label
25739 name "sub:Accents-in-Text"
25747 \begin_layout Plain Layout
25756 \begin_layout Standard
25757 With the following commands all letters can be accented.
25758 The commands must be inserted in TeX-mode.
25761 \begin_layout Standard
25762 \begin_inset space \hfill{}
25766 \begin_inset Tabular
25767 <lyxtabular version="3" rows="8" columns="2">
25769 <column alignment="block" valignment="top" width="0">
25770 <column alignment="block" valignment="top" width="0">
25772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25775 \begin_layout Plain Layout
25781 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25784 \begin_layout Plain Layout
25792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25795 \begin_layout Plain Layout
25799 \begin_inset Quotes grd
25807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25810 \begin_layout Plain Layout
25814 \begin_layout Plain Layout
25830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25833 \begin_layout Plain Layout
25841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25844 \begin_layout Plain Layout
25848 \begin_layout Plain Layout
25864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25867 \begin_layout Plain Layout
25874 \begin_layout Plain Layout
25888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25891 \begin_layout Plain Layout
25895 \begin_layout Plain Layout
25911 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25914 \begin_layout Plain Layout
25922 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25925 \begin_layout Plain Layout
25929 \begin_layout Plain Layout
25945 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25948 \begin_layout Plain Layout
25955 \begin_layout Plain Layout
25969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25972 \begin_layout Plain Layout
25976 \begin_layout Plain Layout
25992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25995 \begin_layout Plain Layout
26002 \begin_layout Plain Layout
26016 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26019 \begin_layout Plain Layout
26023 \begin_layout Plain Layout
26039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26042 \begin_layout Plain Layout
26049 \begin_layout Plain Layout
26063 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26066 \begin_layout Plain Layout
26070 \begin_layout Plain Layout
26090 \begin_inset space \hfill{}
26094 \begin_inset Tabular
26095 <lyxtabular version="3" rows="8" columns="2">
26097 <column alignment="block" valignment="top" width="0">
26098 <column alignment="center" valignment="top" width="0">
26100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26103 \begin_layout Plain Layout
26109 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26112 \begin_layout Plain Layout
26120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26123 \begin_layout Plain Layout
26130 \begin_layout Plain Layout
26144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26147 \begin_layout Plain Layout
26151 \begin_layout Plain Layout
26167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26170 \begin_layout Plain Layout
26178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26181 \begin_layout Plain Layout
26185 \begin_layout Plain Layout
26201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26204 \begin_layout Plain Layout
26211 \begin_layout Plain Layout
26222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26225 \begin_layout Plain Layout
26229 \begin_layout Plain Layout
26245 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26248 \begin_layout Plain Layout
26256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26259 \begin_layout Plain Layout
26263 \begin_layout Plain Layout
26279 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26282 \begin_layout Plain Layout
26289 \begin_layout Plain Layout
26303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26306 \begin_layout Plain Layout
26310 \begin_layout Plain Layout
26326 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26329 \begin_layout Plain Layout
26336 \begin_layout Plain Layout
26350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26353 \begin_layout Plain Layout
26357 \begin_layout Plain Layout
26373 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26376 \begin_layout Plain Layout
26383 \begin_layout Plain Layout
26397 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26400 \begin_layout Plain Layout
26404 \begin_layout Plain Layout
26424 \begin_inset space \hfill{}
26430 \begin_layout Standard
26431 \begin_inset VSpace medskip
26440 also two different characters can be accented.
26449 \begin_layout Plain Layout
26464 \begin_layout Plain Layout
26476 \begin_layout Standard
26489 can in combination with vowels directly be inserted with the keyboard without
26491 The same applies for the tilde
26495 \begin_layout Plain Layout
26496 This only applies for keyboards where the tilde is defined as accent.
26505 in combination with
26520 \begin_layout Standard
26563 , and accents inserted directly with the keyboard are also available in
26565 For the other accents there are special math commands to be used in formulas,
26567 \begin_inset CommandInset ref
26569 reference "sub:Accents-for-one"
26576 \begin_layout Standard
26577 \begin_inset VSpace bigskip
26580 Furthermore, with the command
26590 \begin_layout Plain Layout
26598 all numbers and letters can be set into a circle, quasi accented with a
26599 circle, similar to the the copyright symbol.
26602 \begin_layout Standard
26604 \begin_inset Tabular
26605 <lyxtabular version="3" rows="3" columns="2">
26607 <column alignment="center" valignment="top" width="0">
26608 <column alignment="center" valignment="top" width="0">
26610 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26613 \begin_layout Plain Layout
26619 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26622 \begin_layout Plain Layout
26624 \begin_inset Note Note
26627 \begin_layout Plain Layout
26634 is only used as spacer.
26646 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26649 \begin_layout Plain Layout
26657 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26660 \begin_layout Plain Layout
26664 \begin_layout Plain Layout
26680 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26683 \begin_layout Plain Layout
26694 raisebox{-1.5pt}{W}}
26699 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26702 \begin_layout Plain Layout
26703 \begin_inset Formula $\raisebox{4.5mm}{}$
26710 \begin_layout Plain Layout
26728 \begin_inset Formula $\raisebox{-2mm}{}$
26744 \begin_layout Standard
26745 One has to take care that the character fits in the circle.
26756 \begin_layout Plain Layout
26758 \begin_inset CommandInset ref
26760 reference "sub:Font-Sizes"
26769 specifies thereby the size of the circle.
26780 \begin_layout Plain Layout
26782 \begin_inset CommandInset ref
26784 reference "sub:Boxes-without-Frame"
26793 the character can be centered.
26796 \begin_layout Subsection
26801 \begin_layout Plain Layout
26810 \begin_layout Standard
26811 Minuscule numbers are created with the command
26821 \begin_layout Plain Layout
26830 The command can be used in formulas and in TeX-mode.
26831 The command scheme is:
26834 \begin_layout Standard
26839 oldstylenums{number}
26842 \begin_layout Standard
26847 oldstylenums{0123456789
26850 \begin_inset Formula $\oldstylenums{0123456789}$
26856 \begin_layout Subsection
26857 Miscellaneous Special Characters
26858 \begin_inset CommandInset label
26860 name "sub:Miscellaneous-Special-Characters"
26868 \begin_layout Plain Layout
26869 Special characters ! miscellaneous
26877 \begin_layout Standard
26878 The following characters can only be inserted to formulas by using commands:
26881 \begin_layout Standard
26883 \begin_inset Tabular
26884 <lyxtabular version="3" rows="4" columns="2">
26886 <column alignment="center" valignment="top" width="0">
26887 <column alignment="center" valignment="top" width="0">
26889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26892 \begin_layout Plain Layout
26898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26901 \begin_layout Plain Layout
26909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26912 \begin_layout Plain Layout
26919 \begin_layout Plain Layout
26933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26936 \begin_layout Plain Layout
26937 \begin_inset Formula $\mathcircumflex$
26947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26950 \begin_layout Plain Layout
26958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26961 \begin_layout Plain Layout
26962 \begin_inset Formula $\_$
26972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26975 \begin_layout Plain Layout
26980 \begin_layout Plain Layout
26995 \begin_layout Plain Layout
27006 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27009 \begin_layout Plain Layout
27010 \begin_inset Formula $^{\circ}$
27026 \begin_layout Standard
27027 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27028 contains the following line
27032 \begin_layout Plain Layout
27033 More about this is described in
27034 \begin_inset CommandInset ref
27036 reference "sub:Text-Characters-in"
27048 \begin_layout Standard
27053 DeclareInputtext{176}{
27066 \begin_layout Section
27068 \begin_inset CommandInset label
27070 name "sec:Formula-Styles"
27078 \begin_layout Plain Layout
27087 \begin_layout Itemize
27088 There are two different alignment styles:
27092 \begin_layout Description
27093 Centered is the predefined standard
27096 \begin_layout Description
27097 Indented for this the option
27101 must be inserted in the menu
27103 Document\SpecialChar \menuseparator
27109 \begin_inset space ~
27115 \begin_layout Standard
27120 is used, the indentation can be adjusted with the length
27130 \begin_layout Plain Layout
27139 Should the distance be 15
27140 \begin_inset space \thinspace{}
27143 mm, the following command line is inserted in the LaTeX-preamble
27146 \begin_layout Standard
27156 \begin_layout Standard
27157 When no length is specified, the predefined value of 30
27158 \begin_inset space \thinspace{}
27165 \begin_layout Itemize
27166 And two different numbering styles:
27170 \begin_layout Description
27171 Right is the predefined standard
27174 \begin_layout Description
27175 Left for this the option
27179 must be inserted in the menu
27181 Document\SpecialChar \menuseparator
27187 \begin_inset space ~
27194 \begin_layout Standard
27203 can also be used together.
27204 In this case both options are inserted, separated by a comma.
27207 \begin_layout Standard
27208 The chosen styles are used for all displayed formulas of the document.
27209 When both, centered and indented formulas should be created in a document,
27215 The indented formulas are then set in a flalign environment, see
27216 \begin_inset CommandInset ref
27218 reference "sub:Flalign-Environment"
27225 \begin_layout Section
27227 \begin_inset CommandInset label
27229 name "sec:Multiline-Formulas"
27237 \begin_layout Plain Layout
27238 Formula ! multiline
27246 \begin_layout Subsection
27250 \begin_layout Standard
27251 In LyX multiline formulas are created by pressing
27262 that is described in
27263 \begin_inset CommandInset ref
27265 reference "sub:Standard-align-Environment"
27272 \begin_layout Standard
27273 There are other multiline formula environments that can be created via the
27276 Insert\SpecialChar \menuseparator
27280 These environments are described in the following sections.
27283 \begin_layout Standard
27284 In all multiline formula environments a new line is created by pressing
27290 To add or delete lines, the math toolbar buttons
27291 \begin_inset Graphics
27292 filename ../images/tabular-feature_append-row.png
27298 \begin_inset Graphics
27299 filename ../images/tabular-feature_delete-row.png
27304 , respectively, or the menu
27306 Edit\SpecialChar \menuseparator
27312 \begin_layout Subsubsection
27314 \begin_inset CommandInset label
27316 name "sub:Line-Separation"
27324 \begin_layout Plain Layout
27325 Formula ! multiline ! Line separation
27333 \begin_layout Standard
27334 There is sometimes not enough space in multiline formulas between the lines:
27335 \begin_inset Formula \begin{eqnarray*}
27336 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}\\
27337 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*}
27344 \begin_layout Standard
27345 In LaTeX additional line space is specified as optional argument of the
27347 This is not yet possible in LyX
27351 \begin_layout Plain Layout
27353 \begin_inset CommandInset href
27355 name "LyX-bug #1505"
27356 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27365 , therefore the whole formula must be inserted in TeX-mode.
27366 To add in our example space, the command
27374 is inserted at the end of the first line.
27379 \begin_layout Plain Layout
27386 \begin_layout Plain Layout
27388 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27391 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27398 \begin_layout Plain Layout
27402 left(B^{2}+x_{0}^{2}
27410 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27415 \begin_layout Plain Layout
27427 \begin_layout Standard
27428 \begin_inset VSpace bigskip
27431 To set the the line separation for all lines in a formula, the length
27441 \begin_layout Plain Layout
27451 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27462 \begin_inset space \thinspace{}
27467 \begin_inset space \thinspace{}
27470 mm additional line separation as in the previous example, the command
27473 \begin_layout Standard
27483 \begin_layout Standard
27484 is inserted in TeX-mode before the formula.
27485 This requires that the LaTeX-package
27493 \begin_layout Plain Layout
27498 is part of every LaTeX standard installation.
27507 \begin_layout Plain Layout
27513 was loaded in LaTeX-preamble with the line
27516 \begin_layout Standard
27524 \begin_layout Standard
27529 \begin_layout Plain Layout
27541 \begin_inset Formula \begin{eqnarray*}
27542 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}\\
27543 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*}
27550 \begin_layout Standard
27554 \begin_layout Plain Layout
27565 To get back to the predefined distance,
27571 is set to the value 3
27572 \begin_inset space \thinspace{}
27578 \begin_layout Subsubsection
27580 \begin_inset CommandInset label
27582 name "sub:Column-Separation"
27590 \begin_layout Plain Layout
27591 Formula ! multiline ! Column separation
27599 \begin_layout Standard
27600 Multiline formulas form a matrix.
27601 A formula in the eqnarray environment is for example a matrix with three
27603 By changing the column separation in this environment, the space beside
27604 the relation sign can be changed.
27607 \begin_layout Standard
27608 The column separation is specified with the length
27618 \begin_layout Plain Layout
27627 \begin_inset Newline newline
27630 column separation = 2
27631 \begin_inset space \thinspace{}
27641 \begin_inset Newline newline
27647 \begin_layout Standard
27657 \begin_layout Standard
27658 inserted in TeX-mode, sets for all following formulas a column separation
27660 \begin_inset space \thinspace{}
27664 To get back to the predefined distance,
27671 \begin_inset space \thinspace{}
27677 \begin_layout Standard
27679 \begin_inset space \thinspace{}
27682 cm column separation:
27686 \begin_layout Plain Layout
27698 \begin_inset Formula \begin{eqnarray*}
27700 C & \ne & A\end{eqnarray*}
27704 A formula with the predefined column separation for matrices of 10
27705 \begin_inset space \thinspace{}
27712 \begin_layout Plain Layout
27724 \begin_inset Formula \begin{eqnarray*}
27726 C & \ne & A\end{eqnarray*}
27733 \begin_layout Subsubsection
27738 \begin_layout Plain Layout
27747 \begin_layout Standard
27748 Long formulas can be typeset using these methods:
27751 \begin_layout Itemize
27752 When one side of the equation is much shorther than the line width, this
27753 one is chosen for the left side and the right side is typeset over two
27758 \begin_layout Plain Layout
27768 \begin_inset Formula \begin{eqnarray}
27769 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 \\
27770 & & -\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}
27778 \begin_layout Plain Layout
27788 \begin_inset Newline newline
27791 The minus sign at the beginning of the second line does normally not appear
27792 as operator because it is the first character of the line.
27793 Thus it would not be surrounded by space and could not be distinguished
27794 from the fraction bar.
27795 To avoid this, space was inserted behind the minus sign with the command
27806 \begin_layout Plain Layout
27814 \begin_inset CommandInset ref
27816 reference "sub:Variable-Space"
27829 \begin_layout Plain Layout
27840 \begin_layout Itemize
27841 When both sides of the equation are too long, the command
27851 \begin_layout Plain Layout
27860 It is inserted to the first column of the first line and effects that all
27861 further insertions overwrite the following columns:
27865 \begin_layout Plain Layout
27875 \begin_inset Formula \begin{eqnarray}
27876 \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 \\
27877 & & -\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 \\
27878 & & =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}
27886 \begin_layout Plain Layout
27896 \begin_inset Newline newline
27899 After the insertion of
27905 , the cursor is in a purple box that is a bit shifted to the left from the
27907 In this the formula is inserted.
27911 \begin_layout Plain Layout
27921 \begin_inset Newline newline
27924 The content of the further lines is inserted to the second or another formula
27926 The greater the column number where it was inserted, the larger the indentation.
27930 \begin_layout Plain Layout
27940 \begin_inset Newline newline
27944 \begin_inset Note Greyedout
27947 \begin_layout Plain Layout
27948 Note the following when using
27957 \begin_layout Itemize
27958 The formula doesn't use the full page width.
27960 \begin_inset space \thinspace{}
27964 \begin_inset space ~
27968 \begin_inset Formula $-B^{2}$
27971 is added to the first line in the above example, it would have been outside
27973 To better use the width, negative space can be inserted at the beginning
27977 \begin_layout Itemize
27978 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27983 \begin_layout Plain Layout
27984 \begin_inset CommandInset href
27986 name "LyX-bug #1429"
27987 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
27996 One can only set the cursor at the beginning of the line and move it with
28005 \begin_layout Itemize
28006 Other methods to set long formulas are offered by the environments described
28008 \begin_inset CommandInset ref
28010 reference "sub:Multline-Environment"
28015 \begin_inset CommandInset ref
28017 reference "sub:Multiline-Formula-Parts"
28024 \begin_layout Subsubsection
28026 \begin_inset CommandInset label
28028 name "sub:Multiline-Brackets"
28036 \begin_layout Plain Layout
28037 Brackets ! for multiline expressions
28045 \begin_layout Standard
28046 For brackets spanning multiple lines the following problem occurs:
28047 \begin_inset Formula \begin{eqnarray*}
28048 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28049 & & \left.\cdots+B-D\right]\end{eqnarray*}
28056 \begin_layout Standard
28057 The closing bracket is smaller than the opening bracket because brackets
28058 with variable size may not span multiple lines.
28061 \begin_layout Standard
28062 To set the bracket size for the second line correctly, the first line is
28073 \begin_layout Plain Layout
28081 and the second line with
28089 \begin_layout Plain Layout
28103 \begin_inset CommandInset ref
28105 reference "sub:Automatic-Bracket-Size"
28120 \begin_layout Plain Layout
28146 \begin_layout Plain Layout
28165 \begin_layout Plain Layout
28184 \begin_layout Plain Layout
28196 \begin_inset Formula $\downarrow$
28205 \begin_layout Plain Layout
28213 is inserted, because the multiplication operator with its limits is the
28214 largest symbol in the first line and this should be the size for the bracket
28215 in the second line.
28218 \begin_layout Standard
28219 The result is this:
28220 \begin_inset Formula \begin{eqnarray*}
28221 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28222 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28229 \begin_layout Subsection
28233 \begin_layout Standard
28234 Align environments can be used for every kind of multiline formulas.
28235 They are specially useful to set several formulas side by side.
28238 \begin_layout Standard
28239 Align environments consist of columns.
28240 The odd columns are right aligned, the even ones left aligned.
28241 Every line in an Align environment can be numbered.
28244 \begin_layout Standard
28245 Align environments are created via the menu
28247 Insert\SpecialChar \menuseparator
28253 Edit\SpecialChar \menuseparator
28254 Math\SpecialChar \menuseparator
28255 Change Formula Type
28257 already existing formulas can be converted to Align environments.
28260 \begin_layout Standard
28261 To add or delete columns, the math toolbar buttons
28262 \begin_inset Graphics
28263 filename ../images/tabular-feature_append-column.png
28269 \begin_inset Graphics
28270 filename ../images/tabular-feature_delete-column.png
28275 , respectively, or the menu
28277 Edit\SpecialChar \menuseparator
28283 \begin_layout Subsubsection
28284 Standard align Environment
28285 \begin_inset CommandInset label
28287 name "sub:Standard-align-Environment"
28295 \begin_layout Plain Layout
28296 Formula ! multiline ! align environment
28304 \begin_layout Standard
28305 This Align environment is created by presssing
28309 in a formula or by the menu
28311 Insert\SpecialChar \menuseparator
28312 Math\SpecialChar \menuseparator
28313 AMS align Environment
28318 \begin_layout Standard
28319 An example for two formulas set side by side, that are created with a four
28320 column align environment:
28321 \begin_inset Formula \begin{align*}
28322 A & =\sin(B) & C & =D\\
28323 C & \ne A & B & \ne D\end{align*}
28327 As it can be seen, the formulas in this environment are placed so as if
28336 \begin_layout Plain Layout
28344 \begin_inset CommandInset ref
28346 reference "sub:Variable-Space"
28357 before the first and after every even column.
28358 When the formula style
28364 \begin_layout Plain Layout
28366 \begin_inset CommandInset ref
28368 reference "sec:Formula-Styles"
28379 is used, the formula is set without the
28385 before the first column.
28388 \begin_layout Subsubsection
28389 Alignat Environment
28393 \begin_layout Plain Layout
28394 Formula ! multiline ! alignat environment
28402 \begin_layout Standard
28403 The alignat environment has no predefined column separation.
28404 It can be inserted manually with the spaces that are described
28405 \begin_inset CommandInset ref
28407 reference "sub:Space"
28414 \begin_layout Standard
28415 The above example in the alignat environment where 1
28416 \begin_inset space \thinspace{}
28419 cm space was inserted at the beginning of the second formula:
28420 \begin_inset Formula \begin{alignat*}{2}
28421 A & =\sin(B) & \hspace{1cm}C & =D\\
28422 C & \ne A & B & \ne D\end{alignat*}
28426 Because the column separation can be set separately for every column, this
28427 environment is especially suitable to set three and more formulas side
28431 \begin_layout Subsubsection
28432 Flalign Environment
28433 \begin_inset CommandInset label
28435 name "sub:Flalign-Environment"
28443 \begin_layout Plain Layout
28444 Formula ! multiline ! flalign environment
28452 \begin_layout Standard
28453 In this environment the first two columns are always set as much as possible
28454 to the left and the last two ones to the right.
28456 \begin_inset Formula \begin{flalign*}
28457 A & =1 & B & =2 & C & =3\\
28458 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28465 \begin_layout Standard
28466 By creating a flalign environment with an odd number of columns where an
28467 empty TeX-brace is inserted to the last column, several formulas in a document
28468 can be set to the left, although the formula style
28473 As example the indented formula
28474 \begin_inset CommandInset ref
28476 reference "eq:VolInt"
28481 \begin_inset Formula \begin{flalign}
28482 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28486 The first two columns contain the formula.
28487 To indent it as with the formula style
28492 \begin_inset space \thinspace{}
28495 pt space was inserted at the beginning of the first column.
28498 \begin_layout Subsection
28499 Eqnarray Environment
28503 \begin_layout Plain Layout
28504 Formula ! multiline ! eqnarray environment
28512 \begin_layout Standard
28513 When this environment has been created, three blue boxes appear.
28514 The content of the first box is right aligned, the content of the last
28516 The content of the middle box appears centered and a bit smaller, because
28517 it is designed to insert there only relation characters.
28518 \begin_inset Formula \begin{eqnarray*}
28519 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28521 A & = & A\end{eqnarray*}
28528 \begin_layout Subsection
28533 \begin_layout Plain Layout
28534 Formula ! multiline ! gather environment
28542 \begin_layout Standard
28543 This environment consists of only one centered column.
28544 Every line can be numbered.
28545 \begin_inset Formula \begin{gather}
28547 X=\textrm{-}1\end{gather}
28554 \begin_layout Subsection
28555 Multline Environment
28556 \begin_inset CommandInset label
28558 name "sub:Multline-Environment"
28566 \begin_layout Plain Layout
28567 Formula ! multiline ! multline environment
28575 \begin_layout Standard
28576 The multline environment consists, like the gather environment, of only
28578 But the first line is left aligned, the last one right aligned.
28579 All other lines are centered.
28580 Therefore this environment is suitable for long formulas.
28582 \begin_inset CommandInset ref
28584 reference "eq:lefteqn"
28588 in the multline environment:
28589 \begin_inset Formula \begin{multline}
28590 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}\\
28591 -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}\\
28592 =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}
28599 \begin_layout Standard
28600 In the output only the last (first) line of a multline environment appears
28601 numbered when the document numbering is right (left).
28605 \begin_layout Plain Layout
28606 numbering styles see
28607 \begin_inset CommandInset ref
28609 reference "sec:Formula-Styles"
28621 \begin_layout Standard
28630 \begin_layout Plain Layout
28648 \begin_layout Plain Layout
28658 a centered line can be right or left aligned, respectively.
28659 The commands are used as follows:
28662 \begin_layout Standard
28667 shoveright{line content}
28673 shoveleft{line content}
28676 \begin_layout Standard
28677 \begin_inset VSpace medskip
28688 \begin_layout Plain Layout
28698 specifies the distance of the first line from the left page margin.
28699 Predefined is the length 0
28700 \begin_inset space \thinspace{}
28706 \begin_layout Standard
28707 As example the above formula where the command
28710 \begin_layout Standard
28720 \begin_layout Standard
28721 was inserted in TeX-mode before:
28725 \begin_layout Plain Layout
28737 \begin_inset Formula \begin{multline}
28738 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}\\
28739 \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}}\\
28740 =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}
28748 \begin_layout Plain Layout
28759 The second line was left aligned using
28768 \begin_layout Subsection
28769 Multiline Formula Parts
28770 \begin_inset CommandInset label
28772 name "sub:Multiline-Formula-Parts"
28780 \begin_layout Plain Layout
28781 Formula ! multiline ! formula parts
28789 \begin_layout Standard
28790 To display only parts of a formula with multiple lines, one of the following
28791 environments are used:
28808 They can be inserted via the menu
28810 Insert\SpecialChar \menuseparator
28813 or by using the commands described in this section.
28816 \begin_layout Standard
28817 The first three have the same properties as the corresponding multiline
28818 formula environments, but it is possible to set further formula parts beside
28821 \begin_inset Formula \[
28822 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28823 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28824 \right\} \textrm{Uncertainty relations}\]
28831 \begin_layout Standard
28832 To get this formula, a displayed formula is created where the command
28840 \begin_layout Plain Layout
28851 A purple box appears around the blue formula box where now columns and
28852 lines can be added.
28853 Outside the multiline environment other formula parts can be set, like
28857 \begin_layout Standard
28858 The aligned environment is also suitable for long formulas whose lines are
28859 horizontally aligned.
28860 Using aligned in a displayed formula has the advantage that the formula
28861 number is vertically centered behind the lines.
28863 \begin_inset CommandInset ref
28865 reference "eq:kurzlang"
28869 in the aligned environment:
28870 \begin_inset Formula \begin{equation}
28871 \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}|}\\
28872 & -\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}
28880 \begin_layout Standard
28881 To use the environments
28903 \begin_layout Plain Layout
28921 \begin_layout Plain Layout
28939 \begin_layout Plain Layout
28947 are inserted, respectively.
28948 The split environment has the same properties as the aligned environment
28949 but it can only have two columns.
28952 \begin_layout Subsection
28953 Text in multiline Formulas
28954 \begin_inset CommandInset label
28956 name "sub:Text-in-multiline"
28964 \begin_layout Plain Layout
28974 \begin_layout Plain Layout
28975 Formula ! multiline ! text
28983 \begin_layout Standard
28984 In the Align environments, and the multline and gather environment, text
28985 can be inserted that will appear in a separate line and doesn't affect
28986 the column alignment.
28987 To do this, the command
28995 \begin_layout Plain Layout
29005 is used in the following scheme:
29008 \begin_layout Standard
29016 \begin_layout Standard
29017 The text should not be longer than a line because it cannot be hyphenated.
29018 As LyX doesn't yet support
29024 directly, the text is written as mathematical text.
29031 must hereby be at the beginning of a line and appears in the output above
29033 An example where the text was inserted at the beginning of the second line:
29034 \begin_inset Formula \begin{align}
29035 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29036 \intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29043 \begin_layout Section
29048 \begin_layout Plain Layout
29058 \begin_layout Plain Layout
29059 Formula ! numbering|see
29063 \begin_layout Plain Layout
29074 \begin_layout Plain Layout
29089 \begin_layout Subsection
29093 \begin_layout Standard
29094 Numbered formulas can be created with the menu
29096 Insert\SpecialChar \menuseparator
29097 Math\SpecialChar \menuseparator
29099 \begin_inset space ~
29107 \begin_inset space ~
29113 Existing formulas can be numbered with the menu
29115 Edit\SpecialChar \menuseparator
29116 Math\SpecialChar \menuseparator
29118 \begin_inset space ~
29126 \begin_inset space ~
29132 The formula number is displayed in LyX behind the formula as number sign
29134 The number sign is replaced in the output by the formula number.
29137 \begin_layout Standard
29138 When numbering is turned on in multiline formulas, all lines will be numbered.
29139 But the numbering can be controlled with the menu
29141 Edit\SpecialChar \menuseparator
29142 Math\SpecialChar \menuseparator
29144 \begin_inset space ~
29148 \begin_inset space ~
29152 \begin_inset space ~
29160 \begin_inset space ~
29168 \begin_layout Standard
29169 Except of inline formulas, all formulas can be numbered with two different
29171 \begin_inset CommandInset ref
29173 reference "sec:Formula-Styles"
29180 \begin_layout Subsection
29182 \begin_inset CommandInset label
29184 name "sub:Cross-References"
29192 \begin_layout Plain Layout
29193 Cross-references ! to formulas
29201 \begin_layout Standard
29202 All labeled formulas can be cross-referenced.
29203 A label is added by the menu
29205 Insert\SpecialChar \menuseparator
29208 or the toolbar button
29209 \begin_inset Graphics
29210 filename ../images/label-insert.png
29216 The cursor must hereby be inside a displayed formula.
29217 A dialog pops up displaying the prefix
29222 The label is inserted there behind the prefix.
29223 The predefined prefix means
29224 \begin_inset Quotes eld
29228 \begin_inset Quotes erd
29231 and makes it easier to find labels in large documents because it marks
29232 it as formula label to divide it from e.
29233 \begin_inset space \thinspace{}
29237 \begin_inset space ~
29241 To change a label, the menu
29243 Insert\SpecialChar \menuseparator
29249 \begin_layout Standard
29250 The name of the label is displayed in LyX within two parentheses behind
29252 A formula with a label is always numbered.
29255 \begin_layout Standard
29256 Cross-references are inserted via the menu
29258 Insert\SpecialChar \menuseparator
29261 or with the toolbar button
29262 \begin_inset Graphics
29263 filename ../images/dialog-show-new-inset_ref.png
29269 A formula cross-reference appears in the output as formula number.
29270 When in the cross-reference dialog window the format
29274 is chosen, the cross-reference appears in the output as formula number
29276 \begin_inset Newline newline
29279 By right-clicking on a cross-reference in LyX, one jumps to the formula
29280 that is referenced.
29283 \begin_layout Standard
29284 Here are as examples cross-references to formulas of the following subsections:
29285 \begin_inset Note Note
29288 \begin_layout Plain Layout
29289 Note the different cross-reference types.
29297 \begin_layout Standard
29299 \begin_inset CommandInset ref
29306 \begin_inset CommandInset ref
29314 \begin_inset CommandInset ref
29320 ) big Latin letters are used for the numbering in contrary to (
29321 \begin_inset CommandInset ref
29330 \begin_layout Standard
29331 \begin_inset VSpace medskip
29334 When the argument of
29342 \begin_layout Plain Layout
29350 \begin_inset CommandInset ref
29352 reference "sub:User-defined-Numbering"
29363 contains a box like in
29364 \begin_inset CommandInset ref
29366 reference "sub:Paragraph-Boxes"
29370 , the formula cannot be referenced.
29373 \begin_layout Subsection
29378 \begin_layout Plain Layout
29379 Formula numbering ! subnumbering
29387 \begin_layout Standard
29388 With the help of the commands
29392 begin{subequations}
29400 formulas can be subnumbered.
29401 Both commands are inserted in TeX-mode.
29404 \begin_layout Standard
29406 \begin_inset Formula \begin{equation}
29407 A=C-B\label{eq:a}\end{equation}
29415 \begin_layout Plain Layout
29419 addtocounter{equation}{-1}
29428 \begin_layout Plain Layout
29432 begin{subequations}
29438 \begin_inset VSpace -5mm
29442 \begin_inset Formula \begin{equation}
29443 B=C-A\label{eq:b}\end{equation}
29448 \begin_inset Formula \begin{equation}
29449 C=A+B\label{eq:c}\end{equation}
29456 \begin_layout Standard
29460 \begin_layout Plain Layout
29472 \begin_layout Standard
29473 To create the example, the following is done:
29476 \begin_layout Enumerate
29477 first formula is inserted
29480 \begin_layout Enumerate
29485 addtocounter{equation}{-1}
29487 begin{subequations}
29491 \begin_layout Plain Layout
29500 \begin_inset Newline newline
29505 is inserted after the first formula
29508 \begin_layout Enumerate
29509 second formula is inserted
29512 \begin_layout Enumerate
29513 third formula is inserted
29516 \begin_layout Enumerate
29523 is inserted after the third formula
29526 \begin_layout Standard
29527 Every formula between the commands
29539 is subnumbered as a, b,
29540 \begin_inset Newline linebreak
29543 c, \SpecialChar \ldots{}
29544 For multiline formulas every line will be subnumbered.
29545 All subnumbered formulas are treated as
29550 But as every numbered formula increases the counter
29554 by one, the command
29560 is needed to decrease it.
29561 Otherwise the formulas
29562 \begin_inset CommandInset ref
29569 \begin_inset CommandInset ref
29576 \begin_inset CommandInset ref
29582 would be numbered as
29583 \begin_inset CommandInset ref
29590 \begin_inset CommandInset ref
29597 \begin_inset CommandInset ref
29606 \begin_layout Standard
29607 By inserting the commands in TeX-mode, a space is created between the first
29610 \begin_inset space \thinspace{}
29613 mm vertical space is inserted after the command
29617 begin{subequations}
29620 When the formula style
29626 \begin_layout Plain Layout
29628 \begin_inset CommandInset ref
29630 reference "sec:Formula-Styles"
29642 \begin_inset space \thinspace{}
29645 mm space is inserted instead.
29648 \begin_layout Standard
29649 Here is an example for a multiline formula where the numbering was turned
29650 off for the second line:
29654 \begin_layout Plain Layout
29658 begin{subequations}
29664 \begin_inset Formula \begin{eqnarray}
29665 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29666 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
29667 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29675 \begin_layout Plain Layout
29687 \begin_layout Subsection
29688 User-defined Numbering
29689 \begin_inset CommandInset label
29691 name "sub:User-defined-Numbering"
29699 \begin_layout Plain Layout
29700 Formula numbering ! user-defined
29708 \begin_layout Standard
29712 \begin_layout Plain Layout
29713 Formula numbering ! self-defined delimiters
29718 With the standard numbering parentheses are set around the formula number.
29719 To replace the parentheses for example by vertical bars, the following
29720 line is added to the LaTeX-preamble:
29723 \begin_layout Standard
29735 \begin_inset Note Note
29738 \begin_layout Plain Layout
29739 This macro is already declared in the LaTeX-preamble for testing.
29740 To activate it, remove the percent sign at the beginning.
29748 \begin_layout Standard
29749 To use other characters, the vertical bars besides the
29753 are replaced by one ore more characters.
29754 To get only the formula number the vertical bars are omitted.
29757 \begin_layout Standard
29758 \begin_inset VSpace bigskip
29761 When there should be an expression of your choice instead of the consecutive
29762 formula number in parentheses behind the formula, the command
29772 \begin_layout Plain Layout
29781 \begin_inset Formula \begin{equation}
29782 A+B=C\tag{something}\label{eq:tag}\end{equation}
29786 In this example the command
29794 \begin_layout Plain Layout
29805 was inserted to the formula.
29808 \begin_layout Standard
29817 \begin_layout Plain Layout
29828 is inserted instead, the star prevents the parentheses around the expression:
29829 \begin_inset Formula \[
29830 A+B=C\tag*{something}\]
29837 \begin_layout Standard
29838 \begin_inset VSpace bigskip
29841 To restart the formula numbering with new document parts or sections, the
29842 following command is used:
29845 \begin_layout Standard
29850 @addtoreset{equation}{part}
29856 \begin_layout Plain Layout
29861 \begin_layout Plain Layout
29872 \begin_layout Plain Layout
29885 \begin_layout Plain Layout
29896 \begin_layout Plain Layout
29909 \begin_inset Newline newline
29913 \begin_inset Newline newline
29920 @addtoreset{equation}{section}
29923 \begin_layout Standard
29924 To be able to use these commands in TeX-mode, the
29925 \begin_inset Quotes eld
29929 \begin_inset Quotes erd
29932 character has to be made
29933 \begin_inset Quotes eld
29937 \begin_inset Quotes erd
29940 for LaTeX using the command
29954 So the command sequence in TeX-mode is:
29957 \begin_layout Standard
29963 \begin_inset Newline newline
29968 @addtoreset{equation}{section}
29969 \begin_inset Newline newline
29977 \begin_layout Standard
29978 In the LaTeX-preamble
29990 can be omitted as they are automatically internally inserted by LyX.
29993 \begin_layout Standard
30008 \begin_layout Plain Layout
30013 is part of the LaTeX-package
30021 \begin_layout Plain Layout
30022 Packages ! carlisle
30027 that is part of every LaTeX standard installation.
30036 \begin_layout Plain Layout
30037 Packages ! remreset
30042 has to be loaded in the LaTeX-preamble with the line
30045 \begin_layout Standard
30050 usepackage{remreset}
30053 \begin_layout Standard
30064 \begin_layout Plain Layout
30069 \begin_layout Plain Layout
30080 \begin_layout Plain Layout
30093 \begin_layout Plain Layout
30104 \begin_layout Plain Layout
30116 can be used with the same scheme as
30125 \begin_layout Standard
30126 \begin_inset VSpace bigskip
30129 Sometimes formulas should be numbered in the following form:
30132 \begin_layout Standard
30135 (section number.formula number)
30138 \begin_layout Standard
30139 The formula number should start with every section with
30140 \begin_inset Quotes eld
30144 \begin_inset Quotes erd
30150 \begin_layout Standard
30151 For this case there is the command
30161 \begin_layout Plain Layout
30169 , which is used with the following scheme:
30172 \begin_layout Standard
30177 numberwithin{counter}{sectioning}
30180 \begin_layout Standard
30181 Counter denotes what kind of numbering is affected, sectioning denotes what
30182 number is before the dot.
30185 \begin_layout Standard
30186 Thus in our case the following LaTeX-preamble or ERT line is used:
30189 \begin_layout Standard
30194 numberwithin{equation}{section}
30197 \begin_layout Standard
30198 This is the result:
30202 \begin_layout Plain Layout
30206 numberwithin{equation}{section}
30212 \begin_inset Formula \begin{equation}
30213 A+B=C\end{equation}
30220 \begin_layout Standard
30222 \begin_inset space \thinspace{}
30226 \begin_inset space ~
30229 tables so that the number of the part is the sectioning,
30230 \begin_inset Newline newline
30237 numberwithin{table}{part}
30242 \begin_layout Standard
30243 To go back to the standard numbering or to prevent this kind of numbering
30244 when it is defined by the document class, the following command is inserted
30245 as ERT or to the LaTeX-preamble:
30248 \begin_layout Standard
30261 \begin_layout Plain Layout
30275 \begin_layout Plain Layout
30291 \begin_inset Newline newline
30299 \begin_inset Newline newline
30311 \begin_layout Standard
30318 uses internally the command
30324 , described above, that also needs to be reverted.
30328 \begin_layout Plain Layout
30335 \begin_layout Plain Layout
30339 @removefromreset{equation}{section}
30342 \begin_layout Plain Layout
30354 \begin_layout Subsection
30355 Numbering with Roman Numbers and Letters
30356 \begin_inset CommandInset label
30358 name "sub:Numbering-with-Roman"
30366 \begin_layout Plain Layout
30367 Formula numbering ! with letters
30376 \begin_layout Plain Layout
30377 Formula numbering ! with Roman numbers
30385 \begin_layout Standard
30386 Formulas can also be numbered with Roman numbers and Latin letters.
30387 To number for example with small Roman numbers, the command
30390 \begin_layout Standard
30402 \begin_layout Standard
30403 is inserted before the formula in TeX-mode.
30414 \begin_layout Plain Layout
30422 redefines the predefined command
30438 \begin_layout Plain Layout
30445 has the same scheme like the command
30451 that is described in
30452 \begin_inset CommandInset ref
30454 reference "sec:User-defined-commands"
30468 is the formula counter.
30475 is used as prefix for a counter, the value of the counter is output as
30477 When a formula is numbered, LaTeX sets internally the command
30483 behind the formula.
30492 \begin_layout Plain Layout
30502 outputs the counter as small Roman number.
30505 \begin_layout Standard
30506 All formulas behind the command
30516 are now numbered Roman.
30517 To switch to numbering with big Roman numbers, the command is inserted
30534 \begin_layout Plain Layout
30546 \begin_inset Quotes eld
30550 \begin_inset Quotes erd
30553 with small Latin letters there is the command
30563 \begin_layout Plain Layout
30571 , for big ones there is the command
30581 \begin_layout Plain Layout
30594 \begin_layout Standard
30595 \begin_inset Note Greyedout
30598 \begin_layout Plain Layout
30603 Only maximal 26 formulas can be numbered with Latin letters in one document.
30611 \begin_layout Standard
30615 \begin_layout Plain Layout
30631 \begin_layout Standard
30632 \begin_inset Formula \begin{equation}
30633 A=\textrm{small roman}\label{eq:rom}\end{equation}
30641 \begin_layout Plain Layout
30655 \begin_inset Formula \begin{equation}
30656 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30664 \begin_layout Plain Layout
30678 \begin_inset Formula \begin{equation}
30679 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30687 \begin_layout Plain Layout
30701 \begin_inset Formula \begin{equation}
30702 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30709 \begin_layout Standard
30710 To switch back to the default numbering, insert the command:
30713 \begin_layout Standard
30726 \begin_layout Plain Layout
30737 \begin_layout Standard
30741 \begin_layout Plain Layout
30755 \begin_inset Formula \begin{equation}
30756 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30763 \begin_layout Standard
30764 \begin_inset VSpace medskip
30767 As you see, formulas are numbered serially independent from the numbering
30769 When then numbering should start with
30770 \begin_inset Quotes eld
30774 \begin_inset Quotes erd
30777 when the style is changed, new equation counters have to be defined.
30778 A description about this can be found in the file
30779 \begin_inset CommandInset href
30781 target "Formula-numbering.lyx"
30788 \begin_layout Section
30789 User-defined commands
30790 \begin_inset CommandInset label
30792 name "sec:User-defined-commands"
30800 \begin_layout Plain Layout
30801 User-defined commands
30809 \begin_layout Standard
30810 Many LaTeX-commands are too long to be used frequently.
30811 But it is possible to define with the command
30821 \begin_layout Plain Layout
30829 new shorter commands.
30832 \begin_layout Standard
30833 The command scheme of
30842 \begin_layout Standard
30847 newcommand{new command name}[number of arguments][optional
30852 \begin_inset Newline newline
30859 \begin_layout Plain Layout
30874 \begin_layout Plain Layout
30881 {command definition}
30884 \begin_layout Standard
30885 \begin_inset Note Greyedout
30888 \begin_layout Plain Layout
30893 Assure that the name of the new command is not already used in your document
30894 or by LaTeX-packages that you use.
30895 When you for example define the command
30907 , you get an error message because
30913 is already defined as command for
30914 \begin_inset Quotes eld
30918 \begin_inset Formula $\le$
30922 \begin_inset Quotes erd
30933 \begin_layout Standard
30934 \begin_inset Note Greyedout
30937 \begin_layout Plain Layout
30942 The names of user-defined commands may only consist of Latin letters.
30950 \begin_layout Standard
30951 The number of arguments is an integer in the range 0
30952 \begin_inset space \thinspace{}
30956 \begin_inset space \thinspace{}
30959 9 and specifies how many arguments the new command should have.
30960 With the optional value a value for an optional argument can be predefined.
30961 When this is done, the
30969 rgument of the new command is automatically an optional one.
30972 \begin_layout Standard
30973 Here are some examples:
30976 \begin_layout Itemize
30977 To define the command
30989 , the LaTeX-preamble line is:
30993 \begin_layout Plain Layout
31005 \begin_inset Newline newline
31017 \begin_layout Itemize
31018 To define the command
31030 , the argument (that should be underlined) must be taken into account.
31031 For this the preamble line is:
31035 \begin_layout Plain Layout
31047 \begin_inset Newline newline
31062 \begin_layout Plain Layout
31074 \begin_inset Newline newline
31083 acts as argument placeholder, the
31087 behind it denotes that it is the placeholder for the first argument.
31090 \begin_layout Itemize
31098 \begin_inset space \thinspace{}
31102 \begin_inset space ~
31115 \begin_layout Plain Layout
31127 \begin_inset Newline newline
31136 framebox#1#2{$#3$}}
31142 \begin_layout Plain Layout
31154 \begin_inset Newline newline
31159 The two Dollar signs creates the extra formula needed for
31166 \begin_inset CommandInset ref
31168 reference "sub:Boxes-with-Frame"
31175 \begin_layout Itemize
31176 To create a new command for
31182 where the color for the box needn't to be specified, the argument for the
31183 color is defined optional:
31187 \begin_layout Plain Layout
31199 \begin_inset Newline newline
31208 fcolorbox{#2}{#1}{$#3$}}
31214 \begin_layout Plain Layout
31224 \begin_inset Newline newline
31227 When the color is not specified when using
31233 , the predefined color
31240 \begin_layout Standard
31241 A test of the new defined commands:
31244 \begin_layout Standard
31246 \begin_inset Tabular
31247 <lyxtabular version="3" rows="6" columns="2">
31249 <column alignment="center" valignment="top" width="0">
31250 <column alignment="center" valignment="top" width="0">
31252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31255 \begin_layout Plain Layout
31261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31264 \begin_layout Plain Layout
31266 \begin_inset Note Note
31269 \begin_layout Plain Layout
31276 is only used as spacer.
31288 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31291 \begin_layout Plain Layout
31298 \begin_layout Plain Layout
31312 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31315 \begin_layout Plain Layout
31316 \begin_inset Formula $A\gr B$
31326 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31329 \begin_layout Plain Layout
31337 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31340 \begin_layout Plain Layout
31341 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
31351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31354 \begin_layout Plain Layout
31358 \begin_inset Formula $\to$
31364 \begin_inset Formula $\to$
31375 \begin_layout Plain Layout
31389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31392 \begin_layout Plain Layout
31393 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
31403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31406 \begin_layout Plain Layout
31410 \begin_inset Formula $\to$
31421 \begin_layout Plain Layout
31435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31438 \begin_layout Plain Layout
31439 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
31449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31452 \begin_layout Plain Layout
31458 \begin_inset Formula $\to$
31469 \begin_layout Plain Layout
31483 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31486 \begin_layout Plain Layout
31487 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
31503 \begin_layout Section
31508 \begin_layout Plain Layout
31517 \begin_layout Standard
31518 To create diagrams, the LaTeX-package
31524 \begin_layout Plain Layout
31529 is part of every LaTeX standard installation.
31540 \begin_layout Plain Layout
31547 It is loaded in the LaTeX-preamble with the line
31550 \begin_layout Standard
31558 \begin_layout Standard
31559 Diagrams visualize relations and look like this:
31560 \begin_inset Formula \[
31561 \begin{CD}A@>>>B@>>>C\\
31563 F@<<<E@<<<D\end{CD}\]
31570 \begin_layout Standard
31571 To get them, the command
31579 \begin_layout Plain Layout
31589 is inserted to a formula.
31590 A blue box appears with two dashed lines where further commands can be
31596 a new line is created.
31597 Horizontal relations are inserted in odd, vertical in even formula lines.
31600 \begin_layout Standard
31601 To create the relations there are the following commands:
31604 \begin_layout Itemize
31609 creates a left arrow,
31620 \begin_layout Itemize
31625 creates an up arrow,
31633 a vertical equal sign
31636 \begin_layout Itemize
31642 is a placeholder for non-existent relations
31645 \begin_layout Standard
31646 All arrows can be labeled as follows:
31649 \begin_layout Itemize
31650 Is text inserted between the first and second < or >, resp., it is placed
31652 When it is inserted between the second and third one, it appears under
31656 \begin_layout Itemize
31657 When text for vertical arrows is inserted between the first and second A
31658 or V, resp., it is placed left beside the arrow.
31659 When it is inserted between the second and third one, it appears right
31661 If the text contains an A or V, these letters must be set into a TeX-brace.
31664 \begin_layout Standard
31665 As example a diagram with all possible relations:
31668 \begin_layout Standard
31669 \begin_inset Formula \[
31670 \begin{CD}A@>j>>B@>>k>C@=F\\
31672 D@<<j<E@>k>>F@=C\end{CD}\]
31679 \begin_layout Standard
31680 The command for this is:
31681 \begin_inset Newline newline
31692 \begin_layout Plain Layout
31701 A@>j>>B@>>k>C@=F Ctrl-Enter
31702 \begin_inset Newline newline
31709 \begin_layout Plain Layout
31724 \begin_layout Plain Layout
31737 \begin_layout Plain Layout
31749 \begin_inset Formula $\to$
31755 \begin_inset Newline newline
31762 \begin_layout Plain Layout
31777 \begin_layout Plain Layout
31790 \begin_layout Plain Layout
31800 \begin_layout Standard
31801 \begin_inset Newpage newpage
31807 \begin_layout Section
31812 \begin_layout Plain Layout
31825 \begin_layout Plain Layout
31826 Other useful math tips can be found in
31827 \begin_inset CommandInset citation
31842 \begin_layout Plain Layout
31850 \begin_inset Note Note
31853 \begin_layout Plain Layout
31856 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31859 \begin_layout Plain Layout
31862 texorpdfstring is in section
31863 \begin_inset CommandInset ref
31865 reference "sub:Formulas-in-Section"
31878 \begin_layout Plain Layout
31888 \begin_layout Plain Layout
31893 \begin_layout Plain Layout
31900 Chemical characters
31904 \begin_layout Plain Layout
31919 \begin_layout Subsection
31920 Chemical Symbols and Equations
31921 \begin_inset CommandInset label
31923 name "sub:Chemical-Symbols-and"
31931 \begin_layout Plain Layout
31932 Chemical characters ! Symbols
31941 \begin_layout Plain Layout
31951 \begin_layout Plain Layout
31960 \begin_layout Standard
31961 An example text from chemistry:
31964 \begin_layout Quote
31966 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31969 -ion reacts with two
31970 \begin_inset Formula $\mathrm{Na^{+}}$
31973 -ions to sodium sulfate
31974 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31978 The chemical equation for this is:
31979 \begin_inset Formula \[
31980 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
31987 \begin_layout Standard
31988 This chemical equation can directly be created as formula.
31989 To avoid that the symbols appear italic, everything is highlighted and
31990 changed by the shortcut
31993 \begin_inset space ~
31998 to the upright font style.
32002 \begin_layout Plain Layout
32008 \begin_inset CommandInset ref
32010 reference "sub:Font-Styles"
32022 \begin_layout Subsection
32027 \begin_layout Plain Layout
32036 \begin_layout Standard
32037 Negative numbers often look ugly in formulas because the minus sign before
32038 the number is set with the same length as the minus operator sign.
32039 When writing the negative number in normal text, the minus sign appears
32043 \begin_layout Standard
32044 Thus, the problem disappears when converting the minus sign to mathematical
32048 \begin_layout Standard
32049 An example to visualize the problem:
32052 \begin_layout Standard
32054 \begin_inset Tabular
32055 <lyxtabular version="3" rows="3" columns="2">
32057 <column alignment="right" valignment="top" width="0">
32058 <column alignment="left" valignment="top" width="0">
32060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32063 \begin_layout Plain Layout
32069 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32072 \begin_layout Plain Layout
32080 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32083 \begin_layout Plain Layout
32089 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32092 \begin_layout Plain Layout
32093 \begin_inset Formula $x=-2$
32103 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32106 \begin_layout Plain Layout
32112 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32115 \begin_layout Plain Layout
32116 \begin_inset Formula $x=\textrm{-}2$
32132 \begin_layout Subsection
32133 Comma as Decimal Separator
32137 \begin_layout Plain Layout
32146 \begin_layout Standard
32147 In LaTeX a comma inside a formula is used, according to the English convention,
32148 as number group separator.
32149 So there will be space added behind all commas in formulas.
32152 \begin_layout Standard
32153 To avoid this, the comma is highlighted and changed to mathematical text
32157 \begin_inset space ~
32165 \begin_layout Standard
32166 To use all formula commas in the document as decimal separator, the file
32175 \begin_layout Plain Layout
32180 is part of the LaTeX-package
32188 \begin_layout Plain Layout
32193 \begin_layout Plain Layout
32216 \begin_layout Plain Layout
32222 is loaded with the LaTeX-preamble line
32225 \begin_layout Standard
32233 \begin_layout Subsection
32235 \begin_inset CommandInset label
32237 name "sub:Physical-Vectors"
32245 \begin_layout Plain Layout
32254 \begin_layout Standard
32255 Predefined vectors are offered by the LaTeX-package
32263 \begin_layout Plain Layout
32268 should be part of every LaTeX standard installation.
32277 \begin_layout Plain Layout
32283 that is loaded with the LaTeX-preamble line
32286 \begin_layout Standard
32294 \begin_layout Standard
32298 \begin_layout Plain Layout
32308 \begin_inset Note Note
32311 \begin_layout Plain Layout
32312 The following table will only be displayed when the LaTeX-package
32321 The following commands are defined:
32324 \begin_layout Standard
32326 \begin_inset Tabular
32327 <lyxtabular version="3" rows="4" columns="2">
32329 <column alignment="center" valignment="top" width="0">
32330 <column alignment="center" valignment="top" width="0">
32332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32335 \begin_layout Plain Layout
32341 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32344 \begin_layout Plain Layout
32352 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32355 \begin_layout Plain Layout
32365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32368 \begin_layout Plain Layout
32369 \begin_inset Formula $\Bra{\psi}$
32379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32382 \begin_layout Plain Layout
32392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32395 \begin_layout Plain Layout
32396 \begin_inset Formula $\Ket{\psi}$
32406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32409 \begin_layout Plain Layout
32421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32424 \begin_layout Plain Layout
32425 \begin_inset Formula $\Braket{\psi|\phi}$
32441 \begin_layout Standard
32448 assures that all vertical bars are set in the size of the surrounding brackets:
32449 \begin_inset Formula \[
32450 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32458 \begin_layout Plain Layout
32468 \begin_inset Note Note
32471 \begin_layout Plain Layout
32472 The following will be displayed when the LaTeX-package
32484 \begin_layout Standard
32485 You need to install the LaTeX-package
32489 to see the rest of this subsection in the output.
32492 \begin_layout Standard
32496 \begin_layout Plain Layout
32508 \begin_layout Standard
32515 can also be achieved using the command
32521 , that is described in
32522 \begin_inset CommandInset ref
32524 reference "sub:Automatic-Bracket-Size"
32531 \begin_layout Subsection
32532 Self-defined Fractions
32533 \begin_inset CommandInset label
32535 name "sub:Self-defined-Fractions"
32543 \begin_layout Plain Layout
32544 Fractions ! self-defined
32552 \begin_layout Standard
32553 To define custom commands for fractions, the command
32563 \begin_layout Plain Layout
32571 is used in the following scheme:
32574 \begin_layout Standard
32587 bracket}{fraction bar thickness}{style}
32588 \begin_inset Newline newline
32595 \begin_layout Plain Layout
32610 \begin_layout Plain Layout
32617 {numerator}{denominator}
32620 \begin_layout Standard
32621 The style is a number in the range of 0
32622 \begin_inset space \thinspace{}
32626 \begin_inset space \thinspace{}
32632 \begin_layout Standard
32634 \begin_inset Tabular
32635 <lyxtabular version="3" rows="5" columns="2">
32637 <column alignment="center" valignment="top" width="0">
32638 <column alignment="center" valignment="top" width="0">
32640 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32643 \begin_layout Plain Layout
32649 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32652 \begin_layout Plain Layout
32660 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32663 \begin_layout Plain Layout
32669 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32672 \begin_layout Plain Layout
32673 display style formula
32680 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32683 \begin_layout Plain Layout
32689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32692 \begin_layout Plain Layout
32700 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32703 \begin_layout Plain Layout
32709 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32712 \begin_layout Plain Layout
32720 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32723 \begin_layout Plain Layout
32729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32732 \begin_layout Plain Layout
32746 \begin_layout Standard
32747 When no style is given, the size is adjusted to the surrounding environment
32748 like for the command
32757 \begin_layout Standard
32758 When no fraction bar thickness is given, the predefined value of 0.4
32759 \begin_inset space \thinspace{}
32765 \begin_layout Standard
32766 \begin_inset VSpace medskip
32769 For example, the commands
32782 \begin_inset CommandInset ref
32784 reference "sub:Fractions"
32788 are defined with the commands
32791 \begin_layout Standard
32800 genfrac{}{}{}{0}{#1}{#2}}
32803 \begin_layout Standard
32807 \begin_layout Standard
32816 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32819 \begin_layout Standard
32820 \begin_inset VSpace medskip
32823 To define a fraction where the fraction bar thickness can be given as optional
32824 argument, the following line is inserted to the LaTeX-preamble:
32827 \begin_layout Standard
32836 genfrac{}{}{#1}{}{#2}{#3}}
32839 \begin_layout Standard
32841 \begin_inset Formula \begin{align*}
32842 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32843 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
32847 As one can see, the distance of the numerator and the denominator to the
32848 fraction bar is round about three times the bar thickness.
32851 \begin_layout Subsection
32853 \begin_inset CommandInset label
32855 name "sub:Canceled-Formulas"
32863 \begin_layout Plain Layout
32872 \begin_layout Standard
32873 To cancel formulas or formula parts, the LaTeX-package
32881 \begin_layout Plain Layout
32886 is part of every LaTeX standard installation.
32895 \begin_layout Plain Layout
32901 has to be loaded with the LaTeX-preamble line
32904 \begin_layout Standard
32909 usepackage[samesize]{cancel}
32912 \begin_layout Standard
32913 There are four ways to cancel formulas:
32916 \begin_layout Standard
32918 \begin_inset Tabular
32919 <lyxtabular version="3" rows="5" columns="2">
32921 <column alignment="center" valignment="top" width="0">
32922 <column alignment="center" valignment="top" width="0">
32924 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32927 \begin_layout Plain Layout
32933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32936 \begin_layout Plain Layout
32938 \begin_inset Note Note
32941 \begin_layout Plain Layout
32954 are used here as spacer.
32966 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32969 \begin_layout Plain Layout
32978 \begin_layout Plain Layout
32992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32995 \begin_layout Plain Layout
32996 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
33006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33009 \begin_layout Plain Layout
33018 \begin_layout Plain Layout
33032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33035 \begin_layout Plain Layout
33036 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
33046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33049 \begin_layout Plain Layout
33058 \begin_layout Plain Layout
33072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33075 \begin_layout Plain Layout
33076 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
33086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33089 \begin_layout Plain Layout
33093 \begin_inset Formula $\to$
33104 \begin_layout Plain Layout
33118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33121 \begin_layout Plain Layout
33122 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
33138 \begin_layout Standard
33145 is especially suitable to visualize the reduction of fractions within formulas:
33146 \begin_inset Formula \[
33147 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
33154 \begin_layout Subsection
33155 Formulas in Section Headings
33156 \begin_inset CommandInset label
33158 name "sub:Formulas-in-Section"
33166 \begin_layout Plain Layout
33167 Formula ! in section headings
33175 \begin_layout Standard
33176 When formulas are used in section headings, the following has to be taken
33180 \begin_layout Standard
33181 \begin_inset Note Greyedout
33184 \begin_layout Plain Layout
33193 \begin_layout Plain Layout
33194 Packages ! hyperref
33199 support is enabled in the document settings dialog under
33202 \begin_inset space ~
33207 , PDF-bookmarks are created for every section heading in the table of contents.
33208 If a section heading contains formulas, they are incorrectly displayed
33209 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33218 \begin_layout Standard
33219 Both problems can be solved by inserting at the end of the section heading
33220 a short title with the menu
33222 Insert\SpecialChar \menuseparator
33224 \begin_inset space ~
33230 Short titles are used as alternative for multiline section headings to
33231 keep the table of contents clearly arranged.
33232 Only the short title appears in the table of contents and therefore also
33233 in the PDF-bookmark.
33236 \begin_layout Standard
33237 When formulas should be used in the table of contents but
33241 is used, one can use the following command in TeX-mode:
33244 \begin_layout Standard
33249 texorpdfstring{part}{alternative}
33253 \begin_layout Plain Layout
33264 \begin_layout Standard
33265 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33266 This can be characters, formulas, footnotes, but also cross-references.
33267 The alternative is used instead of the part for the bookmark.
33270 \begin_layout Standard
33271 Here are two example headings:
33272 \begin_inset VSpace -3mm
33279 \begin_layout Plain Layout
33291 \begin_layout Subsubsection
33292 Heading without formula in table of contents
33293 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33297 \begin_inset OptArg
33300 \begin_layout Plain Layout
33301 Heading without formula in table of contents
33309 \begin_layout Subsubsection
33310 Heading with formula in table of contents
33314 \begin_layout Plain Layout
33324 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33331 \begin_layout Plain Layout
33341 \begin_layout Standard
33345 \begin_layout Plain Layout
33354 In the first heading a short title was used, in the second one
33363 \begin_layout Standard
33364 To get the same formatting as for the other headings, the complete heading
33367 boldmath environment
33373 \begin_layout Plain Layout
33375 \begin_inset CommandInset ref
33377 reference "sub:Bold-Formulas"
33389 \begin_layout Subsection
33390 Formulas in multi-column Text
33394 \begin_layout Plain Layout
33395 Formula ! in multi-column text
33403 \begin_layout Standard
33404 Formulas in multi-column text are often too wide to fit into a column and
33405 thus need to be set over the whole page width.
33406 This is done by using the LaTeX-package
33414 \begin_layout Plain Layout
33419 is part of every LaTeX standard installation.
33428 \begin_layout Plain Layout
33429 Packages ! multicol
33434 , that is loaded with the LaTeX-preamble line
33437 \begin_layout Standard
33442 usepackage{multicol}
33445 \begin_layout Standard
33446 \begin_inset Note Greyedout
33449 \begin_layout Plain Layout
33450 Note herby that the setting
33453 \begin_inset space ~
33460 Document\SpecialChar \menuseparator
33466 \begin_inset space ~
33486 \begin_layout Standard
33487 Before the multi-column text the command
33490 \begin_layout Standard
33495 begin{multicols}{column number}
33498 \begin_layout Standard
33499 is written in TeX-mode.
33500 The column number is a number in the range of 2
33501 \begin_inset space \thinspace{}
33505 \begin_inset space \thinspace{}
33509 Before the formula the multi-column text is ended by inserting the command
33512 \begin_layout Standard
33520 \begin_layout Standard
33524 \begin_layout Standard
33525 Due to the command some space is automatically added before the formula.
33527 \begin_inset space \thinspace{}
33530 mm vertical space is inserted before the formula.
33531 When the formula style
33537 \begin_layout Plain Layout
33539 \begin_inset CommandInset ref
33541 reference "sec:Formula-Styles"
33553 \begin_inset space \thinspace{}
33556 mm space is inserted instead.
33559 \begin_layout Standard
33560 As example a multi-column text with a displayed formula:
33563 \begin_layout Standard
33567 \begin_layout Plain Layout
33571 begin{multicols}{2}
33576 Das Spektrum wird fouriertransformiert.
33577 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33578 , Lösungsmittel) zu trennen.
33579 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33580 nun das Aussehen des Ausgangssignals.
33581 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33582 über alle Phasen integrieren muss.
33584 \begin_inset Formula $S$
33587 unser normiertes Ausgangssignal and
33588 \begin_inset Formula $P$
33591 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33595 \begin_layout Plain Layout
33605 \begin_inset VSpace -6mm
33609 \begin_inset Formula \begin{equation}
33610 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33618 \begin_layout Plain Layout
33622 begin{multicols}{2}
33628 \begin_inset Formula $S_{0}$
33631 das Signal ohne Gradient ist and the Normierungsbedingung
33632 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33636 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33638 \begin_inset Formula $\nicefrac{\pi}{2}$
33642 \begin_inset space \thinspace{}
33645 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33646 das Signal zusätzlich abschwächt.
33647 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33649 \begin_inset Formula $T_{2}$
33655 \begin_layout Standard
33659 \begin_layout Plain Layout
33671 \begin_layout Subsection
33672 Formulas with Description of Variables
33676 \begin_layout Plain Layout
33677 Formula ! with description of variables
33685 \begin_layout Standard
33686 To describe variables within a formula, like in formula
33687 \begin_inset CommandInset ref
33689 reference "eq:within"
33698 \begin_inset Formula $n$
33702 \begin_inset space ~
33705 matrix is used with left aligned columns for the
33706 \begin_inset Formula $n$
33713 \begin_layout Plain Layout
33715 \begin_inset CommandInset ref
33717 reference "sec:Matrices"
33726 To set the description in a smaller size, before the matrix e.
33727 \begin_inset space \thinspace{}
33731 \begin_inset space ~
33744 \begin_layout Plain Layout
33746 \begin_inset CommandInset ref
33748 reference "sub:Font-Sizes"
33760 \begin_layout Standard
33761 When the formula style
33767 \begin_layout Plain Layout
33769 \begin_inset CommandInset ref
33771 reference "sec:Formula-Styles"
33792 \begin_layout Plain Layout
33799 only works in formulas with the style
33804 \begin_inset CommandInset ref
33806 reference "sub:Variable-Space"
33815 is inserted before and after the matrix to have the same separation of
33816 the matrix from the equation and the side margin.
33819 \begin_layout Standard
33820 When the formula style
33824 is used, the method described in
33825 \begin_inset CommandInset ref
33827 reference "sub:Flalign-Environment"
33831 is used to indent formulas.
33833 \begin_inset CommandInset ref
33835 reference "eq:within"
33839 consists of five columns whereas in the first two columns contain the equation,
33840 the third the matrix, and the last one an empty TeX-brace.
33841 \begin_inset Formula \begin{flalign}
33842 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
33843 \rho & \textrm{density}\\
33844 V & \textrm{volume}\\
33845 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33852 \begin_layout Subsection
33853 Upright small Greek Letters
33854 \begin_inset CommandInset label
33856 name "sub:Upright-small-Greek"
33864 \begin_layout Plain Layout
33865 Greek letters ! upright
33873 \begin_layout Standard
33874 Most of the math fonts only provide italic small Greek letters.
33875 But for symbols of elementary particles like pions and neutrinos, upright
33876 Greek letters are needed.
33885 \begin_layout Plain Layout
33890 is part of the LaTeX-package
33898 \begin_layout Plain Layout
33903 \begin_layout Plain Layout
33926 \begin_layout Plain Layout
33932 that is loaded with the LaTeX-preamble line
33935 \begin_layout Standard
33940 usepackage{upgreek}
33943 \begin_layout Standard
33949 \begin_layout Plain Layout
33959 \begin_inset Note Note
33962 \begin_layout Plain Layout
33963 The following table will only be displayed when the LaTeX-package
33972 They are created when the command for a small Greek letters is started
33978 For example the command
33985 \begin_inset Formula $\uptau$
33991 \begin_layout Standard
33992 With these commands reactions of elementary particles can be typeset:
33993 \begin_inset Formula \[
33994 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
34001 \begin_layout Standard
34002 The upright letters are more bold and wider than the italic ones.
34003 They should therefore not be used for units like
34004 \begin_inset Quotes eld
34008 \begin_inset Quotes erd
34014 \begin_layout Standard
34018 \begin_layout Plain Layout
34028 \begin_inset Note Note
34031 \begin_layout Plain Layout
34032 The following will be displayed when the LaTeX-package
34044 \begin_layout Standard
34045 You need to install the LaTeX-package
34049 to see the rest of this subsection in the output.
34052 \begin_layout Standard
34056 \begin_layout Plain Layout
34068 \begin_layout Subsection
34069 Text Characters in Formulas
34070 \begin_inset CommandInset label
34072 name "sub:Text-Characters-in"
34080 \begin_layout Plain Layout
34089 \begin_layout Standard
34090 In some cases you might want to insert text characters directly into formulas.
34091 When for example the centered dot · is often used in formulas like
34092 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34095 , one would have to insert the command
34105 \begin_layout Plain Layout
34107 \begin_inset CommandInset ref
34109 reference "sub:Binary-Operators"
34118 all the time, because this character is defined in all encodings as text
34120 But the encoding can be changed by this LaTeX-preamble line:
34123 \begin_layout Standard
34128 Declare Inputtext{183}{
34138 f\SpecialChar \textcompwordmark{}
34142 \begin_layout Standard
34143 The character encoding (menu
34145 Document\SpecialChar \menuseparator
34146 Settings\SpecialChar \menuseparator
34149 ) specifies what character appears when a keyboard key is pressed.
34150 When the key for the character '·' is pressed, internally the command
34157 But this command is not available in a formula so that you would get LaTeX-erro
34159 With the changed encoding the right command is chosen automatically, depending
34160 on if the character was inserted into a formula or not.
34163 \begin_layout Standard
34164 The encoding of several characters is saved in definition files.
34165 Fore example the encoding
34169 is defined in the file
34173 that is in the installation folder of LaTeX.
34174 Encodings should only be changed via the LaTeX-preamble and not in the
34176 Otherwise own documents could not be edited by other LyX users working
34177 on other computers.
34180 \begin_layout Standard
34181 \begin_inset VSpace medskip
34184 Besides the centered dot, in this document the degree sign ° is defined
34185 with the following LaTeX-preamble line so that it can directly be inserted
34189 \begin_layout Standard
34194 DeclareInputtext{176}{
34204 f\SpecialChar \textcompwordmark{}
34208 \begin_layout Standard
34209 \begin_inset Newpage newpage
34215 \begin_layout Section
34217 Typographic Advises
34221 \begin_layout Plain Layout
34222 Typographic Advises
34230 \begin_layout Standard
34231 This section is a summary of the most important typographic rules, listed
34236 \begin_layout Plain Layout
34237 This collection was partly taken from the German semi-official dictionary
34239 \begin_inset Quotes eld
34243 \begin_inset Quotes erd
34247 \begin_inset CommandInset citation
34253 that lists some of the ISO rules.
34261 \begin_layout Itemize
34270 \begin_layout Plain Layout
34271 done with font styles, see
34272 \begin_inset CommandInset ref
34274 reference "sub:Font-Styles"
34284 \begin_inset space \thinspace{}
34288 \begin_inset Newline newline
34291 Between the value and the unit is the smallest space, see
34292 \begin_inset CommandInset ref
34294 reference "sub:Predefined-Space"
34301 \begin_layout Itemize
34302 Percent and perthousand signs are set like physical units:
34303 \begin_inset Newline newline
34307 \begin_inset space \thinspace{}
34313 \begin_layout Itemize
34314 The degree sign follows directly on the value: 15°, but not when it is used
34316 \begin_inset space \thinspace{}
34322 \begin_layout Itemize
34323 In numbers with more than four digits the smallest space is inserted before
34324 every third digit to group them:
34334 \begin_inset space \thinspace{}
34338 \begin_inset space \thinspace{}
34344 \begin_layout Itemize
34345 For dimensionings like 120×90×40
34346 \begin_inset space \thinspace{}
34349 cm the multiplication sign
34350 \begin_inset Quotes eld
34354 \begin_inset Quotes erd
34358 It is available with the LaTeX-command
34364 , but can also directly be inserted with some keyboard definitions.
34367 \begin_layout Itemize
34368 Functions with names consisting of several letters are set upright to avoid
34370 \begin_inset CommandInset ref
34372 reference "sub:Predefined-Functions"
34379 \begin_layout Itemize
34380 Indices consisting of several letters, are set upright:
34381 \begin_inset Formula $E_{\mathrm{kin}}$
34385 \begin_inset Newline newline
34388 Components of matrices are set italic:
34389 \begin_inset Formula $\hat{H}_{kl}$
34395 \begin_layout Itemize
34396 The differentiation/integration operator 'd', the Euler's number 'e', and
34397 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34401 \begin_layout Standard
34402 \begin_inset Newpage newpage
34408 \begin_layout Section
34413 \begin_layout Plain Layout
34422 \begin_layout Standard
34423 Some characters and symbols can be created with several commands.
34424 Here is a list of the synonym commands:
34427 \begin_layout Standard
34428 \begin_inset VSpace bigskip
34432 \begin_inset space \hfill{}
34436 \begin_inset Tabular
34437 <lyxtabular version="3" rows="12" columns="2">
34439 <column alignment="center" valignment="top" width="0pt">
34440 <column alignment="center" valignment="top" width="0pt">
34442 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34445 \begin_layout Plain Layout
34451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34454 \begin_layout Plain Layout
34456 \begin_inset Note Note
34459 \begin_layout Plain Layout
34466 is only used as spacer.
34478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34481 \begin_layout Plain Layout
34489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34492 \begin_layout Plain Layout
34496 \begin_layout Plain Layout
34509 \begin_layout Plain Layout
34523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34526 \begin_layout Plain Layout
34534 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34537 \begin_layout Plain Layout
34547 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34550 \begin_layout Plain Layout
34558 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34561 \begin_layout Plain Layout
34571 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34574 \begin_layout Plain Layout
34582 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34585 \begin_layout Plain Layout
34593 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34596 \begin_layout Plain Layout
34604 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34607 \begin_layout Plain Layout
34615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34618 \begin_layout Plain Layout
34626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34629 \begin_layout Plain Layout
34639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34642 \begin_layout Plain Layout
34650 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34653 \begin_layout Plain Layout
34663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34666 \begin_layout Plain Layout
34674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34677 \begin_layout Plain Layout
34687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34690 \begin_layout Plain Layout
34698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34701 \begin_layout Plain Layout
34711 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34714 \begin_layout Plain Layout
34722 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34725 \begin_layout Plain Layout
34733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34736 \begin_layout Plain Layout
34744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34747 \begin_layout Plain Layout
34759 \begin_inset space \hfill{}
34763 \begin_inset Tabular
34764 <lyxtabular version="3" rows="12" columns="2">
34766 <column alignment="center" valignment="top" width="0pt">
34767 <column alignment="center" valignment="top" width="0pt">
34769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34772 \begin_layout Plain Layout
34778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34781 \begin_layout Plain Layout
34789 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34792 \begin_layout Plain Layout
34800 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34803 \begin_layout Plain Layout
34815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34818 \begin_layout Plain Layout
34826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34829 \begin_layout Plain Layout
34839 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34842 \begin_layout Plain Layout
34850 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34853 \begin_layout Plain Layout
34863 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34866 \begin_layout Plain Layout
34874 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34877 \begin_layout Plain Layout
34885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34888 \begin_layout Plain Layout
34896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34899 \begin_layout Plain Layout
34907 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34910 \begin_layout Plain Layout
34918 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34921 \begin_layout Plain Layout
34931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34934 \begin_layout Plain Layout
34942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34945 \begin_layout Plain Layout
34955 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34958 \begin_layout Plain Layout
34966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34969 \begin_layout Plain Layout
34979 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34982 \begin_layout Plain Layout
34990 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34993 \begin_layout Plain Layout
35003 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35006 \begin_layout Plain Layout
35014 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35017 \begin_layout Plain Layout
35027 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35030 \begin_layout Plain Layout
35038 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35041 \begin_layout Plain Layout
35055 \begin_inset space \hfill{}
35061 \begin_layout Standard
35062 \begin_inset Newpage newpage
35068 \begin_layout Bibliography
35069 \begin_inset CommandInset bibitem
35070 LatexCommand bibitem
35082 The LaTeX Companion
35085 Addison Wesley, 2004
35088 \begin_layout Bibliography
35089 \begin_inset CommandInset bibitem
35090 LatexCommand bibitem
35096 \begin_inset CommandInset href
35099 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35103 of LaTeX's math abilities
35106 \begin_layout Bibliography
35107 \begin_inset CommandInset bibitem
35108 LatexCommand bibitem
35113 LaTeX tips and tricks-
35114 \begin_inset CommandInset href
35117 target "http://tug.org/TeXnik/"
35124 \begin_layout Bibliography
35125 \begin_inset CommandInset bibitem
35126 LatexCommand bibitem
35132 \begin_inset CommandInset href
35135 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35143 \begin_layout Plain Layout
35155 \begin_layout Bibliography
35156 \begin_inset CommandInset bibitem
35157 LatexCommand bibitem
35163 \begin_inset CommandInset href
35166 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35170 of all symbols available with LaTeX-packages
35173 \begin_layout Bibliography
35174 \begin_inset CommandInset bibitem
35175 LatexCommand bibitem
35181 \begin_inset CommandInset href
35183 name "Documentation"
35184 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35188 of the LaTeX-package
35196 \begin_layout Plain Layout
35197 Packages ! hyperref
35205 \begin_layout Bibliography
35206 \begin_inset CommandInset bibitem
35207 LatexCommand bibitem
35213 \begin_inset CommandInset href
35216 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35227 \begin_inset CommandInset ref
35229 reference "sub:Operator-Limits"
35237 \begin_layout Plain Layout
35248 \begin_layout Bibliography
35249 \begin_inset CommandInset bibitem
35250 LatexCommand bibitem
35261 Auflage, Duden 2001
35264 \begin_layout Subsubsection*
35265 \begin_inset CommandInset index_print
35266 LatexCommand printindex