1 #LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
7 % DO NOT ALTER THIS PREAMBLE!!!
9 % This preamble is designed to ensure that the file prints
10 % out as advertised. If you mess with this preamble,
11 % parts of this document may not print out as expected. If you
12 % have problems LaTeXing this file, please contact
13 % the documentation team
14 % email: lyx-docs@lists.lyx.org
21 % set fonts for nicer pdf view
22 \IfFileExists{lmodern.sty}
23 {\usepackage{lmodern}}{}
25 \fi % end if pdflatex is used
27 % Folgendes Problem lösen:
28 % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
29 % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
30 % die Kapitelnummer geschrieben.
31 % Als Lösung wird mehr Platz zwischen Nummer und
32 % Überschrift eingefügt.
33 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
34 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
36 % To be able to enter the character ° and · directly in LyX,
38 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
39 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
41 % increase link area for cross-references and autoname them,
43 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
44 %\renewcommand{\sectionautorefname}{sec.\negthinspace}
45 \renewcommand{\subsectionautorefname}{sec.\negthinspace}
46 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
48 \settowidth{\abc}{\space}
49 \renewcommand{\equationautorefname}{\hspace{-\abc}}
51 % don't load packages twice
52 % see first footnote in sec. 9.3
53 \@ifundefined{textcolor}{\usepackage{color}}{}
55 % the pages of the TOC are numbered roman
56 % and a PDF-bookmark for the TOC is added
58 \let\myTOC\tableofcontents
59 \renewcommand{\tableofcontents}{%
61 \pdfbookmark[1]{Contents}{}
64 \pagenumbering{arabic}}
66 % insert additional vertical space of 1.5 mm between footnotes,
69 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
71 % provides caption formatting
72 \setkomafont{captionlabel}{\bfseries}
78 \usepackage[samesize]{cancel}
80 % enables calculation of values,
83 % for multiple table row and column cells
93 % center multirows (e.g. in sec. 13.3)
94 \renewcommand{\multirowsetup}{\centering}
96 % define a color, used in sec.9.3
97 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
99 % declare operators (see sec. 10.4 and sec. 15.2)
100 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
101 \DeclareMathOperator{\sgn}{sgn}
103 \newcommand{\spce}{\textvisiblespace}
105 % example definitions for sec. 20.1
106 \newcommand{\gr}{\Longrightarrow}
107 \newcommand{\us}[1]{\underline{#1}}
108 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
109 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
110 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
112 % example macro from sec. 19.4
113 %\def\tagform@#1{\maketag@@@{|#1|}}
115 % macro from sec. 10.2
116 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
117 \def\mathclap {\mathpalette \mathclapinternal}
118 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
120 % redefine the greyed out note
121 \renewenvironment{lyxgreyedout}
122 {\textcolor{blue}\bgroup}{\egroup}
124 % check for package eurosym
125 % used for the Euro symbol
127 \IfFileExists{eurosym.sty}
128 {\usepackage[gennarrow]{eurosym}
129 \setboolean{eurosym}{true}}
130 {\setboolean{eurosym}{false}}
132 % needed in sec. 22.4
133 % check for package braket
135 \IfFileExists{braket.sty}
137 \setboolean{braket}{true}}
138 {\setboolean{braket}{false}}
140 % needed in sec. 22.10
141 % check for package upgreek
143 \IfFileExists{upgreek.sty}
144 {\usepackage{upgreek}
145 \setboolean{upgreek}{true}}
146 {\setboolean{upgreek}{false}}
148 \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
153 \font_typewriter default
154 \font_default_family default
163 \pdf_title "LyX's Math Manual"
164 \pdf_author "LyX Team, Uwe Stöhr"
165 \pdf_subject "LyX-documentation about math"
166 \pdf_keywords "LyX, Mathed"
168 \pdf_bookmarksnumbered true
169 \pdf_bookmarksopen true
170 \pdf_bookmarksopenlevel 1
171 \pdf_breaklinks false
175 \pdf_pagebackref false
176 \pdf_pdfusetitle false
177 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels"
184 \paperorientation portrait
187 \paragraph_separation skip
189 \quotes_language english
192 \paperpagestyle plain
196 \tracking_changes false
197 \output_changes false
200 \extra_embedded_files ""
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
496 \begin_inset Newline newline
499 To create a display style formula
503 \begin_layout Plain Layout
504 Formula ! display style
509 that will appear bigger and in an own paragraph, press
516 \begin_layout Standard
517 To change a display style formula to an inline formula, set the cursor into
518 the formula and press
524 Edit\SpecialChar \menuseparator
525 Math\SpecialChar \menuseparator
529 The same way is used to change an inline formula to a display style formula.
532 \begin_layout Standard
533 To display parts of an inline formula in the size of a display style formula,
542 \begin_layout Plain Layout
553 Then a new blue box appears in which the desired formula part is inserted.
556 \begin_layout Standard
557 Only inline formulas are allowed inside tables.
560 \begin_layout Standard
565 can be turned on in the menu
567 View\SpecialChar \menuseparator
571 When you click there on
572 \begin_inset Quotes eld
576 \begin_inset Quotes erd
579 the toolbar will be shown permanently at the bottom; this state is visualized
584 menu with a checkmark.
585 When you click in this state again on
586 \begin_inset Quotes eld
590 \begin_inset Quotes erd
601 is only shown when the cursor is within a formula; this state is visualized
602 by the renaming of the menu entry from
603 \begin_inset Quotes eld
607 \begin_inset Quotes erd
611 \begin_inset Quotes eld
619 \begin_inset Quotes erd
625 \begin_layout Standard
630 \begin_layout Plain Layout
635 \begin_layout Plain Layout
643 \begin_layout Plain Layout
654 \begin_layout Plain Layout
671 is invoked by pressing the toolbar button
672 \begin_inset Graphics
673 filename ../images/ert-insert.png
681 Insert\SpecialChar \menuseparator
686 \begin_layout Plain Layout
697 \begin_layout Plain Layout
711 \begin_inset Note Note
714 \begin_layout Plain Layout
715 In LyX there are three
716 \begin_inset Quotes eld
720 \begin_inset Quotes erd
723 that appear in the output with sub- and superscript letters: TeX, LaTeX,
727 \begin_layout Plain Layout
728 To avoid that these names are recognized as proper names, TeX-braces are
729 set around one of the letters of the name.
737 \begin_layout Standard
738 To change the LaTeX-preamble
742 \begin_layout Plain Layout
750 Document\SpecialChar \menuseparator
751 Settings\SpecialChar \menuseparator
756 \begin_layout Plain Layout
767 \begin_layout Plain Layout
783 \begin_layout Standard
784 To edit matrices, case differentiations, and multiline formulas subsequently,
787 Edit\SpecialChar \menuseparator
792 Edit\SpecialChar \menuseparator
794 \begin_inset Space \thinspace{}
798 \begin_inset Space \thinspace{}
808 When lines and columns are swapped via the menu, the column or line where
809 the cursor is in is exchanged with the column to the right or the line
811 Is the cursor in the last column or row, the exchange is done with the
812 column to the left or the line above.
815 \begin_layout Standard
816 To write text in formulas
820 \begin_layout Plain Layout
821 For multiline formulas the command
828 \begin_inset CommandInset ref
830 reference "sub:Text-in-multiline"
847 \begin_layout Plain Layout
857 \begin_layout Plain Layout
864 This mode is invoked with the the shortcut
872 or by the insertion of the command
880 \begin_layout Plain Layout
891 The text appears black in LyX and can therefore be distinguished from the
892 other formula parts that appear blue.
893 In the output mathematical text is set upright, in contrary to other formula
897 \begin_layout Subsection*
901 \begin_layout Standard
902 Most of the LaTeX-commands for math constructs have the following scheme:
905 \begin_layout Standard
921 \begin_layout Standard
922 A command starts always with a backslash
923 \begin_inset Quotes gld
933 \begin_inset Quotes grd
937 To omit optional arguments, also omit the associated brackets.
938 The braces around the required arguments are named in this document as
943 \begin_layout Plain Layout
948 \begin_layout Plain Layout
956 \begin_layout Plain Layout
967 \begin_layout Plain Layout
985 If you add in a formula a left brace to a command name, LyX creates automatical
987 In all other cases TeX-braces are created in formulas with the command
995 TeX-braces appear red in LyX, in contrary to normal braces that appear
997 In TeX-mode no command is needed to get TeX-braces.
998 TeX-braces don't appear in the output.
1001 \begin_layout Standard
1002 When commands without arguments, like commands for symbols are entered in
1003 TeX-mode, a space character must
1007 be behind the command to end it.
1008 This space doesn't appear in the output.
1009 When the space should appear in the output, the space must be followed
1010 by a protected space in normal text.
1013 \begin_layout Standard
1014 A protected space is inserted with
1021 \begin_layout Subsection*
1022 \begin_inset Newpage newpage
1028 \begin_layout Itemize
1033 \begin_layout Plain Layout
1034 This visible space character can be created with the command
1044 \begin_layout Plain Layout
1052 , inserted in TeX-mode.
1061 \begin_layout Plain Layout
1071 \begin_inset Space ~
1074 denotes a space character to be input.
1077 \begin_layout Itemize
1079 \begin_inset Formula $\to$
1082 denotes the usage of the corresponding arrow key on the keyboard.
1085 \begin_layout Subsection*
1089 \begin_layout Standard
1091 \begin_inset Float table
1097 \begin_layout Plain Layout
1099 \begin_inset Caption
1101 \begin_layout Plain Layout
1102 \begin_inset CommandInset label
1104 name "tab:Used-units"
1116 \begin_layout Plain Layout
1118 \begin_inset Tabular
1119 <lyxtabular version="3" rows="13" columns="2">
1121 <column alignment="center" valignment="top" width="0">
1122 <column alignment="center" valignment="top" width="0">
1124 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1127 \begin_layout Plain Layout
1133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1136 \begin_layout Plain Layout
1144 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1147 \begin_layout Plain Layout
1153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1156 \begin_layout Plain Layout
1164 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1167 \begin_layout Plain Layout
1173 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1176 \begin_layout Plain Layout
1184 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1187 \begin_layout Plain Layout
1193 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1196 \begin_layout Plain Layout
1198 \begin_inset Space \thinspace{}
1202 \begin_inset Space \thinspace{}
1212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1215 \begin_layout Plain Layout
1221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1224 \begin_layout Plain Layout
1226 \begin_inset Space \thinspace{}
1230 \begin_inset Space \thinspace{}
1240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1243 \begin_layout Plain Layout
1249 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1252 \begin_layout Plain Layout
1254 \begin_inset Space \thinspace{}
1258 \begin_inset Space \thinspace{}
1268 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1271 \begin_layout Plain Layout
1277 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1280 \begin_layout Plain Layout
1282 \begin_inset Space \thinspace{}
1286 \begin_inset Space \thinspace{}
1296 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1299 \begin_layout Plain Layout
1305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1308 \begin_layout Plain Layout
1310 \begin_inset Space \thinspace{}
1314 \begin_inset Space \thinspace{}
1324 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1336 \begin_layout Plain Layout
1338 \begin_inset Space \thinspace{}
1342 \begin_inset Formula $\approx$
1346 \begin_inset Space \thinspace{}
1356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1359 \begin_layout Plain Layout
1365 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1368 \begin_layout Plain Layout
1370 \begin_inset Space \thinspace{}
1374 \begin_inset Space \thinspace{}
1384 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1387 \begin_layout Plain Layout
1393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1396 \begin_layout Plain Layout
1400 \begin_inset Quotes eld
1406 \begin_inset Quotes erd
1416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1419 \begin_layout Plain Layout
1425 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1428 \begin_layout Plain Layout
1430 \begin_inset Quotes eld
1438 \begin_inset Quotes erd
1448 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1451 \begin_layout Plain Layout
1457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1460 \begin_layout Plain Layout
1462 \begin_inset Space \thinspace{}
1466 \begin_inset Formula $\nicefrac{1}{18}$
1470 \begin_inset Space \thinspace{}
1491 \begin_layout Standard
1492 \begin_inset Newpage newpage
1498 \begin_layout Section
1502 \begin_layout Subsection
1507 \begin_layout Plain Layout
1517 \begin_layout Plain Layout
1527 \begin_layout Plain Layout
1532 \begin_layout Plain Layout
1543 \begin_layout Plain Layout
1559 \begin_layout Plain Layout
1564 \begin_layout Plain Layout
1575 \begin_layout Plain Layout
1590 \begin_layout Standard
1591 Indices are created with an underscore
1592 \begin_inset Quotes eld
1596 \begin_inset Quotes erd
1599 or via the math toolbar button
1600 \begin_inset Graphics
1601 filename ../images/math-subscript.png
1607 , exponents with a caret
1608 \begin_inset Quotes eld
1612 \begin_inset Quotes erd
1615 or via the math toolbar button
1616 \begin_inset Graphics
1617 filename ../images/math-superscript.png
1626 \begin_layout Standard
1628 \begin_inset Tabular
1629 <lyxtabular version="3" rows="4" columns="2">
1631 <column alignment="center" valignment="top" width="0pt">
1632 <column alignment="center" valignment="top" width="0pt">
1634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1637 \begin_layout Plain Layout
1643 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1646 \begin_layout Plain Layout
1648 \begin_inset Note Note
1651 \begin_layout Plain Layout
1658 is only used as spacer.
1670 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1673 \begin_layout Plain Layout
1679 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1682 \begin_layout Plain Layout
1683 \begin_inset Formula $B_{V}$
1693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1696 \begin_layout Plain Layout
1702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1705 \begin_layout Plain Layout
1706 \begin_inset Formula $\raisebox {5mm}{}B^{V}$
1716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1719 \begin_layout Plain Layout
1724 \begin_layout Plain Layout
1738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1741 \begin_layout Plain Layout
1742 \begin_inset Formula $\raisebox {5mm}{}B^{A}$
1758 \begin_layout Standard
1759 As the caret is in some languages an accent, vowels will be accentuated
1760 in this case and not set as exponents
1764 \begin_layout Plain Layout
1765 Depending on the used keyboard settings this can also happen for other character
1772 To get in this case exponents, press
1776 after the caret as in the last example.
1779 \begin_layout Subsection
1781 \begin_inset CommandInset label
1783 name "sub:Fractions"
1791 \begin_layout Plain Layout
1800 \begin_layout Standard
1801 Fractions are generated with the command
1811 \begin_layout Plain Layout
1819 or via the math toolbar button
1820 \begin_inset Graphics
1821 filename ../images/math/frac.png
1828 The font size is adjusted automatically, depending on whether the fraction
1829 is in an inline or display style formula.
1830 With the math toolbar button
1831 \begin_inset Graphics
1832 filename ../images/math/frac-square.png
1838 you can select different fraction types.
1841 \begin_layout Standard
1850 \begin_layout Plain Layout
1860 a fraction can be created that has in any case the size of a display style
1870 \begin_layout Plain Layout
1880 the fraction appears always with the size of an inline formula.
1884 \begin_layout Standard
1885 A line with the fraction
1886 \begin_inset Formula $\frac{1}{2}$
1889 that was created with the command
1898 \begin_layout Standard
1899 A line with the fraction
1900 \begin_inset Formula $\dfrac{1}{2}$
1903 that was created with the command
1912 \begin_layout Standard
1914 \begin_inset Tabular
1915 <lyxtabular version="3" rows="4" columns="2">
1917 <column alignment="center" valignment="top" width="0pt">
1918 <column alignment="center" valignment="top" width="0pt">
1920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1923 \begin_layout Plain Layout
1929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1932 \begin_layout Plain Layout
1934 \begin_inset Note Note
1937 \begin_layout Plain Layout
1944 is only used as spacer.
1956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1959 \begin_layout Plain Layout
1966 \begin_layout Plain Layout
1976 \begin_inset Formula $\downarrow$
1984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1987 \begin_layout Plain Layout
1988 \begin_inset Formula $\raisebox {4.5mm}{}\frac{A}{B}\raisebox {-2.5mm}{}$
1998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2001 \begin_layout Plain Layout
2008 \begin_layout Plain Layout
2018 \begin_inset Formula $\downarrow$
2026 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2029 \begin_layout Plain Layout
2030 \begin_inset Formula $\raisebox {7mm}{}\dfrac{A}{B}\raisebox {-4mm}{}$
2040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2043 \begin_layout Plain Layout
2050 \begin_layout Plain Layout
2063 \begin_layout Plain Layout
2078 \begin_layout Plain Layout
2088 \begin_inset Formula $\downarrow$
2092 \begin_inset Formula $\downarrow\downarrow$
2100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2103 \begin_layout Plain Layout
2104 \begin_inset Formula $\raisebox {8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox {-4mm}{}$
2120 \begin_layout Standard
2121 \begin_inset VSpace bigskip
2125 \begin_inset Newpage newpage
2128 For nested fractions the command
2138 \begin_layout Plain Layout
2148 \begin_inset VSpace -3mm
2154 \begin_layout Standard
2155 \begin_inset Formula \begin{align*}
2156 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2157 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac {A}{B+\cfrac {C+\cfrac {E}{F}}{D}}\end{align*}
2164 \begin_layout Standard
2165 The command for the example above is:
2168 \begin_layout Standard
2174 \begin_inset Formula $\to$
2184 \begin_inset Formula $\to$
2190 \begin_inset Formula $\to\to$
2198 \begin_layout Standard
2199 \begin_inset VSpace medskip
2205 \begin_layout Standard
2212 sets the fraction always in the size of a displayed formula, also when
2213 it is part of another fraction.
2220 has the following command scheme:
2223 \begin_layout Standard
2228 cfrac[numerator position]{numerator}{denominator}
2231 \begin_layout Standard
2232 The numerator position can be
2245 l or r aligns the numerator to the left or right, resp.
2246 \begin_inset Space ~
2249 with the fraction stroke.
2254 or no position is given, the numerator appears centered.
2255 These fractions demonstrate the different alignments:
2256 \begin_inset Newline newline
2262 \begin_inset Formula $\cfrac [l]{A}{B+C}$
2266 \begin_inset Formula $\cfrac {A}{B+C}$
2270 \begin_inset Formula $\cfrac [r]{A}{B+C}$
2276 \begin_layout Standard
2277 \begin_inset VSpace medskip
2280 It is often advantageous to combine
2293 \begin_inset Formula \[
2294 \cfrac {A}{B+\cfrac {C+\frac{E}{F}}{D}}\]
2301 \begin_layout Standard
2302 For inline fractions with a sloped fraction stroke you can use the command
2311 \begin_layout Plain Layout
2322 \begin_inset Formula $\nicefrac{5}{31}$
2328 \begin_layout Standard
2329 How to define own fractions where the fraction stroke can be changed, is
2331 \begin_inset CommandInset ref
2333 reference "sub:Self-defined-Fractions"
2340 \begin_layout Subsection
2345 \begin_layout Plain Layout
2354 \begin_layout Standard
2355 Square roots are created with
2365 \begin_layout Plain Layout
2373 or the math toolbar button
2374 \begin_inset Graphics
2375 filename ../images/math/sqrt.png
2381 , all other roots with the command
2391 \begin_layout Plain Layout
2399 or with the math toolbar button
2400 \begin_inset Graphics
2401 filename ../images/math/root.png
2410 \begin_layout Standard
2412 \begin_inset Tabular
2413 <lyxtabular version="3" rows="3" columns="2">
2415 <column alignment="center" valignment="top" width="0pt">
2416 <column alignment="center" valignment="top" width="0pt">
2418 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2421 \begin_layout Plain Layout
2427 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2430 \begin_layout Plain Layout
2432 \begin_inset Note Note
2435 \begin_layout Plain Layout
2442 is only used as spacer.
2454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2457 \begin_layout Plain Layout
2464 \begin_layout Plain Layout
2478 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2481 \begin_layout Plain Layout
2482 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt{A-B}$
2492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2495 \begin_layout Plain Layout
2502 \begin_layout Plain Layout
2512 \begin_inset Formula $\downarrow$
2520 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2523 \begin_layout Plain Layout
2524 \begin_inset Formula $\raisebox {4.5mm}{}\sqrt[3]{A-B}$
2540 \begin_layout Standard
2541 A square root can also be created with
2547 when the root index field is left empty.
2550 \begin_layout Standard
2551 With certain indices the distance to the root is too small, like in this
2553 \begin_inset Formula $\sqrt[\beta]{B}$
2557 \begin_inset Newline newline
2561 \begin_inset Formula $\beta$
2565 To avoid this, the commands
2575 \begin_layout Plain Layout
2593 \begin_layout Plain Layout
2601 are used with the following scheme:
2604 \begin_layout Standard
2618 \begin_layout Standard
2619 Distance is the number of Big Points (unit bp;
2620 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2623 ), that the index should be moved to the left or top, resp..
2624 The commands are written to the index.
2625 This way the command
2626 \begin_inset Newline newline
2636 \begin_inset Formula $\to$
2642 \begin_inset Formula $\to$
2651 \begin_layout Plain Layout
2661 \begin_inset Formula $\to$
2665 \begin_inset Newline newline
2670 produces a correct typeset formula:
2671 \begin_inset Formula $\sqrt[\leftroot {-1}\uproot {2}\beta]{B}$
2677 \begin_layout Subsection
2678 Binomial coefficients
2682 \begin_layout Plain Layout
2683 Binomial coefficient s
2691 \begin_layout Standard
2692 Binomial coefficients are inserted with the command
2702 \begin_layout Plain Layout
2710 or with the submenu of the math toolbar button
2711 \begin_inset Graphics
2712 filename ../images/math/frac-square.png
2719 Analog to fractions (
2739 \begin_layout Plain Layout
2759 \begin_layout Plain Layout
2770 \begin_layout Standard
2772 \begin_inset Tabular
2773 <lyxtabular version="3" rows="4" columns="2">
2775 <column alignment="center" valignment="top" width="0pt">
2776 <column alignment="center" valignment="top" width="0pt">
2778 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2781 \begin_layout Plain Layout
2787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2790 \begin_layout Plain Layout
2792 \begin_inset Note Note
2795 \begin_layout Plain Layout
2802 is only used as spacer.
2814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2817 \begin_layout Plain Layout
2824 \begin_layout Plain Layout
2834 \begin_inset Formula $\downarrow$
2842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2845 \begin_layout Plain Layout
2846 \begin_inset Formula $\raisebox {5mm}{}\binom{A}{B}\raisebox {-2.5mm}{}$
2856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2859 \begin_layout Plain Layout
2866 \begin_layout Plain Layout
2876 \begin_inset Formula $\downarrow$
2884 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2887 \begin_layout Plain Layout
2888 \begin_inset Formula $\raisebox {5mm}{}\dbinom{A}{B}\raisebox {-2.5mm}{}$
2898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2901 \begin_layout Plain Layout
2908 \begin_layout Plain Layout
2918 \begin_inset Formula $\downarrow$
2926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2929 \begin_layout Plain Layout
2930 \begin_inset Formula $\raisebox {5mm}{}\tbinom{A}{B}\raisebox {-2.5mm}{}$
2946 \begin_layout Subsection
2947 Case differentiations
2951 \begin_layout Plain Layout
2952 Case differentiations
2960 \begin_layout Standard
2962 \begin_inset Tabular
2963 <lyxtabular version="3" rows="3" columns="2">
2965 <column alignment="center" valignment="top" width="0pt">
2966 <column alignment="center" valignment="top" width="0pt">
2968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2971 \begin_layout Plain Layout
2977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2980 \begin_layout Plain Layout
2988 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2991 \begin_layout Plain Layout
2998 \begin_layout Plain Layout
3008 \begin_inset Formula $\to$
3015 \begin_layout Plain Layout
3028 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3031 \begin_layout Plain Layout
3032 \begin_inset Formula $\begin{cases}
3043 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3046 \begin_layout Plain Layout
3053 \begin_layout Plain Layout
3067 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3070 \begin_layout Plain Layout
3071 \begin_inset Formula $\begin{cases}
3072 A & \textrm{for }x>0\\
3073 B & \textrm{for }x=0\end{cases}$
3089 \begin_layout Standard
3096 or the usage of the math toolbar button
3097 \begin_inset Graphics
3098 filename ../images/math/cases.png
3104 you can create new lines with the shortcut
3108 or the table toolbar button
3109 \begin_inset Graphics
3110 filename ../images/tabular-feature_append-row.png
3119 \begin_layout Standard
3126 is also available via the menu
3128 Insert\SpecialChar \menuseparator
3129 Math\SpecialChar \menuseparator
3135 \begin_layout Subsection
3140 \begin_layout Plain Layout
3149 \begin_layout Standard
3160 \begin_layout Plain Layout
3168 every character can be displayed canceled.
3169 The characters are quasi accentuated by a slash.
3172 \begin_layout Standard
3174 \begin_inset Tabular
3175 <lyxtabular version="3" rows="4" columns="2">
3177 <column alignment="center" valignment="top" width="0pt">
3178 <column alignment="center" valignment="top" width="0pt">
3180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3183 \begin_layout Plain Layout
3189 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3192 \begin_layout Plain Layout
3200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3203 \begin_layout Plain Layout
3211 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3214 \begin_layout Plain Layout
3215 \begin_inset Formula $\not=$
3225 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3228 \begin_layout Plain Layout
3238 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3241 \begin_layout Plain Layout
3242 \begin_inset Formula $\not\le$
3252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3255 \begin_layout Plain Layout
3265 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3268 \begin_layout Plain Layout
3269 \begin_inset Formula $\not\parallel$
3285 \begin_layout Standard
3286 The last example shows, that not all negations look good.
3287 Therefore there are for some negations special commands (see
3288 \begin_inset CommandInset ref
3290 reference "sub:Mathematical-Symbols"
3295 \begin_inset CommandInset ref
3297 reference "sec:Relations"
3304 \begin_layout Subsection
3306 \begin_inset CommandInset label
3308 name "sub:Placeholders"
3316 \begin_layout Plain Layout
3326 \begin_layout Plain Layout
3327 Chemical characters ! Isotopes
3336 \begin_layout Plain Layout
3341 \begin_layout Plain Layout
3352 \begin_layout Plain Layout
3367 \begin_layout Standard
3369 \begin_inset Space \thinspace{}
3373 \begin_inset Space ~
3380 \begin_layout Plain Layout
3381 More about chemical symbols is written in
3382 \begin_inset CommandInset ref
3384 reference "sub:Chemical-Symbols-and"
3393 the following problem occurs:
3396 \begin_layout Standard
3398 \begin_inset Tabular
3399 <lyxtabular version="3" rows="2" columns="2">
3401 <column alignment="center" valignment="top" width="0pt">
3402 <column alignment="center" valignment="top" width="0pt">
3404 <cell alignment="center" valignment="top" usebox="none">
3407 \begin_layout Plain Layout
3408 Indices created with sub- and superscripts:
3413 <cell alignment="center" valignment="top" usebox="none">
3416 \begin_layout Plain Layout
3417 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox {-3mm}{}$
3427 <cell alignment="center" valignment="top" usebox="none">
3430 \begin_layout Plain Layout
3436 <cell alignment="center" valignment="top" usebox="none">
3439 \begin_layout Plain Layout
3440 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3454 \begin_inset Note Note
3457 \begin_layout Plain Layout
3464 is only used as spacer.
3472 \begin_layout Standard
3473 The shorter index is by default placed below or above the first character
3474 of the longer index.
3475 To avoid this there is the command
3485 \begin_layout Plain Layout
3493 or the math toolbar button
3494 \begin_inset Space \thinspace{}
3501 \begin_layout Plain Layout
3502 can be found in the submenu of the toolbar button
3503 \begin_inset Graphics
3504 filename ../images/math/space.png
3516 \begin_inset Graphics
3517 filename ../images/math/phantom.png
3523 that creates one or more phantom characters.
3530 a small blue box appears that is superposed with two red arrows.
3531 The arrows indicate that the complete width and height of the box content
3532 will be created as placeholder.
3533 Phantom characters are accordingly placeholders with the size of the characters.
3536 \begin_layout Standard
3538 \begin_inset Tabular
3539 <lyxtabular version="3" rows="4" columns="2">
3541 <column alignment="center" valignment="top" width="0">
3542 <column alignment="center" valignment="top" width="0">
3544 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3547 \begin_layout Plain Layout
3553 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3556 \begin_layout Plain Layout
3558 \begin_inset Note Note
3561 \begin_layout Plain Layout
3568 is only used as spacer.
3580 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3583 \begin_layout Plain Layout
3588 \begin_layout Plain Layout
3603 \begin_layout Plain Layout
3613 \begin_inset Formula $\to$
3620 \begin_layout Plain Layout
3634 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3637 \begin_layout Plain Layout
3638 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox {-2.5mm}{}$
3648 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3651 \begin_layout Plain Layout
3656 \begin_layout Plain Layout
3671 \begin_layout Plain Layout
3681 \begin_inset Formula $\to$
3688 \begin_layout Plain Layout
3702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3705 \begin_layout Plain Layout
3706 \begin_inset Formula $\raisebox {4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox {-2.5mm}{}$
3716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3719 \begin_layout Plain Layout
3726 \begin_layout Plain Layout
3741 \begin_layout Plain Layout
3751 \begin_inset Formula $\to$
3758 \begin_layout Plain Layout
3772 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3775 \begin_layout Plain Layout
3776 \begin_inset Formula $\raisebox {4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox {-2.5mm}{}$
3792 \begin_layout Standard
3793 Furthermore there are the commands
3803 \begin_layout Plain Layout
3812 \begin_inset Space ~
3816 \begin_inset Graphics
3817 filename ../images/math/vphantom.png
3833 \begin_layout Plain Layout
3842 \begin_inset Space ~
3846 \begin_inset Graphics
3847 filename ../images/math/hphantom.png
3860 creates only space for the maximal height of the characters in the box
3861 but not for its width.
3868 creates only space for the width of the box content.
3869 Therefore the boxes of both commands have only one red arrow.
3872 \begin_layout Standard
3883 \begin_layout Plain Layout
3898 space for the height of the integral sign,
3902 \begin_layout Plain Layout
3909 creates an integral sign, see
3910 \begin_inset CommandInset ref
3912 reference "sub:Big-Operators"
3921 because this is the larger character.
3922 An example application is in
3923 \begin_inset CommandInset ref
3925 reference "sub:Multiline-Brackets"
3932 \begin_layout Subsection
3937 \begin_layout Plain Layout
3947 \begin_layout Plain Layout
3948 Formula ! underlined
3956 \begin_layout Standard
3958 \begin_inset Tabular
3959 <lyxtabular version="3" rows="4" columns="2">
3961 <column alignment="center" valignment="top" width="0pt">
3962 <column alignment="center" valignment="top" width="0pt">
3964 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3967 \begin_layout Plain Layout
3973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3976 \begin_layout Plain Layout
3978 \begin_inset Note Note
3981 \begin_layout Plain Layout
3988 is only used as spacer.
4000 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4003 \begin_layout Plain Layout
4010 \begin_layout Plain Layout
4023 \begin_layout Plain Layout
4036 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4039 \begin_layout Plain Layout
4040 \begin_inset Formula $\raisebox {5mm}{}\overline{A+B}$
4050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4053 \begin_layout Plain Layout
4060 \begin_layout Plain Layout
4073 \begin_layout Plain Layout
4086 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4089 \begin_layout Plain Layout
4090 \begin_inset Formula $\underline{A+B}\raisebox {-2.5mm}{}$
4100 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4103 \begin_layout Plain Layout
4110 \begin_layout Plain Layout
4125 \begin_layout Plain Layout
4139 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4142 \begin_layout Plain Layout
4143 \begin_inset Formula $\raisebox {5mm}{}\overline{\underline{A+B}}\raisebox {-2.5mm}{}$
4159 \begin_layout Standard
4160 In the last example it doesn't matter if first
4175 \begin_layout Standard
4176 To double underline e.
4177 \begin_inset Space \thinspace{}
4190 \begin_layout Standard
4191 It is possible to place up to 6 lines above or below characters.
4194 \begin_layout Subsection
4199 \begin_layout Plain Layout
4208 \begin_layout Standard
4209 There are different types of ellipses available.
4213 \begin_layout Plain Layout
4214 In the math toolbar in the submenu of the button
4215 \begin_inset Graphics
4216 filename ../images/math/ldots.png
4227 For listings dots at the baseline are used (
4237 \begin_layout Plain Layout
4245 ), while for operations dots are needed that are on the same height as the
4256 \begin_layout Plain Layout
4265 When using the command
4275 \begin_layout Plain Layout
4283 , LaTeX decides on the basis of the next character what type is used.
4286 \begin_layout Standard
4288 \begin_inset Tabular
4289 <lyxtabular version="3" rows="8" columns="2">
4291 <column alignment="center" valignment="top" width="0pt">
4292 <column alignment="center" valignment="top" width="0pt">
4294 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4297 \begin_layout Plain Layout
4303 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4306 \begin_layout Plain Layout
4314 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4317 \begin_layout Plain Layout
4322 \begin_layout Plain Layout
4337 \begin_layout Plain Layout
4351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4354 \begin_layout Plain Layout
4355 \begin_inset Formula $A_{1},\dots,A_{n}$
4365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4368 \begin_layout Plain Layout
4373 \begin_layout Plain Layout
4388 \begin_layout Plain Layout
4402 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4405 \begin_layout Plain Layout
4406 \begin_inset Formula $A_{1}+\dots+A_{n}$
4416 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4419 \begin_layout Plain Layout
4424 \begin_layout Plain Layout
4439 \begin_layout Plain Layout
4453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4456 \begin_layout Plain Layout
4457 \begin_inset Formula $A_{1},\ldots,A_{n}$
4467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4470 \begin_layout Plain Layout
4475 \begin_layout Plain Layout
4490 \begin_layout Plain Layout
4504 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4507 \begin_layout Plain Layout
4508 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4518 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4521 \begin_layout Plain Layout
4529 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4532 \begin_layout Plain Layout
4533 \begin_inset Formula $\vdots$
4543 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4546 \begin_layout Plain Layout
4554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4557 \begin_layout Plain Layout
4558 \begin_inset Formula $\ddots$
4568 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4571 \begin_layout Plain Layout
4573 \begin_inset Space \thinspace{}
4576 matrix with the different dots
4581 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4584 \begin_layout Plain Layout
4585 \begin_inset Formula $\begin{array}{ccc}
4586 A_{11} & \cdots & A_{1m}\\
4587 \vdots & \ddots & \vdots\\
4588 A_{n1} & \cdots & A_{nm}\end{array}$
4604 \begin_layout Standard
4605 The ellipses available in menu
4607 Insert\SpecialChar \menuseparator
4609 \begin_inset Space ~
4623 \begin_layout Standard
4624 \begin_inset VSpace medskip
4627 Specially for matrices there are ellipses that span over several columns.
4628 They are created with the command
4638 \begin_layout Plain Layout
4646 , that has the following scheme:
4649 \begin_layout Standard
4654 hdotsfor[distance]{number of columns}
4657 \begin_layout Standard
4658 The number of columns specifies how many columns should be spanned.
4659 Distance is a factor for the distance between the dots.
4662 \begin_layout Standard
4663 In the following matrix the command
4669 was inserted in the first box of the second line, to get an ellipsis with
4670 a dot distance twice as long as with the command
4677 \begin_inset Formula \[
4678 \left(\begin{array}{cccc}
4681 q & w & e & r\end{array}\right)\]
4685 Note that the matrix fields that should be spanned must be empty, otherwise
4686 you get LaTeX-errors.
4689 \begin_layout Standard
4690 \begin_inset VSpace bigskip
4693 Furthermore you can fill with the command
4703 \begin_layout Plain Layout
4711 the rest of a line with dots.
4712 The effect of these commands is the same like with
4719 \begin_inset CommandInset ref
4721 reference "sub:Variable-Space"
4728 \begin_layout Standard
4729 For example the command
4737 \begin_layout Plain Layout
4751 \begin_layout Standard
4752 \begin_inset Formula $A\dotfill B$
4758 \begin_layout Standard
4765 there is for a line the command
4775 \begin_layout Plain Layout
4786 \begin_layout Standard
4787 \begin_inset Formula $A\hrulefill B$
4793 \begin_layout Standard
4794 To use the commands for text, they have to be inserted in TeX-mode.
4797 \begin_layout Section
4799 \begin_inset CommandInset label
4809 \begin_layout Plain Layout
4818 \begin_layout Standard
4819 Matrices can be inserted via the math toolbar button
4820 \begin_inset Graphics
4821 filename ../images/dialog-show_mathmatrix.png
4829 Insert\SpecialChar \menuseparator
4830 Math\SpecialChar \menuseparator
4834 You will be asked for the number of matrix columns and rows, and the alignment.
4835 The vertical alignment is hereby only of importance for matrices in inline
4839 \begin_layout Standard
4840 The first matrix is top
4841 \begin_inset Formula $\begin{array}[t]{cccc}
4844 C & F & I & L\end{array}$
4848 \begin_inset Formula $\begin{array}{cccc}
4851 C & F & I & L\end{array}$
4854 , and the third bottom
4855 \begin_inset Formula $\begin{array}[b]{cccc}
4858 C & F & I & L\end{array}$
4864 \begin_layout Standard
4865 The horizontal alignment specifies how the column entries should be aligned.
4866 It is set by entering a letter for every column.
4871 denotes left aligned,
4880 To create for example a 4
4885 \begin_inset Space ~
4888 matrix where the first column is left aligned, the second and third are
4889 centered, and the last one is right aligned, one enters for the horizontal
4895 Normally are in a matrix all columns centered, therefore the default is
4896 for every column is a
4903 \begin_layout Standard
4904 Horizontal alignment:
4907 \begin_layout Standard
4913 \begin_inset Formula $\begin{array}{lll}
4916 C & F & 10000\end{array}$
4924 \begin_inset Formula $\begin{array}{ccc}
4927 C & F & 10000\end{array}$
4935 \begin_inset Formula $\begin{array}{rrr}
4938 C & F & 10000\end{array}$
4944 \begin_layout Standard
4945 To add or delete rows and columns subsequently, the math toolbar buttons
4947 \begin_inset Graphics
4948 filename ../images/tabular-feature_append-row.png
4955 \begin_inset Graphics
4956 filename ../images/tabular-feature_delete-row.png
4963 \begin_inset Space \thinspace{}
4968 Edit\SpecialChar \menuseparator
4972 New rows can also be created with
4979 \begin_layout Standard
4980 \begin_inset VSpace bigskip
4983 Parentheses around a matrix can can either be created with the commands
4994 \begin_layout Plain Layout
5012 \begin_layout Plain Layout
5023 \begin_inset Space ~
5029 \begin_inset CommandInset ref
5031 reference "sub:Automatic-Bracket-Size"
5035 , or by using the following commands:
5036 \begin_inset VSpace medskip
5042 \begin_layout Standard
5043 \begin_inset Space \hfill{}
5047 \begin_inset Tabular
5048 <lyxtabular version="3" rows="4" columns="2">
5050 <column alignment="center" valignment="top" width="0">
5051 <column alignment="center" valignment="top" width="0">
5053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5056 \begin_layout Plain Layout
5062 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5065 \begin_layout Plain Layout
5067 \begin_inset Note Note
5070 \begin_layout Plain Layout
5077 is only used as spacer.
5089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5092 \begin_layout Plain Layout
5099 \begin_layout Plain Layout
5113 \begin_inset Space \thinspace{}
5121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5124 \begin_layout Plain Layout
5125 \begin_inset Formula $\raisebox {7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5126 0 & \textrm{-}\mathrm{i}\\
5127 \mathrm{i} & 0\end{array}\end{bmatrix}\raisebox {-5.3mm}{}$
5137 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5140 \begin_layout Plain Layout
5147 \begin_layout Plain Layout
5161 \begin_inset Space \thinspace{}
5169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5172 \begin_layout Plain Layout
5173 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5174 0 & \textrm{-}\mathrm{i}\\
5175 \mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox {-5.3mm}{}$
5185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5188 \begin_layout Plain Layout
5195 \begin_layout Plain Layout
5209 \begin_inset Space \thinspace{}
5217 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5220 \begin_layout Plain Layout
5221 \begin_inset Formula $\raisebox {7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5222 0 & \textrm{-}\mathrm{i}\\
5223 \mathrm{i} & 0\end{array}\end{pmatrix}\raisebox {-5.3mm}{}$
5237 \begin_inset Space \hfill{}
5241 \begin_inset Tabular
5242 <lyxtabular version="3" rows="4" columns="2">
5244 <column alignment="center" valignment="top" width="0">
5245 <column alignment="center" valignment="top" width="0">
5247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5250 \begin_layout Plain Layout
5256 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5259 \begin_layout Plain Layout
5267 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5270 \begin_layout Plain Layout
5277 \begin_layout Plain Layout
5291 \begin_inset Space \thinspace{}
5299 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5302 \begin_layout Plain Layout
5303 \begin_inset Formula $\raisebox {7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5304 0 & \textrm{-}\mathrm{i}\\
5305 \mathrm{i} & 0\end{array}\end{vmatrix}\raisebox {-5.3mm}{}$
5315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5318 \begin_layout Plain Layout
5325 \begin_layout Plain Layout
5339 \begin_inset Space \thinspace{}
5347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5350 \begin_layout Plain Layout
5351 \begin_inset Formula $\raisebox {7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5352 0 & \textrm{-}\mathrm{i}\\
5353 \mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox {-5.3mm}{}$
5363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5366 \begin_layout Plain Layout
5373 \begin_layout Plain Layout
5387 \begin_inset Space \thinspace{}
5395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5398 \begin_layout Plain Layout
5399 \begin_inset Formula $\raisebox {7.5mm}{}\begin{matrix}\begin{array}{cc}
5400 0 & \textrm{-}\mathrm{i}\\
5401 \mathrm{i} & 0\end{array}\end{matrix}\raisebox {-5.3mm}{}$
5415 \begin_inset Space \hfill{}
5421 \begin_layout Standard
5422 \begin_inset VSpace medskip
5426 \begin_inset Space \thinspace{}
5430 \begin_inset Space ~
5439 is inserted, a blue box appears between two vertical lines where the matrix
5443 \begin_layout Standard
5444 \begin_inset VSpace bigskip
5447 As all multiline formulas are matrices, the length
5457 \begin_layout Plain Layout
5465 that is described in
5466 \begin_inset CommandInset ref
5468 reference "sub:Column-Separation"
5472 can also be used to change the column separation of matrices.
5475 \begin_layout Standard
5476 To change the row separation, the command
5486 \begin_layout Plain Layout
5495 It is used as follows:
5498 \begin_layout Standard
5505 arraystretch}{stretch factor}
5509 \begin_layout Plain Layout
5520 \begin_layout Standard
5527 assigns the stretch factor to the predefined command
5535 \begin_inset Space \thinspace{}
5539 \begin_inset Space ~
5542 the row separation, use the factor 2.
5543 This is then used for all following matrices.
5544 To go back to the original separation, assign the factor 1 to
5553 \begin_layout Standard
5554 To set matrices into a text line, the command
5564 \begin_layout Plain Layout
5573 When it is inserted a blue box with two dashed lines appears.
5574 In this box the matrix is inserted.
5577 \begin_layout Standard
5579 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5580 C & D\end{smallmatrix}\right)$
5586 \begin_layout Section
5587 Brackets and Delimiters
5591 \begin_layout Plain Layout
5601 \begin_layout Plain Layout
5610 \begin_layout Subsection
5611 Vertical Brackets and Delimiters
5615 \begin_layout Plain Layout
5624 \begin_layout Standard
5625 \begin_inset Space \hfill{}
5629 \begin_inset Tabular
5630 <lyxtabular version="3" rows="9" columns="2">
5632 <column alignment="center" valignment="top" width="0pt">
5633 <column alignment="center" valignment="top" width="0pt">
5635 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5638 \begin_layout Plain Layout
5644 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5647 \begin_layout Plain Layout
5655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5658 \begin_layout Plain Layout
5664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5667 \begin_layout Plain Layout
5668 \begin_inset Formula $($
5678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5681 \begin_layout Plain Layout
5687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5690 \begin_layout Plain Layout
5691 \begin_inset Formula $\{$
5701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5704 \begin_layout Plain Layout
5710 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5713 \begin_layout Plain Layout
5714 \begin_inset Formula $[$
5724 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5727 \begin_layout Plain Layout
5735 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5738 \begin_layout Plain Layout
5739 \begin_inset Formula $\langle$
5749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5752 \begin_layout Plain Layout
5760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5763 \begin_layout Plain Layout
5764 \begin_inset Formula $\lceil$
5774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5777 \begin_layout Plain Layout
5785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5788 \begin_layout Plain Layout
5789 \begin_inset Formula $\lfloor$
5799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5802 \begin_layout Plain Layout
5808 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5811 \begin_layout Plain Layout
5812 \begin_inset Formula $/$
5822 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5825 \begin_layout Plain Layout
5831 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5834 \begin_layout Plain Layout
5835 \begin_inset Formula $|$
5849 \begin_inset Space \hfill{}
5853 \begin_inset Tabular
5854 <lyxtabular version="3" rows="9" columns="2">
5856 <column alignment="center" valignment="top" width="0pt">
5857 <column alignment="center" valignment="top" width="0pt">
5859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5862 \begin_layout Plain Layout
5868 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5871 \begin_layout Plain Layout
5879 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5882 \begin_layout Plain Layout
5888 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5891 \begin_layout Plain Layout
5892 \begin_inset Formula $)$
5902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5905 \begin_layout Plain Layout
5911 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5914 \begin_layout Plain Layout
5915 \begin_inset Formula $\}$
5925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5928 \begin_layout Plain Layout
5934 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5937 \begin_layout Plain Layout
5938 \begin_inset Formula $]$
5948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5951 \begin_layout Plain Layout
5959 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5962 \begin_layout Plain Layout
5963 \begin_inset Formula $\rangle$
5973 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5976 \begin_layout Plain Layout
5984 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5987 \begin_layout Plain Layout
5988 \begin_inset Formula $\rceil$
5998 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6001 \begin_layout Plain Layout
6009 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6012 \begin_layout Plain Layout
6013 \begin_inset Formula $\rfloor$
6023 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6026 \begin_layout Plain Layout
6036 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6039 \begin_layout Plain Layout
6040 \begin_inset Formula $\backslash$
6050 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6053 \begin_layout Plain Layout
6061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6064 \begin_layout Plain Layout
6065 \begin_inset Formula $\|$
6079 \begin_inset Space \hfill{}
6085 \begin_layout Standard
6088 \begin_inset Note Greyedout
6091 \begin_layout Plain Layout
6096 In TeX-mode the command
6106 \begin_layout Plain Layout
6114 must be used for the backslash, because the command
6122 produces there a line break.
6130 \begin_layout Standard
6131 For all characters listed above the size can be adjusted with the commands
6132 described in the following two subsections.
6133 When using these commands, the characters < and > can directly be used
6134 instead of the commands
6149 \begin_layout Subsubsection
6151 \begin_inset CommandInset label
6153 name "sub:Manual-Bracket-Size"
6161 \begin_layout Plain Layout
6162 Bracket size ! manual
6170 \begin_layout Standard
6171 The bracket size can be specified manually by the LaTeX-commands
6181 \begin_layout Plain Layout
6214 denotes the smallest and
6220 the largest bracket size.
6223 \begin_layout Standard
6224 These commands are used to emphasize levels of brackets:
6227 \begin_layout Standard
6229 \begin_inset Tabular
6230 <lyxtabular version="3" rows="2" columns="2">
6232 <column alignment="center" valignment="top" width="0pt">
6233 <column alignment="center" valignment="top" width="0pt">
6235 <cell alignment="center" valignment="top" usebox="none">
6238 \begin_layout Plain Layout
6239 all brackets in the same size:
6244 <cell alignment="center" valignment="top" usebox="none">
6247 \begin_layout Plain Layout
6248 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox {-4mm}{}$
6258 <cell alignment="center" valignment="top" usebox="none">
6261 \begin_layout Plain Layout
6267 <cell alignment="center" valignment="top" usebox="none">
6270 \begin_layout Plain Layout
6271 \begin_inset Formula $\Big ((A+B)(A-B)\Big )^{C}$
6285 \begin_inset Note Note
6288 \begin_layout Plain Layout
6295 is only used as spacer.
6303 \begin_layout Standard
6304 For the second formula the command
6314 \begin_layout Plain Layout
6328 \begin_layout Standard
6329 Here is an overview about all bracket sizes:
6332 \begin_layout Standard
6352 \begin_layout Plain Layout
6369 \begin_layout Plain Layout
6382 \begin_layout Plain Layout
6398 \begin_layout Standard
6400 \begin_inset Formula $\Bigg (\exp\bigg <\Big [\big \{\ln(3x)\big \}^{2}\sin(x)\Big ]^{A}\bigg >\Bigg )^{0,5}$
6406 \begin_layout Standard
6407 \begin_inset Newpage newpage
6416 -commands there is the variant
6426 \begin_layout Plain Layout
6434 that adds a bit more space between the bracket and its content, and the
6451 \begin_layout Plain Layout
6461 , that don't add additional space.
6466 at the end of the command
6472 is for a left bracket; for a right bracket this will be replaced by an
6478 A left or right bracket can each be an opening or closing bracket.
6481 \begin_layout Standard
6482 In the following table is a comparison of the variants:
6485 \begin_layout Standard
6487 \begin_inset Tabular
6488 <lyxtabular version="3" rows="5" columns="2">
6490 <column alignment="center" valignment="middle" width="0">
6491 <column alignment="center" valignment="middle" width="0">
6493 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6496 \begin_layout Plain Layout
6502 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6505 \begin_layout Plain Layout
6507 \begin_inset Note Note
6510 \begin_layout Plain Layout
6517 is only used as spacer.
6529 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6532 \begin_layout Plain Layout
6547 \begin_layout Plain Layout
6565 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6568 \begin_layout Plain Layout
6569 \begin_inset Formula $\raisebox {5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox {-3.25mm}{}$
6579 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6582 \begin_layout Plain Layout
6597 \begin_layout Plain Layout
6615 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6618 \begin_layout Plain Layout
6619 \begin_inset Formula $\raisebox {5.5mm}{}\Big (\big (\ln(3x)\big )^{2}\Big )\raisebox {-3.25mm}{}$
6629 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6632 \begin_layout Plain Layout
6647 \begin_layout Plain Layout
6665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6668 \begin_layout Plain Layout
6669 \begin_inset Formula $\raisebox {5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox {-3.25mm}{}$
6679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6682 \begin_layout Plain Layout
6694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6697 \begin_layout Plain Layout
6698 \begin_inset Formula $\raisebox {4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox {-2mm}{}$
6714 \begin_layout Subsubsection
6715 Automatic Bracket Size
6716 \begin_inset CommandInset label
6718 name "sub:Automatic-Bracket-Size"
6726 \begin_layout Plain Layout
6727 Bracket size ! automatic
6735 \begin_layout Standard
6736 Brackets with variable size can be inserted with the commands
6746 \begin_layout Plain Layout
6764 \begin_layout Plain Layout
6772 or via the math toolbar button
6773 \begin_inset Graphics
6774 filename ../images/dialog-show_mathdelimiter.png
6793 the wanted bracket must be inserted.
6794 The bracket size will then automatically be calculated for the output.
6797 \begin_layout Standard
6799 normal bracket: The command
6809 \begin_layout Plain Layout
6819 \begin_inset Formula $\downarrow$
6826 \begin_layout Plain Layout
6838 \begin_inset Formula \[
6846 \begin_layout Standard
6848 multiline bracket: The command
6860 \begin_layout Plain Layout
6870 \begin_inset Formula $\downarrow$
6877 \begin_layout Plain Layout
6891 \begin_inset Formula \[
6892 \ln\left(\frac{A}{C}\right)\]
6899 \begin_layout Standard
6915 \begin_inset Space ~
6921 This has the advantage that you can see in LyX immediately the real bracket
6922 size and that the matching right bracket will be created too.
6923 \begin_inset Newline newline
6926 The command for the last example would then be:
6940 \begin_layout Plain Layout
6950 \begin_inset Formula $\downarrow$
6956 \begin_layout Standard
6957 To omit a left or right bracket, a dot is inserted for the omitted bracket.
6958 For example the command
6968 \begin_layout Plain Layout
6978 \begin_inset Formula $\downarrow$
6985 \begin_layout Plain Layout
7001 \begin_inset Formula \[
7002 \left.\frac{A}{B}\right\} \]
7020 will be converted by LyX to brackets in the right size when the document
7021 is reloaded and an omitted bracket will appear as dashed line.
7024 \begin_layout Standard
7025 \begin_inset VSpace bigskip
7028 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7039 \begin_layout Plain Layout
7047 is additionally available for all brackets and limits.
7048 With this command the height of the following character is adapted to the
7049 one of the surrounding brackets, what is e.
7050 \begin_inset Space \thinspace{}
7054 \begin_inset Space ~
7057 needed for physical vectors:
7058 \begin_inset Formula \[
7059 \left\langle \phi\:\middle |\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
7063 For physical vectors there is a special LaTeX-package, described in
7064 \begin_inset CommandInset ref
7066 reference "sub:Physical-Vectors"
7073 \begin_layout Subsection
7078 \begin_layout Plain Layout
7079 Brackets ! horizontal
7087 \begin_layout Standard
7089 \begin_inset Tabular
7090 <lyxtabular version="3" rows="4" columns="2">
7092 <column alignment="center" valignment="top" width="0pt">
7093 <column alignment="center" valignment="top" width="0pt">
7095 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7098 \begin_layout Plain Layout
7100 \begin_inset Note Note
7103 \begin_layout Plain Layout
7110 is only used as spacer.
7120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7123 \begin_layout Plain Layout
7131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7134 \begin_layout Plain Layout
7138 \begin_layout Plain Layout
7153 \begin_layout Plain Layout
7166 \begin_layout Plain Layout
7179 \begin_layout Plain Layout
7192 \begin_layout Plain Layout
7203 \begin_layout Plain Layout
7216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7219 \begin_layout Plain Layout
7220 \begin_inset Formula $\overbrace{A+B}^{3}$
7230 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7233 \begin_layout Plain Layout
7237 \begin_layout Plain Layout
7252 \begin_layout Plain Layout
7265 \begin_layout Plain Layout
7278 \begin_layout Plain Layout
7289 \begin_layout Plain Layout
7302 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7305 \begin_layout Plain Layout
7306 \begin_inset Formula $\underbrace{A+B}_{5}$
7316 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7319 \begin_layout Plain Layout
7326 \begin_layout Plain Layout
7341 \begin_layout Plain Layout
7354 \begin_layout Plain Layout
7367 \begin_layout Plain Layout
7380 \begin_layout Plain Layout
7393 \begin_layout Plain Layout
7406 \begin_layout Plain Layout
7420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7423 \begin_layout Plain Layout
7424 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7440 \begin_layout Standard
7441 In the last example it doesn't matter if
7453 is inserted at first.
7456 \begin_layout Standard
7457 \begin_inset VSpace bigskip
7460 When brackets are needed that overlap each other, multiline formulas, as
7462 \begin_inset CommandInset ref
7464 reference "sec:Multiline-Formulas"
7469 \begin_inset Formula \begin{eqnarray*}
7470 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7471 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
7475 In the first row the formula is inserted together with the first brace.
7476 It is hereby important that the space command
7480 \begin_layout Plain Layout
7481 Space commands are explained in
7482 \begin_inset CommandInset ref
7484 reference "sub:Predefined-Space"
7499 is inserted before the first
7500 \begin_inset Formula $d$
7503 , because the brace that ends behind the
7504 \begin_inset Formula $q$
7507 prevents that the following
7508 \begin_inset Quotes eld
7512 \begin_inset Quotes erd
7515 is surrounded by space.
7519 \begin_layout Plain Layout
7520 because a bracket is not handled as character, see
7521 \begin_inset CommandInset ref
7523 reference "sub:Binary-Operators"
7532 In the second row the second brace is inserted.
7533 As it should begin before the
7534 \begin_inset Formula $b$
7549 \begin_layout Plain Layout
7557 \begin_inset CommandInset ref
7559 reference "sub:Placeholders"
7568 This space is needed because the
7569 \begin_inset Quotes eld
7573 \begin_inset Quotes erd
7576 is also surrounded by space in the formula.
7577 The brace is placed under the command
7586 \begin_layout Standard
7587 It gets more complicated when brackets overlap each other, like in the following
7592 \begin_layout Plain Layout
7604 \begin_inset Formula \begin{eqnarray*}
7605 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
7606 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
7614 \begin_layout Plain Layout
7625 The first formula row is the same as the second row of the previous example,
7626 with the difference that the brace is above.
7627 The second row contains the formula together with the second brace.
7628 To avoid that there is space between the upper brace in the first row and
7629 the formula, the row spacing need to be reduced.
7630 This is not easily possible due to a bug in LyX
7634 \begin_layout Plain Layout
7635 \begin_inset CommandInset href
7637 name "LyX-bug #1505"
7638 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
7648 As solution for the problem, the global formula row separation
7658 \begin_layout Plain Layout
7666 must be changed to -6
7667 \begin_inset Space \thinspace{}
7670 pt before the formula with the command
7685 is set back after the formula to the standard value of 3
7686 \begin_inset Space \thinspace{}
7689 pt using the same command.
7690 More about the row separation in formulas is explained in
7691 \begin_inset CommandInset ref
7693 reference "sub:Line-Separation"
7700 \begin_layout Section
7705 \begin_layout Plain Layout
7714 \begin_layout Standard
7715 Arrows can be inserted via the math toolbar button
7716 \begin_inset Graphics
7717 filename ../images/math/leftarrow.png
7723 or the commands listed in the following subsections.
7726 \begin_layout Subsection
7731 \begin_layout Plain Layout
7740 \begin_layout Standard
7741 \begin_inset Space \hfill{}
7745 \begin_inset Tabular
7746 <lyxtabular version="3" rows="8" columns="2">
7748 <column alignment="center" valignment="top" width="0pt">
7749 <column alignment="center" valignment="top" width="0pt">
7751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7754 \begin_layout Plain Layout
7760 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7763 \begin_layout Plain Layout
7771 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7774 \begin_layout Plain Layout
7782 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7785 \begin_layout Plain Layout
7786 \begin_inset Formula $\gets$
7796 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7799 \begin_layout Plain Layout
7807 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7810 \begin_layout Plain Layout
7811 \begin_inset Formula $\Leftarrow$
7821 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7824 \begin_layout Plain Layout
7832 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7835 \begin_layout Plain Layout
7836 \begin_inset Formula $\longleftarrow$
7846 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7849 \begin_layout Plain Layout
7857 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7860 \begin_layout Plain Layout
7861 \begin_inset Formula $\Longleftarrow$
7871 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7874 \begin_layout Plain Layout
7882 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7885 \begin_layout Plain Layout
7886 \begin_inset Formula $\leftharpoonup$
7896 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7899 \begin_layout Plain Layout
7907 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7910 \begin_layout Plain Layout
7911 \begin_inset Formula $\leftharpoondown$
7921 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
7924 \begin_layout Plain Layout
7932 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
7935 \begin_layout Plain Layout
7936 \begin_inset Formula $\hookleftarrow$
7950 \begin_inset Space \hfill{}
7954 \begin_inset Tabular
7955 <lyxtabular version="3" rows="8" columns="2">
7957 <column alignment="center" valignment="top" width="0pt">
7958 <column alignment="center" valignment="top" width="0pt">
7960 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7963 \begin_layout Plain Layout
7969 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7972 \begin_layout Plain Layout
7980 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7983 \begin_layout Plain Layout
7991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7994 \begin_layout Plain Layout
7995 \begin_inset Formula $\to$
8005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8008 \begin_layout Plain Layout
8016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8019 \begin_layout Plain Layout
8020 \begin_inset Formula $\Rightarrow$
8030 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8033 \begin_layout Plain Layout
8041 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8044 \begin_layout Plain Layout
8045 \begin_inset Formula $\longrightarrow$
8055 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8058 \begin_layout Plain Layout
8066 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8069 \begin_layout Plain Layout
8070 \begin_inset Formula $\Longrightarrow$
8080 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8083 \begin_layout Plain Layout
8091 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8094 \begin_layout Plain Layout
8095 \begin_inset Formula $\rightharpoonup$
8105 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8108 \begin_layout Plain Layout
8116 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8119 \begin_layout Plain Layout
8120 \begin_inset Formula $\rightharpoondown$
8130 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8133 \begin_layout Plain Layout
8141 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8144 \begin_layout Plain Layout
8145 \begin_inset Formula $\hookrightarrow$
8159 \begin_inset Space \hfill{}
8165 \begin_layout Standard
8166 \begin_inset Space \hfill{}
8170 \begin_inset Tabular
8171 <lyxtabular version="3" rows="6" columns="2">
8173 <column alignment="center" valignment="top" width="0pt">
8174 <column alignment="center" valignment="top" width="0pt">
8176 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8179 \begin_layout Plain Layout
8185 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8188 \begin_layout Plain Layout
8196 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8199 \begin_layout Plain Layout
8207 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8210 \begin_layout Plain Layout
8211 \begin_inset Formula $\leftrightarrow$
8221 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8224 \begin_layout Plain Layout
8232 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8235 \begin_layout Plain Layout
8236 \begin_inset Formula $\Leftrightarrow$
8246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8249 \begin_layout Plain Layout
8257 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8260 \begin_layout Plain Layout
8261 \begin_inset Formula $\longleftrightarrow$
8271 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8274 \begin_layout Plain Layout
8282 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8285 \begin_layout Plain Layout
8286 \begin_inset Formula $\Longleftrightarrow$
8296 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8299 \begin_layout Plain Layout
8307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8310 \begin_layout Plain Layout
8311 \begin_inset Formula $\rightleftharpoons$
8325 \begin_inset Space \hspace{}
8330 \begin_inset Space \hfill{}
8334 \begin_inset Tabular
8335 <lyxtabular version="3" rows="5" columns="2">
8337 <column alignment="center" valignment="top" width="0pt">
8338 <column alignment="center" valignment="top" width="0pt">
8340 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8343 \begin_layout Plain Layout
8349 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8352 \begin_layout Plain Layout
8360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8363 \begin_layout Plain Layout
8371 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8374 \begin_layout Plain Layout
8375 \begin_inset Formula $\mapsto$
8385 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8388 \begin_layout Plain Layout
8396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8399 \begin_layout Plain Layout
8400 \begin_inset Formula $\longmapsto$
8410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8413 \begin_layout Plain Layout
8421 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8424 \begin_layout Plain Layout
8425 \begin_inset Formula $\leadsto$
8435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8438 \begin_layout Plain Layout
8446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8449 \begin_layout Plain Layout
8450 \begin_inset Formula $\dasharrow$
8464 \begin_inset Space \hfill{}
8470 \begin_layout Standard
8471 \begin_inset VSpace medskip
8474 Arrows used as accent like e.
8475 \begin_inset Space \thinspace{}
8479 \begin_inset Space ~
8482 vector arrows are listed in
8483 \begin_inset CommandInset ref
8485 reference "sec:Accents"
8492 \begin_layout Standard
8493 \begin_inset VSpace bigskip
8496 Furthermore there are the labeled arrows
8500 \begin_layout Plain Layout
8516 \begin_layout Plain Layout
8534 \begin_layout Plain Layout
8538 \begin_inset VSpace 4mm
8547 When inserting one of these commands in a formula, an arrow with two blue
8548 boxes appear where the label can be inserted.
8549 The length of the arrow adapts to the label width.
8552 \begin_layout Standard
8554 \begin_inset Tabular
8555 <lyxtabular version="3" rows="3" columns="2">
8557 <column alignment="center" valignment="top" width="0pt">
8558 <column alignment="center" valignment="top" width="0pt">
8560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8563 \begin_layout Plain Layout
8569 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8572 \begin_layout Plain Layout
8574 \begin_inset Note Note
8577 \begin_layout Plain Layout
8584 is only used as spacer.
8596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8599 \begin_layout Plain Layout
8606 \begin_layout Plain Layout
8616 \begin_inset Formula $\downarrow$
8620 \begin_inset Formula $\to$
8628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8631 \begin_layout Plain Layout
8632 \begin_inset Formula $\raisebox {5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox {-4mm}{}$
8642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8645 \begin_layout Plain Layout
8652 \begin_layout Plain Layout
8662 \begin_inset Formula $\downarrow$
8666 \begin_inset Formula $\to$
8674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8677 \begin_layout Plain Layout
8678 \begin_inset Formula $\raisebox {5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox {-4mm}{}$
8694 \begin_layout Subsection
8695 Vertical and diagonal Arrows
8699 \begin_layout Plain Layout
8709 \begin_layout Plain Layout
8718 \begin_layout Standard
8719 \begin_inset Space \hfill{}
8723 \begin_inset Tabular
8724 <lyxtabular version="3" rows="7" columns="2">
8726 <column alignment="center" valignment="top" width="0pt">
8727 <column alignment="center" valignment="top" width="0pt">
8729 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8732 \begin_layout Plain Layout
8738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8741 \begin_layout Plain Layout
8749 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8752 \begin_layout Plain Layout
8760 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8763 \begin_layout Plain Layout
8764 \begin_inset Formula $\uparrow$
8774 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8777 \begin_layout Plain Layout
8785 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8788 \begin_layout Plain Layout
8789 \begin_inset Formula $\Uparrow$
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8802 \begin_layout Plain Layout
8810 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8813 \begin_layout Plain Layout
8814 \begin_inset Formula $\updownarrow$
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8827 \begin_layout Plain Layout
8835 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8838 \begin_layout Plain Layout
8839 \begin_inset Formula $\Updownarrow$
8849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8852 \begin_layout Plain Layout
8860 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8863 \begin_layout Plain Layout
8864 \begin_inset Formula $\Downarrow$
8874 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8877 \begin_layout Plain Layout
8885 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8888 \begin_layout Plain Layout
8889 \begin_inset Formula $\downarrow$
8903 \begin_inset Space \hfill{}
8907 \begin_inset Tabular
8908 <lyxtabular version="3" rows="5" columns="2">
8910 <column alignment="center" valignment="top" width="0pt">
8911 <column alignment="center" valignment="top" width="0pt">
8913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8916 \begin_layout Plain Layout
8922 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8925 \begin_layout Plain Layout
8933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8936 \begin_layout Plain Layout
8944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8947 \begin_layout Plain Layout
8948 \begin_inset Formula $\nearrow$
8958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8961 \begin_layout Plain Layout
8969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8972 \begin_layout Plain Layout
8973 \begin_inset Formula $\searrow$
8983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8986 \begin_layout Plain Layout
8994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8997 \begin_layout Plain Layout
8998 \begin_inset Formula $\swarrow$
9008 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9011 \begin_layout Plain Layout
9019 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9022 \begin_layout Plain Layout
9023 \begin_inset Formula $\nwarrow$
9037 \begin_inset Space \hfill{}
9043 \begin_layout Standard
9044 \begin_inset VSpace medskip
9047 Vertical arrows can be used also as delimiter together with the commands
9049 \begin_inset CommandInset ref
9051 reference "sub:Manual-Bracket-Size"
9056 \begin_inset CommandInset ref
9058 reference "sub:Automatic-Bracket-Size"
9065 \begin_layout Standard
9066 \begin_inset Newpage newpage
9072 \begin_layout Section
9074 \begin_inset CommandInset label
9084 \begin_layout Plain Layout
9093 \begin_layout Standard
9094 Accents can be inserted via the math toolbar button
9095 \begin_inset Graphics
9096 filename ../images/math/hat.png
9102 or the commands listed in the following subsections.
9105 \begin_layout Subsection
9106 Accents for one Character
9110 \begin_layout Plain Layout
9123 \begin_layout Plain Layout
9125 \begin_inset CommandInset ref
9127 reference "sub:Accents-in-Text"
9140 \begin_layout Plain Layout
9148 \begin_inset Note Note
9151 \begin_layout Plain Layout
9154 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
9157 \begin_layout Plain Layout
9160 texorpdfstring is in section
9161 \begin_inset CommandInset ref
9163 reference "sub:Formulas-in-Section"
9173 \begin_inset CommandInset label
9175 name "sub:Accents-for-one"
9183 \begin_layout Plain Layout
9184 Accents ! for one character
9192 \begin_layout Standard
9193 \begin_inset Space \hfill{}
9197 \begin_inset Tabular
9198 <lyxtabular version="3" rows="8" columns="2">
9200 <column alignment="center" valignment="top" width="0pt">
9201 <column alignment="center" valignment="top" width="0pt">
9203 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9206 \begin_layout Plain Layout
9212 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9215 \begin_layout Plain Layout
9217 \begin_inset Note Note
9220 \begin_layout Plain Layout
9227 is only used as spacer.
9239 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9242 \begin_layout Plain Layout
9249 \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
9267 \begin_inset Formula $\raisebox {5mm}{}\dot{A}$
9277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9280 \begin_layout Plain Layout
9287 \begin_layout Plain Layout
9301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9304 \begin_layout Plain Layout
9305 \begin_inset Formula $\raisebox {5mm}{}\ddot{A}$
9315 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9318 \begin_layout Plain Layout
9325 \begin_layout Plain Layout
9339 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9342 \begin_layout Plain Layout
9343 \begin_inset Formula $\raisebox {5mm}{}\dddot{A}$
9353 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9356 \begin_layout Plain Layout
9364 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9367 \begin_layout Plain Layout
9368 \begin_inset Formula $\raisebox {5mm}{}\ddddot {A}$
9378 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9381 \begin_layout Plain Layout
9388 \begin_layout Plain Layout
9401 \begin_layout Plain Layout
9412 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9415 \begin_layout Plain Layout
9416 \begin_inset Formula $\raisebox {5mm}{}\vec{A}$
9426 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9429 \begin_layout Plain Layout
9436 \begin_layout Plain Layout
9450 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9453 \begin_layout Plain Layout
9454 \begin_inset Formula $\raisebox {5mm}{}\bar{A}$
9464 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9467 \begin_layout Plain Layout
9474 \begin_layout Plain Layout
9488 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9491 \begin_layout Plain Layout
9492 \begin_inset Formula $\raisebox {5mm}{}\mathring{A}$
9506 \begin_inset Space \hfill{}
9510 \begin_inset Tabular
9511 <lyxtabular version="3" rows="7" columns="2">
9513 <column alignment="center" valignment="top" width="0pt">
9514 <column alignment="center" valignment="top" width="0pt">
9516 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9519 \begin_layout Plain Layout
9525 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9528 \begin_layout Plain Layout
9536 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9539 \begin_layout Plain Layout
9546 \begin_layout Plain Layout
9560 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9563 \begin_layout Plain Layout
9564 \begin_inset Formula $\raisebox {5mm}{}\tilde{A}$
9574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9577 \begin_layout Plain Layout
9584 \begin_layout Plain Layout
9598 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9601 \begin_layout Plain Layout
9602 \begin_inset Formula $\raisebox {5mm}{}\hat{A}$
9612 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9615 \begin_layout Plain Layout
9622 \begin_layout Plain Layout
9636 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9639 \begin_layout Plain Layout
9640 \begin_inset Formula $\raisebox {5mm}{}\check{A}$
9650 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9653 \begin_layout Plain Layout
9660 \begin_layout Plain Layout
9674 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9677 \begin_layout Plain Layout
9678 \begin_inset Formula $\raisebox {5mm}{}\acute{A}$
9688 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9691 \begin_layout Plain Layout
9698 \begin_layout Plain Layout
9712 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9715 \begin_layout Plain Layout
9716 \begin_inset Formula $\raisebox {5mm}{}\grave{A}$
9726 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9729 \begin_layout Plain Layout
9736 \begin_layout Plain Layout
9750 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9753 \begin_layout Plain Layout
9754 \begin_inset Formula $\raisebox {5mm}{}\breve{A}$
9768 \begin_inset Space \hfill{}
9774 \begin_layout Standard
9775 \begin_inset VSpace bigskip
9782 \begin_layout Plain Layout
9788 in formulas, a quotation mark is inserted before the vowel.
9789 These two characters are then treated by LaTeX as
9793 character when the formula part with the umlaut is marked as German.
9801 \begin_inset Quotes eld
9805 \begin_inset Quotes erd
9808 umlauts are created as demonstrated in the following example:
9811 \begin_layout Standard
9812 \begin_inset VSpace -2mm
9818 \begin_layout Standard
9820 \begin_inset Tabular
9821 <lyxtabular version="3" rows="3" columns="2">
9823 <column alignment="center" valignment="top" width="0">
9824 <column alignment="center" valignment="top" width="0">
9826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9829 \begin_layout Plain Layout
9835 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9838 \begin_layout Plain Layout
9840 \begin_inset Note Note
9843 \begin_layout Plain Layout
9850 is only used as spacer.
9862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9865 \begin_layout Plain Layout
9868 \begin_inset Quotes grd
9876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9879 \begin_layout Plain Layout
9882 \begin_inset Formula $"i$
9892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9895 \begin_layout Plain Layout
9902 \begin_layout Plain Layout
9916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9919 \begin_layout Plain Layout
9920 \begin_inset Formula $\raisebox {5mm}{}\ddot{i}$
9936 \begin_layout Standard
9937 Another advantage to
9943 is that umlauts can directly be converted to mathematical text because
9944 the accent commands above are
9950 in mathematical text
9953 To convert an accented character to mathematical text, only the character
9954 under the accent may be converted.
9955 This applies also for all other conversions, e.
9956 \begin_inset Space \thinspace{}
9960 \begin_inset Space ~
9966 \begin_layout Standard
9967 In mathematical text, umlauts and other accented characters can directly
9971 \begin_layout Subsection
9972 Accents for Operators
9976 \begin_layout Plain Layout
9977 Accents ! for operators
9985 \begin_layout Standard
9996 \begin_layout Plain Layout
10014 \begin_layout Plain Layout
10022 characters can be placed above or below an operator, respectively, to accent
10034 \begin_layout Plain Layout
10042 characters can be set before and behind an operator.
10043 The command scheme is:
10046 \begin_layout Standard
10062 \begin_layout Standard
10069 must always be before the operator that should be accented.
10070 You can accent with several characters and even with other operators and
10078 for example only characters behind an operator, write nothing between the
10079 first braces but don't omit the braces.
10082 \begin_layout Standard
10083 For example the command
10088 \begin_inset Formula $\to$
10098 \begin_inset Formula $\to$
10107 \begin_layout Plain Layout
10123 \begin_inset Formula \[
10124 \sideset {}{'}\sum_{k=1}^{n}\]
10131 \begin_layout Standard
10140 \begin_layout Plain Layout
10155 \begin_layout Plain Layout
10167 \begin_inset Formula $\uparrow$
10175 \begin_inset Formula \[
10176 \overset{a}{\maltese}\]
10180 As seen in the last example, with
10192 also symbols and characters can be accented; with
10198 this is not possible.
10201 \begin_layout Subsection
10202 Accents for several Characters
10203 \begin_inset CommandInset label
10205 name "sub:Accents-for-several"
10213 \begin_layout Plain Layout
10214 Accents ! for several characters
10222 \begin_layout Standard
10223 \begin_inset Space \hfill{}
10227 \begin_inset Tabular
10228 <lyxtabular version="3" rows="5" columns="2">
10230 <column alignment="center" valignment="top" width="0pt">
10231 <column alignment="center" valignment="top" width="0pt">
10233 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10236 \begin_layout Plain Layout
10242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10245 \begin_layout Plain Layout
10247 \begin_inset Note Note
10250 \begin_layout Plain Layout
10257 is only used as spacer.
10269 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10272 \begin_layout Plain Layout
10279 \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
10297 \begin_inset Formula $\raisebox {6mm}{}\overleftarrow{A=B}\raisebox {-2mm}{}$
10307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10310 \begin_layout Plain Layout
10317 \begin_layout Plain Layout
10331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10334 \begin_layout Plain Layout
10335 \begin_inset Formula $\raisebox {5mm}{}\underleftarrow{A=B}\raisebox {-3mm}{}$
10345 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10348 \begin_layout Plain Layout
10355 \begin_layout Plain Layout
10369 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10372 \begin_layout Plain Layout
10373 \begin_inset Formula $\raisebox {6mm}{}\overleftrightarrow{A=B}\raisebox {-2mm}{}$
10383 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10386 \begin_layout Plain Layout
10389 underleftrightarrow
10393 \begin_layout Plain Layout
10407 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10410 \begin_layout Plain Layout
10411 \begin_inset Formula $\raisebox {5mm}{}\underleftrightarrow{A=B}\raisebox {-3mm}{}$
10425 \begin_inset Space \hfill{}
10429 \begin_inset Tabular
10430 <lyxtabular version="3" rows="5" columns="2">
10432 <column alignment="center" valignment="top" width="0pt">
10433 <column alignment="center" valignment="top" width="0pt">
10435 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10438 \begin_layout Plain Layout
10444 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10447 \begin_layout Plain Layout
10455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10458 \begin_layout Plain Layout
10465 \begin_layout Plain Layout
10479 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10482 \begin_layout Plain Layout
10483 \begin_inset Formula $\raisebox {6mm}{}\overrightarrow{A=B}\raisebox {-2mm}{}$
10493 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10496 \begin_layout Plain Layout
10503 \begin_layout Plain Layout
10517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10520 \begin_layout Plain Layout
10521 \begin_inset Formula $\raisebox {5mm}{}\underrightarrow{A=B}\raisebox {-3mm}{}$
10531 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10534 \begin_layout Plain Layout
10541 \begin_layout Plain Layout
10555 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10558 \begin_layout Plain Layout
10559 \begin_inset Formula $\raisebox {6mm}{}\widetilde{A=B}\raisebox {-2mm}{}$
10569 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10572 \begin_layout Plain Layout
10579 \begin_layout Plain Layout
10593 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10596 \begin_layout Plain Layout
10597 \begin_inset Formula $\raisebox {6mm}{}\widehat{A=B}\raisebox {-2mm}{}$
10611 \begin_inset Space \hfill{}
10617 \begin_layout Standard
10618 \begin_inset VSpace medskip
10621 With these commands as many characters as you like can be accented.
10634 will only be set in the output with a length of three characters, as shown
10635 in the following example:
10636 \begin_inset Formula \[
10637 \widetilde{A+B=C-D}\]
10644 \begin_layout Standard
10655 \begin_layout Plain Layout
10673 \begin_layout Plain Layout
10681 described in the previous subsection it is also possible to accent several
10691 \begin_layout Plain Layout
10701 \begin_inset Formula $\downarrow$
10707 \begin_inset Formula \[
10708 \underset{***}{A=B}\]
10715 \begin_layout Section
10717 \begin_inset CommandInset label
10727 \begin_layout Plain Layout
10736 \begin_layout Subsection
10738 \begin_inset CommandInset label
10740 name "sub:Predefined-Space"
10748 \begin_layout Plain Layout
10749 Space ! horizontal ! predefined
10757 \begin_layout Standard
10758 Sometimes it is necessary to insert horizontal space to a formula.
10759 This is done by inserting a protected space (shortcut
10765 \begin_inset Quotes eld
10775 \begin_layout Plain Layout
10788 \begin_inset Quotes erd
10791 appears and by pressing
10795 several times one can select one of eight different space sizes.
10796 The spaces can also be inserted using the math toolbar button
10797 \begin_inset Graphics
10798 filename ../images/math/space.png
10804 or special commands.
10805 Independent from the inserted command, one can select the size again by
10813 \begin_layout Standard
10816 \begin_inset VSpace -5mm
10820 \begin_inset Tabular
10821 <lyxtabular version="3" rows="3" columns="7">
10823 <column alignment="center" valignment="middle" width="6.8cm">
10824 <column alignment="center" valignment="top" width="0">
10825 <column alignment="center" valignment="top" width="0">
10826 <column alignment="center" valignment="top" width="0">
10827 <column alignment="center" valignment="top" width="0">
10828 <column alignment="center" valignment="top" width="0">
10829 <column alignment="center" valignment="top" width="0">
10831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10834 \begin_layout Plain Layout
10840 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10843 \begin_layout Plain Layout
10851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10854 \begin_layout Plain Layout
10862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10865 \begin_layout Plain Layout
10873 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10876 \begin_layout Plain Layout
10884 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10887 \begin_layout Plain Layout
10895 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10898 \begin_layout Plain Layout
10908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10911 \begin_layout Plain Layout
10916 keystrokes after inserting the protected space
10921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10924 \begin_layout Plain Layout
10930 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10933 \begin_layout Plain Layout
10939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10942 \begin_layout Plain Layout
10948 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10951 \begin_layout Plain Layout
10957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10960 \begin_layout Plain Layout
10966 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10969 \begin_layout Plain Layout
10977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10980 \begin_layout Plain Layout
10986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10989 \begin_layout Plain Layout
10990 \begin_inset Formula $A\, B$
10998 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11001 \begin_layout Plain Layout
11002 \begin_inset Formula $A\: B$
11010 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11013 \begin_layout Plain Layout
11014 \begin_inset Formula $A\; B$
11022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11025 \begin_layout Plain Layout
11026 \begin_inset Formula $A\quad B$
11034 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11037 \begin_layout Plain Layout
11038 \begin_inset Formula $A\qquad B$
11046 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11049 \begin_layout Plain Layout
11050 \begin_inset Formula $A\! B$
11066 \begin_layout Standard
11067 The last size seem to produce no space.
11068 It is displayed red in LyX contrary to the other sizes, because it is a
11070 There are two more negative spaces:
11073 \begin_layout Standard
11075 \begin_inset Tabular
11076 <lyxtabular version="3" rows="3" columns="3">
11078 <column alignment="center" valignment="middle" width="6.8cm">
11079 <column alignment="center" valignment="top" width="0pt">
11080 <column alignment="center" valignment="top" width="0pt">
11082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11085 \begin_layout Plain Layout
11091 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11094 \begin_layout Plain Layout
11102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11105 \begin_layout Plain Layout
11115 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11118 \begin_layout Plain Layout
11123 keystrokes after inserting the protected space
11128 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11131 \begin_layout Plain Layout
11137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11140 \begin_layout Plain Layout
11148 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11151 \begin_layout Plain Layout
11157 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11160 \begin_layout Plain Layout
11161 \begin_inset Formula $A\negmedspace B$
11169 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11172 \begin_layout Plain Layout
11173 \begin_inset Formula $A\negthickspace B$
11189 \begin_layout Standard
11190 Negative spaces can lead to characters overlapping each other.
11191 Thus they can be used to enforce ligatures, what is e.
11192 \begin_inset Space \thinspace{}
11196 \begin_inset Space ~
11199 useful for summation operators:
11202 \begin_layout Standard
11204 \begin_inset Tabular
11205 <lyxtabular version="3" rows="3" columns="2">
11207 <column alignment="center" valignment="top" width="0">
11208 <column alignment="center" valignment="top" width="0">
11210 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11213 \begin_layout Plain Layout
11219 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11222 \begin_layout Plain Layout
11224 \begin_inset Note Note
11227 \begin_layout Plain Layout
11234 is only used as spacer.
11246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11249 \begin_layout Plain Layout
11258 \begin_layout Plain Layout
11272 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11275 \begin_layout Plain Layout
11276 \begin_inset Formula $\raisebox {4.5mm}{}\sum\sum f_{kl}\raisebox {-2.5mm}{}$
11286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11289 \begin_layout Plain Layout
11300 \begin_layout Plain Layout
11314 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11317 \begin_layout Plain Layout
11318 \begin_inset Formula $\raisebox {4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox {-2.5mm}{}$
11334 \begin_layout Standard
11335 Relations like for example equal signs, are always surrounded by space.
11336 To suppress this, the equal sign is placed into a TeX-brace.
11337 The following example demonstrates this:
11340 \begin_layout Standard
11342 \begin_inset Tabular
11343 <lyxtabular version="3" rows="2" columns="2">
11345 <column alignment="center" valignment="top" width="0pt">
11346 <column alignment="center" valignment="top" width="0pt">
11348 <cell alignment="center" valignment="top" usebox="none">
11351 \begin_layout Plain Layout
11357 <cell alignment="center" valignment="top" usebox="none">
11360 \begin_layout Plain Layout
11361 \begin_inset Formula $A=B$
11371 <cell alignment="center" valignment="top" usebox="none">
11374 \begin_layout Plain Layout
11375 \begin_inset Note Note
11378 \begin_layout Plain Layout
11385 is only used as spacer.
11391 \begin_inset Formula $\raisebox {5mm}{}$
11394 equation without space
11399 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11402 \begin_layout Plain Layout
11403 \begin_inset Formula $A{=}B$
11419 \begin_layout Standard
11421 The command for the last formula is:
11426 \begin_inset Formula $\to$
11432 \begin_layout Standard
11433 \begin_inset VSpace bigskip
11436 Spaces are needed for physical units, because the space between the value
11437 and the unit is the smallest one and not a normal space.
11438 For units in text, the smallest space is inserted via the menu
11440 Insert\SpecialChar \menuseparator
11441 Formatting\SpecialChar \menuseparator
11443 \begin_inset Space ~
11455 \begin_layout Standard
11456 An example to visualize the difference:
11459 \begin_layout Standard
11460 \begin_inset Tabular
11461 <lyxtabular version="3" rows="2" columns="2">
11463 <column alignment="left" valignment="top" width="0">
11464 <column alignment="left" valignment="top" width="0">
11466 <cell alignment="center" valignment="top" usebox="none">
11469 \begin_layout Plain Layout
11471 \begin_inset Formula $\cdot$
11479 <cell alignment="center" valignment="top" usebox="none">
11482 \begin_layout Plain Layout
11483 space between value and unit
11490 <cell alignment="center" valignment="top" usebox="none">
11493 \begin_layout Plain Layout
11495 \begin_inset Space \thinspace{}
11499 \begin_inset Formula $\cdot$
11507 <cell alignment="center" valignment="top" usebox="none">
11510 \begin_layout Plain Layout
11511 smallest space between value and unit
11524 \begin_layout Subsection
11529 \begin_layout Plain Layout
11542 \begin_layout Plain Layout
11543 for vertical space in formulas see
11544 \begin_inset CommandInset ref
11546 reference "sub:Line-Separation"
11559 \begin_layout Plain Layout
11567 \begin_inset Note Note
11570 \begin_layout Plain Layout
11573 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11576 \begin_layout Plain Layout
11579 texorpdfstring is in section
11580 \begin_inset CommandInset ref
11582 reference "sub:Formulas-in-Section"
11592 \begin_inset CommandInset label
11594 name "sub:Variable-Space"
11602 \begin_layout Plain Layout
11603 Space ! horizontal ! variable
11611 \begin_layout Standard
11612 Space with a defined length can be inserted in LyX with the command
11613 \begin_inset Newline newline
11626 \begin_layout Plain Layout
11635 For the length all units listed in
11636 \begin_inset CommandInset ref
11638 reference "tab:Used-units"
11642 are allowed, except of the unit
11643 \begin_inset Quotes eld
11647 \begin_inset Quotes erd
11651 The length may also be negative.
11652 To insert so many space that the formula uses all available space, the
11663 \begin_layout Plain Layout
11674 \begin_layout Standard
11675 \begin_inset VSpace -1mm
11681 \begin_layout Standard
11683 \begin_inset Tabular
11684 <lyxtabular version="3" rows="4" columns="2">
11686 <column alignment="center" valignment="top" width="0">
11687 <column alignment="center" valignment="top" width="0">
11689 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11692 \begin_layout Plain Layout
11698 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11701 \begin_layout Plain Layout
11709 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11712 \begin_layout Plain Layout
11716 \begin_inset Formula $\to$
11726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11729 \begin_layout Plain Layout
11730 \begin_inset Formula $A=B\hspace {3cm}A\not=C$
11740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11743 \begin_layout Plain Layout
11747 \begin_inset Formula $\to$
11757 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11760 \begin_layout Plain Layout
11761 \begin_inset Formula $A\hspace {-1mm}A\not=A$
11771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11774 \begin_layout Plain Layout
11781 \begin_layout Plain Layout
11795 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11798 \begin_layout Plain Layout
11799 \begin_inset Formula $A=A\hfill B=B$
11815 \begin_layout Standard
11816 In the last example the available space is given by the longest column entry
11818 In an inline formula the space depends on the length of the line in which
11826 Thus, when the line uses the full width, no space will be created.
11833 only has an effect on displayed formulas when the formula style
11838 (Formula styles are explained in
11839 \begin_inset CommandInset ref
11841 reference "sec:Formula-Styles"
11848 \begin_layout Standard
11849 For text, variable space can be inserted via the menu
11851 Insert\SpecialChar \menuseparator
11852 Formatting\SpecialChar \menuseparator
11854 \begin_inset Space ~
11859 , what is not possible in formulas:
11862 \begin_layout Standard
11863 This is a line with
11864 \begin_inset Space \hspace{}
11869 \begin_inset Space \thinspace{}
11875 \begin_layout Standard
11876 This is a line with
11877 \begin_inset Space \hfill{}
11883 \begin_layout Subsection
11884 Space besides inline Formulas
11888 \begin_layout Plain Layout
11889 Space ! besides inline formulas
11897 \begin_layout Standard
11898 The space that surrounds inline formulas can be adjusted with the length
11907 \begin_layout Plain Layout
11918 The value of a length is set with the command
11926 \begin_layout Plain Layout
11936 that has the following scheme:
11939 \begin_layout Standard
11944 setlength{length name}{value}
11947 \begin_layout Standard
11955 \begin_inset Space \thinspace{}
11961 \begin_layout Standard
11971 \begin_layout Standard
11972 is inserted in TeX-mode.
11974 \begin_inset Space \thinspace{}
11977 mm space will now be set around all inline formulas:
11981 \begin_layout Plain Layout
11995 \begin_layout Standard
11996 This is a line with an inline formula
11997 \begin_inset Formula $A=B$
12001 \begin_inset Space \thinspace{}
12004 mm surrounding space.
12008 \begin_layout Plain Layout
12022 \begin_layout Standard
12023 To return to the predefined value,
12029 is set to the value 0
12030 \begin_inset Space \thinspace{}
12036 \begin_layout Section
12041 \begin_layout Plain Layout
12051 \begin_layout Plain Layout
12056 \begin_layout Plain Layout
12067 \begin_layout Plain Layout
12082 \begin_layout Standard
12083 Boxes for text are described in chapter
12090 \begin_inset Space ~
12098 \begin_layout Subsection
12100 \begin_inset CommandInset label
12102 name "sub:Boxes-with-Frame"
12110 \begin_layout Plain Layout
12119 \begin_layout Standard
12120 It is possible to frame formulas or parts of it with the commands
12130 \begin_layout Plain Layout
12148 \begin_layout Plain Layout
12159 \begin_layout Standard
12160 When one of these commands is inserted to a formula, a blue box appears
12161 within a frame to enter formula parts.
12168 an additional formula has to be created by
12176 \begin_layout Plain Layout
12177 Due to a bug in LyX it is not possible to create a new formula with
12182 \begin_inset CommandInset href
12184 name "LyX-bug #1435"
12185 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12194 , because the box content will otherwise be treated as mathematical text.
12201 is used, a new formula is automatically created inside the frame.
12204 \begin_layout Standard
12211 is not suitable to frame displayed formulas, because the formula will always
12212 be set in the size of the text.
12219 is in contrary not suitable to frame inline formulas, because the formula
12220 will always be set in the size of a displayed formula.
12223 \begin_layout Standard
12230 there is the command
12240 \begin_layout Plain Layout
12248 where additionally the frame width and the alignment can be specified.
12255 is used in the following scheme:
12258 \begin_layout Standard
12263 framebox[frame width][position]{box content}
12266 \begin_layout Standard
12267 The position can either be
12284 right aligns the formula in the box.
12285 When no position is given, the formula will be centered.
12286 \begin_inset Newline newline
12289 Is no width given, also no position can be given.
12290 In this case the frame width is adjusted to the box content like for
12299 \begin_layout Standard
12306 is inserted, a box appears containing three blue boxes.
12307 The first two boxes are surrounded by brackets and denote the two optional
12309 The third box is for formula parts like for
12318 \begin_layout Standard
12320 \begin_inset Note Note
12323 \begin_layout Plain Layout
12324 The table has been set into a minipage to make the footnote appearing.
12325 Otherwise the footnote text would not be displayed.
12331 \begin_inset Box Frameless
12340 height_special "totalheight"
12343 \begin_layout Plain Layout
12345 \begin_inset Tabular
12346 <lyxtabular version="3" rows="5" columns="2">
12348 <column alignment="center" valignment="top" width="0">
12349 <column alignment="center" valignment="top" width="0">
12351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12354 \begin_layout Plain Layout
12359 \begin_layout Plain Layout
12360 Due to a bug in LyX it is not possible to create a new formula with
12365 \begin_inset CommandInset href
12367 name "LyX-bug #1435"
12368 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
12382 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12385 \begin_layout Plain Layout
12387 \begin_inset Note Note
12390 \begin_layout Plain Layout
12397 is only used as spacer.
12409 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12412 \begin_layout Plain Layout
12419 \begin_layout Plain Layout
12438 \begin_layout Plain Layout
12452 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12455 \begin_layout Plain Layout
12456 \begin_inset Formula \raisebox {6mm}{}\fbox{$\int A=B$}\raisebox {-4mm}{}
12467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12470 \begin_layout Plain Layout
12477 \begin_layout Plain Layout
12492 \begin_layout Plain Layout
12506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12509 \begin_layout Plain Layout
12510 \begin_inset Formula $\raisebox {8.5mm}{}\boxed{\int A=B}\raisebox {-6.5mm}{}$
12520 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12523 \begin_layout Plain Layout
12530 \begin_layout Plain Layout
12544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12547 \begin_layout Plain Layout
12548 \begin_inset Formula $\raisebox {6mm}{}A+\fbox{B}\raisebox {-3mm}{}$
12558 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12561 \begin_layout Plain Layout
12568 \begin_layout Plain Layout
12578 \begin_inset Formula $\to$
12582 \begin_inset Formula $\to$
12595 \begin_layout Plain Layout
12605 \begin_inset Formula $\downarrow$
12613 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12616 \begin_layout Plain Layout
12617 \begin_inset Formula $\raisebox {6mm}{}$
12621 \begin_inset Formula $\framebox[20mm][]{$\frac{A}{B}$}$
12625 \begin_inset Formula $\raisebox {-4mm}{}$
12646 \begin_layout Standard
12647 The frame thickness can also be adjusted.
12648 To do this the following commands have to be inserted in TeX-mode before
12652 \begin_layout Standard
12662 \begin_inset Quotes eld
12666 \begin_inset Quotes erd
12680 \begin_inset Quotes eld
12684 \begin_inset Quotes erd
12690 \begin_layout Standard
12691 \begin_inset Quotes eld
12695 \begin_inset Quotes erd
12698 specifies the minimal distance between the frame and the first character
12700 An example for this is the following framed formula:
12704 \begin_layout Plain Layout
12716 \begin_inset Formula \[
12721 Before this formula the commands
12724 \begin_layout Standard
12746 \begin_layout Standard
12747 were inserted in TeX-mode.
12748 The given values are used for all following boxes.
12751 \begin_layout Standard
12752 To return to the standard frame size, the command
12755 \begin_layout Standard
12780 \begin_layout Plain Layout
12794 \begin_layout Standard
12795 is inserted in TeX-mode before the next formula.
12798 \begin_layout Subsection
12799 Boxes without Frame
12800 \begin_inset CommandInset label
12802 name "sub:Boxes-without-Frame"
12810 \begin_layout Plain Layout
12811 Boxes ! without frame
12819 \begin_layout Standard
12820 For boxes without a frame there are the following box commands:
12830 \begin_layout Plain Layout
12848 \begin_layout Plain Layout
12866 \begin_layout Plain Layout
12877 \begin_layout Standard
12884 a box can be super- or subscripted.
12885 But in contrary to normal super- and subscripting, the characters in the
12886 box keep their font size.
12893 is used in the following scheme:
12896 \begin_layout Standard
12901 raisebox{height}{box content}
12904 \begin_layout Standard
12905 When the box should contain a formula, an extra formula is needed like for
12915 \begin_layout Standard
12917 \begin_inset Tabular
12918 <lyxtabular version="3" rows="4" columns="2">
12920 <column alignment="center" valignment="top" width="0">
12921 <column alignment="center" valignment="top" width="0">
12923 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12926 \begin_layout Plain Layout
12932 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12935 \begin_layout Plain Layout
12943 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12946 \begin_layout Plain Layout
12950 \begin_inset Formula $\to$
12956 \begin_inset Formula $\to$
12964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12967 \begin_layout Plain Layout
12968 \begin_inset Formula $H\raisebox {2mm}{al}lo$
12978 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12981 \begin_layout Plain Layout
12985 \begin_inset Formula $\to$
12991 \begin_inset Formula $\to$
12999 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13002 \begin_layout Plain Layout
13003 \begin_inset Formula $H\raisebox {-2mm}{al}lo$
13013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13016 \begin_layout Plain Layout
13020 \begin_inset Formula $\to$
13035 \begin_layout Plain Layout
13049 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13052 \begin_layout Plain Layout
13056 \begin_layout Plain Layout
13080 \begin_layout Standard
13081 The last formula can currently only be created using TeX-mode because LyX
13082 inserts a box instead of the needed extra formula.
13086 \begin_layout Plain Layout
13088 \begin_inset CommandInset href
13090 name "LyX-bug #1435"
13091 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13103 \begin_layout Standard
13128 , with the difference that there is no frame.
13131 \begin_layout Subsection
13133 \begin_inset CommandInset label
13135 name "sub:Colored-Boxes"
13143 \begin_layout Plain Layout
13152 \begin_layout Standard
13153 To be able to use all commands explained in this section, the LaTeX-package
13162 \begin_layout Plain Layout
13167 is part of every LaTeX standard installation.
13176 \begin_layout Plain Layout
13182 has to be loaded in the LaTeX-preamble with the line
13186 \begin_layout Plain Layout
13187 When text is colored somewhere in the document with a predefined color,
13188 LyX loads the LaTeX-package
13193 Thus it is possible that the package is loaded twice, but this doesn't
13200 \begin_inset Note Note
13203 \begin_layout Plain Layout
13204 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13213 \begin_layout Standard
13221 \begin_layout Standard
13222 \begin_inset VSpace medskip
13225 To color boxes, the command
13235 \begin_layout Plain Layout
13243 is used in the following scheme:
13246 \begin_layout Standard
13251 colorbox{color}{box content}
13254 \begin_layout Standard
13255 The box content can also be a box and a
13261 can also be part of another box (see the 2nd and 3rd example).
13262 When the box should contain a formula, an extra formula has to be created,
13273 \begin_layout Plain Layout
13274 This also applies for the command
13282 \begin_inset CommandInset href
13284 name "LyX-bug #1435"
13285 target "http://bugzilla.lyx.org/show_bug.cgi?id=1435"
13297 \begin_layout Standard
13298 One of the following predefined colors can be chosen:
13301 \begin_layout Standard
13335 \begin_layout Standard
13337 \begin_inset Tabular
13338 <lyxtabular version="3" rows="4" columns="2">
13340 <column alignment="center" valignment="top" width="0">
13341 <column alignment="center" valignment="top" width="0">
13343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13346 \begin_layout Plain Layout
13352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13355 \begin_layout Plain Layout
13357 \begin_inset Note Note
13360 \begin_layout Plain Layout
13367 is only used as spacer.
13379 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13382 \begin_layout Plain Layout
13386 \begin_inset Formula $\to$
13396 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13399 \begin_layout Plain Layout
13400 \begin_inset Formula $\raisebox {6mm}{}\colorbox {yellow}{A=B}\raisebox {-3mm}{}$
13410 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13413 \begin_layout Plain Layout
13417 \begin_inset Formula $\to$
13428 \begin_layout Plain Layout
13442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13445 \begin_layout Plain Layout
13446 \begin_inset Formula $\raisebox {6mm}{}\colorbox {green}{\fbox{A=B}}\raisebox {-3mm}{}$
13456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13459 \begin_layout Plain Layout
13466 \begin_layout Plain Layout
13478 \begin_inset Formula $\to$
13488 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13491 \begin_layout Plain Layout
13492 \begin_inset Formula $\raisebox {6mm}{}\fbox{\colorbox {green}{A=B}}\raisebox {-3mm}{}$
13508 \begin_layout Standard
13515 only colors the box but not the characters in the box.
13516 To color all characters, the whole formula is highlighted and the wanted
13517 color is chosen in the
13520 \begin_inset Space ~
13526 The dialog can be called with the toolbar button
13527 \begin_inset Graphics
13528 filename ../images/dialog-show_character.png
13536 Edit\SpecialChar \menuseparator
13538 \begin_inset Space ~
13541 Style\SpecialChar \menuseparator
13545 The formula number has then the same color as the formula.
13546 When the formula number should get another color than the formula characters,
13547 the color must be changed within the formula.
13550 \begin_layout Standard
13554 \begin_layout Standard
13557 \begin_inset Formula \begin{equation}
13558 \int A=B\label{eq:red}\end{equation}
13565 \begin_inset Formula \begin{equation}
13566 \textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
13573 \begin_layout Standard
13575 \begin_inset CommandInset ref
13581 is completely colored red.
13582 \begin_inset Newline newline
13586 \begin_inset CommandInset ref
13588 reference "eq:redgreen"
13592 was first completely colored green to set the color for the formula number.
13593 Subsequently the formula characters were colored red.
13596 \begin_layout Standard
13597 \begin_inset VSpace bigskip
13600 To color the frame different than the rest of the box, the command
13610 \begin_layout Plain Layout
13618 is used in the following scheme:
13621 \begin_layout Standard
13626 fcolorbox{frame color}{color}{box content}
13629 \begin_layout Standard
13636 is an extension of the command
13643 The frame width is set, like for
13666 \begin_layout Plain Layout
13678 \begin_inset Formula \[
13679 \fcolorbox {cyan}{magenta}{A=B}\]
13687 \begin_layout Plain Layout
13701 \begin_layout Standard
13702 This formula was created with the command
13703 \begin_inset Newline newline
13711 \begin_inset Formula $\to$
13717 \begin_inset Formula $\to$
13727 \begin_layout Standard
13728 \begin_inset VSpace bigskip
13731 To use other colors than the predefined ones, they have to be defined first.
13734 \begin_layout Standard
13735 One can for example define the color
13736 \begin_inset Quotes eld
13744 \begin_inset Quotes erd
13747 with the LaTeX-preamble line:
13750 \begin_layout Standard
13755 definecolor{darkgreen}{cmyk}{0.5,
13773 \begin_layout Plain Layout
13784 \begin_layout Standard
13789 is the color space that denotes the colors
13806 The four comma separated numbers are the portion factor for the corresponding
13807 colors of the color space.
13808 The factors can be in the range of 0
13809 \begin_inset Space \thinspace{}
13813 \begin_inset Space \thinspace{}
13821 also the color space
13825 can be used for definitions.
13842 , so that there are in this case three portion factors for the corresponding
13844 Furthermore there is the color space
13848 with one portion factor for the gray value.
13851 \begin_layout Standard
13852 As example a framed box with the new defined color
13856 where the characters have been colored
13861 \begin_inset Formula \begin{equation}
13862 \colorbox {darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
13869 \begin_layout Standard
13870 Self-defined colors can also be used for text with the help of the command
13881 \begin_layout Plain Layout
13890 \begin_layout Standard
13894 \begin_layout Plain Layout
13898 textcolor{darkgreen}{
13904 \begin_inset Quotes eld
13908 \begin_inset Quotes erd
13915 \begin_layout Plain Layout
13925 \begin_layout Standard
13936 \begin_layout Plain Layout
13944 is used in the scheme
13948 textcolor{color}{characters to color}
13953 \begin_layout Subsection
13955 \begin_inset CommandInset label
13957 name "sub:Paragraph-Boxes"
13965 \begin_layout Plain Layout
13966 Boxes ! as paragraph
13974 \begin_layout Standard
13975 A box that can contain several lines and paragraphs, a so called paragraph
13976 box (parbox), can be created with the menu
13978 Insert\SpecialChar \menuseparator
13981 or the toolbar button
13982 \begin_inset Graphics
13983 filename ../images/box-insert.png
13992 \begin_layout Standard
13993 The following example shows a framed parbox in a line:
13996 \begin_layout Standard
13997 \begin_inset VSpace medskip
14001 \begin_inset Box Boxed
14010 height_special "totalheight"
14013 \begin_layout Plain Layout
14014 This is a paragraph box.
14016 \begin_inset Space \thinspace{}
14019 cm long and can also contain formulas:
14020 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14031 \begin_layout Standard
14032 \begin_inset VSpace medskip
14038 \begin_layout Standard
14039 Such a box is created by right-clicking on the gray box inset.
14040 A dialog pops up showing the box properties.
14054 \begin_inset Space \thinspace{}
14059 Vertical Box Alignment
14064 \begin_layout Standard
14065 \begin_inset VSpace medskip
14068 In LaTeX a parbox is created with the command
14078 \begin_layout Plain Layout
14086 that has the following scheme:
14089 \begin_layout Standard
14094 parbox[position]{width}{box content}
14097 \begin_layout Standard
14111 for bottom means that the box is aligned within the surrounding text with
14117 for top this is done with the first line.
14118 When no position is given, the box will be vertically centered, see section
14126 \begin_inset Space ~
14131 manual for examples.
14134 \begin_layout Standard
14135 \begin_inset VSpace bigskip
14138 To frame formulas completely, including the formula number, the formula
14139 must be set into a parbox.
14140 To do this, the command
14154 is inserted in TeX-mode before the formula.
14163 \begin_layout Plain Layout
14173 is hereby the line width set for the document.
14174 Because the frame is outside the parbox, 2
14175 \begin_inset Space \thinspace{}
14178 times the frame separation and the frame thickness must be subtracted from
14180 As this is not automatically done by LyX due to a bug
14184 \begin_layout Plain Layout
14185 \begin_inset CommandInset href
14187 name "LyX-bug #4483"
14188 target "http://bugzilla.lyx.org/show_bug.cgi?id=4483"
14197 , TeX-mode has to be used.
14198 To be able to multiply and subtract in arguments, the LaTeX-package
14206 \begin_layout Plain Layout
14211 is part of every LaTeX standard installation.
14220 \begin_layout Plain Layout
14226 must be loaded in the LaTeX-preamble with the line
14229 \begin_layout Standard
14237 \begin_layout Standard
14238 Behind the formula both boxes are closed by entering
14243 Here is an example:
14247 \begin_layout Plain Layout
14261 \begin_layout Standard
14265 \begin_layout Plain Layout
14283 \begin_inset Formula \begin{equation}
14284 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
14292 \begin_layout Plain Layout
14303 \begin_layout Plain Layout
14317 \begin_layout Standard
14318 \begin_inset VSpace medskip
14321 As a parbox is used as argument of
14327 , there is in this case no difference between
14342 \begin_layout Standard
14343 \begin_inset VSpace bigskip
14346 Paragraph boxes are very useful to comment formulas directly.
14353 is used in combination with the command
14367 \begin_inset CommandInset ref
14369 reference "sub:User-defined-Numbering"
14376 \begin_layout Standard
14377 An example of a formula commented with
14386 \begin_layout Standard
14390 \begin_layout Plain Layout
14403 This is a description.
14404 It is distinctly separated from the formula and multiline.
14408 \begin_layout Plain Layout
14420 \begin_layout Standard
14421 Such a formula must be inserted completely in TeX-mode because LyX does
14422 not yet support the command
14429 The formula is created with the following command sequence:
14432 \begin_layout Standard
14445 is inserted in TeX-mode.
14449 \begin_layout Plain Layout
14450 When the formula style
14462 can also be replaced by
14469 (formula styles see
14470 \begin_inset CommandInset ref
14472 reference "sec:Formula-Styles"
14481 Then the description follows as normal text, and finally
14487 is inserted in TeX-mode.
14500 hereby create a displayed formula.
14503 \begin_layout Standard
14510 can be seen in this example that was
14511 \begin_inset Quotes eld
14515 \begin_inset Quotes erd
14518 using the mathematical textmode:
14519 \begin_inset Formula \[
14520 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
14527 \begin_layout Section
14532 \begin_layout Plain Layout
14541 \begin_layout Subsection
14543 \begin_inset CommandInset label
14545 name "sub:Big-Operators"
14553 \begin_layout Plain Layout
14563 \begin_layout Plain Layout
14573 \begin_layout Plain Layout
14582 \begin_layout Standard
14583 To be able to use all integral operators listed here, the option
14585 Use esint package automatically
14587 must be set in the document settings under
14590 \begin_inset Space ~
14598 \begin_layout Standard
14599 \begin_inset Space \hfill{}
14603 \begin_inset Tabular
14604 <lyxtabular version="3" rows="11" columns="2">
14606 <column alignment="center" valignment="top" width="0pt">
14607 <column alignment="center" valignment="top" width="0pt">
14609 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14612 \begin_layout Plain Layout
14618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14621 \begin_layout Plain Layout
14629 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14632 \begin_layout Plain Layout
14639 \begin_layout Plain Layout
14652 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14655 \begin_layout Plain Layout
14656 \begin_inset Formula $\sum$
14666 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14669 \begin_layout Plain Layout
14676 \begin_layout Plain Layout
14689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14692 \begin_layout Plain Layout
14693 \begin_inset Formula $\int$
14703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14706 \begin_layout Plain Layout
14714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14717 \begin_layout Plain Layout
14718 \begin_inset Formula $\intop$
14728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14731 \begin_layout Plain Layout
14739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14742 \begin_layout Plain Layout
14743 \begin_inset Formula $\oint$
14753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14756 \begin_layout Plain Layout
14764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14767 \begin_layout Plain Layout
14768 \begin_inset Formula $\ointop$
14778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14781 \begin_layout Plain Layout
14789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14792 \begin_layout Plain Layout
14793 \begin_inset Formula $\ointctrclockwise$
14803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14806 \begin_layout Plain Layout
14814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14817 \begin_layout Plain Layout
14818 \begin_inset Formula $\ointclockwise$
14828 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14831 \begin_layout Plain Layout
14839 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14842 \begin_layout Plain Layout
14843 \begin_inset Formula $\sqint$
14853 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14856 \begin_layout Plain Layout
14864 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14867 \begin_layout Plain Layout
14868 \begin_inset Formula $\bigcap$
14878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14881 \begin_layout Plain Layout
14889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14892 \begin_layout Plain Layout
14893 \begin_inset Formula $\bigcup$
14907 \begin_inset Space \hfill{}
14911 \begin_inset Tabular
14912 <lyxtabular version="3" rows="10" columns="2">
14914 <column alignment="center" valignment="top" width="0pt">
14915 <column alignment="center" valignment="top" width="0pt">
14917 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14920 \begin_layout Plain Layout
14926 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14929 \begin_layout Plain Layout
14937 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14940 \begin_layout Plain Layout
14947 \begin_layout Plain Layout
14960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14963 \begin_layout Plain Layout
14964 \begin_inset Formula $\prod$
14974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14977 \begin_layout Plain Layout
14985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14988 \begin_layout Plain Layout
14989 \begin_inset Formula $\coprod$
14999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15002 \begin_layout Plain Layout
15010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15013 \begin_layout Plain Layout
15014 \begin_inset Formula $\bigodot$
15024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15027 \begin_layout Plain Layout
15035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15038 \begin_layout Plain Layout
15039 \begin_inset Formula $\bigotimes$
15049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15052 \begin_layout Plain Layout
15060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15063 \begin_layout Plain Layout
15064 \begin_inset Formula $\bigoplus$
15074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15077 \begin_layout Plain Layout
15085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15088 \begin_layout Plain Layout
15089 \begin_inset Formula $\bigwedge$
15099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15102 \begin_layout Plain Layout
15110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15113 \begin_layout Plain Layout
15114 \begin_inset Formula $\bigvee$
15124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15127 \begin_layout Plain Layout
15135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15138 \begin_layout Plain Layout
15139 \begin_inset Formula $\bigsqcup$
15149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15152 \begin_layout Plain Layout
15160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15163 \begin_layout Plain Layout
15164 \begin_inset Formula $\biguplus$
15178 \begin_inset Space \hfill{}
15184 \begin_layout Standard
15185 All big operators can also be inserted via the math toolbar button
15186 \begin_inset Graphics
15187 filename ../images/math/intop.png
15196 \begin_layout Standard
15197 The operators are called big because they are bigger than the sometimes
15198 equal looking binary operators.
15199 All big operators can have limits as described in the next subsection.
15202 \begin_layout Standard
15228 \begin_inset Space ~
15231 in the style the operator limits are displayed, see
15232 \begin_inset CommandInset ref
15234 reference "sub:Operator-Limits"
15242 \begin_layout Subsubsection*
15243 Advices for Integrals
15246 \begin_layout Standard
15251 in an integral is an operator, that therefore has to be set upright.
15252 This is done by highlighting the
15256 and using the keyboard shortcut
15259 \begin_inset Space ~
15268 \begin_layout Plain Layout
15274 \begin_inset CommandInset ref
15276 reference "sub:Font-Styles"
15286 Finally the smallest space is inserted before the
15290 , as this is usual for operators.
15294 \begin_layout Standard
15296 \begin_inset Formula $\int A(x)dx$
15300 \begin_inset Newline newline
15307 \begin_layout Plain Layout
15317 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15323 \begin_layout Standard
15324 For multiple integrals there are the following commands:
15325 \begin_inset VSpace medskip
15331 \begin_layout Standard
15332 \begin_inset Space \hfill{}
15336 \begin_inset Tabular
15337 <lyxtabular version="3" rows="4" columns="2">
15339 <column alignment="center" valignment="top" width="0">
15340 <column alignment="center" valignment="top" width="0">
15342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15345 \begin_layout Plain Layout
15351 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15354 \begin_layout Plain Layout
15356 \begin_inset Note Note
15359 \begin_layout Plain Layout
15366 is only used as spacer.
15378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15381 \begin_layout Plain Layout
15389 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15392 \begin_layout Plain Layout
15393 \begin_inset Formula $\raisebox {4.5mm}{}\iint\raisebox {-2.5mm}{}$
15403 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15406 \begin_layout Plain Layout
15414 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15417 \begin_layout Plain Layout
15418 \begin_inset Formula $\raisebox {4.5mm}{}\oiint\raisebox {-2.5mm}{}$
15428 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15431 \begin_layout Plain Layout
15439 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15442 \begin_layout Plain Layout
15443 \begin_inset Formula $\raisebox {4.5mm}{}\sqiint\raisebox {-2.5mm}{}$
15457 \begin_inset Space \hfill{}
15461 \begin_inset Tabular
15462 <lyxtabular version="3" rows="4" columns="2">
15464 <column alignment="center" valignment="top" width="0">
15465 <column alignment="center" valignment="top" width="0">
15467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15470 \begin_layout Plain Layout
15476 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15479 \begin_layout Plain Layout
15487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15490 \begin_layout Plain Layout
15498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15501 \begin_layout Plain Layout
15502 \begin_inset Formula $\raisebox {4.5mm}{}\iiint\raisebox {-2.5mm}{}$
15512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15515 \begin_layout Plain Layout
15523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15526 \begin_layout Plain Layout
15527 \begin_inset Formula $\raisebox {4.5mm}{}\iiiint\raisebox {-2.5mm}{}$
15537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15540 \begin_layout Plain Layout
15548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15551 \begin_layout Plain Layout
15552 \begin_inset Formula $\raisebox {4.5mm}{}\dotsint\raisebox {-2.5mm}{}$
15566 \begin_inset Space \hfill{}
15572 \begin_layout Subsection
15574 \begin_inset CommandInset label
15576 name "sub:Operator-Limits"
15584 \begin_layout Plain Layout
15593 \begin_layout Standard
15594 Limits are created by super- and subscripts:
15597 \begin_layout Standard
15599 \begin_inset Tabular
15600 <lyxtabular version="3" rows="2" columns="2">
15602 <column alignment="center" valignment="top" width="0pt">
15603 <column alignment="center" valignment="top" width="0pt">
15605 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15608 \begin_layout Plain Layout
15614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15617 \begin_layout Plain Layout
15619 \begin_inset Note Note
15622 \begin_layout Plain Layout
15629 is only used as spacer.
15641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15644 \begin_layout Plain Layout
15653 \begin_layout Plain Layout
15663 \begin_inset Formula $\to$
15667 \begin_inset Formula $\to$
15675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15678 \begin_layout Plain Layout
15679 \begin_inset Formula $\raisebox {5mm}{}\prod_{0}^{\infty}A(x)\raisebox {-2.5mm}{}$
15695 \begin_layout Standard
15696 Limits of inline formulas are set right beside the operator.
15697 Limits in displayed formulas are set above or below the operator, except
15698 of integral limits.
15701 \begin_layout Standard
15702 To force that the limits are set beside the operator, the cursor is set
15703 directly behind the operator and the limits type is changed with the menu
15706 Edit\SpecialChar \menuseparator
15707 Math\SpecialChar \menuseparator
15719 \begin_inset Space ~
15728 \begin_layout Standard
15729 The default limits type is this:
15730 \begin_inset Formula \[
15731 \sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
15735 This is how it looks when the limits type was changed to
15742 \begin_inset Formula \[
15743 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
15747 For integrals, except of
15759 , the limits are by default set beside the operator.
15760 But for multiple integrals the limits are often set below the operator.
15761 In the following example the limits type was therefore set to
15765 and so set below the integrals:
15766 \begin_inset Formula \begin{equation}
15767 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
15774 \begin_layout Standard
15775 \begin_inset VSpace medskip
15778 To specify conditions for limits, the commands
15788 \begin_layout Plain Layout
15806 \begin_layout Plain Layout
15815 To create for example this expression
15816 \begin_inset Formula \begin{equation}
15817 \sum_{\begin{subarray}{c}
15819 \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
15826 \begin_layout Standard
15827 the following has to be done:
15828 \begin_inset Newline newline
15843 \begin_layout Plain Layout
15855 One is now in a blue box under the summation operator and insert there
15864 \begin_layout Plain Layout
15876 The blue box is now within a purple box and now several lines can be written
15878 A new line is created by inserting a line break (
15884 \begin_inset Newline newline
15889 0<k<1000 Ctrl-Return
15890 \begin_inset Newline newline
15895 is typed in, a new box appears below for the new line.
15898 \begin_layout Standard
15899 The alignment of the lines can be changed to left aligned with the
15909 Edit\SpecialChar \menuseparator
15913 To get right alignment,
15921 \begin_layout Plain Layout
15932 is inserted at the beginning of the line.
15935 \begin_layout Standard
15948 with the difference that the lines are always centered.
15951 \begin_layout Standard
15952 \begin_inset VSpace bigskip
15956 \begin_inset CommandInset ref
15958 reference "eq:substack"
15962 there can be too much space beside an operator, because the characters
15963 following the operator are set beside the limits.
15966 \begin_layout Standard
15967 To avoid this, the following macro can be used in the LaTeX-preamble:
15970 \begin_layout Standard
15984 \begin_inset Newline newline
15996 \begin_inset Newline newline
16003 mathclapinternal #1#2{
16007 mathsurround =0pt #1{#2}$}}
16010 \begin_layout Standard
16011 This defines the command
16021 \begin_layout Plain Layout
16029 that sets the width of the limit to 0
16030 \begin_inset Space \thinspace{}
16034 The command scheme is
16037 \begin_layout Standard
16045 \begin_layout Standard
16046 where the limit can consist of several conditions.
16049 \begin_layout Standard
16051 \begin_inset CommandInset ref
16053 reference "eq:substack"
16057 , one uses the command
16060 \begin_layout Standard
16073 \begin_layout Plain Layout
16082 0<k<1000 Ctrl-Enter
16085 \begin_layout Standard
16086 to create the lower limit.
16087 The summand is now directly behind the summation operator:
16088 \begin_inset Formula \[
16089 \sum_{\mathclap {\substack{0<k<1000\\
16090 \\k\,\in\,\mathbb{N}}
16098 \begin_layout Standard
16099 \begin_inset VSpace bigskip
16102 How to use one limit for several operators is described in
16103 \begin_inset CommandInset ref
16105 reference "sub:Self-defined-Operators"
16112 \begin_layout Subsection
16114 \begin_inset CommandInset label
16116 name "sub:Binary-Operators"
16124 \begin_layout Plain Layout
16133 \begin_layout Standard
16134 Binary operators are surrounded by space when there is a character before
16136 \begin_inset VSpace medskip
16142 \begin_layout Standard
16143 \begin_inset Space \hfill{}
16147 \begin_inset Tabular
16148 <lyxtabular version="3" rows="13" columns="2">
16150 <column alignment="center" valignment="top" width="0pt">
16151 <column alignment="center" valignment="top" width="0pt">
16153 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16156 \begin_layout Plain Layout
16158 \begin_inset Note Note
16161 \begin_layout Plain Layout
16168 is only used as spacer.
16178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16181 \begin_layout Plain Layout
16189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16192 \begin_layout Plain Layout
16198 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16201 \begin_layout Plain Layout
16202 \begin_inset Formula $+$
16212 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16215 \begin_layout Plain Layout
16221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16224 \begin_layout Plain Layout
16225 \begin_inset Formula $-$
16235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16238 \begin_layout Plain Layout
16246 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16249 \begin_layout Plain Layout
16250 \begin_inset Formula $\pm$
16260 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16263 \begin_layout Plain Layout
16271 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16274 \begin_layout Plain Layout
16275 \begin_inset Formula $\mp$
16285 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16288 \begin_layout Plain Layout
16296 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16299 \begin_layout Plain Layout
16300 \begin_inset Formula $\cdot$
16310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16313 \begin_layout Plain Layout
16321 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16324 \begin_layout Plain Layout
16325 \begin_inset Formula $\times$
16335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16338 \begin_layout Plain Layout
16346 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16349 \begin_layout Plain Layout
16350 \begin_inset Formula $\div$
16360 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16363 \begin_layout Plain Layout
16367 \begin_layout Plain Layout
16380 \begin_layout Plain Layout
16392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16395 \begin_layout Plain Layout
16396 \begin_inset Formula $*$
16406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16409 \begin_layout Plain Layout
16417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16420 \begin_layout Plain Layout
16421 \begin_inset Formula $\star$
16431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16434 \begin_layout Plain Layout
16442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16445 \begin_layout Plain Layout
16446 \begin_inset Formula $\circ$
16456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16459 \begin_layout Plain Layout
16467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16470 \begin_layout Plain Layout
16471 \begin_inset Formula $\diamond$
16481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16484 \begin_layout Plain Layout
16492 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16495 \begin_layout Plain Layout
16496 \begin_inset Formula $\bullet$
16510 \begin_inset Space \hfill{}
16514 \begin_inset Tabular
16515 <lyxtabular version="3" rows="13" columns="2">
16517 <column alignment="center" valignment="top" width="0pt">
16518 <column alignment="center" valignment="top" width="0pt">
16520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16523 \begin_layout Plain Layout
16529 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16532 \begin_layout Plain Layout
16540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16543 \begin_layout Plain Layout
16551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16554 \begin_layout Plain Layout
16555 \begin_inset Formula $\nabla$
16565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16568 \begin_layout Plain Layout
16576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16579 \begin_layout Plain Layout
16580 \begin_inset Formula $\bigtriangledown$
16590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16593 \begin_layout Plain Layout
16601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16604 \begin_layout Plain Layout
16605 \begin_inset Formula $\bigtriangleup$
16615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16618 \begin_layout Plain Layout
16626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16629 \begin_layout Plain Layout
16630 \begin_inset Formula $\Box$
16640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16643 \begin_layout Plain Layout
16651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16654 \begin_layout Plain Layout
16655 \begin_inset Formula $\cap$
16665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16668 \begin_layout Plain Layout
16676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16679 \begin_layout Plain Layout
16680 \begin_inset Formula $\cup$
16690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16693 \begin_layout Plain Layout
16701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16704 \begin_layout Plain Layout
16705 \begin_inset Formula $\dagger$
16715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16718 \begin_layout Plain Layout
16726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16729 \begin_layout Plain Layout
16730 \begin_inset Formula $\ddagger$
16740 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16743 \begin_layout Plain Layout
16751 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16754 \begin_layout Plain Layout
16755 \begin_inset Formula $\wr$
16765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16768 \begin_layout Plain Layout
16776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16779 \begin_layout Plain Layout
16780 \begin_inset Formula $\bigcirc$
16790 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16793 \begin_layout Plain Layout
16801 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16804 \begin_layout Plain Layout
16805 \begin_inset Formula $\wedge$
16815 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16818 \begin_layout Plain Layout
16826 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16829 \begin_layout Plain Layout
16830 \begin_inset Formula $\vee$
16844 \begin_inset Space \hfill{}
16848 \begin_inset Tabular
16849 <lyxtabular version="3" rows="13" columns="2">
16851 <column alignment="center" valignment="top" width="0pt">
16852 <column alignment="center" valignment="top" width="0pt">
16854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16857 \begin_layout Plain Layout
16863 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16866 \begin_layout Plain Layout
16874 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16877 \begin_layout Plain Layout
16885 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16888 \begin_layout Plain Layout
16889 \begin_inset Formula $\oplus$
16899 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16902 \begin_layout Plain Layout
16910 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16913 \begin_layout Plain Layout
16914 \begin_inset Formula $\ominus$
16924 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16927 \begin_layout Plain Layout
16935 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16938 \begin_layout Plain Layout
16939 \begin_inset Formula $\otimes$
16949 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16952 \begin_layout Plain Layout
16960 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16963 \begin_layout Plain Layout
16964 \begin_inset Formula $\oslash$
16974 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16977 \begin_layout Plain Layout
16985 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16988 \begin_layout Plain Layout
16989 \begin_inset Formula $\odot$
16999 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17002 \begin_layout Plain Layout
17010 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17013 \begin_layout Plain Layout
17014 \begin_inset Formula $\amalg$
17024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17027 \begin_layout Plain Layout
17035 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17038 \begin_layout Plain Layout
17039 \begin_inset Formula $\uplus$
17049 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17052 \begin_layout Plain Layout
17060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17063 \begin_layout Plain Layout
17064 \begin_inset Formula $\setminus$
17074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17077 \begin_layout Plain Layout
17085 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17088 \begin_layout Plain Layout
17089 \begin_inset Formula $\sqcap$
17099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17102 \begin_layout Plain Layout
17110 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17113 \begin_layout Plain Layout
17114 \begin_inset Formula $\sqcup$
17124 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17127 \begin_layout Plain Layout
17135 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17138 \begin_layout Plain Layout
17139 \begin_inset Formula $\triangleleft$
17149 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17152 \begin_layout Plain Layout
17160 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17163 \begin_layout Plain Layout
17164 \begin_inset Formula $\triangleright$
17178 \begin_inset Space \hfill{}
17184 \begin_layout Standard
17185 All binary operators can also be inserted via the math toolbar button
17186 \begin_inset Graphics
17187 filename ../images/math/pm.png
17196 \begin_layout Standard
17197 To typeset the Laplace operator also
17214 \begin_inset Formula $\nabla^{2}$
17217 ) can be used instead of
17226 \begin_layout Standard
17233 Insert\SpecialChar \menuseparator
17245 \begin_layout Subsection
17246 Self-defined Operators
17247 \begin_inset CommandInset label
17249 name "sub:Self-defined-Operators"
17257 \begin_layout Plain Layout
17258 Operators ! self-defined
17266 \begin_layout Standard
17267 With the help of the command
17271 DeclareMathOperator
17277 \begin_layout Plain Layout
17282 DeclareMathOperator
17287 custom operators can be defined in the LaTeX-preamble.
17288 Its command scheme is:
17291 \begin_layout Standard
17296 DeclareMathOperator{new command}{display}
17299 \begin_layout Standard
17300 Display can be characters or symbols that define how the operator looks
17302 To define a big operator a * is set behind the command.
17303 All self-defined big operators can have limits as described in
17304 \begin_inset CommandInset ref
17306 reference "sub:Operator-Limits"
17313 \begin_layout Standard
17314 For example the LaTeX-preamble line
17317 \begin_layout Standard
17322 DeclareMathOperator*{
17329 \begin_layout Standard
17330 defines the command
17336 , that inserts a big operator consisting of the lozenge symbol from
17337 \begin_inset CommandInset ref
17339 reference "sub:Miscellaneous-Symbols"
17344 \begin_inset Formula \[
17345 \Lozenge _{n=1}^{\infty}\]
17349 The command for this formula is:
17360 \begin_inset Formula $\to$
17366 \begin_layout Standard
17367 \begin_inset VSpace bigskip
17370 When self-defined operators are not used several times in the document,
17371 they can also be defined with the commands
17381 \begin_layout Plain Layout
17399 \begin_layout Plain Layout
17407 , which have the following scheme:
17410 \begin_layout Standard
17424 \begin_layout Standard
17431 defines big operators,
17440 \begin_layout Standard
17448 \begin_inset Space \thinspace{}
17452 \begin_inset Space ~
17455 be used to use one limit for several operators:
17458 \begin_layout Standard
17459 \begin_inset Formula \[
17460 \mathop {\sum\negmedspace\sum}_{i,j=1}^{N}\]
17467 \begin_layout Standard
17468 The command for the formula above is:
17469 \begin_inset Newline newline
17488 \begin_layout Plain Layout
17500 \begin_inset Formula $\to$
17509 \begin_layout Plain Layout
17523 \begin_layout Section
17528 \begin_layout Plain Layout
17537 \begin_layout Subsection
17539 \begin_inset CommandInset label
17541 name "sub:Font-Styles"
17549 \begin_layout Plain Layout
17558 \begin_layout Standard
17559 Latin letters in formulas can be set in one of the following font styles:
17560 \begin_inset VSpace -2mm
17566 \begin_layout Standard
17568 \begin_inset Tabular
17569 <lyxtabular version="3" rows="6" columns="3">
17571 <column alignment="center" valignment="top" width="0">
17572 <column alignment="center" valignment="top" width="0">
17573 <column alignment="center" valignment="top" width="0">
17575 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17578 \begin_layout Plain Layout
17584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17587 \begin_layout Plain Layout
17593 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17596 \begin_layout Plain Layout
17604 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17607 \begin_layout Plain Layout
17616 \begin_layout Plain Layout
17632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17635 \begin_layout Plain Layout
17636 \begin_inset Formula $\mathbb{ABC}$
17644 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17647 \begin_layout Plain Layout
17655 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17658 \begin_layout Plain Layout
17667 \begin_layout Plain Layout
17683 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17686 \begin_layout Plain Layout
17687 \begin_inset Formula $\mathbf{AbC}$
17695 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17698 \begin_layout Plain Layout
17706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17709 \begin_layout Plain Layout
17718 \begin_layout Plain Layout
17734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17737 \begin_layout Plain Layout
17738 \begin_inset Formula $\boldsymbol{AbC}$
17746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17749 \begin_layout Plain Layout
17757 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17760 \begin_layout Plain Layout
17769 \begin_layout Plain Layout
17785 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17788 \begin_layout Plain Layout
17789 \begin_inset Formula $\mathcal{ABC}$
17797 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17800 \begin_layout Plain Layout
17808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17811 \begin_layout Plain Layout
17820 \begin_layout Plain Layout
17836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17839 \begin_layout Plain Layout
17840 \begin_inset Formula $\mathfrak{AbC}$
17848 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17851 \begin_layout Plain Layout
17865 \begin_layout Standard
17867 \begin_inset Tabular
17868 <lyxtabular version="3" rows="5" columns="3">
17870 <column alignment="center" valignment="top" width="0">
17871 <column alignment="center" valignment="top" width="0">
17872 <column alignment="center" valignment="top" width="0">
17874 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17877 \begin_layout Plain Layout
17883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17886 \begin_layout Plain Layout
17892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17895 \begin_layout Plain Layout
17903 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17906 \begin_layout Plain Layout
17915 \begin_layout Plain Layout
17931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17934 \begin_layout Plain Layout
17935 \begin_inset Formula $\mathit{AbC}$
17943 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17946 \begin_layout Plain Layout
17954 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17957 \begin_layout Plain Layout
17966 \begin_layout Plain Layout
17982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17985 \begin_layout Plain Layout
17986 \begin_inset Formula $\mathrm{AbC}$
17994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17997 \begin_layout Plain Layout
18005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18008 \begin_layout Plain Layout
18017 \begin_layout Plain Layout
18033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18036 \begin_layout Plain Layout
18037 \begin_inset Formula $\mathsf{AbC}$
18045 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18048 \begin_layout Plain Layout
18056 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18059 \begin_layout Plain Layout
18068 \begin_layout Plain Layout
18084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18087 \begin_layout Plain Layout
18088 \begin_inset Formula $\mathtt{AbC}$
18096 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18099 \begin_layout Plain Layout
18113 \begin_layout Standard
18114 \begin_inset Note Greyedout
18117 \begin_layout Plain Layout
18134 can only be used for big letters.
18142 \begin_layout Standard
18143 Predefined is the style
18152 \begin_layout Standard
18153 The style commands work also for letters in mathematical constructs:
18154 \begin_inset Formula \[
18155 \mathfrak{A=\frac{b}{C}}\]
18162 \begin_layout Standard
18163 Characters in mathematical text don't appear in a math font style but in
18164 the text font style
18171 That their style can't be set correctly via the text style dialog is a
18176 \begin_layout Plain Layout
18177 \begin_inset CommandInset href
18179 name "LyX-bug #4091"
18180 target "http://bugzilla.lyx.org/show_bug.cgi?id=4091"
18192 \begin_layout Standard
18193 Instead of the style commands the dialog
18195 Edit\SpecialChar \menuseparator
18196 Math\SpecialChar \menuseparator
18199 or the toolbar button
18200 \begin_inset Graphics
18201 filename ../images/math/font.png
18210 \begin_layout Subsection
18212 \begin_inset CommandInset label
18214 name "sub:Bold-Formulas"
18222 \begin_layout Plain Layout
18231 \begin_layout Standard
18232 To make a complete formula bold, the command
18238 from the previous subsection cannot be used, because it doesn't work for
18239 small Greek letters.
18240 Furthermore it prints Latin letters always upright, like in the following
18244 \begin_layout Standard
18245 \begin_inset Formula \[
18246 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
18253 \begin_layout Standard
18254 To display the formula correctly, the command
18261 \begin_inset Formula \[
18262 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
18266 It is also possible to set the formula in a
18268 boldmath environment
18271 This environment is created by inserting the command
18279 \begin_layout Plain Layout
18290 To end the environment, the command
18298 \begin_layout Plain Layout
18308 is inserted in TeX-mode.
18312 \begin_layout Plain Layout
18322 \begin_inset Formula \[
18323 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
18331 \begin_layout Plain Layout
18343 \begin_layout Subsection
18345 \begin_inset CommandInset label
18347 name "sub:Font-Sizes"
18355 \begin_layout Plain Layout
18364 \begin_layout Standard
18365 For characters in formulas there are, analog to characters in text, the
18366 following size commands:
18369 \begin_layout Standard
18413 \begin_inset Newline newline
18435 \begin_layout Standard
18436 The size produced by the commands depends on the document font size, that
18437 corresponds with the command
18444 The other commands produce smaller or larger sizes than
18451 The font size can however not exceed a certain value.
18452 Is for example the document font size 12
18453 \begin_inset Space \thinspace{}
18462 switches to the same size as
18472 \begin_layout Standard
18473 A size command is inserted in TeX-mode before the formula and sets the size
18474 for all following formula and text characters.
18475 To switch back to the initial size, the command
18481 is inserted behind the formula in TeX-mode.
18484 \begin_layout Standard
18485 Within a formula the size can only be changed for symbols or letters in
18487 To do this, the size command is inserted in mathematical text.
18488 All following characters until the end of the mathematical text or until
18489 another size command will have the selected size.
18491 \begin_inset VSpace -2mm
18497 \begin_layout Standard
18501 \begin_layout Plain Layout
18511 \begin_inset Formula \[
18512 A=\frac{B}{c}\cdot\maltese\]
18517 \begin_inset Formula \[
18518 \maltese A\textrm{\Large \maltese\textit{A}}\textrm{\tiny \maltese\textit{A}}\]
18526 \begin_layout Plain Layout
18538 \begin_layout Standard
18539 \begin_inset VSpace medskip
18542 Before both formulas the command
18549 The command for the second formula is:
18550 \begin_inset Newline newline
18561 \begin_layout Plain Layout
18576 \begin_layout Plain Layout
18591 \begin_layout Plain Layout
18606 \begin_layout Plain Layout
18616 \begin_inset Formula $\to$
18620 \begin_inset Formula $\to$
18624 \begin_inset Newline newline
18628 \begin_inset Space \hspace*{}
18642 \begin_layout Plain Layout
18657 \begin_layout Plain Layout
18672 \begin_layout Plain Layout
18684 \begin_layout Standard
18685 If a symbol cannot be displayed in different sizes, it will always be displayed
18686 in the default size.
18689 \begin_layout Section
18694 \begin_layout Plain Layout
18703 \begin_layout Standard
18704 All Greek letters can also be inserted via the toolbar button
18705 \begin_inset Graphics
18706 filename ../images/math/alpha.png
18715 \begin_layout Subsection
18717 \begin_inset CommandInset label
18719 name "sub:Small-Letters"
18727 \begin_layout Plain Layout
18728 Greek letters ! small
18736 \begin_layout Standard
18737 \begin_inset Space \hfill{}
18741 \begin_inset Tabular
18742 <lyxtabular version="3" rows="11" columns="2">
18744 <column alignment="center" valignment="top" width="0pt">
18745 <column alignment="center" valignment="top" width="0pt">
18747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18750 \begin_layout Plain Layout
18756 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18759 \begin_layout Plain Layout
18767 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18770 \begin_layout Plain Layout
18778 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18781 \begin_layout Plain Layout
18782 \begin_inset Formula $\alpha$
18792 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18795 \begin_layout Plain Layout
18803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18806 \begin_layout Plain Layout
18807 \begin_inset Formula $\beta$
18817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18820 \begin_layout Plain Layout
18828 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18831 \begin_layout Plain Layout
18832 \begin_inset Formula $\gamma$
18842 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18845 \begin_layout Plain Layout
18853 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18856 \begin_layout Plain Layout
18857 \begin_inset Formula $\delta$
18867 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18870 \begin_layout Plain Layout
18878 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18881 \begin_layout Plain Layout
18882 \begin_inset Formula $\epsilon$
18892 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18895 \begin_layout Plain Layout
18903 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18906 \begin_layout Plain Layout
18907 \begin_inset Formula $\varepsilon$
18917 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18920 \begin_layout Plain Layout
18928 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18931 \begin_layout Plain Layout
18932 \begin_inset Formula $\zeta$
18942 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18945 \begin_layout Plain Layout
18953 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18956 \begin_layout Plain Layout
18957 \begin_inset Formula $\eta$
18967 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18970 \begin_layout Plain Layout
18978 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18981 \begin_layout Plain Layout
18982 \begin_inset Formula $\theta$
18992 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18995 \begin_layout Plain Layout
19003 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19006 \begin_layout Plain Layout
19007 \begin_inset Formula $\vartheta$
19021 \begin_inset Space \hfill{}
19025 \begin_inset Tabular
19026 <lyxtabular version="3" rows="12" columns="2">
19028 <column alignment="center" valignment="top" width="0pt">
19029 <column alignment="center" valignment="top" width="0pt">
19031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19034 \begin_layout Plain Layout
19040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19043 \begin_layout Plain Layout
19051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19054 \begin_layout Plain Layout
19062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19065 \begin_layout Plain Layout
19066 \begin_inset Formula $\iota$
19076 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19079 \begin_layout Plain Layout
19087 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19090 \begin_layout Plain Layout
19091 \begin_inset Formula $\kappa$
19101 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19104 \begin_layout Plain Layout
19112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19115 \begin_layout Plain Layout
19116 \begin_inset Formula $\varkappa$
19126 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19129 \begin_layout Plain Layout
19137 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19140 \begin_layout Plain Layout
19141 \begin_inset Formula $\lambda$
19151 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19154 \begin_layout Plain Layout
19162 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19165 \begin_layout Plain Layout
19166 \begin_inset Formula $\mu$
19176 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19179 \begin_layout Plain Layout
19187 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19190 \begin_layout Plain Layout
19191 \begin_inset Formula $\nu$
19201 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19204 \begin_layout Plain Layout
19212 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19215 \begin_layout Plain Layout
19216 \begin_inset Formula $\xi$
19226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19229 \begin_layout Plain Layout
19235 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19238 \begin_layout Plain Layout
19239 \begin_inset Formula $o$
19249 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19252 \begin_layout Plain Layout
19260 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19263 \begin_layout Plain Layout
19264 \begin_inset Formula $\pi$
19274 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19277 \begin_layout Plain Layout
19285 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19288 \begin_layout Plain Layout
19289 \begin_inset Formula $\varpi$
19299 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19302 \begin_layout Plain Layout
19310 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19313 \begin_layout Plain Layout
19314 \begin_inset Formula $\rho$
19328 \begin_inset Space \hfill{}
19332 \begin_inset Tabular
19333 <lyxtabular version="3" rows="11" columns="2">
19335 <column alignment="center" valignment="top" width="0pt">
19336 <column alignment="center" valignment="top" width="0pt">
19338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19341 \begin_layout Plain Layout
19347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19350 \begin_layout Plain Layout
19358 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19361 \begin_layout Plain Layout
19369 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19372 \begin_layout Plain Layout
19373 \begin_inset Formula $\varrho$
19383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19386 \begin_layout Plain Layout
19394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19397 \begin_layout Plain Layout
19398 \begin_inset Formula $\sigma$
19408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19411 \begin_layout Plain Layout
19419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19422 \begin_layout Plain Layout
19423 \begin_inset Formula $\varsigma$
19433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19436 \begin_layout Plain Layout
19444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19447 \begin_layout Plain Layout
19448 \begin_inset Formula $\tau$
19458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19461 \begin_layout Plain Layout
19469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19472 \begin_layout Plain Layout
19473 \begin_inset Formula $\upsilon$
19483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19486 \begin_layout Plain Layout
19494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19497 \begin_layout Plain Layout
19498 \begin_inset Formula $\phi$
19508 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19511 \begin_layout Plain Layout
19519 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19522 \begin_layout Plain Layout
19523 \begin_inset Formula $\varphi$
19533 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19536 \begin_layout Plain Layout
19544 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19547 \begin_layout Plain Layout
19548 \begin_inset Formula $\chi$
19558 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19561 \begin_layout Plain Layout
19569 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19572 \begin_layout Plain Layout
19573 \begin_inset Formula $\psi$
19583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19586 \begin_layout Plain Layout
19594 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19597 \begin_layout Plain Layout
19598 \begin_inset Formula $\omega$
19612 \begin_inset Space \hfill{}
19618 \begin_layout Standard
19619 \begin_inset VSpace medskip
19625 \begin_layout Standard
19626 How to create upright Greek letters is explained in
19627 \begin_inset CommandInset ref
19629 reference "sub:Upright-small-Greek"
19636 \begin_layout Subsection
19641 \begin_layout Plain Layout
19642 Greek letters ! big
19650 \begin_layout Standard
19651 \begin_inset Space \hfill{}
19655 \begin_inset Tabular
19656 <lyxtabular version="3" rows="7" columns="2">
19658 <column alignment="center" valignment="top" width="0pt">
19659 <column alignment="center" valignment="top" width="0pt">
19661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19664 \begin_layout Plain Layout
19670 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19673 \begin_layout Plain Layout
19681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19684 \begin_layout Plain Layout
19692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19695 \begin_layout Plain Layout
19696 \begin_inset Formula $\Gamma$
19706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19709 \begin_layout Plain Layout
19717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19720 \begin_layout Plain Layout
19721 \begin_inset Formula $\Delta$
19731 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19734 \begin_layout Plain Layout
19742 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19745 \begin_layout Plain Layout
19746 \begin_inset Formula $\Theta$
19756 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19759 \begin_layout Plain Layout
19767 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19770 \begin_layout Plain Layout
19771 \begin_inset Formula $\Lambda$
19781 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19784 \begin_layout Plain Layout
19792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19795 \begin_layout Plain Layout
19796 \begin_inset Formula $\Xi$
19806 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19809 \begin_layout Plain Layout
19817 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19820 \begin_layout Plain Layout
19821 \begin_inset Formula $\Pi$
19835 \begin_inset Space \hfill{}
19839 \begin_inset Tabular
19840 <lyxtabular version="3" rows="6" columns="2">
19842 <column alignment="center" valignment="top" width="0pt">
19843 <column alignment="center" valignment="top" width="0pt">
19845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19848 \begin_layout Plain Layout
19854 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19857 \begin_layout Plain Layout
19865 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19868 \begin_layout Plain Layout
19876 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19879 \begin_layout Plain Layout
19880 \begin_inset Formula $\Sigma$
19890 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19893 \begin_layout Plain Layout
19901 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19904 \begin_layout Plain Layout
19905 \begin_inset Formula $\Upsilon$
19915 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19918 \begin_layout Plain Layout
19926 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19929 \begin_layout Plain Layout
19930 \begin_inset Formula $\Phi$
19940 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19943 \begin_layout Plain Layout
19951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19954 \begin_layout Plain Layout
19955 \begin_inset Formula $\Psi$
19965 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19968 \begin_layout Plain Layout
19976 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19979 \begin_layout Plain Layout
19980 \begin_inset Formula $\Omega$
19994 \begin_inset Space \hfill{}
20000 \begin_layout Standard
20001 \begin_inset VSpace medskip
20004 That the big Greek letters appear upright is caused by a design bug when
20006 To get correct italic big letters, begin every command with
20011 For example the command
20018 \begin_inset Formula $\varGamma $
20024 \begin_layout Subsection
20029 \begin_layout Plain Layout
20030 Greek letters ! bold
20038 \begin_layout Standard
20039 Greek letters cannot be set with different font styles like Latin letters.
20040 They can only be made bold with the command
20050 \begin_layout Plain Layout
20061 \begin_layout Standard
20063 \begin_inset Tabular
20064 <lyxtabular version="3" rows="3" columns="2">
20066 <column alignment="center" valignment="top" width="0">
20067 <column alignment="center" valignment="top" width="0">
20069 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20072 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20089 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20092 \begin_layout Plain Layout
20104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20107 \begin_layout Plain Layout
20108 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
20118 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20121 \begin_layout Plain Layout
20133 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20136 \begin_layout Plain Layout
20137 \begin_inset Formula $\theta\boldsymbol{\theta}$
20153 \begin_layout Section
20158 \begin_layout Plain Layout
20171 \begin_layout Plain Layout
20172 A list with all symbols of most of the LaTeX-packages can be found in
20173 \begin_inset CommandInset citation
20188 \begin_layout Plain Layout
20196 \begin_inset Note Note
20199 \begin_layout Plain Layout
20202 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
20205 \begin_layout Plain Layout
20208 texorpdfstring is in section
20209 \begin_inset CommandInset ref
20211 reference "sub:Formulas-in-Section"
20224 \begin_layout Plain Layout
20233 \begin_layout Standard
20234 Many of the symbols listed in this section can also be inserted via the
20236 \begin_inset Graphics
20237 filename ../images/math/nabla.png
20244 \begin_inset Graphics
20245 filename ../images/math/digamma.png
20254 \begin_layout Subsection
20255 Mathematical Symbols
20256 \begin_inset CommandInset label
20258 name "sub:Mathematical-Symbols"
20266 \begin_layout Plain Layout
20267 Symbols ! mathematical
20275 \begin_layout Standard
20276 \begin_inset Space \hfill{}
20280 \begin_inset Tabular
20281 <lyxtabular version="3" rows="10" columns="2">
20283 <column alignment="center" valignment="top" width="0pt">
20284 <column alignment="center" valignment="top" width="0pt">
20286 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20289 \begin_layout Plain Layout
20295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20298 \begin_layout Plain Layout
20306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20309 \begin_layout Plain Layout
20317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20320 \begin_layout Plain Layout
20321 \begin_inset Formula $\neg$
20331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20334 \begin_layout Plain Layout
20342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20345 \begin_layout Plain Layout
20346 \begin_inset Formula $\Im$
20356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20359 \begin_layout Plain Layout
20367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20370 \begin_layout Plain Layout
20371 \begin_inset Formula $\Re$
20381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20384 \begin_layout Plain Layout
20392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20395 \begin_layout Plain Layout
20396 \begin_inset Formula $\aleph$
20406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20409 \begin_layout Plain Layout
20417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20420 \begin_layout Plain Layout
20421 \begin_inset Formula $\partial$
20431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20434 \begin_layout Plain Layout
20442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20445 \begin_layout Plain Layout
20446 \begin_inset Formula $\infty$
20456 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20459 \begin_layout Plain Layout
20467 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20470 \begin_layout Plain Layout
20471 \begin_inset Formula $\wp$
20481 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20484 \begin_layout Plain Layout
20492 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20495 \begin_layout Plain Layout
20496 \begin_inset Formula $\imath$
20506 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20509 \begin_layout Plain Layout
20517 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20520 \begin_layout Plain Layout
20521 \begin_inset Formula $\jmath$
20535 \begin_inset Space \hfill{}
20539 \begin_inset Tabular
20540 <lyxtabular version="3" rows="10" columns="2">
20542 <column alignment="center" valignment="top" width="0pt">
20543 <column alignment="center" valignment="top" width="0pt">
20545 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20548 \begin_layout Plain Layout
20554 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20557 \begin_layout Plain Layout
20559 \begin_inset Note Note
20562 \begin_layout Plain Layout
20569 is only used as spacer.
20581 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20584 \begin_layout Plain Layout
20592 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20595 \begin_layout Plain Layout
20596 \begin_inset Formula $\forall$
20606 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20609 \begin_layout Plain Layout
20617 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20620 \begin_layout Plain Layout
20621 \begin_inset Formula $\exists$
20631 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20634 \begin_layout Plain Layout
20642 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20645 \begin_layout Plain Layout
20646 \begin_inset Formula $\nexists$
20656 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20659 \begin_layout Plain Layout
20667 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20670 \begin_layout Plain Layout
20671 \begin_inset Formula $\emptyset$
20681 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20684 \begin_layout Plain Layout
20692 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20695 \begin_layout Plain Layout
20696 \begin_inset Formula $\varnothing$
20706 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20709 \begin_layout Plain Layout
20717 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20720 \begin_layout Plain Layout
20721 \begin_inset Formula $\dag $
20731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20734 \begin_layout Plain Layout
20742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20745 \begin_layout Plain Layout
20746 \begin_inset Formula $\ddag $
20756 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20759 \begin_layout Plain Layout
20767 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20770 \begin_layout Plain Layout
20774 \begin_layout Plain Layout
20784 \begin_inset Formula $\complement$
20791 \begin_layout Plain Layout
20805 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
20808 \begin_layout Plain Layout
20816 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
20819 \begin_layout Plain Layout
20820 \begin_inset Formula $\Bbbk$
20834 \begin_inset Space \hfill{}
20838 \begin_inset Tabular
20839 <lyxtabular version="3" rows="10" columns="2">
20841 <column alignment="center" valignment="top" width="0pt">
20842 <column alignment="center" valignment="top" width="0pt">
20844 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20847 \begin_layout Plain Layout
20853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20856 \begin_layout Plain Layout
20864 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20867 \begin_layout Plain Layout
20875 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20878 \begin_layout Plain Layout
20879 \begin_inset Formula $\prime$
20889 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20892 \begin_layout Plain Layout
20900 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20903 \begin_layout Plain Layout
20904 \begin_inset Formula $\backprime$
20914 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20917 \begin_layout Plain Layout
20925 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20928 \begin_layout Plain Layout
20929 \begin_inset Formula $\mho$
20939 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20942 \begin_layout Plain Layout
20950 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20953 \begin_layout Plain Layout
20954 \begin_inset Formula $\triangle$
20964 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20967 \begin_layout Plain Layout
20975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20978 \begin_layout Plain Layout
20979 \begin_inset Formula $\angle$
20989 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20992 \begin_layout Plain Layout
21000 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21003 \begin_layout Plain Layout
21004 \begin_inset Formula $\measuredangle$
21014 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21017 \begin_layout Plain Layout
21025 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21028 \begin_layout Plain Layout
21029 \begin_inset Formula $\sphericalangle$
21039 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21042 \begin_layout Plain Layout
21050 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21053 \begin_layout Plain Layout
21054 \begin_inset Formula $\top$
21064 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21067 \begin_layout Plain Layout
21075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21078 \begin_layout Plain Layout
21079 \begin_inset Formula $\bot$
21093 \begin_inset Space \hfill{}
21099 \begin_layout Standard
21100 \begin_inset Newpage newpage
21106 \begin_layout Subsection
21107 Miscellaneous Symbols
21108 \begin_inset CommandInset label
21110 name "sub:Miscellaneous-Symbols"
21118 \begin_layout Plain Layout
21119 Symbols ! miscellaneous
21127 \begin_layout Standard
21130 \begin_inset Tabular
21131 <lyxtabular version="3" rows="10" columns="2">
21133 <column alignment="center" valignment="top" width="0pt">
21134 <column alignment="center" valignment="top" width="0pt">
21136 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21139 \begin_layout Plain Layout
21145 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21148 \begin_layout Plain Layout
21156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21159 \begin_layout Plain Layout
21167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21170 \begin_layout Plain Layout
21171 \begin_inset Formula $\flat$
21181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21184 \begin_layout Plain Layout
21192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21195 \begin_layout Plain Layout
21196 \begin_inset Formula $\natural$
21206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21209 \begin_layout Plain Layout
21217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21220 \begin_layout Plain Layout
21221 \begin_inset Formula $\sharp$
21231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21234 \begin_layout Plain Layout
21242 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21245 \begin_layout Plain Layout
21246 \begin_inset Formula $\surd$
21256 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21259 \begin_layout Plain Layout
21267 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21270 \begin_layout Plain Layout
21271 \begin_inset Formula $\checkmark$
21281 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21284 \begin_layout Plain Layout
21292 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21295 \begin_layout Plain Layout
21296 \begin_inset Formula $\yen$
21306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21309 \begin_layout Plain Layout
21317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21320 \begin_layout Plain Layout
21321 \begin_inset Formula $\pounds $
21331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21334 \begin_layout Plain Layout
21340 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21343 \begin_layout Plain Layout
21344 \begin_inset Formula $\$$
21354 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21357 \begin_layout Plain Layout
21363 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21366 \begin_layout Plain Layout
21367 \begin_inset Formula $§$
21381 \begin_inset Tabular
21382 <lyxtabular version="3" rows="10" columns="2">
21384 <column alignment="center" valignment="top" width="0">
21385 <column alignment="center" valignment="top" width="0">
21387 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21390 \begin_layout Plain Layout
21396 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21399 \begin_layout Plain Layout
21407 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21410 \begin_layout Plain Layout
21418 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21421 \begin_layout Plain Layout
21422 \begin_inset Formula $\hbar$
21432 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21435 \begin_layout Plain Layout
21443 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21446 \begin_layout Plain Layout
21447 \begin_inset Formula $\hslash$
21457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21460 \begin_layout Plain Layout
21468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21471 \begin_layout Plain Layout
21472 \begin_inset Formula $\clubsuit$
21482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21485 \begin_layout Plain Layout
21493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21496 \begin_layout Plain Layout
21497 \begin_inset Formula $\spadesuit$
21507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21510 \begin_layout Plain Layout
21518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21521 \begin_layout Plain Layout
21522 \begin_inset Formula $\bigstar$
21532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21535 \begin_layout Plain Layout
21543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21546 \begin_layout Plain Layout
21547 \begin_inset Formula $\blacklozenge$
21557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21560 \begin_layout Plain Layout
21568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21571 \begin_layout Plain Layout
21572 \begin_inset Formula $\blacktriangle$
21582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21585 \begin_layout Plain Layout
21593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21596 \begin_layout Plain Layout
21597 \begin_inset Formula $\blacktriangledown$
21607 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21610 \begin_layout Plain Layout
21618 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21621 \begin_layout Plain Layout
21622 \begin_inset Formula $\bullet$
21636 \begin_inset Tabular
21637 <lyxtabular version="3" rows="10" columns="2">
21639 <column alignment="center" valignment="top" width="0pt">
21640 <column alignment="center" valignment="top" width="0pt">
21642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21645 \begin_layout Plain Layout
21651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21654 \begin_layout Plain Layout
21662 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21665 \begin_layout Plain Layout
21673 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21676 \begin_layout Plain Layout
21677 \begin_inset Formula $\diamondsuit$
21687 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21690 \begin_layout Plain Layout
21698 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21701 \begin_layout Plain Layout
21702 \begin_inset Formula $\Diamond$
21712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21715 \begin_layout Plain Layout
21723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21726 \begin_layout Plain Layout
21727 \begin_inset Formula $\heartsuit$
21737 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21740 \begin_layout Plain Layout
21748 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21751 \begin_layout Plain Layout
21752 \begin_inset Formula $\P $
21762 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21765 \begin_layout Plain Layout
21773 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21776 \begin_layout Plain Layout
21777 \begin_inset Formula $\copyright $
21787 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21790 \begin_layout Plain Layout
21798 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21801 \begin_layout Plain Layout
21802 \begin_inset Formula $\circledR$
21812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21815 \begin_layout Plain Layout
21823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21826 \begin_layout Plain Layout
21827 \begin_inset Formula $\maltese$
21837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21840 \begin_layout Plain Layout
21848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21851 \begin_layout Plain Layout
21852 \begin_inset Formula $\diagup$
21862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21865 \begin_layout Plain Layout
21873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21876 \begin_layout Plain Layout
21877 \begin_inset Formula $\diagdown$
21893 \begin_layout Standard
21894 \begin_inset VSpace medskip
21897 More symbols are listed in
21898 \begin_inset CommandInset ref
21900 reference "sub:Miscellaneous-Special-Characters"
21907 \begin_layout Standard
21908 Some symbols can be displayed in different sizes, see
21909 \begin_inset CommandInset ref
21911 reference "sub:Font-Sizes"
21918 \begin_layout Subsection
21923 \begin_layout Plain Layout
21924 Symbols ! Euro-symbol
21933 \begin_layout Plain Layout
21937 \begin_layout Plain Layout
21954 \begin_layout Standard
21955 To use the Euro symbol in formulas, the LaTeX-package
21963 \begin_layout Plain Layout
21969 must be installed and loaded with the LaTeX-preamble line
21972 \begin_layout Standard
21977 usepackage[gennarrow]{eurosym}
21980 \begin_layout Standard
21981 The Euro symbol can now be inserted with the command
21991 \begin_layout Plain Layout
22002 \begin_layout Standard
22003 The Euro symbol can directly be inserted with the € key in mathematical
22004 text, without having
22019 can also be inserted in TeX-mode.
22020 The official currency symbol can then be inserted with the command
22030 \begin_layout Plain Layout
22038 , that is only available in TeX-mode.
22041 \begin_layout Standard
22045 \begin_layout Plain Layout
22055 \begin_inset Note Note
22058 \begin_layout Plain Layout
22059 The following table will only be displayed when the LaTeX-package
22071 \begin_layout Standard
22072 An overview about the different Euro symbols:
22075 \begin_layout Standard
22077 \begin_inset Tabular
22078 <lyxtabular version="3" rows="4" columns="3">
22080 <column alignment="center" valignment="top" width="0pt">
22081 <column alignment="center" valignment="top" width="0pt">
22082 <column alignment="center" valignment="top" width="0pt">
22084 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
22087 \begin_layout Plain Layout
22093 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22096 \begin_layout Plain Layout
22102 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22105 \begin_layout Plain Layout
22113 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22116 \begin_layout Plain Layout
22122 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22125 \begin_layout Plain Layout
22133 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22136 \begin_layout Plain Layout
22137 \begin_inset Formula $\euro $
22147 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22150 \begin_layout Plain Layout
22156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22159 \begin_layout Plain Layout
22165 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22168 \begin_layout Plain Layout
22169 \begin_inset Formula $\mbox{€}$
22179 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22182 \begin_layout Plain Layout
22188 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22191 \begin_layout Plain Layout
22199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22202 \begin_layout Plain Layout
22206 \begin_layout Plain Layout
22228 \begin_layout Standard
22232 \begin_layout Plain Layout
22242 \begin_inset Note Note
22245 \begin_layout Plain Layout
22246 The following will be displayed when the LaTeX-package
22258 \begin_layout Standard
22259 You need to install the LaTeX-package
22263 to see the rest of this subsection in the output.
22266 \begin_layout Standard
22270 \begin_layout Plain Layout
22282 \begin_layout Section
22284 \begin_inset CommandInset label
22286 name "sec:Relations"
22294 \begin_layout Plain Layout
22304 \begin_layout Plain Layout
22309 \begin_layout Plain Layout
22320 \begin_layout Plain Layout
22335 \begin_layout Standard
22336 All relations can also be inserted via the toolbar button
22337 \begin_inset Graphics
22338 filename ../images/math/leq.png
22347 \begin_layout Standard
22348 \begin_inset Space \hfill{}
22352 \begin_inset Tabular
22353 <lyxtabular version="3" rows="17" columns="2">
22355 <column alignment="center" valignment="top" width="0pt">
22356 <column alignment="center" valignment="top" width="0pt">
22358 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22361 \begin_layout Plain Layout
22367 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22370 \begin_layout Plain Layout
22378 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22381 \begin_layout Plain Layout
22387 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22390 \begin_layout Plain Layout
22391 \begin_inset Formula $<$
22401 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22404 \begin_layout Plain Layout
22412 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22415 \begin_layout Plain Layout
22416 \begin_inset Formula $\le$
22426 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22429 \begin_layout Plain Layout
22437 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22440 \begin_layout Plain Layout
22441 \begin_inset Formula $\ll$
22451 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22454 \begin_layout Plain Layout
22462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22465 \begin_layout Plain Layout
22466 \begin_inset Formula $\prec$
22476 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22479 \begin_layout Plain Layout
22487 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22490 \begin_layout Plain Layout
22491 \begin_inset Formula $\preceq$
22501 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22504 \begin_layout Plain Layout
22512 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22515 \begin_layout Plain Layout
22516 \begin_inset Formula $\subset$
22526 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22529 \begin_layout Plain Layout
22537 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22540 \begin_layout Plain Layout
22541 \begin_inset Formula $\subseteq$
22551 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22554 \begin_layout Plain Layout
22562 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22565 \begin_layout Plain Layout
22566 \begin_inset Formula $\sqsubseteq$
22576 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22579 \begin_layout Plain Layout
22587 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22590 \begin_layout Plain Layout
22591 \begin_inset Formula $\in$
22601 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22604 \begin_layout Plain Layout
22612 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22615 \begin_layout Plain Layout
22616 \begin_inset Formula $\vdash$
22626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22629 \begin_layout Plain Layout
22637 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22640 \begin_layout Plain Layout
22641 \begin_inset Formula $\smile$
22651 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22654 \begin_layout Plain Layout
22662 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22665 \begin_layout Plain Layout
22666 \begin_inset Formula $\lhd$
22676 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22679 \begin_layout Plain Layout
22687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22690 \begin_layout Plain Layout
22691 \begin_inset Formula $\unlhd$
22701 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22704 \begin_layout Plain Layout
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22715 \begin_layout Plain Layout
22716 \begin_inset Formula $\gtrless$
22726 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22729 \begin_layout Plain Layout
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22740 \begin_layout Plain Layout
22741 \begin_inset Formula $\mid$
22751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22754 \begin_layout Plain Layout
22762 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22765 \begin_layout Plain Layout
22766 \begin_inset Formula $\nmid$
22780 \begin_inset Space \hfill{}
22784 \begin_inset Tabular
22785 <lyxtabular version="3" rows="17" columns="2">
22787 <column alignment="center" valignment="top" width="0pt">
22788 <column alignment="center" valignment="top" width="0pt">
22790 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22793 \begin_layout Plain Layout
22799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22802 \begin_layout Plain Layout
22810 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22813 \begin_layout Plain Layout
22819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22822 \begin_layout Plain Layout
22823 \begin_inset Formula $=$
22833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22836 \begin_layout Plain Layout
22844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22847 \begin_layout Plain Layout
22848 \begin_inset Formula $\not=$
22858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22861 \begin_layout Plain Layout
22869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22872 \begin_layout Plain Layout
22873 \begin_inset Formula $\equiv$
22883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22886 \begin_layout Plain Layout
22894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22897 \begin_layout Plain Layout
22898 \begin_inset Formula $\sim$
22908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22911 \begin_layout Plain Layout
22919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22922 \begin_layout Plain Layout
22923 \begin_inset Formula $\simeq$
22933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22936 \begin_layout Plain Layout
22944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22947 \begin_layout Plain Layout
22948 \begin_inset Formula $\approx$
22958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22961 \begin_layout Plain Layout
22969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22972 \begin_layout Plain Layout
22973 \begin_inset Formula $\cong$
22983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22986 \begin_layout Plain Layout
22994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22997 \begin_layout Plain Layout
22998 \begin_inset Formula $\bowtie$
23008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23011 \begin_layout Plain Layout
23019 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23022 \begin_layout Plain Layout
23023 \begin_inset Formula $\notin$
23033 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23036 \begin_layout Plain Layout
23044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23047 \begin_layout Plain Layout
23048 \begin_inset Formula $\perp$
23058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23061 \begin_layout Plain Layout
23069 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23072 \begin_layout Plain Layout
23073 \begin_inset Formula $\propto$
23083 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23086 \begin_layout Plain Layout
23094 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23097 \begin_layout Plain Layout
23098 \begin_inset Formula $\asymp$
23108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23111 \begin_layout Plain Layout
23119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23122 \begin_layout Plain Layout
23123 \begin_inset Formula $\doteq$
23133 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23136 \begin_layout Plain Layout
23144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23147 \begin_layout Plain Layout
23148 \begin_inset Formula $\circeq$
23158 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23161 \begin_layout Plain Layout
23169 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23172 \begin_layout Plain Layout
23173 \begin_inset Formula $\models$
23183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23186 \begin_layout Plain Layout
23194 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23197 \begin_layout Plain Layout
23198 \begin_inset Formula $\widehat{=}$
23212 \begin_inset Space \hfill{}
23216 \begin_inset Tabular
23217 <lyxtabular version="3" rows="17" columns="2">
23219 <column alignment="center" valignment="top" width="0pt">
23220 <column alignment="center" valignment="top" width="0pt">
23222 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23225 \begin_layout Plain Layout
23231 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23234 \begin_layout Plain Layout
23242 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23245 \begin_layout Plain Layout
23251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23254 \begin_layout Plain Layout
23255 \begin_inset Formula $>$
23265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23268 \begin_layout Plain Layout
23276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23279 \begin_layout Plain Layout
23280 \begin_inset Formula $\ge$
23290 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23293 \begin_layout Plain Layout
23301 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23304 \begin_layout Plain Layout
23305 \begin_inset Formula $\gg$
23315 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23318 \begin_layout Plain Layout
23326 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23329 \begin_layout Plain Layout
23330 \begin_inset Formula $\succ$
23340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23343 \begin_layout Plain Layout
23351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23354 \begin_layout Plain Layout
23355 \begin_inset Formula $\succeq$
23365 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23368 \begin_layout Plain Layout
23376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23379 \begin_layout Plain Layout
23380 \begin_inset Formula $\supset$
23390 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23393 \begin_layout Plain Layout
23401 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23404 \begin_layout Plain Layout
23405 \begin_inset Formula $\supseteq$
23415 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23418 \begin_layout Plain Layout
23426 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23429 \begin_layout Plain Layout
23430 \begin_inset Formula $\sqsupseteq$
23440 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23443 \begin_layout Plain Layout
23451 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23454 \begin_layout Plain Layout
23455 \begin_inset Formula $\ni$
23465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23468 \begin_layout Plain Layout
23476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23479 \begin_layout Plain Layout
23480 \begin_inset Formula $\dashv$
23490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23493 \begin_layout Plain Layout
23501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23504 \begin_layout Plain Layout
23505 \begin_inset Formula $\frown$
23515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23518 \begin_layout Plain Layout
23526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23529 \begin_layout Plain Layout
23530 \begin_inset Formula $\rhd$
23540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23543 \begin_layout Plain Layout
23551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23554 \begin_layout Plain Layout
23555 \begin_inset Formula $\unrhd$
23565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23568 \begin_layout Plain Layout
23576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23579 \begin_layout Plain Layout
23580 \begin_inset Formula $\lessgtr$
23590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23593 \begin_layout Plain Layout
23601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23604 \begin_layout Plain Layout
23605 \begin_inset Formula $\parallel$
23615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23618 \begin_layout Plain Layout
23626 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23629 \begin_layout Plain Layout
23630 \begin_inset Formula $\nparallel$
23644 \begin_inset Space \hfill{}
23650 \begin_layout Standard
23651 \begin_inset VSpace medskip
23666 are bigger than the equal looking operators
23681 \begin_layout Standard
23682 Relations are, in contrary to symbols, always surrounded by space.
23685 \begin_layout Standard
23686 Relations with labels can be created with the command
23696 \begin_layout Plain Layout
23707 \begin_layout Standard
23709 \begin_inset Tabular
23710 <lyxtabular version="3" rows="2" columns="2">
23712 <column alignment="center" valignment="top" width="0">
23713 <column alignment="center" valignment="top" width="0">
23715 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23718 \begin_layout Plain Layout
23724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23727 \begin_layout Plain Layout
23729 \begin_inset Note Note
23732 \begin_layout Plain Layout
23739 is only used as spacer.
23751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23754 \begin_layout Plain Layout
23761 \begin_layout Plain Layout
23778 \begin_layout Plain Layout
23788 \begin_inset Formula $\downarrow$
23797 \begin_layout Plain Layout
23810 \begin_layout Plain Layout
23824 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23827 \begin_layout Plain Layout
23828 \begin_inset Formula $\raisebox {5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
23844 \begin_layout Section
23848 \begin_layout Subsection
23849 Predefined Functions
23850 \begin_inset CommandInset label
23852 name "sub:Predefined-Functions"
23860 \begin_layout Plain Layout
23861 Functions ! predefined
23869 \begin_layout Standard
23870 In general, variables are set
23874 in mathematical expressions, but not function names, because
23875 \begin_inset Formula $sin$
23878 could be misunderstood as
23879 \begin_inset Formula $s\cdot i\cdot n$
23883 Therefore there are predefined functions, that are additionally a bit separated
23885 They are inserted as commands starting with a backslash before their name.
23888 \begin_layout Standard
23890 \begin_inset Tabular
23891 <lyxtabular version="3" rows="2" columns="4">
23893 <column alignment="center" valignment="top" width="0pt">
23894 <column alignment="center" valignment="top" width="0pt">
23895 <column alignment="center" valignment="top" width="0pt">
23896 <column alignment="center" valignment="top" width="0pt">
23898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23901 \begin_layout Plain Layout
23907 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23910 \begin_layout Plain Layout
23916 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23919 \begin_layout Plain Layout
23925 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23928 \begin_layout Plain Layout
23936 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23939 \begin_layout Plain Layout
23945 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23948 \begin_layout Plain Layout
23949 \begin_inset Formula $Asin(x)+B$
23957 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23960 \begin_layout Plain Layout
23968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23971 \begin_layout Plain Layout
23972 \begin_inset Formula $A\sin(x)+B$
23986 \begin_inset Newpage pagebreak
23992 \begin_layout Standard
23993 The following functions are predefined:
23996 \begin_layout Standard
23997 \begin_inset VSpace -2mm
24003 \begin_layout Standard
24005 \begin_inset Tabular
24006 <lyxtabular version="3" rows="9" columns="4">
24008 <column alignment="center" valignment="top" width="0pt">
24009 <column alignment="center" valignment="top" width="0pt">
24010 <column alignment="center" valignment="top" width="0pt">
24011 <column alignment="center" valignment="top" width="0pt">
24013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24016 \begin_layout Plain Layout
24022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24025 \begin_layout Plain Layout
24031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24034 \begin_layout Plain Layout
24040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24043 \begin_layout Plain Layout
24051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24054 \begin_layout Plain Layout
24062 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24065 \begin_layout Plain Layout
24073 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24076 \begin_layout Plain Layout
24084 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24087 \begin_layout Plain Layout
24097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24100 \begin_layout Plain Layout
24108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24111 \begin_layout Plain Layout
24119 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24122 \begin_layout Plain Layout
24130 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24133 \begin_layout Plain Layout
24143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24146 \begin_layout Plain Layout
24154 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24157 \begin_layout Plain Layout
24165 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24168 \begin_layout Plain Layout
24176 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24179 \begin_layout Plain Layout
24189 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24192 \begin_layout Plain Layout
24200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24203 \begin_layout Plain Layout
24211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24214 \begin_layout Plain Layout
24222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24225 \begin_layout Plain Layout
24235 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24238 \begin_layout Plain Layout
24246 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24249 \begin_layout Plain Layout
24257 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24260 \begin_layout Plain Layout
24268 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24271 \begin_layout Plain Layout
24281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24284 \begin_layout Plain Layout
24292 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24295 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24306 \begin_layout Plain Layout
24314 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24317 \begin_layout Plain Layout
24327 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24330 \begin_layout Plain Layout
24338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24341 \begin_layout Plain Layout
24349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24352 \begin_layout Plain Layout
24360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24363 \begin_layout Plain Layout
24373 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24376 \begin_layout Plain Layout
24384 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24387 \begin_layout Plain Layout
24395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24398 \begin_layout Plain Layout
24406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24409 \begin_layout Plain Layout
24425 \begin_layout Standard
24426 They can also be inserted with the math toolbar button
24427 \begin_inset Graphics
24428 filename ../images/math/functions.png
24437 \begin_layout Subsection
24438 Self-defined Functions
24442 \begin_layout Plain Layout
24443 Functions ! self-defined
24451 \begin_layout Standard
24452 To use a function that is not predefined, like for example the sign function
24453 sgn(x), there are two possibilities:
24456 \begin_layout Itemize
24457 Define the function by inserting the following line to the LaTeX-preamble
24461 \begin_layout Plain Layout
24466 DeclareMathOperator
24469 \begin_inset CommandInset ref
24471 reference "sub:Self-defined-Operators"
24481 \begin_inset Newline newline
24485 \begin_inset VSpace -3mm
24489 \begin_inset Newline newline
24496 DeclareMathOperator{
24504 \begin_layout Plain Layout
24509 DeclareMathOperator
24515 \begin_inset Newline newline
24519 \begin_inset VSpace -2mm
24523 \begin_inset Newline newline
24526 Now the new defined function can be called with the command
24535 \begin_layout Itemize
24536 Write the the formula as usual, mark the formula name, in our example the
24541 , and change it to mathematical text.
24542 At last a space is inserted between prefactor and function.
24545 \begin_layout Standard
24546 The result is the same with both methods as with a predefined function
24550 \begin_layout Plain Layout
24551 In LyX self-defined functions are displayed red, predefined ones black.
24559 \begin_layout Standard
24561 \begin_inset Tabular
24562 <lyxtabular version="3" rows="3" columns="2">
24564 <column alignment="center" valignment="top" width="0pt">
24565 <column alignment="center" valignment="top" width="0pt">
24567 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24576 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24579 \begin_layout Plain Layout
24587 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24590 \begin_layout Plain Layout
24598 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24601 \begin_layout Plain Layout
24602 \begin_inset Formula $A\sgn (x)+B$
24612 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24615 \begin_layout Plain Layout
24619 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
24627 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24630 \begin_layout Plain Layout
24631 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
24647 \begin_layout Standard
24648 The first method is more suitable when the self-defined function should
24649 be used several times.
24652 \begin_layout Subsection
24657 \begin_layout Plain Layout
24666 \begin_layout Standard
24667 For limits there are defined besides
24677 \begin_layout Plain Layout
24697 furthermore the following functions:
24700 \begin_layout Standard
24702 \begin_inset Tabular
24703 <lyxtabular version="3" rows="5" columns="2">
24705 <column alignment="center" valignment="top" width="0">
24706 <column alignment="center" valignment="top" width="0">
24708 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24711 \begin_layout Plain Layout
24717 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24720 \begin_layout Plain Layout
24722 \begin_inset Note Note
24725 \begin_layout Plain Layout
24732 is only used as spacer.
24744 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24747 \begin_layout Plain Layout
24755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24758 \begin_layout Plain Layout
24759 \begin_inset Formula $\varliminf $
24769 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24772 \begin_layout Plain Layout
24780 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24783 \begin_layout Plain Layout
24784 \begin_inset Formula $\varlimsup $
24794 <cell alignment="center" valignment="top" leftline="true" usebox="none">
24797 \begin_layout Plain Layout
24805 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
24808 \begin_layout Plain Layout
24809 \begin_inset Formula $\varprojlim $
24819 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
24822 \begin_layout Plain Layout
24830 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
24833 \begin_layout Plain Layout
24834 \begin_inset Formula $\varinjlim $
24838 \begin_inset Formula $\raisebox {-2.5mm}{}$
24854 \begin_layout Standard
24855 \begin_inset VSpace medskip
24858 The limit is created by inserting a subscript.
24859 It is set right beside the function in an inline formula:
24862 \begin_layout Standard
24864 \begin_inset Tabular
24865 <lyxtabular version="3" rows="2" columns="2">
24867 <column alignment="center" valignment="top" width="0pt">
24868 <column alignment="center" valignment="top" width="0pt">
24870 <cell alignment="center" valignment="top" usebox="none">
24873 \begin_layout Plain Layout
24879 <cell alignment="center" valignment="top" usebox="none">
24882 \begin_layout Plain Layout
24883 \begin_inset Space \hspace{}
24888 \begin_inset Note Note
24891 \begin_layout Plain Layout
24904 are used here as spacer.
24916 <cell alignment="center" valignment="top" usebox="none">
24919 \begin_layout Plain Layout
24928 \begin_layout Plain Layout
24941 \begin_layout Plain Layout
24955 <cell alignment="center" valignment="top" usebox="none">
24958 \begin_layout Plain Layout
24959 \begin_inset Formula $\hspace {1cm}\raisebox {5mm}{}\lim_{x\to A}x=B$
24975 \begin_layout Standard
24976 In a displayed formula the limit is set below the formula, as usual:
24977 \begin_inset Formula \[
24985 \begin_layout Subsection
24990 \begin_layout Plain Layout
24991 Functions ! modulo-
24999 \begin_layout Standard
25000 The modulo-function is special, because it exists in four variants.
25003 \begin_layout Standard
25004 The variants in a displayed formula:
25005 \begin_inset Formula \begin{align*}
25006 \underline{\textrm{Command}\raisebox {-0.9mm}{}} & & \underline{\textrm{Result}}\\
25007 \mathrm{a\backslash mod\textrm{\spce }b} & & a\mod b\\
25008 \mathrm{a\backslash pmod\textrm{\spce }b} & & a\pmod b\\
25009 \mathrm{a\backslash bmod\textrm{\spce }b} & & a\bmod b\\
25010 \mathrm{a\backslash pod\textrm{\spce }b} & & a\pod b\end{align*}
25017 \begin_layout Standard
25018 In an inline formula less space is set before the function names for all
25022 \begin_layout Section
25027 \begin_layout Plain Layout
25036 \begin_layout Subsection
25037 Special Characters in Mathematical Text
25040 \begin_layout Standard
25041 The following commands can only be used in mathematical text or in TeX-mode:
25044 \begin_layout Standard
25045 \begin_inset Space \hfill{}
25049 \begin_inset Tabular
25050 <lyxtabular version="3" rows="8" columns="2">
25052 <column alignment="block" valignment="top" width="0">
25053 <column alignment="block" valignment="top" width="0">
25055 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25058 \begin_layout Plain Layout
25064 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25067 \begin_layout Plain Layout
25075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25078 \begin_layout Plain Layout
25086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25089 \begin_layout Plain Layout
25090 \begin_inset Formula $\textrm{\oe }$
25100 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25103 \begin_layout Plain Layout
25111 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25114 \begin_layout Plain Layout
25115 \begin_inset Formula $\textrm{\OE }$
25125 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25128 \begin_layout Plain Layout
25136 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25139 \begin_layout Plain Layout
25140 \begin_inset Formula $\textrm{\ae }$
25150 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25153 \begin_layout Plain Layout
25161 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25164 \begin_layout Plain Layout
25165 \begin_inset Formula $\textrm{\AE }$
25175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25178 \begin_layout Plain Layout
25186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25189 \begin_layout Plain Layout
25190 \begin_inset Formula $\textrm{\aa }$
25200 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25203 \begin_layout Plain Layout
25210 \begin_layout Plain Layout
25214 \begin_layout Plain Layout
25222 \begin_layout Plain Layout
25233 \begin_layout Plain Layout
25249 \begin_layout Plain Layout
25257 \begin_layout Plain Layout
25268 \begin_layout Plain Layout
25284 \begin_layout Plain Layout
25295 \begin_layout Plain Layout
25303 \begin_layout Plain Layout
25314 \begin_layout Plain Layout
25330 \begin_layout Plain Layout
25347 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25350 \begin_layout Plain Layout
25351 \begin_inset Formula $\textrm{\AA}$
25361 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25364 \begin_layout Plain Layout
25372 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25375 \begin_layout Plain Layout
25376 \begin_inset Formula $\textrm{\i }$
25390 \begin_inset Space \hfill{}
25394 \begin_inset Tabular
25395 <lyxtabular version="3" rows="8" columns="2">
25397 <column alignment="block" valignment="top" width="0">
25398 <column alignment="center" valignment="top" width="0">
25400 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25403 \begin_layout Plain Layout
25405 \begin_inset Note Note
25408 \begin_layout Plain Layout
25415 is used for separation, because otherwise the output will be ¡ and ¿ respective
25426 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25429 \begin_layout Plain Layout
25437 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25440 \begin_layout Plain Layout
25448 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25451 \begin_layout Plain Layout
25452 \begin_inset Formula $\textrm{\o }$
25462 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25465 \begin_layout Plain Layout
25473 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25476 \begin_layout Plain Layout
25477 \begin_inset Formula $\textrm{\O}$
25487 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25490 \begin_layout Plain Layout
25498 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25501 \begin_layout Plain Layout
25502 \begin_inset Formula $\textrm{\l }$
25512 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25515 \begin_layout Plain Layout
25523 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25526 \begin_layout Plain Layout
25527 \begin_inset Formula $\textrm{\L }$
25537 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25540 \begin_layout Plain Layout
25542 \begin_inset Space \hspace{}
25550 \begin_layout Plain Layout
25564 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25567 \begin_layout Plain Layout
25568 \begin_inset Formula $\textrm{!`}$
25578 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25581 \begin_layout Plain Layout
25583 \begin_inset Space \hspace{}
25591 \begin_layout Plain Layout
25605 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25608 \begin_layout Plain Layout
25609 \begin_inset Formula $\textrm{?`}$
25619 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25622 \begin_layout Plain Layout
25630 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25633 \begin_layout Plain Layout
25634 \begin_inset Formula $\textrm{\j }$
25648 \begin_inset Space \hfill{}
25654 \begin_layout Standard
25656 \begin_inset Formula $\textrm{\textrm{Å}}$
25660 \begin_inset Formula $\textrm{\textrm{Ø}}$
25663 can also be inserted via the math toolbar button
25664 \begin_inset Graphics
25665 filename ../images/math/digamma.png
25674 \begin_layout Standard
25675 An exception are the commands
25678 \begin_inset Space \hspace{}
25687 \begin_inset Space \hspace{}
25693 , because they can be inserted in LyX directly to text.
25696 \begin_layout Subsection
25698 \begin_inset CommandInset label
25700 name "sub:Accents-in-Text"
25708 \begin_layout Plain Layout
25717 \begin_layout Standard
25718 With the following commands all letters can be accented.
25719 The commands must be inserted in TeX-mode.
25722 \begin_layout Standard
25723 \begin_inset Space \hfill{}
25727 \begin_inset Tabular
25728 <lyxtabular version="3" rows="8" columns="2">
25730 <column alignment="block" valignment="top" width="0">
25731 <column alignment="block" valignment="top" width="0">
25733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25736 \begin_layout Plain Layout
25742 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25745 \begin_layout Plain Layout
25753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25756 \begin_layout Plain Layout
25760 \begin_inset Quotes grd
25768 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25771 \begin_layout Plain Layout
25775 \begin_layout Plain Layout
25791 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25794 \begin_layout Plain Layout
25802 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25805 \begin_layout Plain Layout
25809 \begin_layout Plain Layout
25825 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25828 \begin_layout Plain Layout
25835 \begin_layout Plain Layout
25849 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25852 \begin_layout Plain Layout
25856 \begin_layout Plain Layout
25872 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25875 \begin_layout Plain Layout
25883 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25886 \begin_layout Plain Layout
25890 \begin_layout Plain Layout
25906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25909 \begin_layout Plain Layout
25916 \begin_layout Plain Layout
25930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25933 \begin_layout Plain Layout
25937 \begin_layout Plain Layout
25953 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25956 \begin_layout Plain Layout
25963 \begin_layout Plain Layout
25977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25980 \begin_layout Plain Layout
25984 \begin_layout Plain Layout
26000 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26003 \begin_layout Plain Layout
26010 \begin_layout Plain Layout
26024 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26027 \begin_layout Plain Layout
26031 \begin_layout Plain Layout
26051 \begin_inset Space \hfill{}
26055 \begin_inset Tabular
26056 <lyxtabular version="3" rows="8" columns="2">
26058 <column alignment="block" valignment="top" width="0">
26059 <column alignment="center" valignment="top" width="0">
26061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26064 \begin_layout Plain Layout
26070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26073 \begin_layout Plain Layout
26081 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26084 \begin_layout Plain Layout
26091 \begin_layout Plain Layout
26105 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26108 \begin_layout Plain Layout
26112 \begin_layout Plain Layout
26128 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26131 \begin_layout Plain Layout
26139 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26142 \begin_layout Plain Layout
26146 \begin_layout Plain Layout
26162 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26165 \begin_layout Plain Layout
26172 \begin_layout Plain Layout
26183 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26186 \begin_layout Plain Layout
26190 \begin_layout Plain Layout
26206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26209 \begin_layout Plain Layout
26217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26220 \begin_layout Plain Layout
26224 \begin_layout Plain Layout
26240 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26243 \begin_layout Plain Layout
26250 \begin_layout Plain Layout
26264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26267 \begin_layout Plain Layout
26271 \begin_layout Plain Layout
26287 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26290 \begin_layout Plain Layout
26297 \begin_layout Plain Layout
26311 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26314 \begin_layout Plain Layout
26318 \begin_layout Plain Layout
26334 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26337 \begin_layout Plain Layout
26344 \begin_layout Plain Layout
26358 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26361 \begin_layout Plain Layout
26365 \begin_layout Plain Layout
26385 \begin_inset Space \hfill{}
26391 \begin_layout Standard
26392 \begin_inset VSpace medskip
26401 also two different characters can be accented.
26410 \begin_layout Plain Layout
26425 \begin_layout Plain Layout
26437 \begin_layout Standard
26450 can in combination with vowels directly be inserted with the keyboard without
26452 The same applies for the tilde
26456 \begin_layout Plain Layout
26457 This only applies for keyboards where the tilde is defined as accent.
26466 in combination with
26481 \begin_layout Standard
26524 , and accents inserted directly with the keyboard are also available in
26526 For the other accents there are special math commands to be used in formulas,
26528 \begin_inset CommandInset ref
26530 reference "sub:Accents-for-one"
26537 \begin_layout Standard
26538 \begin_inset VSpace bigskip
26541 Furthermore, with the command
26551 \begin_layout Plain Layout
26559 all numbers and letters can be set into a circle, quasi accented with a
26560 circle, similar to the the copyright symbol.
26563 \begin_layout Standard
26565 \begin_inset Tabular
26566 <lyxtabular version="3" rows="3" columns="2">
26568 <column alignment="center" valignment="top" width="0">
26569 <column alignment="center" valignment="top" width="0">
26571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26574 \begin_layout Plain Layout
26580 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26583 \begin_layout Plain Layout
26585 \begin_inset Note Note
26588 \begin_layout Plain Layout
26595 is only used as spacer.
26607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26610 \begin_layout Plain Layout
26618 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26621 \begin_layout Plain Layout
26625 \begin_layout Plain Layout
26641 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26644 \begin_layout Plain Layout
26655 raisebox{-1.5pt}{W}}
26660 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26663 \begin_layout Plain Layout
26664 \begin_inset Formula $\raisebox {4.5mm}{}$
26671 \begin_layout Plain Layout
26689 \begin_inset Formula $\raisebox {-2mm}{}$
26705 \begin_layout Standard
26706 One has to take care that the character fits in the circle.
26717 \begin_layout Plain Layout
26719 \begin_inset CommandInset ref
26721 reference "sub:Font-Sizes"
26730 specifies thereby the size of the circle.
26741 \begin_layout Plain Layout
26743 \begin_inset CommandInset ref
26745 reference "sub:Boxes-without-Frame"
26754 the character can be centered.
26757 \begin_layout Subsection
26762 \begin_layout Plain Layout
26771 \begin_layout Standard
26772 Minuscule numbers are created with the command
26782 \begin_layout Plain Layout
26791 The command can be used in formulas and in TeX-mode.
26792 The command scheme is:
26795 \begin_layout Standard
26800 oldstylenums{number}
26803 \begin_layout Standard
26808 oldstylenums{0123456789
26811 \begin_inset Formula $\oldstylenums {0123456789}$
26817 \begin_layout Subsection
26818 Miscellaneous Special Characters
26819 \begin_inset CommandInset label
26821 name "sub:Miscellaneous-Special-Characters"
26829 \begin_layout Plain Layout
26830 Special characters ! miscellaneous
26838 \begin_layout Standard
26839 The following characters can only be inserted to formulas by using commands:
26842 \begin_layout Standard
26844 \begin_inset Tabular
26845 <lyxtabular version="3" rows="4" columns="2">
26847 <column alignment="center" valignment="top" width="0">
26848 <column alignment="center" valignment="top" width="0">
26850 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26853 \begin_layout Plain Layout
26859 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26862 \begin_layout Plain Layout
26870 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26873 \begin_layout Plain Layout
26880 \begin_layout Plain Layout
26894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26897 \begin_layout Plain Layout
26898 \begin_inset Formula $\mathcircumflex$
26908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26911 \begin_layout Plain Layout
26919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26922 \begin_layout Plain Layout
26923 \begin_inset Formula $\_{} {}{}{}{}{}$
26933 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26936 \begin_layout Plain Layout
26941 \begin_layout Plain Layout
26956 \begin_layout Plain Layout
26967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26971 \begin_inset Formula $^{\circ}$
26987 \begin_layout Standard
26988 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
26989 contains the following line
26993 \begin_layout Plain Layout
26994 More about this is described in
26995 \begin_inset CommandInset ref
26997 reference "sub:Text-Characters-in"
27009 \begin_layout Standard
27014 DeclareInputtext{176}{
27024 f\SpecialChar \textcompwordmark{}
27028 \begin_layout Section
27030 \begin_inset CommandInset label
27032 name "sec:Formula-Styles"
27040 \begin_layout Plain Layout
27049 \begin_layout Itemize
27050 There are two different alignment styles:
27054 \begin_layout Description
27055 Centered is the predefined standard
27058 \begin_layout Description
27059 Indented for this the option
27063 must be inserted in the menu
27065 Document\SpecialChar \menuseparator
27071 \begin_inset Space ~
27077 \begin_layout Standard
27082 is used, the indentation can be adjusted with the length
27092 \begin_layout Plain Layout
27101 Should the distance be 15
27102 \begin_inset Space \thinspace{}
27105 mm, the following command line is inserted in the LaTeX-preamble
27108 \begin_layout Standard
27118 \begin_layout Standard
27119 When no length is specified, the predefined value of 30
27120 \begin_inset Space \thinspace{}
27127 \begin_layout Itemize
27128 And two different numbering styles:
27132 \begin_layout Description
27133 Right is the predefined standard
27136 \begin_layout Description
27137 Left for this the option
27141 must be inserted in the menu
27143 Document\SpecialChar \menuseparator
27149 \begin_inset Space ~
27156 \begin_layout Standard
27165 can also be used together.
27166 In this case both options are inserted, separated by a comma.
27169 \begin_layout Standard
27170 The chosen styles are used for all displayed formulas of the document.
27171 When both, centered and indented formulas should be created in a document,
27177 The indented formulas are then set in a flalign environment, see
27178 \begin_inset CommandInset ref
27180 reference "sub:Flalign-Environment"
27187 \begin_layout Section
27189 \begin_inset CommandInset label
27191 name "sec:Multiline-Formulas"
27199 \begin_layout Plain Layout
27200 Formula ! multiline
27208 \begin_layout Subsection
27212 \begin_layout Standard
27213 In LyX multiline formulas are created by pressing
27224 that is described in
27225 \begin_inset CommandInset ref
27227 reference "sub:Standard-align-Environment"
27234 \begin_layout Standard
27235 There are other multiline formula environments that can be created via the
27238 Insert\SpecialChar \menuseparator
27242 These environments are described in the following sections.
27245 \begin_layout Standard
27246 In all multiline formula environments a new line is created by pressing
27252 To add or delete lines, the math toolbar buttons
27253 \begin_inset Graphics
27254 filename ../images/tabular-feature_append-row.png
27261 \begin_inset Graphics
27262 filename ../images/tabular-feature_delete-row.png
27268 , respectively, or the menu
27270 Edit\SpecialChar \menuseparator
27276 \begin_layout Subsubsection
27278 \begin_inset CommandInset label
27280 name "sub:Line-Separation"
27288 \begin_layout Plain Layout
27289 Formula ! multiline ! Line separation
27297 \begin_layout Standard
27298 There is sometimes not enough space in multiline formulas between the lines:
27299 \begin_inset Formula \begin{eqnarray*}
27300 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}\\
27301 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*}
27308 \begin_layout Standard
27309 In LaTeX additional line space is specified as optional argument of the
27311 This is not yet possible in LyX
27315 \begin_layout Plain Layout
27317 \begin_inset CommandInset href
27319 name "LyX-bug #1505"
27320 target "http://bugzilla.lyx.org/show_bug.cgi?id=1505"
27329 , therefore the whole formula must be inserted in TeX-mode.
27330 To add in our example space, the command
27338 is inserted at the end of the first line.
27343 \begin_layout Plain Layout
27350 \begin_layout Plain Layout
27352 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
27355 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
27362 \begin_layout Plain Layout
27366 left(B^{2}+x_{0}^{2}
27374 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
27379 \begin_layout Plain Layout
27391 \begin_layout Standard
27392 \begin_inset VSpace bigskip
27395 To set the the line separation for all lines in a formula, the length
27405 \begin_layout Plain Layout
27415 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
27426 \begin_inset Space \thinspace{}
27431 \begin_inset Space \thinspace{}
27434 mm additional line separation as in the previous example, the command
27437 \begin_layout Standard
27447 \begin_layout Standard
27448 is inserted in TeX-mode before the formula.
27449 This requires that the LaTeX-package
27457 \begin_layout Plain Layout
27462 is part of every LaTeX standard installation.
27471 \begin_layout Plain Layout
27477 was loaded in LaTeX-preamble with the line
27480 \begin_layout Standard
27488 \begin_layout Standard
27493 \begin_layout Plain Layout
27505 \begin_inset Formula \begin{eqnarray*}
27506 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}\\
27507 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*}
27514 \begin_layout Standard
27518 \begin_layout Plain Layout
27529 To get back to the predefined distance,
27535 is set to the value 3
27536 \begin_inset Space \thinspace{}
27542 \begin_layout Subsubsection
27544 \begin_inset CommandInset label
27546 name "sub:Column-Separation"
27554 \begin_layout Plain Layout
27555 Formula ! multiline ! Column separation
27563 \begin_layout Standard
27564 Multiline formulas form a matrix.
27565 A formula in the eqnarray environment is for example a matrix with three
27567 By changing the column separation in this environment, the space beside
27568 the relation sign can be changed.
27571 \begin_layout Standard
27572 The column separation is specified with the length
27582 \begin_layout Plain Layout
27591 \begin_inset Newline newline
27594 column separation = 2
27595 \begin_inset Space \thinspace{}
27605 \begin_inset Newline newline
27611 \begin_layout Standard
27621 \begin_layout Standard
27622 inserted in TeX-mode, sets for all following formulas a column separation
27624 \begin_inset Space \thinspace{}
27628 To get back to the predefined distance,
27635 \begin_inset Space \thinspace{}
27641 \begin_layout Standard
27643 \begin_inset Space \thinspace{}
27646 cm column separation:
27650 \begin_layout Plain Layout
27662 \begin_inset Formula \begin{eqnarray*}
27664 C & \ne & A\end{eqnarray*}
27668 A formula with the predefined column separation for matrices of 10
27669 \begin_inset Space \thinspace{}
27676 \begin_layout Plain Layout
27688 \begin_inset Formula \begin{eqnarray*}
27690 C & \ne & A\end{eqnarray*}
27697 \begin_layout Subsubsection
27702 \begin_layout Plain Layout
27711 \begin_layout Standard
27712 Long formulas can be typeset using these methods:
27715 \begin_layout Itemize
27716 When one side of the equation is much shorther than the line width, this
27717 one is chosen for the left side and the right side is typeset over two
27722 \begin_layout Plain Layout
27732 \begin_inset Formula \begin{eqnarray}
27733 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 \\
27734 & & -\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}
27742 \begin_layout Plain Layout
27752 \begin_inset Newline newline
27755 The minus sign at the beginning of the second line does normally not appear
27756 as operator because it is the first character of the line.
27757 Thus it would not be surrounded by space and could not be distinguished
27758 from the fraction bar.
27759 To avoid this, space was inserted behind the minus sign with the command
27770 \begin_layout Plain Layout
27778 \begin_inset CommandInset ref
27780 reference "sub:Variable-Space"
27793 \begin_layout Plain Layout
27804 \begin_layout Itemize
27805 When both sides of the equation are too long, the command
27815 \begin_layout Plain Layout
27824 It is inserted to the first column of the first line and effects that all
27825 further insertions overwrite the following columns:
27829 \begin_layout Plain Layout
27839 \begin_inset Formula \begin{eqnarray}
27840 \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 \\
27841 & & -\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 \\
27842 & & =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}
27850 \begin_layout Plain Layout
27860 \begin_inset Newline newline
27863 After the insertion of
27869 , the cursor is in a purple box that is a bit shifted to the left from the
27871 In this the formula is inserted.
27875 \begin_layout Plain Layout
27885 \begin_inset Newline newline
27888 The content of the further lines is inserted to the second or another formula
27890 The greater the column number where it was inserted, the larger the indentation.
27894 \begin_layout Plain Layout
27904 \begin_inset Newline newline
27908 \begin_inset Note Greyedout
27911 \begin_layout Plain Layout
27912 Note the following when using
27921 \begin_layout Itemize
27922 The formula doesn't use the full page width.
27924 \begin_inset Space \thinspace{}
27928 \begin_inset Space ~
27932 \begin_inset Formula $-B^{2}$
27935 is added to the first line in the above example, it would have been outside
27937 To better use the width, negative space can be inserted at the beginning
27941 \begin_layout Itemize
27942 Due to a bug in LyX the cursor cannot be set with the mouse into the first
27947 \begin_layout Plain Layout
27948 \begin_inset CommandInset href
27950 name "LyX-bug #1429"
27951 target "http://bugzilla.lyx.org/show_bug.cgi?id=1429"
27960 One can only set the cursor at the beginning of the line and move it with
27969 \begin_layout Itemize
27970 Other methods to set long formulas are offered by the environments described
27972 \begin_inset CommandInset ref
27974 reference "sub:Multline-Environment"
27979 \begin_inset CommandInset ref
27981 reference "sub:Multiline-Formula-Parts"
27988 \begin_layout Subsubsection
27990 \begin_inset CommandInset label
27992 name "sub:Multiline-Brackets"
28000 \begin_layout Plain Layout
28001 Brackets ! for multiline expressions
28009 \begin_layout Standard
28010 For brackets spanning multiple lines the following problem occurs:
28011 \begin_inset Formula \begin{eqnarray*}
28012 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28013 & & \left.\cdots+B-D\right]\end{eqnarray*}
28020 \begin_layout Standard
28021 The closing bracket is smaller than the opening bracket because brackets
28022 with variable size may not span multiple lines.
28025 \begin_layout Standard
28026 To set the bracket size for the second line correctly, the first line is
28037 \begin_layout Plain Layout
28045 and the second line with
28053 \begin_layout Plain Layout
28067 \begin_inset CommandInset ref
28069 reference "sub:Automatic-Bracket-Size"
28084 \begin_layout Plain Layout
28110 \begin_layout Plain Layout
28129 \begin_layout Plain Layout
28148 \begin_layout Plain Layout
28160 \begin_inset Formula $\downarrow$
28169 \begin_layout Plain Layout
28177 is inserted, because the multiplication operator with its limits is the
28178 largest symbol in the first line and this should be the size for the bracket
28179 in the second line.
28182 \begin_layout Standard
28183 The result is this:
28184 \begin_inset Formula \begin{eqnarray*}
28185 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28186 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
28193 \begin_layout Subsection
28197 \begin_layout Standard
28198 Align environments can be used for every kind of multiline formulas.
28199 They are specially useful to set several formulas side by side.
28202 \begin_layout Standard
28203 Align environments consist of columns.
28204 The odd columns are right aligned, the even ones left aligned.
28205 Every line in an Align environment can be numbered.
28208 \begin_layout Standard
28209 Align environments are created via the menu
28211 Insert\SpecialChar \menuseparator
28217 Edit\SpecialChar \menuseparator
28218 Math\SpecialChar \menuseparator
28219 Change Formula Type
28221 already existing formulas can be converted to Align environments.
28224 \begin_layout Standard
28225 To add or delete columns, the math toolbar buttons
28226 \begin_inset Graphics
28227 filename ../images/tabular-feature_append-column.png
28234 \begin_inset Graphics
28235 filename ../images/tabular-feature_delete-column.png
28241 , respectively, or the menu
28243 Edit\SpecialChar \menuseparator
28249 \begin_layout Subsubsection
28250 Standard align Environment
28251 \begin_inset CommandInset label
28253 name "sub:Standard-align-Environment"
28261 \begin_layout Plain Layout
28262 Formula ! multiline ! align environment
28270 \begin_layout Standard
28271 This Align environment is created by presssing
28275 in a formula or by the menu
28277 Insert\SpecialChar \menuseparator
28278 Math\SpecialChar \menuseparator
28279 AMS align Environment
28284 \begin_layout Standard
28285 An example for two formulas set side by side, that are created with a four
28286 column align environment:
28287 \begin_inset Formula \begin{align*}
28288 A & =\sin(B) & C & =D\\
28289 C & \ne A & B & \ne D\end{align*}
28293 As it can be seen, the formulas in this environment are placed so as if
28302 \begin_layout Plain Layout
28310 \begin_inset CommandInset ref
28312 reference "sub:Variable-Space"
28323 before the first and after every even column.
28324 When the formula style
28330 \begin_layout Plain Layout
28332 \begin_inset CommandInset ref
28334 reference "sec:Formula-Styles"
28345 is used, the formula is set without the
28351 before the first column.
28354 \begin_layout Subsubsection
28355 Alignat Environment
28359 \begin_layout Plain Layout
28360 Formula ! multiline ! alignat environment
28368 \begin_layout Standard
28369 The alignat environment has no predefined column separation.
28370 It can be inserted manually with the spaces that are described
28371 \begin_inset CommandInset ref
28373 reference "sub:Space"
28380 \begin_layout Standard
28381 The above example in the alignat environment where 1
28382 \begin_inset Space \thinspace{}
28385 cm space was inserted at the beginning of the second formula:
28386 \begin_inset Formula \begin{alignat*}{2}
28387 A & =\sin(B) & \hspace {1cm}C & =D\\
28388 C & \ne A & B & \ne D\end{alignat*}
28392 Because the column separation can be set separately for every column, this
28393 environment is especially suitable to set three and more formulas side
28397 \begin_layout Subsubsection
28398 Flalign Environment
28399 \begin_inset CommandInset label
28401 name "sub:Flalign-Environment"
28409 \begin_layout Plain Layout
28410 Formula ! multiline ! flalign environment
28418 \begin_layout Standard
28419 In this environment the first two columns are always set as much as possible
28420 to the left and the last two ones to the right.
28422 \begin_inset Formula \begin{flalign*}
28423 A & =1 & B & =2 & C & =3\\
28424 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
28431 \begin_layout Standard
28432 By creating a flalign environment with an odd number of columns where an
28433 empty TeX-brace is inserted to the last column, several formulas in a document
28434 can be set to the left, although the formula style
28439 As example the indented formula
28440 \begin_inset CommandInset ref
28442 reference "eq:VolInt"
28447 \begin_inset Formula \begin{flalign}
28448 \hspace {30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
28452 The first two columns contain the formula.
28453 To indent it as with the formula style
28458 \begin_inset Space \thinspace{}
28461 pt space was inserted at the beginning of the first column.
28464 \begin_layout Subsection
28465 Eqnarray Environment
28469 \begin_layout Plain Layout
28470 Formula ! multiline ! eqnarray environment
28478 \begin_layout Standard
28479 When this environment has been created, three blue boxes appear.
28480 The content of the first box is right aligned, the content of the last
28482 The content of the middle box appears centered and a bit smaller, because
28483 it is designed to insert there only relation characters.
28484 \begin_inset Formula \begin{eqnarray*}
28485 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
28487 A & = & A\end{eqnarray*}
28494 \begin_layout Subsection
28499 \begin_layout Plain Layout
28500 Formula ! multiline ! gather environment
28508 \begin_layout Standard
28509 This environment consists of only one centered column.
28510 Every line can be numbered.
28511 \begin_inset Formula \begin{gather}
28513 X=\textrm{-}1\end{gather}
28520 \begin_layout Subsection
28521 Multline Environment
28522 \begin_inset CommandInset label
28524 name "sub:Multline-Environment"
28532 \begin_layout Plain Layout
28533 Formula ! multiline ! multline environment
28541 \begin_layout Standard
28542 The multline environment consists, like the gather environment, of only
28544 But the first line is left aligned, the last one right aligned.
28545 All other lines are centered.
28546 Therefore this environment is suitable for long formulas.
28548 \begin_inset CommandInset ref
28550 reference "eq:lefteqn"
28554 in the multline environment:
28555 \begin_inset Formula \begin{multline}
28556 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}\\
28557 -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}\\
28558 =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}
28565 \begin_layout Standard
28566 In the output only the last (first) line of a multline environment appears
28567 numbered when the document numbering is right (left).
28571 \begin_layout Plain Layout
28572 numbering styles see
28573 \begin_inset CommandInset ref
28575 reference "sec:Formula-Styles"
28587 \begin_layout Standard
28596 \begin_layout Plain Layout
28614 \begin_layout Plain Layout
28624 a centered line can be right or left aligned, respectively.
28625 The commands are used as follows:
28628 \begin_layout Standard
28633 shoveright{line content}
28639 shoveleft{line content}
28642 \begin_layout Standard
28643 \begin_inset VSpace medskip
28654 \begin_layout Plain Layout
28664 specifies the distance of the first line from the left page margin.
28665 Predefined is the length 0
28666 \begin_inset Space \thinspace{}
28672 \begin_layout Standard
28673 As example the above formula where the command
28676 \begin_layout Standard
28686 \begin_layout Standard
28687 was inserted in TeX-mode before:
28691 \begin_layout Plain Layout
28703 \begin_inset Formula \begin{multline}
28704 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}\\
28705 \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}}\\
28706 =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}
28714 \begin_layout Plain Layout
28725 The second line was left aligned using
28734 \begin_layout Subsection
28735 Multiline Formula Parts
28736 \begin_inset CommandInset label
28738 name "sub:Multiline-Formula-Parts"
28746 \begin_layout Plain Layout
28747 Formula ! multiline ! formula parts
28755 \begin_layout Standard
28756 To display only parts of a formula with multiple lines, one of the following
28757 environments are used:
28774 They can be inserted via the menu
28776 Insert\SpecialChar \menuseparator
28779 or by using the commands described in this section.
28782 \begin_layout Standard
28783 The first three have the same properties as the corresponding multiline
28784 formula environments, but it is possible to set further formula parts beside
28787 \begin_inset Formula \[
28788 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
28789 \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
28790 \right\} \textrm{Uncertainty relations}\]
28797 \begin_layout Standard
28798 To get this formula, a displayed formula is created where the command
28806 \begin_layout Plain Layout
28817 A purple box appears around the blue formula box where now columns and
28818 lines can be added.
28819 Outside the multiline environment other formula parts can be set, like
28823 \begin_layout Standard
28824 The aligned environment is also suitable for long formulas whose lines are
28825 horizontally aligned.
28826 Using aligned in a displayed formula has the advantage that the formula
28827 number is vertically centered behind the lines.
28829 \begin_inset CommandInset ref
28831 reference "eq:kurzlang"
28835 in the aligned environment:
28836 \begin_inset Formula \begin{equation}
28837 \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}|}\\
28838 & -\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}
28846 \begin_layout Standard
28847 To use the environments
28869 \begin_layout Plain Layout
28887 \begin_layout Plain Layout
28905 \begin_layout Plain Layout
28913 are inserted, respectively.
28914 The split environment has the same properties as the aligned environment
28915 but it can only have two columns.
28918 \begin_layout Subsection
28919 Text in multiline Formulas
28920 \begin_inset CommandInset label
28922 name "sub:Text-in-multiline"
28930 \begin_layout Plain Layout
28940 \begin_layout Plain Layout
28941 Formula ! multiline ! text
28949 \begin_layout Standard
28950 In the Align environments, and the multline and gather environment, text
28951 can be inserted that will appear in a separate line and doesn't affect
28952 the column alignment.
28953 To do this, the command
28961 \begin_layout Plain Layout
28971 is used in the following scheme:
28974 \begin_layout Standard
28982 \begin_layout Standard
28983 The text should not be longer than a line because it cannot be hyphenated.
28984 As LyX doesn't yet support
28990 directly, the text is written as mathematical text.
28997 must hereby be at the beginning of a line and appears in the output above
28999 An example where the text was inserted at the beginning of the second line:
29000 \begin_inset Formula \begin{align}
29001 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29002 \intertext {\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
29009 \begin_layout Section
29014 \begin_layout Plain Layout
29024 \begin_layout Plain Layout
29025 Formula ! numbering|see
29029 \begin_layout Plain Layout
29040 \begin_layout Plain Layout
29055 \begin_layout Subsection
29059 \begin_layout Standard
29060 Numbered formulas can be created with the menu
29062 Insert\SpecialChar \menuseparator
29063 Math\SpecialChar \menuseparator
29065 \begin_inset Space ~
29073 \begin_inset Space ~
29079 Existing formulas can be numbered with the menu
29081 Edit\SpecialChar \menuseparator
29082 Math\SpecialChar \menuseparator
29084 \begin_inset Space ~
29092 \begin_inset Space ~
29098 The formula number is displayed in LyX behind the formula as number sign
29100 The number sign is replaced in the output by the formula number.
29103 \begin_layout Standard
29104 When numbering is turned on in multiline formulas, all lines will be numbered.
29105 But the numbering can be controlled with the menu
29107 Edit\SpecialChar \menuseparator
29108 Math\SpecialChar \menuseparator
29110 \begin_inset Space ~
29114 \begin_inset Space ~
29118 \begin_inset Space ~
29126 \begin_inset Space ~
29134 \begin_layout Standard
29135 Except of inline formulas, all formulas can be numbered with two different
29137 \begin_inset CommandInset ref
29139 reference "sec:Formula-Styles"
29146 \begin_layout Subsection
29148 \begin_inset CommandInset label
29150 name "sub:Cross-References"
29158 \begin_layout Plain Layout
29159 Cross-references ! to formulas
29167 \begin_layout Standard
29168 All labeled formulas can be cross-referenced.
29169 A label is added by the menu
29171 Insert\SpecialChar \menuseparator
29174 or the toolbar button
29175 \begin_inset Graphics
29176 filename ../images/label-insert.png
29183 The cursor must hereby be inside a displayed formula.
29184 A dialog pops up displaying the prefix
29189 The label is inserted there behind the prefix.
29190 The predefined prefix means
29191 \begin_inset Quotes eld
29195 \begin_inset Quotes erd
29198 and makes it easier to find labels in large documents because it marks
29199 it as formula label to divide it from e.
29200 \begin_inset Space \thinspace{}
29204 \begin_inset Space ~
29208 To change a label, the menu
29210 Insert\SpecialChar \menuseparator
29216 \begin_layout Standard
29217 The name of the label is displayed in LyX within two parentheses behind
29219 A formula with a label is always numbered.
29222 \begin_layout Standard
29223 Cross-references are inserted via the menu
29225 Insert\SpecialChar \menuseparator
29228 or with the toolbar button
29229 \begin_inset Graphics
29230 filename ../images/dialog-show-new-inset_ref.png
29237 A formula cross-reference appears in the output as formula number.
29238 When in the cross-reference dialog window the format
29242 is chosen, the cross-reference appears in the output as formula number
29244 \begin_inset Newline newline
29247 By right-clicking on a cross-reference in LyX, one jumps to the formula
29248 that is referenced.
29251 \begin_layout Standard
29252 Here are as examples cross-references to formulas of the following subsections:
29253 \begin_inset Note Note
29256 \begin_layout Plain Layout
29257 Note the different cross-reference types.
29265 \begin_layout Standard
29267 \begin_inset CommandInset ref
29274 \begin_inset CommandInset ref
29282 \begin_inset CommandInset ref
29288 ) big Latin letters are used for the numbering in contrary to (
29289 \begin_inset CommandInset ref
29298 \begin_layout Standard
29299 \begin_inset VSpace medskip
29302 When the argument of
29310 \begin_layout Plain Layout
29318 \begin_inset CommandInset ref
29320 reference "sub:User-defined-Numbering"
29331 contains a box like in
29332 \begin_inset CommandInset ref
29334 reference "sub:Paragraph-Boxes"
29338 , the formula cannot be referenced.
29341 \begin_layout Subsection
29346 \begin_layout Plain Layout
29347 Formula numbering ! subnumbering
29355 \begin_layout Standard
29356 With the help of the commands
29360 begin{subequations}
29368 formulas can be subnumbered.
29369 Both commands are inserted in TeX-mode.
29372 \begin_layout Standard
29374 \begin_inset Formula \begin{equation}
29375 A=C-B\label{eq:a}\end{equation}
29383 \begin_layout Plain Layout
29387 addtocounter{equation}{-1}
29396 \begin_layout Plain Layout
29400 begin{subequations}
29406 \begin_inset VSpace -5mm
29410 \begin_inset Formula \begin{equation}
29411 B=C-A\label{eq:b}\end{equation}
29416 \begin_inset Formula \begin{equation}
29417 C=A+B\label{eq:c}\end{equation}
29424 \begin_layout Standard
29428 \begin_layout Plain Layout
29440 \begin_layout Standard
29441 To create the example, the following is done:
29444 \begin_layout Enumerate
29445 first formula is inserted
29448 \begin_layout Enumerate
29453 addtocounter{equation}{-1}
29455 begin{subequations}
29459 \begin_layout Plain Layout
29468 \begin_inset Newline newline
29473 is inserted after the first formula
29476 \begin_layout Enumerate
29477 second formula is inserted
29480 \begin_layout Enumerate
29481 third formula is inserted
29484 \begin_layout Enumerate
29491 is inserted after the third formula
29494 \begin_layout Standard
29495 Every formula between the commands
29507 is subnumbered as a, b,
29508 \begin_inset Newline linebreak
29511 c, \SpecialChar \ldots{}
29512 For multiline formulas every line will be subnumbered.
29513 All subnumbered formulas are treated as
29518 But as every numbered formula increases the counter
29522 by one, the command
29528 is needed to decrease it.
29529 Otherwise the formulas
29530 \begin_inset CommandInset ref
29537 \begin_inset CommandInset ref
29544 \begin_inset CommandInset ref
29550 would be numbered as
29551 \begin_inset CommandInset ref
29558 \begin_inset CommandInset ref
29565 \begin_inset CommandInset ref
29574 \begin_layout Standard
29575 By inserting the commands in TeX-mode, a space is created between the first
29578 \begin_inset Space \thinspace{}
29581 mm vertical space is inserted after the command
29585 begin{subequations}
29588 When the formula style
29594 \begin_layout Plain Layout
29596 \begin_inset CommandInset ref
29598 reference "sec:Formula-Styles"
29610 \begin_inset Space \thinspace{}
29613 mm space is inserted instead.
29616 \begin_layout Standard
29617 Here is an example for a multiline formula where the numbering was turned
29618 off for the second line:
29622 \begin_layout Plain Layout
29626 begin{subequations}
29632 \begin_inset Formula \begin{eqnarray}
29633 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
29634 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
29635 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
29643 \begin_layout Plain Layout
29655 \begin_layout Subsection
29656 User-defined Numbering
29657 \begin_inset CommandInset label
29659 name "sub:User-defined-Numbering"
29667 \begin_layout Plain Layout
29668 Formula numbering ! user-defined
29676 \begin_layout Standard
29680 \begin_layout Plain Layout
29681 Formula numbering ! self-defined delimiters
29686 With the standard numbering parentheses are set around the formula number.
29687 To replace the parentheses for example by vertical bars, the following
29688 line is added to the LaTeX-preamble:
29691 \begin_layout Standard
29703 \begin_inset Note Note
29706 \begin_layout Plain Layout
29707 This macro is already declared in the LaTeX-preamble for testing.
29708 To activate it, remove the percent sign at the beginning.
29716 \begin_layout Standard
29717 To use other characters, the vertical bars besides the
29721 are replaced by one ore more characters.
29722 To get only the formula number the vertical bars are omitted.
29725 \begin_layout Standard
29726 \begin_inset VSpace bigskip
29729 When there should be an expression of your choice instead of the consecutive
29730 formula number in parentheses behind the formula, the command
29740 \begin_layout Plain Layout
29749 \begin_inset Formula \begin{equation}
29750 A+B=C\tag{something}\label{eq:tag}\end{equation}
29754 In this example the command
29762 \begin_layout Plain Layout
29773 was inserted to the formula.
29776 \begin_layout Standard
29785 \begin_layout Plain Layout
29796 is inserted instead, the star prevents the parentheses around the expression:
29797 \begin_inset Formula \[
29798 A+B=C\tag*{something}\]
29805 \begin_layout Standard
29806 \begin_inset VSpace bigskip
29809 To restart the formula numbering with new document parts or sections, the
29810 following command is used:
29813 \begin_layout Standard
29818 @addtoreset{equation}{part}
29824 \begin_layout Plain Layout
29829 \begin_layout Plain Layout
29840 \begin_layout Plain Layout
29853 \begin_layout Plain Layout
29864 \begin_layout Plain Layout
29877 \begin_inset Newline newline
29881 \begin_inset Newline newline
29888 @addtoreset{equation}{section}
29891 \begin_layout Standard
29892 To be able to use these commands in TeX-mode, the
29893 \begin_inset Quotes eld
29897 \begin_inset Quotes erd
29900 character has to be made
29901 \begin_inset Quotes eld
29905 \begin_inset Quotes erd
29908 for LaTeX using the command
29922 So the command sequence in TeX-mode is:
29925 \begin_layout Standard
29931 \begin_inset Newline newline
29936 @addtoreset{equation}{section}
29937 \begin_inset Newline newline
29945 \begin_layout Standard
29946 In the LaTeX-preamble
29958 can be omitted as they are automatically internally inserted by LyX.
29961 \begin_layout Standard
29976 \begin_layout Plain Layout
29981 is part of the LaTeX-package
29989 \begin_layout Plain Layout
29990 Packages ! carlisle
29995 that is part of every LaTeX standard installation.
30004 \begin_layout Plain Layout
30005 Packages ! remreset
30010 has to be loaded in the LaTeX-preamble with the line
30013 \begin_layout Standard
30018 usepackage{remreset}
30021 \begin_layout Standard
30032 \begin_layout Plain Layout
30037 \begin_layout Plain Layout
30048 \begin_layout Plain Layout
30061 \begin_layout Plain Layout
30072 \begin_layout Plain Layout
30084 can be used with the same scheme as
30093 \begin_layout Standard
30094 \begin_inset VSpace bigskip
30097 Sometimes formulas should be numbered in the following form:
30100 \begin_layout Standard
30103 (section number.formula number)
30106 \begin_layout Standard
30107 The formula number should start with every section with
30108 \begin_inset Quotes eld
30112 \begin_inset Quotes erd
30118 \begin_layout Standard
30119 For this case there is the command
30129 \begin_layout Plain Layout
30137 , which is used with the following scheme:
30140 \begin_layout Standard
30145 numberwithin{counter}{sectioning}
30148 \begin_layout Standard
30149 Counter denotes what kind of numbering is affected, sectioning denotes what
30150 number is before the dot.
30153 \begin_layout Standard
30154 Thus in our case the following LaTeX-preamble or ERT line is used:
30157 \begin_layout Standard
30162 numberwithin{equation}{section}
30165 \begin_layout Standard
30166 This is the result:
30170 \begin_layout Plain Layout
30174 numberwithin{equation}{section}
30180 \begin_inset Formula \begin{equation}
30181 A+B=C\end{equation}
30188 \begin_layout Standard
30190 \begin_inset Space \thinspace{}
30194 \begin_inset Space ~
30197 tables so that the number of the part is the sectioning,
30198 \begin_inset Newline newline
30205 numberwithin{table}{part}
30210 \begin_layout Standard
30211 To go back to the standard numbering or to prevent this kind of numbering
30212 when it is defined by the document class, the following command is inserted
30213 as ERT or to the LaTeX-preamble:
30216 \begin_layout Standard
30229 \begin_layout Plain Layout
30243 \begin_layout Plain Layout
30259 \begin_inset Newline newline
30267 \begin_inset Newline newline
30279 \begin_layout Standard
30286 uses internally the command
30292 , described above, that also needs to be reverted.
30296 \begin_layout Plain Layout
30303 \begin_layout Plain Layout
30307 @removefromreset{equation}{section}
30310 \begin_layout Plain Layout
30322 \begin_layout Subsection
30323 Numbering with Roman Numbers and Letters
30324 \begin_inset CommandInset label
30326 name "sub:Numbering-with-Roman"
30334 \begin_layout Plain Layout
30335 Formula numbering ! with letters
30344 \begin_layout Plain Layout
30345 Formula numbering ! with Roman numbers
30353 \begin_layout Standard
30354 Formulas can also be numbered with Roman numbers and Latin letters.
30355 To number for example with small Roman numbers, the command
30358 \begin_layout Standard
30370 \begin_layout Standard
30371 is inserted before the formula in TeX-mode.
30382 \begin_layout Plain Layout
30390 redefines the predefined command
30406 \begin_layout Plain Layout
30413 has the same scheme like the command
30419 that is described in
30420 \begin_inset CommandInset ref
30422 reference "sec:User-defined-commands"
30436 is the formula counter.
30443 is used as prefix for a counter, the value of the counter is output as
30445 When a formula is numbered, LaTeX sets internally the command
30451 behind the formula.
30460 \begin_layout Plain Layout
30470 outputs the counter as small Roman number.
30473 \begin_layout Standard
30474 All formulas behind the command
30484 are now numbered Roman.
30485 To switch to numbering with big Roman numbers, the command is inserted
30502 \begin_layout Plain Layout
30514 \begin_inset Quotes eld
30518 \begin_inset Quotes erd
30521 with small Latin letters there is the command
30531 \begin_layout Plain Layout
30539 , for big ones there is the command
30549 \begin_layout Plain Layout
30562 \begin_layout Standard
30563 \begin_inset Note Greyedout
30566 \begin_layout Plain Layout
30571 Only maximal 26 formulas can be numbered with Latin letters in one document.
30579 \begin_layout Standard
30583 \begin_layout Plain Layout
30599 \begin_layout Standard
30600 \begin_inset Formula \begin{equation}
30601 A=\textrm{small roman}\label{eq:rom}\end{equation}
30609 \begin_layout Plain Layout
30623 \begin_inset Formula \begin{equation}
30624 B=\textrm{big Roman}\label{eq:Rom}\end{equation}
30632 \begin_layout Plain Layout
30646 \begin_inset Formula \begin{equation}
30647 C=\textrm{small Latin}\label{eq:lat}\end{equation}
30655 \begin_layout Plain Layout
30669 \begin_inset Formula \begin{equation}
30670 D=\textrm{big Latin}\label{eq:Lat}\end{equation}
30677 \begin_layout Standard
30678 To switch back to the default numbering, insert the command:
30681 \begin_layout Standard
30694 \begin_layout Plain Layout
30705 \begin_layout Standard
30709 \begin_layout Plain Layout
30723 \begin_inset Formula \begin{equation}
30724 E=\textrm{Arabic}\label{eq:arab}\end{equation}
30731 \begin_layout Standard
30732 \begin_inset VSpace medskip
30735 As you see, formulas are numbered serially independent from the numbering
30737 When then numbering should start with
30738 \begin_inset Quotes eld
30742 \begin_inset Quotes erd
30745 when the style is changed, new equation counters have to be defined.
30746 A description about this can be found in the file
30747 \begin_inset CommandInset href
30749 target "Formula-numbering.lyx"
30756 \begin_layout Section
30757 User-defined commands
30758 \begin_inset CommandInset label
30760 name "sec:User-defined-commands"
30768 \begin_layout Plain Layout
30769 User-defined commands
30777 \begin_layout Standard
30778 Many LaTeX-commands are too long to be used frequently.
30779 But it is possible to define with the command
30789 \begin_layout Plain Layout
30797 new shorter commands.
30800 \begin_layout Standard
30801 The command scheme of
30810 \begin_layout Standard
30815 newcommand{new command name}[number of arguments][optional
30820 \begin_inset Newline newline
30827 \begin_layout Plain Layout
30842 \begin_layout Plain Layout
30849 {command definition}
30852 \begin_layout Standard
30853 \begin_inset Note Greyedout
30856 \begin_layout Plain Layout
30861 Assure that the name of the new command is not already used in your document
30862 or by LaTeX-packages that you use.
30863 When you for example define the command
30875 , you get an error message because
30881 is already defined as command for
30882 \begin_inset Quotes eld
30886 \begin_inset Formula $\le$
30890 \begin_inset Quotes erd
30901 \begin_layout Standard
30902 \begin_inset Note Greyedout
30905 \begin_layout Plain Layout
30910 The names of user-defined commands may only consist of Latin letters.
30918 \begin_layout Standard
30919 The number of arguments is an integer in the range 0
30920 \begin_inset Space \thinspace{}
30924 \begin_inset Space \thinspace{}
30927 9 and specifies how many arguments the new command should have.
30928 With the optional value a value for an optional argument can be predefined.
30929 When this is done, the
30937 rgument of the new command is automatically an optional one.
30940 \begin_layout Standard
30941 Here are some examples:
30944 \begin_layout Itemize
30945 To define the command
30957 , the LaTeX-preamble line is:
30961 \begin_layout Plain Layout
30973 \begin_inset Newline newline
30985 \begin_layout Itemize
30986 To define the command
30998 , the argument (that should be underlined) must be taken into account.
30999 For this the preamble line is:
31003 \begin_layout Plain Layout
31015 \begin_inset Newline newline
31030 \begin_layout Plain Layout
31042 \begin_inset Newline newline
31051 acts as argument placeholder, the
31055 behind it denotes that it is the placeholder for the first argument.
31058 \begin_layout Itemize
31066 \begin_inset Space \thinspace{}
31070 \begin_inset Space ~
31083 \begin_layout Plain Layout
31095 \begin_inset Newline newline
31104 framebox#1#2{$#3$}}
31110 \begin_layout Plain Layout
31122 \begin_inset Newline newline
31127 The two Dollar signs creates the extra formula needed for
31134 \begin_inset CommandInset ref
31136 reference "sub:Boxes-with-Frame"
31143 \begin_layout Itemize
31144 To create a new command for
31150 where the color for the box needn't to be specified, the argument for the
31151 color is defined optional:
31155 \begin_layout Plain Layout
31167 \begin_inset Newline newline
31176 fcolorbox{#2}{#1}{$#3$}}
31182 \begin_layout Plain Layout
31192 \begin_inset Newline newline
31195 When the color is not specified when using
31201 , the predefined color
31208 \begin_layout Standard
31209 A test of the new defined commands:
31212 \begin_layout Standard
31214 \begin_inset Tabular
31215 <lyxtabular version="3" rows="6" columns="2">
31217 <column alignment="center" valignment="top" width="0">
31218 <column alignment="center" valignment="top" width="0">
31220 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31223 \begin_layout Plain Layout
31229 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31232 \begin_layout Plain Layout
31234 \begin_inset Note Note
31237 \begin_layout Plain Layout
31244 is only used as spacer.
31256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31259 \begin_layout Plain Layout
31266 \begin_layout Plain Layout
31280 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31283 \begin_layout Plain Layout
31284 \begin_inset Formula $A\gr B$
31294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31297 \begin_layout Plain Layout
31305 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31308 \begin_layout Plain Layout
31309 \begin_inset Formula $\raisebox {4.5mm}{}\us {ABcd}\raisebox {-2mm}{}$
31319 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31322 \begin_layout Plain Layout
31326 \begin_inset Formula $\to$
31332 \begin_inset Formula $\to$
31343 \begin_layout Plain Layout
31357 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31360 \begin_layout Plain Layout
31361 \begin_inset Formula $\raisebox {6mm}{}\fb {[2cm]}{}{\int A=B}\raisebox {-4mm}{}$
31371 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31374 \begin_layout Plain Layout
31378 \begin_inset Formula $\to$
31389 \begin_layout Plain Layout
31403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31406 \begin_layout Plain Layout
31407 \begin_inset Formula $\raisebox {6mm}{}\cb {red}{\int A=B}\raisebox {-4mm}{}$
31417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31420 \begin_layout Plain Layout
31426 \begin_inset Formula $\to$
31437 \begin_layout Plain Layout
31451 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31454 \begin_layout Plain Layout
31455 \begin_inset Formula $\raisebox {6mm}{}\cb [green]{red}{\int A=B}\raisebox {-4mm}{}$
31471 \begin_layout Section
31476 \begin_layout Plain Layout
31485 \begin_layout Standard
31486 To create diagrams, the LaTeX-package
31492 \begin_layout Plain Layout
31497 is part of every LaTeX standard installation.
31508 \begin_layout Plain Layout
31515 It is loaded in the LaTeX-preamble with the line
31518 \begin_layout Standard
31526 \begin_layout Standard
31527 Diagrams visualize relations and look like this:
31528 \begin_inset Formula \[
31529 \begin{CD}A@>>>B@>>>C\\
31531 F@<<<E@<<<D\end{CD}\]
31538 \begin_layout Standard
31539 To get them, the command
31547 \begin_layout Plain Layout
31557 is inserted to a formula.
31558 A blue box appears with two dashed lines where further commands can be
31564 a new line is created.
31565 Horizontal relations are inserted in odd, vertical in even formula lines.
31568 \begin_layout Standard
31569 To create the relations there are the following commands:
31572 \begin_layout Itemize
31577 creates a left arrow,
31588 \begin_layout Itemize
31593 creates an up arrow,
31601 a vertical equal sign
31604 \begin_layout Itemize
31610 is a placeholder for non-existent relations
31613 \begin_layout Standard
31614 All arrows can be labeled as follows:
31617 \begin_layout Itemize
31618 Is text inserted between the first and second < or >, resp., it is placed
31620 When it is inserted between the second and third one, it appears under
31624 \begin_layout Itemize
31625 When text for vertical arrows is inserted between the first and second A
31626 or V, resp., it is placed left beside the arrow.
31627 When it is inserted between the second and third one, it appears right
31629 If the text contains an A or V, these letters must be set into a TeX-brace.
31632 \begin_layout Standard
31633 As example a diagram with all possible relations:
31636 \begin_layout Standard
31637 \begin_inset Formula \[
31638 \begin{CD}A@>j>>B@>>k>C@=F\\
31640 D@<<j<E@>k>>F@=C\end{CD}\]
31647 \begin_layout Standard
31648 The command for this is:
31649 \begin_inset Newline newline
31660 \begin_layout Plain Layout
31669 A@>j>>B@>>k>C@=F Ctrl-Enter
31670 \begin_inset Newline newline
31677 \begin_layout Plain Layout
31692 \begin_layout Plain Layout
31705 \begin_layout Plain Layout
31717 \begin_inset Formula $\to$
31723 \begin_inset Newline newline
31730 \begin_layout Plain Layout
31745 \begin_layout Plain Layout
31758 \begin_layout Plain Layout
31768 \begin_layout Standard
31769 \begin_inset Newpage newpage
31775 \begin_layout Section
31780 \begin_layout Plain Layout
31793 \begin_layout Plain Layout
31794 Other useful math tips can be found in
31795 \begin_inset CommandInset citation
31810 \begin_layout Plain Layout
31818 \begin_inset Note Note
31821 \begin_layout Plain Layout
31824 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
31827 \begin_layout Plain Layout
31830 texorpdfstring is in section
31831 \begin_inset CommandInset ref
31833 reference "sub:Formulas-in-Section"
31846 \begin_layout Plain Layout
31856 \begin_layout Plain Layout
31861 \begin_layout Plain Layout
31868 Chemical characters
31872 \begin_layout Plain Layout
31887 \begin_layout Subsection
31888 Chemical Symbols and Equations
31889 \begin_inset CommandInset label
31891 name "sub:Chemical-Symbols-and"
31899 \begin_layout Plain Layout
31900 Chemical characters ! Symbols
31909 \begin_layout Plain Layout
31919 \begin_layout Plain Layout
31928 \begin_layout Standard
31929 An example text from chemistry:
31932 \begin_layout Quote
31934 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31937 -ion reacts with two
31938 \begin_inset Formula $\mathrm{Na^{+}}$
31941 -ions to sodium sulfate
31942 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31946 The chemical equation for this is:
31947 \begin_inset Formula \[
31948 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
31955 \begin_layout Standard
31956 This chemical equation can directly be created as formula.
31957 To avoid that the symbols appear italic, everything is highlighted and
31958 changed by the shortcut
31961 \begin_inset Space ~
31966 to the upright font style.
31970 \begin_layout Plain Layout
31976 \begin_inset CommandInset ref
31978 reference "sub:Font-Styles"
31990 \begin_layout Subsection
31995 \begin_layout Plain Layout
32004 \begin_layout Standard
32005 Negative numbers often look ugly in formulas because the minus sign before
32006 the number is set with the same length as the minus operator sign.
32007 When writing the negative number in normal text, the minus sign appears
32011 \begin_layout Standard
32012 Thus, the problem disappears when converting the minus sign to mathematical
32016 \begin_layout Standard
32017 An example to visualize the problem:
32020 \begin_layout Standard
32022 \begin_inset Tabular
32023 <lyxtabular version="3" rows="3" columns="2">
32025 <column alignment="right" valignment="top" width="0">
32026 <column alignment="left" valignment="top" width="0">
32028 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32031 \begin_layout Plain Layout
32037 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
32040 \begin_layout Plain Layout
32048 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32051 \begin_layout Plain Layout
32057 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32060 \begin_layout Plain Layout
32061 \begin_inset Formula $x=-2$
32071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32074 \begin_layout Plain Layout
32080 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
32083 \begin_layout Plain Layout
32084 \begin_inset Formula $x=\textrm{-}2$
32100 \begin_layout Subsection
32101 Comma as Decimal Separator
32105 \begin_layout Plain Layout
32114 \begin_layout Standard
32115 In LaTeX a comma inside a formula is used, according to the English convention,
32116 as number group separator.
32117 So there will be space added behind all commas in formulas.
32120 \begin_layout Standard
32121 To avoid this, the comma is highlighted and changed to mathematical text
32125 \begin_inset Space ~
32133 \begin_layout Standard
32134 To use all formula commas in the document as decimal separator, the file
32143 \begin_layout Plain Layout
32148 is part of the LaTeX-package
32156 \begin_layout Plain Layout
32158 \begin_inset VSpace 4mm
32175 \begin_layout Plain Layout
32181 is loaded with the LaTeX-preamble line
32184 \begin_layout Standard
32192 \begin_layout Subsection
32194 \begin_inset CommandInset label
32196 name "sub:Physical-Vectors"
32204 \begin_layout Plain Layout
32213 \begin_layout Standard
32214 Predefined vectors are offered by the LaTeX-package
32222 \begin_layout Plain Layout
32227 should be part of every LaTeX standard installation.
32236 \begin_layout Plain Layout
32242 that is loaded with the LaTeX-preamble line
32245 \begin_layout Standard
32253 \begin_layout Standard
32257 \begin_layout Plain Layout
32267 \begin_inset Note Note
32270 \begin_layout Plain Layout
32271 The following table will only be displayed when the LaTeX-package
32280 The following commands are defined:
32283 \begin_layout Standard
32285 \begin_inset Tabular
32286 <lyxtabular version="3" rows="4" columns="2">
32288 <column alignment="center" valignment="top" width="0">
32289 <column alignment="center" valignment="top" width="0">
32291 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32294 \begin_layout Plain Layout
32300 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32303 \begin_layout Plain Layout
32311 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32314 \begin_layout Plain Layout
32324 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32327 \begin_layout Plain Layout
32328 \begin_inset Formula $\Bra {\psi}$
32338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32341 \begin_layout Plain Layout
32351 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32354 \begin_layout Plain Layout
32355 \begin_inset Formula $\Ket {\psi}$
32365 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32368 \begin_layout Plain Layout
32380 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32383 \begin_layout Plain Layout
32384 \begin_inset Formula $\Braket {\psi|\phi}$
32400 \begin_layout Standard
32407 assures that all vertical bars are set in the size of the surrounding brackets:
32408 \begin_inset Formula \[
32409 \Braket {\phi|J=\frac{3}{2}\,,\, M_{J}}\]
32417 \begin_layout Plain Layout
32427 \begin_inset Note Note
32430 \begin_layout Plain Layout
32431 The following will be displayed when the LaTeX-package
32443 \begin_layout Standard
32444 You need to install the LaTeX-package
32448 to see the rest of this subsection in the output.
32451 \begin_layout Standard
32455 \begin_layout Plain Layout
32467 \begin_layout Standard
32474 can also be achieved using the command
32480 , that is described in
32481 \begin_inset CommandInset ref
32483 reference "sub:Automatic-Bracket-Size"
32490 \begin_layout Subsection
32491 Self-defined Fractions
32492 \begin_inset CommandInset label
32494 name "sub:Self-defined-Fractions"
32502 \begin_layout Plain Layout
32503 Fractions ! self-defined
32511 \begin_layout Standard
32512 To define custom commands for fractions, the command
32522 \begin_layout Plain Layout
32530 is used in the following scheme:
32533 \begin_layout Standard
32546 bracket}{fraction bar thickness}{style}
32547 \begin_inset Newline newline
32554 \begin_layout Plain Layout
32569 \begin_layout Plain Layout
32576 {numerator}{denominator}
32579 \begin_layout Standard
32580 The style is a number in the range of 0
32581 \begin_inset Space \thinspace{}
32585 \begin_inset Space \thinspace{}
32591 \begin_layout Standard
32593 \begin_inset Tabular
32594 <lyxtabular version="3" rows="5" columns="2">
32596 <column alignment="center" valignment="top" width="0">
32597 <column alignment="center" valignment="top" width="0">
32599 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32602 \begin_layout Plain Layout
32608 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32611 \begin_layout Plain Layout
32619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32622 \begin_layout Plain Layout
32628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32631 \begin_layout Plain Layout
32632 display style formula
32639 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32642 \begin_layout Plain Layout
32648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32651 \begin_layout Plain Layout
32659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32662 \begin_layout Plain Layout
32668 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32671 \begin_layout Plain Layout
32679 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32682 \begin_layout Plain Layout
32688 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32691 \begin_layout Plain Layout
32705 \begin_layout Standard
32706 When no style is given, the size is adjusted to the surrounding environment
32707 like for the command
32716 \begin_layout Standard
32717 When no fraction bar thickness is given, the predefined value of 0.4
32718 \begin_inset Space \thinspace{}
32724 \begin_layout Standard
32725 \begin_inset VSpace medskip
32728 For example, the commands
32741 \begin_inset CommandInset ref
32743 reference "sub:Fractions"
32747 are defined with the commands
32750 \begin_layout Standard
32759 genfrac{}{}{}{0}{#1}{#2}}
32762 \begin_layout Standard
32766 \begin_layout Standard
32775 genfrac{(}{)}{0pt}{1}{#1}{#2}}
32778 \begin_layout Standard
32779 \begin_inset VSpace medskip
32782 To define a fraction where the fraction bar thickness can be given as optional
32783 argument, the following line is inserted to the LaTeX-preamble:
32786 \begin_layout Standard
32795 genfrac{}{}{#1}{}{#2}{#3}}
32798 \begin_layout Standard
32800 \begin_inset Formula \begin{align*}
32801 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
32802 \text{Result} & & \fracS [1mm]{A}{B} & & \fracS [5mm]{A}{B}\end{align*}
32806 As one can see, the distance of the numerator and the denominator to the
32807 fraction bar is round about three times the bar thickness.
32810 \begin_layout Subsection
32812 \begin_inset CommandInset label
32814 name "sub:Canceled-Formulas"
32822 \begin_layout Plain Layout
32831 \begin_layout Standard
32832 To cancel formulas or formula parts, the LaTeX-package
32840 \begin_layout Plain Layout
32845 is part of every LaTeX standard installation.
32854 \begin_layout Plain Layout
32860 has to be loaded with the LaTeX-preamble line
32863 \begin_layout Standard
32868 usepackage[samesize]{cancel}
32871 \begin_layout Standard
32872 There are four ways to cancel formulas:
32875 \begin_layout Standard
32877 \begin_inset Tabular
32878 <lyxtabular version="3" rows="5" columns="2">
32880 <column alignment="center" valignment="top" width="0">
32881 <column alignment="center" valignment="top" width="0">
32883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32886 \begin_layout Plain Layout
32892 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32895 \begin_layout Plain Layout
32897 \begin_inset Note Note
32900 \begin_layout Plain Layout
32913 are used here as spacer.
32925 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32928 \begin_layout Plain Layout
32937 \begin_layout Plain Layout
32951 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32954 \begin_layout Plain Layout
32955 \begin_inset Formula $\raisebox {4.5mm}{}\cancel {\int A=B}\raisebox {-2.5mm}{}$
32965 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32968 \begin_layout Plain Layout
32977 \begin_layout Plain Layout
32991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32994 \begin_layout Plain Layout
32995 \begin_inset Formula $\raisebox {4.5mm}{}\bcancel {\int A=B}\raisebox {-2.5mm}{}$
33005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33008 \begin_layout Plain Layout
33017 \begin_layout Plain Layout
33031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33034 \begin_layout Plain Layout
33035 \begin_inset Formula $\raisebox {4.5mm}{}\xcancel {\int A=B}\raisebox {-2.5mm}{}$
33045 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33048 \begin_layout Plain Layout
33052 \begin_inset Formula $\to$
33063 \begin_layout Plain Layout
33077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33080 \begin_layout Plain Layout
33081 \begin_inset Formula $\raisebox {7mm}{}\cancelto {1}{\int A=B}\raisebox {-2.5mm}{}\hspace {3mm}$
33097 \begin_layout Standard
33104 is especially suitable to visualize the reduction of fractions within formulas:
33105 \begin_inset Formula \[
33106 \frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto {2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel {1+b^{2}}}\]
33113 \begin_layout Subsection
33114 Formulas in Section Headings
33115 \begin_inset CommandInset label
33117 name "sub:Formulas-in-Section"
33125 \begin_layout Plain Layout
33126 Formula ! in section headings
33134 \begin_layout Standard
33135 When formulas are used in section headings, the following has to be taken
33139 \begin_layout Standard
33140 \begin_inset Note Greyedout
33143 \begin_layout Plain Layout
33152 \begin_layout Plain Layout
33153 Packages ! hyperref
33158 support is enabled in the document settings dialog under
33161 \begin_inset Space ~
33166 , PDF-bookmarks are created for every section heading in the table of contents.
33167 If a section heading contains formulas, they are incorrectly displayed
33168 in the bookmark text, because formulas in bookmarks infringe the PDF convention
33177 \begin_layout Standard
33178 Both problems can be solved by inserting at the end of the section heading
33179 a short title with the menu
33181 Insert\SpecialChar \menuseparator
33183 \begin_inset Space ~
33189 Short titles are used as alternative for multiline section headings to
33190 keep the table of contents clearly arranged.
33191 Only the short title appears in the table of contents and therefore also
33192 in the PDF-bookmark.
33195 \begin_layout Standard
33196 When formulas should be used in the table of contents but
33200 is used, one can use the following command in TeX-mode:
33203 \begin_layout Standard
33208 texorpdfstring{part}{alternative}
33212 \begin_layout Plain Layout
33223 \begin_layout Standard
33224 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
33225 This can be characters, formulas, footnotes, but also cross-references.
33226 The alternative is used instead of the part for the bookmark.
33229 \begin_layout Standard
33230 Here are two example headings:
33231 \begin_inset VSpace -3mm
33238 \begin_layout Plain Layout
33250 \begin_layout Subsubsection
33251 Heading without formula in table of contents
33252 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33256 \begin_inset OptArg
33259 \begin_layout Plain Layout
33260 Heading without formula in table of contents
33268 \begin_layout Subsubsection
33269 Heading with formula in table of contents
33273 \begin_layout Plain Layout
33283 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
33290 \begin_layout Plain Layout
33300 \begin_layout Standard
33304 \begin_layout Plain Layout
33313 In the first heading a short title was used, in the second one
33322 \begin_layout Standard
33323 To get the same formatting as for the other headings, the complete heading
33326 boldmath environment
33332 \begin_layout Plain Layout
33334 \begin_inset CommandInset ref
33336 reference "sub:Bold-Formulas"
33348 \begin_layout Subsection
33349 Formulas in multi-column Text
33353 \begin_layout Plain Layout
33354 Formula ! in multi-column text
33362 \begin_layout Standard
33363 Formulas in multi-column text are often too wide to fit into a column and
33364 thus need to be set over the whole page width.
33365 This is done by using the LaTeX-package
33373 \begin_layout Plain Layout
33378 is part of every LaTeX standard installation.
33387 \begin_layout Plain Layout
33388 Packages ! multicol
33393 , that is loaded with the LaTeX-preamble line
33396 \begin_layout Standard
33401 usepackage{multicol}
33404 \begin_layout Standard
33405 \begin_inset Note Greyedout
33408 \begin_layout Plain Layout
33409 Note herby that the setting
33412 \begin_inset Space ~
33419 Document\SpecialChar \menuseparator
33425 \begin_inset Space ~
33445 \begin_layout Standard
33446 Before the multi-column text the command
33449 \begin_layout Standard
33454 begin{multicols}{column number}
33457 \begin_layout Standard
33458 is written in TeX-mode.
33459 The column number is a number in the range of 2
33460 \begin_inset Space \thinspace{}
33464 \begin_inset Space \thinspace{}
33468 Before the formula the multi-column text is ended by inserting the command
33471 \begin_layout Standard
33479 \begin_layout Standard
33483 \begin_layout Standard
33484 Due to the command some space is automatically added before the formula.
33486 \begin_inset Space \thinspace{}
33489 mm vertical space is inserted before the formula.
33490 When the formula style
33496 \begin_layout Plain Layout
33498 \begin_inset CommandInset ref
33500 reference "sec:Formula-Styles"
33512 \begin_inset Space \thinspace{}
33515 mm space is inserted instead.
33518 \begin_layout Standard
33519 As example a multi-column text with a displayed formula:
33522 \begin_layout Standard
33526 \begin_layout Plain Layout
33530 begin{multicols}{2}
33535 Das Spektrum wird fouriertransformiert.
33536 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
33537 , Lösungsmittel) zu trennen.
33538 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
33539 nun das Aussehen des Ausgangssignals.
33540 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
33541 über alle Phasen integrieren muss.
33543 \begin_inset Formula $S$
33546 unser normiertes Ausgangssignal and
33547 \begin_inset Formula $P$
33550 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
33554 \begin_layout Plain Layout
33564 \begin_inset VSpace -6mm
33568 \begin_inset Formula \begin{equation}
33569 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
33577 \begin_layout Plain Layout
33581 begin{multicols}{2}
33587 \begin_inset Formula $S_{0}$
33590 das Signal ohne Gradient ist and the Normierungsbedingung
33591 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
33595 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
33597 \begin_inset Formula $\nicefrac{\pi}{2}$
33601 \begin_inset Space \thinspace{}
33604 -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
33605 das Signal zusätzlich abschwächt.
33606 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
33608 \begin_inset Formula $T_{2}$
33614 \begin_layout Standard
33618 \begin_layout Plain Layout
33630 \begin_layout Subsection
33631 Formulas with Description of Variables
33635 \begin_layout Plain Layout
33636 Formula ! with description of variables
33644 \begin_layout Standard
33645 To describe variables within a formula, like in formula
33646 \begin_inset CommandInset ref
33648 reference "eq:within"
33657 \begin_inset Formula $n$
33661 \begin_inset Space ~
33664 matrix is used with left aligned columns for the
33665 \begin_inset Formula $n$
33672 \begin_layout Plain Layout
33674 \begin_inset CommandInset ref
33676 reference "sec:Matrices"
33685 To set the description in a smaller size, before the matrix e.
33686 \begin_inset Space \thinspace{}
33690 \begin_inset Space ~
33703 \begin_layout Plain Layout
33705 \begin_inset CommandInset ref
33707 reference "sub:Font-Sizes"
33719 \begin_layout Standard
33720 When the formula style
33726 \begin_layout Plain Layout
33728 \begin_inset CommandInset ref
33730 reference "sec:Formula-Styles"
33751 \begin_layout Plain Layout
33758 only works in formulas with the style
33763 \begin_inset CommandInset ref
33765 reference "sub:Variable-Space"
33774 is inserted before and after the matrix to have the same separation of
33775 the matrix from the equation and the side margin.
33778 \begin_layout Standard
33779 When the formula style
33783 is used, the method described in
33784 \begin_inset CommandInset ref
33786 reference "sub:Flalign-Environment"
33790 is used to indent formulas.
33792 \begin_inset CommandInset ref
33794 reference "eq:within"
33798 consists of five columns whereas in the first two columns contain the equation,
33799 the third the matrix, and the last one an empty TeX-brace.
33800 \begin_inset Formula \begin{flalign}
33801 \hspace {30pt}F_{A} & =\rho·V·g & \footnotesize \begin{array}{ll}
33802 \rho & \textrm{density}\\
33803 V & \textrm{volume}\\
33804 g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
33811 \begin_layout Subsection
33812 Upright small Greek Letters
33813 \begin_inset CommandInset label
33815 name "sub:Upright-small-Greek"
33823 \begin_layout Plain Layout
33824 Greek letters ! upright
33832 \begin_layout Standard
33833 Most of the math fonts only provide italic small Greek letters.
33834 But for symbols of elementary particles like pions and neutrinos, upright
33835 Greek letters are needed.
33844 \begin_layout Plain Layout
33849 is part of the LaTeX-package
33857 \begin_layout Plain Layout
33859 \begin_inset VSpace 4mm
33876 \begin_layout Plain Layout
33882 that is loaded with the LaTeX-preamble line
33885 \begin_layout Standard
33890 usepackage{upgreek}
33893 \begin_layout Standard
33899 \begin_layout Plain Layout
33909 \begin_inset Note Note
33912 \begin_layout Plain Layout
33913 The following table will only be displayed when the LaTeX-package
33922 They are created when the command for a small Greek letters is started
33928 For example the command
33935 \begin_inset Formula $\uptau $
33941 \begin_layout Standard
33942 With these commands reactions of elementary particles can be typeset:
33943 \begin_inset Formula \[
33944 \uppi ^{+}\to\upmu ^{+}+\upnu _{\upmu }\]
33951 \begin_layout Standard
33952 The upright letters are more bold and wider than the italic ones.
33953 They should therefore not be used for units like
33954 \begin_inset Quotes eld
33958 \begin_inset Quotes erd
33964 \begin_layout Standard
33968 \begin_layout Plain Layout
33978 \begin_inset Note Note
33981 \begin_layout Plain Layout
33982 The following will be displayed when the LaTeX-package
33994 \begin_layout Standard
33995 You need to install the LaTeX-package
33999 to see the rest of this subsection in the output.
34002 \begin_layout Standard
34006 \begin_layout Plain Layout
34018 \begin_layout Subsection
34019 Text Characters in Formulas
34020 \begin_inset CommandInset label
34022 name "sub:Text-Characters-in"
34030 \begin_layout Plain Layout
34039 \begin_layout Standard
34040 In some cases you might want to insert text characters directly into formulas.
34041 When for example the centered dot · is often used in formulas like
34042 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
34045 , one would have to insert the command
34055 \begin_layout Plain Layout
34057 \begin_inset CommandInset ref
34059 reference "sub:Binary-Operators"
34068 all the time, because this character is defined in all encodings as text
34070 But the encoding can be changed by this LaTeX-preamble line:
34073 \begin_layout Standard
34078 Declare Inputtext{183}{
34088 f\SpecialChar \textcompwordmark{}
34092 \begin_layout Standard
34093 The character encoding (menu
34095 Document\SpecialChar \menuseparator
34096 Settings\SpecialChar \menuseparator
34099 ) specifies what character appears when a keyboard key is pressed.
34100 When the key for the character '·' is pressed, internally the command
34107 But this command is not available in a formula so that you would get LaTeX-erro
34109 With the changed encoding the right command is chosen automatically, depending
34110 on if the character was inserted into a formula or not.
34113 \begin_layout Standard
34114 The encoding of several characters is saved in definition files.
34115 Fore example the encoding
34119 is defined in the file
34123 that is in the installation folder of LaTeX.
34124 Encodings should only be changed via the LaTeX-preamble and not in the
34126 Otherwise own documents could not be edited by other LyX users working
34127 on other computers.
34130 \begin_layout Standard
34131 \begin_inset VSpace medskip
34134 Besides the centered dot, in this document the degree sign ° is defined
34135 with the following LaTeX-preamble line so that it can directly be inserted
34139 \begin_layout Standard
34144 DeclareInputtext{176}{
34154 f\SpecialChar \textcompwordmark{}
34158 \begin_layout Standard
34159 \begin_inset Newpage newpage
34165 \begin_layout Section
34167 Typographic Advises
34171 \begin_layout Plain Layout
34172 Typographic Advises
34180 \begin_layout Standard
34181 This section is a summary of the most important typographic rules, listed
34186 \begin_layout Plain Layout
34187 This collection was partly taken from the German semi-official dictionary
34189 \begin_inset Quotes eld
34193 \begin_inset Quotes erd
34197 \begin_inset CommandInset citation
34203 that lists some of the ISO rules.
34211 \begin_layout Itemize
34220 \begin_layout Plain Layout
34221 done with font styles, see
34222 \begin_inset CommandInset ref
34224 reference "sub:Font-Styles"
34234 \begin_inset Space \thinspace{}
34238 \begin_inset Newline newline
34241 Between the value and the unit is the smallest space, see
34242 \begin_inset CommandInset ref
34244 reference "sub:Predefined-Space"
34251 \begin_layout Itemize
34252 Percent and perthousand signs are set like physical units:
34253 \begin_inset Newline newline
34257 \begin_inset Space \thinspace{}
34263 \begin_layout Itemize
34264 The degree sign follows directly on the value: 15°, but not when it is used
34266 \begin_inset Space \thinspace{}
34272 \begin_layout Itemize
34273 In numbers with more than four digits the smallest space is inserted before
34274 every third digit to group them:
34284 \begin_inset Space \thinspace{}
34288 \begin_inset Space \thinspace{}
34294 \begin_layout Itemize
34295 For dimensionings like 120×90×40
34296 \begin_inset Space \thinspace{}
34299 cm the multiplication sign
34300 \begin_inset Quotes eld
34304 \begin_inset Quotes erd
34308 It is available with the LaTeX-command
34314 , but can also directly be inserted with some keyboard definitions.
34317 \begin_layout Itemize
34318 Functions with names consisting of several letters are set upright to avoid
34320 \begin_inset CommandInset ref
34322 reference "sub:Predefined-Functions"
34329 \begin_layout Itemize
34330 Indices consisting of several letters, are set upright:
34331 \begin_inset Formula $E_{\mathrm{kin}}$
34335 \begin_inset Newline newline
34338 Components of matrices are set italic:
34339 \begin_inset Formula $\hat{H}_{kl}$
34345 \begin_layout Itemize
34346 The differentiation/integration operator 'd', the Euler's number 'e', and
34347 the imaginary unit 'i' should be set upright, to avoid mixing them up with
34351 \begin_layout Standard
34352 \begin_inset Newpage newpage
34358 \begin_layout Section
34363 \begin_layout Plain Layout
34372 \begin_layout Standard
34373 Some characters and symbols can be created with several commands.
34374 Here is a list of the synonym commands:
34377 \begin_layout Standard
34378 \begin_inset VSpace bigskip
34382 \begin_inset Space \hfill{}
34386 \begin_inset Tabular
34387 <lyxtabular version="3" rows="12" columns="2">
34389 <column alignment="center" valignment="top" width="0pt">
34390 <column alignment="center" valignment="top" width="0pt">
34392 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34395 \begin_layout Plain Layout
34401 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34404 \begin_layout Plain Layout
34406 \begin_inset Note Note
34409 \begin_layout Plain Layout
34416 is only used as spacer.
34428 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34431 \begin_layout Plain Layout
34439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34442 \begin_layout Plain Layout
34446 \begin_layout Plain Layout
34459 \begin_layout Plain Layout
34473 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34476 \begin_layout Plain Layout
34484 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34487 \begin_layout Plain Layout
34497 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34500 \begin_layout Plain Layout
34508 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34511 \begin_layout Plain Layout
34521 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34524 \begin_layout Plain Layout
34532 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34535 \begin_layout Plain Layout
34543 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34546 \begin_layout Plain Layout
34554 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34557 \begin_layout Plain Layout
34565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34568 \begin_layout Plain Layout
34576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34579 \begin_layout Plain Layout
34589 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34592 \begin_layout Plain Layout
34600 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34603 \begin_layout Plain Layout
34613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34616 \begin_layout Plain Layout
34624 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34627 \begin_layout Plain Layout
34637 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34640 \begin_layout Plain Layout
34648 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34651 \begin_layout Plain Layout
34661 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34664 \begin_layout Plain Layout
34672 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34675 \begin_layout Plain Layout
34683 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34686 \begin_layout Plain Layout
34694 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34697 \begin_layout Plain Layout
34709 \begin_inset Space \hfill{}
34713 \begin_inset Tabular
34714 <lyxtabular version="3" rows="12" columns="2">
34716 <column alignment="center" valignment="top" width="0pt">
34717 <column alignment="center" valignment="top" width="0pt">
34719 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34722 \begin_layout Plain Layout
34728 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34731 \begin_layout Plain Layout
34739 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34742 \begin_layout Plain Layout
34750 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34753 \begin_layout Plain Layout
34765 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34768 \begin_layout Plain Layout
34776 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34779 \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
34813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34816 \begin_layout Plain Layout
34824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34827 \begin_layout Plain Layout
34835 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34838 \begin_layout Plain Layout
34846 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34849 \begin_layout Plain Layout
34857 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34860 \begin_layout Plain Layout
34868 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34871 \begin_layout Plain Layout
34881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34884 \begin_layout Plain Layout
34892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34895 \begin_layout Plain Layout
34905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34908 \begin_layout Plain Layout
34916 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34919 \begin_layout Plain Layout
34929 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34932 \begin_layout Plain Layout
34940 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34943 \begin_layout Plain Layout
34953 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34956 \begin_layout Plain Layout
34964 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
34967 \begin_layout Plain Layout
34977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34980 \begin_layout Plain Layout
34988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
34991 \begin_layout Plain Layout
35005 \begin_inset Space \hfill{}
35011 \begin_layout Standard
35012 \begin_inset Newpage newpage
35018 \begin_layout Bibliography
35019 \begin_inset CommandInset bibitem
35020 LatexCommand bibitem
35032 The LaTeX Companion
35035 Addison Wesley, 2004
35038 \begin_layout Bibliography
35039 \begin_inset CommandInset bibitem
35040 LatexCommand bibitem
35046 \begin_inset CommandInset href
35049 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
35053 of LaTeX's math abilities
35056 \begin_layout Bibliography
35057 \begin_inset CommandInset bibitem
35058 LatexCommand bibitem
35063 LaTeX tips and tricks-
35064 \begin_inset CommandInset href
35067 target "http://tug.org/TeXnik/"
35074 \begin_layout Bibliography
35075 \begin_inset CommandInset bibitem
35076 LatexCommand bibitem
35082 \begin_inset CommandInset href
35085 target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf"
35093 \begin_layout Plain Layout
35105 \begin_layout Bibliography
35106 \begin_inset CommandInset bibitem
35107 LatexCommand bibitem
35113 \begin_inset CommandInset href
35116 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
35120 of all symbols available with LaTeX-packages
35123 \begin_layout Bibliography
35124 \begin_inset CommandInset bibitem
35125 LatexCommand bibitem
35131 \begin_inset CommandInset href
35133 name "Documentation"
35134 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
35138 of the LaTeX-package
35146 \begin_layout Plain Layout
35147 Packages ! hyperref
35155 \begin_layout Bibliography
35156 \begin_inset CommandInset bibitem
35157 LatexCommand bibitem
35163 \begin_inset CommandInset href
35166 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
35177 \begin_inset CommandInset ref
35179 reference "sub:Operator-Limits"
35187 \begin_layout Plain Layout
35198 \begin_layout Bibliography
35199 \begin_inset CommandInset bibitem
35200 LatexCommand bibitem
35211 Auflage, Duden 2001
35214 \begin_layout Subsubsection*
35215 \begin_inset CommandInset index_print
35216 LatexCommand printindex