1 #LyX 2.1 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
20 % set fonts for nicer pdf view
21 \IfFileExists{lmodern.sty}
22 {\usepackage{lmodern}}{}
24 \fi % end if pdflatex is used
26 % solves the following problem:
27 % If the dection number consits of too many numerals the section heading
28 % will be printed in the TOC without a space between it and the section number.
29 % As solution more space between the number and the heading is inserted:
30 \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
31 \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
33 % To be able to enter the character ° and · directly in LyX,
35 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
36 \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
38 % increase link area for cross-references and autoname them,
39 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
40 \@ifundefined{extrasenglish}{\usepackage[english]{babel}}{}
41 \addto\extrasenglish{%
42 \renewcommand*{\equationautorefname}[1]{}%
43 \renewcommand{\sectionautorefname}{sec.\negthinspace}%
44 \renewcommand{\subsectionautorefname}{sec.\negthinspace}%
45 \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}%
48 % don't load packages twice
49 % see first footnote in sec. 9.3
50 \@ifundefined{textcolor}{\usepackage{color}}{}
52 % the pages of the TOC are numbered roman
53 % and a PDF-bookmark for the TOC is added
55 \let\myTOC\tableofcontents
56 \renewcommand{\tableofcontents}{%
58 \pdfbookmark[1]{\contentsname}{}
61 \pagenumbering{arabic}}
63 % insert additional vertical space of 1.5 mm between footnotes,
65 \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
67 % provides caption formatting
68 \setkomafont{captionlabel}{\bfseries}
71 \usepackage[samesize]{cancel}
73 % enables calculation of values
76 % for multiple columns used in sec. 24.7
82 % for the Fourier transformation symbol
85 % define a color, used in sec.9.3
86 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
88 % declare operators (see sec. 10.4 and sec. 15.2)
89 \DeclareMathOperator*{\Lozenge}{\blacklozenge}
90 \DeclareMathOperator{\sgn}{sgn}
92 \newcommand{\spce}{\textvisiblespace}
94 % example definitions for sec. 20.1
95 \newcommand{\gr}{\Longrightarrow}
96 \newcommand{\us}[1]{\underline{#1}}
97 \newcommand{\fb}[3]{\framebox#1#2{$#3$}}
98 \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
99 \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
101 % example macro from sec. 19.4
102 %\def\tagform@#1{\maketag@@@{|#1|}}
104 % macro from sec. 10.2
105 \def\clap#1{\hbox to 0pt{\hss #1\hss}}
106 \def\mathclap {\mathpalette \mathclapinternal}
107 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
110 % ------------------------------------
111 % used to check for needed LaTeX packages
114 % check for package eurosym
115 % used for the Euro symbol
117 \IfFileExists{eurosym.sty}
118 {\usepackage[gennarrow]{eurosym}
119 \setboolean{eurosym}{true}}
120 {\setboolean{eurosym}{false}}
122 % check for package braket
123 % used for physical vectors
125 \IfFileExists{braket.sty}
127 \setboolean{braket}{true}}
128 {\setboolean{braket}{false}}
130 % check for package cancel
132 \IfFileExists{cancel.sty}
134 \setboolean{cancel}{true}}
135 {\setboolean{cancel}{false}}
137 % check for package upgreek
139 \IfFileExists{upgreek.sty}
140 {\usepackage{upgreek}
141 \setboolean{upgreek}{true}}
142 {\setboolean{upgreek}{false}}
144 \options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
145 \use_default_options false
146 \maintain_unincluded_children false
148 \language_package default
153 \font_typewriter default
155 \font_default_family default
156 \use_non_tex_fonts false
162 \default_output_format default
164 \bibtex_command default
165 \index_command default
169 \pdf_title "LyX's Math Manual"
170 \pdf_author "LyX Team, Uwe Stöhr"
171 \pdf_subject "LyX-documentation about math"
172 \pdf_keywords "LyX, Mathed"
174 \pdf_bookmarksnumbered true
175 \pdf_bookmarksopen true
176 \pdf_bookmarksopenlevel 1
177 \pdf_breaklinks false
181 \pdf_pdfusetitle false
182 \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
185 \use_package amsmath 2
186 \use_package amssymb 2
187 \use_package cancel 0
189 \use_package mathdots 1
190 \use_package mathtools 0
191 \use_package mhchem 1
192 \use_package stackrel 0
193 \use_package stmaryrd 0
194 \use_package undertilde 0
196 \cite_engine_type default
200 \paperorientation portrait
204 \notefontcolor #0000ff
211 \paragraph_separation skip
213 \quotes_language english
216 \paperpagestyle plain
220 \tracking_changes false
221 \output_changes false
224 \html_be_strict false
230 LyX's detailed Math manual
238 \begin_layout Plain Layout
240 If you have comments or error corrections, please send them to the LyX Documenta
244 \begin_inset CommandInset href
246 name "lyx-docs@lists.lyx.org"
247 target "lyx-docs@lists.lyx.org?subject=LyX's Math manual"
258 \begin_inset Note Note
261 \begin_layout Plain Layout
268 \begin_inset Newline newline
272 \begin_inset Newline newline
280 \begin_layout Standard
281 \begin_inset CommandInset toc
282 LatexCommand tableofcontents
289 \begin_layout Standard
290 \begin_inset Note Note
293 \begin_layout Plain Layout
294 To export this document to PDF, PS or DVI the LaTeX-packages
296 braket, cancel, eurosym, mathdots, mhchem
303 If they are not installed the document can be exported anyway but the sections
304 where the packages are required will not appear in the output.
309 ; if it is not installed, this file cannot be exported.
312 \begin_layout Plain Layout
313 The latest PDF-version of this document can be found here:
314 \begin_inset Newline newline
319 http://wiki.lyx.org/LyX/DocumentationDevelopment#Math
327 \begin_layout Standard
328 \begin_inset Newpage newpage
334 \begin_layout Section
338 \begin_layout Standard
339 This document explains LyX's math features and is furthermore a collection
340 of LaTeX-commands used for mathematical characters and constructs.
341 The explanations are designed for the usage of commands.
342 It is therefore required that you have read the section
353 \begin_layout Standard
354 Most of the characters and many constructs explained in this manual are
355 also accessible via the menu
359 \SpecialChar \menuseparator
375 But everybody who has to write lots of formulas will notice that it is
376 much faster to use commands instead of the math toolbar.
377 Therefore this manual is focused on commands but also mentions the correspondin
378 g toolbar buttons when available.
381 \begin_layout Standard
382 If not specially mentioned the commands are only available within formulas.
383 To be able to use all commands explained in this document, the option
387 must be checked in the document settings (menu
389 Document\SpecialChar \menuseparator
390 Settings\SpecialChar \menuseparator
401 \begin_layout Plain Layout
404 Use AMS math package automatically
410 \begin_layout Plain Layout
419 -math when math constructs are found that are supported by LyX.
427 \begin_layout Standard
428 This document doesn't list all
432 \begin_layout Plain Layout
445 \begin_layout Plain Layout
450 \begin_layout Plain Layout
459 -math commands is in the file
462 \begin_inset CommandInset href
465 target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf"
471 , which is part of every LaTeX standard installation.
476 for lucidity reasons.
479 \begin_layout Section
483 \begin_layout Standard
484 To create an inline formula
485 \begin_inset Index idx
488 \begin_layout Plain Layout
494 that is embedded into a text line, use one of the shortcuts
500 or the toolbar button
501 \begin_inset Graphics
502 filename ../images/math-mode.png
508 \begin_inset Newline newline
511 To create a display style formula
512 \begin_inset Index idx
515 \begin_layout Plain Layout
516 Formula ! display style
521 which will appear bigger, has a different format, and will be in a separate
522 paragraph, use one of these shortcuts:
531 \begin_layout Standard
532 To change a display style formula to an inline formula, set the cursor into
533 the formula and use one of the shortcuts
541 Edit\SpecialChar \menuseparator
542 Math\SpecialChar \menuseparator
546 The same way is used to change an inline formula to a display style formula.
549 \begin_layout Standard
550 To display parts of an inline formula in the size of a display style formula,
558 \begin_inset Index idx
561 \begin_layout Plain Layout
570 Then a new blue box appears in which the desired formula part is inserted.
573 \begin_layout Standard
574 Only inline formulas are allowed inside tables.
577 \begin_layout Standard
582 can be turned on in the menu
584 View\SpecialChar \menuseparator
588 When you click there on
589 \begin_inset Quotes eld
593 \begin_inset Quotes erd
596 the toolbar will be shown permanently at the bottom; this state is visualized
601 menu with a checkmark.
602 When you click in this state again on
603 \begin_inset Quotes eld
607 \begin_inset Quotes erd
618 is only shown when the cursor is within a formula; this state is visualized
619 by the renaming of the menu entry from
620 \begin_inset Quotes eld
624 \begin_inset Quotes erd
628 \begin_inset Quotes eld
636 \begin_inset Quotes erd
642 \begin_layout Standard
644 \begin_inset Index idx
647 \begin_layout Plain Layout
653 is invoked by pressing the toolbar button
654 \begin_inset Graphics
655 filename ../images/ert-insert.png
662 Insert\SpecialChar \menuseparator
667 \begin_layout Plain Layout
683 \begin_inset Note Note
686 \begin_layout Plain Layout
687 In LyX there are three
688 \begin_inset Quotes eld
692 \begin_inset Quotes erd
695 that appear in the output with sub- and superscript letters: TeX, LaTeX
699 \begin_layout Plain Layout
700 To avoid that these names are recognized as proper names, a TeX-brace pair
709 \begin_layout Standard
710 To change the LaTeX-preamble
711 \begin_inset Index idx
714 \begin_layout Plain Layout
722 Document\SpecialChar \menuseparator
723 Settings\SpecialChar \menuseparator
728 \begin_layout Plain Layout
744 \begin_layout Standard
745 To edit matrices, case differentiations and multiline formulas subsequently,
748 Edit\SpecialChar \menuseparator
753 Edit\SpecialChar \menuseparator
755 \begin_inset space \thinspace{}
759 \begin_inset space \thinspace{}
769 When lines and columns are swapped via the menu, the column or line where
770 the cursor is in is exchanged with the column to the right or the line
772 Is the cursor in the last column or row, the exchange is done with the
773 column to the left or the line above.
776 \begin_layout Standard
777 To write text in formulas
781 \begin_layout Plain Layout
782 For multiline formulas the command
789 \begin_inset CommandInset ref
791 reference "sub:Text-in-multiline"
805 \begin_inset Index idx
808 \begin_layout Plain Layout
815 \begin_inset Index idx
818 \begin_layout Plain Layout
825 This mode is invoked with the shortcut
831 or by the insertion of the command
838 \begin_inset Index idx
841 \begin_layout Plain Layout
850 The text appears black in LyX and can therefore be distinguished from the
851 other formula parts which appear blue.
852 In the output mathematical text is set upright, in contrary to other formula
856 \begin_layout Subsection*
860 \begin_layout Standard
861 Most of the LaTeX-commands for math constructs have the following scheme:
864 \begin_layout Standard
880 \begin_layout Standard
881 A command always starts with a backslash
882 \begin_inset Quotes gld
892 \begin_inset Quotes grd
896 To omit optional arguments, also omit the associated brackets.
897 The braces around the required arguments are named in this document as
899 \begin_inset Index idx
902 \begin_layout Plain Layout
909 If you add in a formula a left brace to a command name, LyX automatically
911 In all other cases TeX-braces are created in formulas with the command
919 TeX-braces appear red in LyX, in contrary to normal braces which appear
921 In TeX-mode no command is needed to get TeX-braces.
922 TeX-braces don't appear in the output.
925 \begin_layout Standard
926 When commands without arguments, like commands for symbols are entered in
927 TeX-mode, a space character must
931 be behind the command to end it.
932 This space doesn't appear in the output.
933 When the space should appear in the output, the space must be followed
934 by a protected space in normal text.
937 \begin_layout Standard
938 A protected space is inserted with
941 arg "command-alternatives space-insert protected ; math-space"
947 \begin_layout Subsection*
948 \begin_inset Newpage newpage
954 \begin_layout Itemize
959 \begin_layout Plain Layout
960 This visible space character can be created with the command
967 \begin_inset Index idx
970 \begin_layout Plain Layout
978 , inserted in TeX-mode.
987 \begin_layout Plain Layout
1000 denotes a space character to be input.
1003 \begin_layout Itemize
1005 \begin_inset Formula $\to$
1008 denotes the usage of the corresponding arrow key on the keyboard.
1013 key can often be used instead of
1014 \begin_inset Formula $\to$
1018 \begin_inset Formula $\downarrow$
1026 \begin_inset Formula $\leftarrow$
1030 \begin_inset Formula $\uparrow$
1036 \begin_layout Subsection*
1040 \begin_layout Standard
1042 \begin_inset Float table
1048 \begin_layout Plain Layout
1050 \begin_inset Caption Standard
1052 \begin_layout Plain Layout
1053 \begin_inset CommandInset label
1055 name "tab:Available-units"
1067 \begin_layout Plain Layout
1069 \begin_inset Tabular
1070 <lyxtabular version="3" rows="13" columns="2">
1071 <features rotate="0" tabularvalignment="middle">
1072 <column alignment="center" valignment="top">
1073 <column alignment="center" valignment="top">
1075 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1078 \begin_layout Plain Layout
1084 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1087 \begin_layout Plain Layout
1095 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1098 \begin_layout Plain Layout
1104 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1107 \begin_layout Plain Layout
1115 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1118 \begin_layout Plain Layout
1124 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1127 \begin_layout Plain Layout
1135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1138 \begin_layout Plain Layout
1144 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1147 \begin_layout Plain Layout
1149 \begin_inset space \thinspace{}
1153 \begin_inset space \thinspace{}
1163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1166 \begin_layout Plain Layout
1172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1175 \begin_layout Plain Layout
1177 \begin_inset space \thinspace{}
1181 \begin_inset space \thinspace{}
1191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1194 \begin_layout Plain Layout
1200 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1203 \begin_layout Plain Layout
1205 \begin_inset space \thinspace{}
1209 \begin_inset space \thinspace{}
1219 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1222 \begin_layout Plain Layout
1228 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1231 \begin_layout Plain Layout
1233 \begin_inset space \thinspace{}
1237 \begin_inset space \thinspace{}
1247 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1250 \begin_layout Plain Layout
1256 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1259 \begin_layout Plain Layout
1261 \begin_inset space \thinspace{}
1265 \begin_inset space \thinspace{}
1275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1278 \begin_layout Plain Layout
1284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1287 \begin_layout Plain Layout
1289 \begin_inset space \thinspace{}
1293 \begin_inset Formula $\approx$
1297 \begin_inset space \thinspace{}
1307 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1310 \begin_layout Plain Layout
1316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1319 \begin_layout Plain Layout
1321 \begin_inset space \thinspace{}
1325 \begin_inset space \thinspace{}
1335 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1338 \begin_layout Plain Layout
1344 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1347 \begin_layout Plain Layout
1351 \begin_inset Quotes eld
1357 \begin_inset Quotes erd
1367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1370 \begin_layout Plain Layout
1376 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1379 \begin_layout Plain Layout
1381 \begin_inset Quotes eld
1389 \begin_inset Quotes erd
1399 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1402 \begin_layout Plain Layout
1408 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1411 \begin_layout Plain Layout
1413 \begin_inset space \thinspace{}
1417 \begin_inset Formula $\nicefrac{1}{18}$
1421 \begin_inset space \thinspace{}
1442 \begin_layout Standard
1443 \begin_inset Newpage newpage
1449 \begin_layout Section
1453 \begin_layout Subsection
1455 \begin_inset Index idx
1458 \begin_layout Plain Layout
1465 \begin_inset Index idx
1468 \begin_layout Plain Layout
1475 \begin_inset Index idx
1478 \begin_layout Plain Layout
1483 \begin_layout Plain Layout
1494 \begin_layout Plain Layout
1507 \begin_inset Index idx
1510 \begin_layout Plain Layout
1515 \begin_layout Plain Layout
1526 \begin_layout Plain Layout
1541 \begin_layout Standard
1542 Indices are created with an underscore
1543 \begin_inset Quotes eld
1547 \begin_inset Quotes erd
1550 or via the math toolbar button
1551 \begin_inset Graphics
1552 filename ../images/math-subscript.png
1557 , exponents with a caret
1558 \begin_inset Quotes eld
1562 \begin_inset Quotes erd
1565 or via the math toolbar button
1566 \begin_inset Graphics
1567 filename ../images/math-superscript.png
1575 \begin_layout Standard
1577 \begin_inset Tabular
1578 <lyxtabular version="3" rows="4" columns="2">
1579 <features rotate="0" tabularvalignment="middle">
1580 <column alignment="center" valignment="top" width="0pt">
1581 <column alignment="center" valignment="top" width="0pt">
1583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1586 \begin_layout Plain Layout
1592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1595 \begin_layout Plain Layout
1597 \begin_inset Note Note
1600 \begin_layout Plain Layout
1607 is only used as spacer.
1619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1622 \begin_layout Plain Layout
1628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1631 \begin_layout Plain Layout
1632 \begin_inset Formula $B_{V}$
1642 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1645 \begin_layout Plain Layout
1651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1654 \begin_layout Plain Layout
1655 \begin_inset Formula $\raisebox{5mm}{}B^{V}$
1665 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1668 \begin_layout Plain Layout
1673 \begin_layout Plain Layout
1687 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1690 \begin_layout Plain Layout
1691 \begin_inset Formula $\raisebox{5mm}{}B^{A}$
1707 \begin_layout Standard
1708 As the caret is in some languages an accent, vowels will be accentuated
1709 in this case and not set as exponents
1713 \begin_layout Plain Layout
1714 Depending on the used keyboard settings this can also happen for characters
1721 To get exponents in this case, press
1725 after the caret as in the last example.
1728 \begin_layout Subsection
1730 \begin_inset CommandInset label
1732 name "sub:Fractions"
1737 \begin_inset Index idx
1740 \begin_layout Plain Layout
1749 \begin_layout Standard
1750 Fractions are generated with the command
1757 \begin_inset Index idx
1760 \begin_layout Plain Layout
1768 or via the math toolbar button
1769 \begin_inset Graphics
1770 filename ../images/math/frac.png
1776 The font size is adjusted automatically, depending on whether the fraction
1777 is in an inline or display style formula.
1778 With the math toolbar button
1779 \begin_inset Graphics
1780 filename ../images/math/frac-square.png
1785 you can select different fraction types.
1788 \begin_layout Standard
1796 \begin_inset Index idx
1799 \begin_layout Plain Layout
1807 a fraction can be created that always has the size of a display style formula.
1815 \begin_inset Index idx
1818 \begin_layout Plain Layout
1826 the fraction appears always with the size of an inline formula.
1830 \begin_layout Standard
1831 A line with the fraction
1832 \begin_inset Formula $\frac{1}{2}$
1835 that was created with the command
1844 \begin_layout Standard
1845 A line with the fraction
1846 \begin_inset Formula $\dfrac{1}{2}$
1849 that was created with the command
1858 \begin_layout Standard
1860 \begin_inset Tabular
1861 <lyxtabular version="3" rows="4" columns="2">
1862 <features rotate="0" tabularvalignment="middle">
1863 <column alignment="center" valignment="top" width="0pt">
1864 <column alignment="center" valignment="top" width="0pt">
1866 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1869 \begin_layout Plain Layout
1875 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
1878 \begin_layout Plain Layout
1880 \begin_inset Note Note
1883 \begin_layout Plain Layout
1890 is only used as spacer.
1902 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1905 \begin_layout Plain Layout
1912 \begin_layout Plain Layout
1922 \begin_inset Formula $\downarrow$
1930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1933 \begin_layout Plain Layout
1934 \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
1944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1947 \begin_layout Plain Layout
1954 \begin_layout Plain Layout
1964 \begin_inset Formula $\downarrow$
1972 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1975 \begin_layout Plain Layout
1976 \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
1986 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
1989 \begin_layout Plain Layout
1996 \begin_layout Plain Layout
2011 \begin_layout Plain Layout
2021 \begin_inset Formula $\downarrow$
2025 \begin_inset Formula $\downarrow\downarrow$
2033 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2036 \begin_layout Plain Layout
2037 \begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
2053 \begin_layout Standard
2054 \begin_inset VSpace bigskip
2058 \begin_inset Newpage newpage
2061 For nested fractions the command
2068 \begin_inset Index idx
2071 \begin_layout Plain Layout
2081 \begin_inset VSpace -3mm
2087 \begin_layout Standard
2088 \begin_inset Formula
2090 \textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
2091 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
2099 \begin_layout Standard
2100 The command for the example above is:
2103 \begin_layout Standard
2112 \begin_layout Plain Layout
2122 \begin_inset Formula $\downarrow$
2131 \begin_layout Plain Layout
2146 \begin_layout Plain Layout
2156 \begin_inset Formula $\downarrow$
2160 \begin_inset Formula $\downarrow$
2166 \begin_layout Standard
2167 \begin_inset VSpace medskip
2173 \begin_layout Standard
2180 sets the fraction always in the size of a displayed formula, also when
2181 it is part of another fraction.
2184 \begin_layout Standard
2185 It is possible to specify the alignment of the numerator.
2192 is used to left align it, the command
2205 centers the numerator.
2206 These fractions demonstrate the different alignments:
2209 \begin_layout Standard
2212 \begin_inset Formula
2214 \cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C}
2222 \begin_layout Standard
2223 \begin_inset Note Greyedout
2226 \begin_layout Plain Layout
2243 are no real LaTeX commands but represent the command
2247 cfrac[alignment]{numerator}{denominator}
2250 Therefore you cannot use them in TeX code.
2258 \begin_layout Standard
2259 \begin_inset VSpace medskip
2262 It is often advantageous to combine
2275 \begin_inset Formula
2277 \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
2285 \begin_layout Standard
2286 For inline fractions with a sloped fraction stroke you can use the command
2294 \begin_inset Index idx
2297 \begin_layout Plain Layout
2306 \begin_inset Formula $\nicefrac{5}{31}$
2316 \begin_inset Index idx
2319 \begin_layout Plain Layout
2328 \begin_inset Formula $\unitfrac{5}{31}$
2331 There is furthermore the command
2337 that offers to write a fraction in combination with a number:
2338 \begin_inset Formula $\unitfrac[2]{1}{3}$
2344 \begin_layout Standard
2345 \begin_inset Note Greyedout
2348 \begin_layout Plain Layout
2359 is not a real LaTeX command but the command
2360 \begin_inset Newline newline
2367 unitfrac[number]{numerator}{denominator}
2370 Therefore you cannot use it in TeX code.
2378 \begin_layout Standard
2379 How to define own fractions where the fraction stroke can be changed, is
2381 \begin_inset CommandInset ref
2383 reference "sub:Self-defined-Fractions"
2390 \begin_layout Standard
2391 \begin_inset Newpage newpage
2397 \begin_layout Subsection
2399 \begin_inset Index idx
2402 \begin_layout Plain Layout
2411 \begin_layout Standard
2412 Square roots are created with
2419 \begin_inset Index idx
2422 \begin_layout Plain Layout
2430 or the math toolbar button
2431 \begin_inset Graphics
2432 filename ../images/math/sqrt.png
2437 , all other roots with the command
2444 \begin_inset Index idx
2447 \begin_layout Plain Layout
2455 or with the math toolbar button
2456 \begin_inset Graphics
2457 filename ../images/math/root.png
2465 \begin_layout Standard
2467 \begin_inset Tabular
2468 <lyxtabular version="3" rows="3" columns="2">
2469 <features rotate="0" tabularvalignment="middle">
2470 <column alignment="center" valignment="top" width="0pt">
2471 <column alignment="center" valignment="top" width="0pt">
2473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2476 \begin_layout Plain Layout
2482 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2485 \begin_layout Plain Layout
2487 \begin_inset Note Note
2490 \begin_layout Plain Layout
2497 is only used as spacer.
2509 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2512 \begin_layout Plain Layout
2519 \begin_layout Plain Layout
2533 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2536 \begin_layout Plain Layout
2537 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
2547 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
2550 \begin_layout Plain Layout
2557 \begin_layout Plain Layout
2567 \begin_inset Formula $\downarrow$
2575 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
2578 \begin_layout Plain Layout
2579 \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
2595 \begin_layout Standard
2596 A square root can also be created with
2602 when the root index field is left empty.
2605 \begin_layout Standard
2606 With certain indices the distance to the root is too small, like in this
2608 \begin_inset Formula $\sqrt[\beta]{B}$
2612 \begin_inset Newline newline
2616 \begin_inset Formula $\beta$
2620 To avoid this, the commands
2627 \begin_inset Index idx
2630 \begin_layout Plain Layout
2645 \begin_inset Index idx
2648 \begin_layout Plain Layout
2656 are used with the following scheme:
2659 \begin_layout Standard
2673 \begin_layout Standard
2674 Distance is the number of Big Points (unit bp;
2675 \begin_inset Formula $\mathrm{72\, bp=1\, inch}$
2678 ), that the index should be moved to the left or top, resp..
2679 The commands are written to the index.
2680 This way the command
2681 \begin_inset Newline newline
2691 \begin_inset Formula $\to$
2697 \begin_inset Formula $\to$
2706 \begin_layout Plain Layout
2716 \begin_inset Formula $\to$
2720 \begin_inset Newline newline
2725 produces a correct typeset formula:
2726 \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
2732 \begin_layout Subsection
2733 Binomial Coefficients
2734 \begin_inset Index idx
2737 \begin_layout Plain Layout
2738 Binomial coefficients
2746 \begin_layout Standard
2747 Binomial coefficients are inserted with the command
2754 \begin_inset Index idx
2757 \begin_layout Plain Layout
2765 or with the submenu of the math toolbar button
2766 \begin_inset Graphics
2767 filename ../images/math/frac-square.png
2785 there are the commands
2792 \begin_inset Index idx
2795 \begin_layout Plain Layout
2810 \begin_inset Index idx
2813 \begin_layout Plain Layout
2822 For other brackets around binomial coeficients there are the commands
2829 \begin_inset Index idx
2832 \begin_layout Plain Layout
2847 \begin_inset Index idx
2850 \begin_layout Plain Layout
2861 \begin_layout Standard
2863 \begin_inset Tabular
2864 <lyxtabular version="3" rows="6" columns="2">
2865 <features rotate="0" tabularvalignment="middle">
2866 <column alignment="center" valignment="top" width="0pt">
2867 <column alignment="center" valignment="top" width="0pt">
2869 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2872 \begin_layout Plain Layout
2878 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
2881 \begin_layout Plain Layout
2883 \begin_inset Note Note
2886 \begin_layout Plain Layout
2893 is only used as spacer.
2905 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2908 \begin_layout Plain Layout
2915 \begin_layout Plain Layout
2925 \begin_inset Formula $\downarrow$
2933 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2936 \begin_layout Plain Layout
2937 \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
2947 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
2950 \begin_layout Plain Layout
2957 \begin_layout Plain Layout
2967 \begin_inset Formula $\downarrow$
2975 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2978 \begin_layout Plain Layout
2979 \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
2989 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
2992 \begin_layout Plain Layout
2999 \begin_layout Plain Layout
3009 \begin_inset Formula $\downarrow$
3017 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3020 \begin_layout Plain Layout
3021 \begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$
3031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3034 \begin_layout Plain Layout
3041 \begin_layout Plain Layout
3051 \begin_inset Formula $\downarrow$
3059 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3062 \begin_layout Plain Layout
3063 \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$
3073 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3076 \begin_layout Plain Layout
3083 \begin_layout Plain Layout
3093 \begin_inset Formula $\downarrow$
3101 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3104 \begin_layout Plain Layout
3105 \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$
3121 \begin_layout Subsection
3122 Case Differentiations
3123 \begin_inset Index idx
3126 \begin_layout Plain Layout
3127 Case differentiations
3135 \begin_layout Standard
3137 \begin_inset Tabular
3138 <lyxtabular version="3" rows="3" columns="2">
3139 <features rotate="0" tabularvalignment="middle">
3140 <column alignment="center" valignment="top" width="0pt">
3141 <column alignment="center" valignment="top" width="0pt">
3143 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3146 \begin_layout Plain Layout
3152 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3155 \begin_layout Plain Layout
3163 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3166 \begin_layout Plain Layout
3173 \begin_layout Plain Layout
3183 \begin_inset Formula $\to$
3187 \begin_inset Index idx
3190 \begin_layout Plain Layout
3203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3206 \begin_layout Plain Layout
3207 \begin_inset Formula $\begin{cases}
3218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3221 \begin_layout Plain Layout
3228 \begin_layout Plain Layout
3240 arg "newline-insert newline"
3248 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3251 \begin_layout Plain Layout
3252 \begin_inset Formula $\begin{cases}
3253 A & \textrm{for }x>0\\
3254 B & \textrm{for }x=0
3271 \begin_layout Standard
3278 or pressing the math toolbar button
3279 \begin_inset Graphics
3280 filename ../images/math/cases.png
3285 you can create new lines with the shortcut
3288 arg "newline-insert newline"
3291 or the table toolbar button
3292 \begin_inset Graphics
3293 filename ../images/tabular-feature_append-row.png
3301 \begin_layout Standard
3308 is also available via the menu
3310 Insert\SpecialChar \menuseparator
3311 Math\SpecialChar \menuseparator
3317 \begin_layout Subsection
3319 \begin_inset Index idx
3322 \begin_layout Plain Layout
3331 \begin_layout Standard
3339 \begin_inset Index idx
3342 \begin_layout Plain Layout
3350 every character can be displayed canceled.
3351 The characters are quasi accentuated by a slash.
3354 \begin_layout Standard
3356 \begin_inset Tabular
3357 <lyxtabular version="3" rows="4" columns="2">
3358 <features rotate="0" tabularvalignment="middle">
3359 <column alignment="center" valignment="top" width="0pt">
3360 <column alignment="center" valignment="top" width="0pt">
3362 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3365 \begin_layout Plain Layout
3371 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3374 \begin_layout Plain Layout
3382 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3385 \begin_layout Plain Layout
3393 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3396 \begin_layout Plain Layout
3397 \begin_inset Formula $\not=$
3407 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3410 \begin_layout Plain Layout
3420 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3423 \begin_layout Plain Layout
3424 \begin_inset Formula $\not\le$
3434 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3437 \begin_layout Plain Layout
3447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3450 \begin_layout Plain Layout
3451 \begin_inset Formula $\not\parallel$
3467 \begin_layout Standard
3468 The last example shows that not all negations look good.
3469 Therefore there are special commands for some negations (see
3470 \begin_inset CommandInset ref
3472 reference "sub:Mathematical-Symbols"
3477 \begin_inset CommandInset ref
3479 reference "sec:Relations"
3486 \begin_layout Subsection
3488 \begin_inset CommandInset label
3490 name "sub:Placeholders"
3495 \begin_inset Index idx
3498 \begin_layout Plain Layout
3505 \begin_inset Index idx
3508 \begin_layout Plain Layout
3509 Chemical characters ! Isotopes
3515 \begin_inset Index idx
3518 \begin_layout Plain Layout
3523 \begin_layout Plain Layout
3534 \begin_layout Plain Layout
3549 \begin_layout Standard
3551 \begin_inset space \thinspace{}
3555 \begin_inset space \space{}
3562 \begin_layout Plain Layout
3563 Typesetting isotopes and chemical symbols is described in
3564 \begin_inset CommandInset ref
3566 reference "sub:Chemical-Symbols-and"
3575 the following problem occurs:
3578 \begin_layout Standard
3580 \begin_inset Tabular
3581 <lyxtabular version="3" rows="2" columns="2">
3582 <features rotate="0" tabularvalignment="middle">
3583 <column alignment="center" valignment="top" width="0pt">
3584 <column alignment="center" valignment="top" width="0pt">
3586 <cell alignment="center" valignment="top" usebox="none">
3589 \begin_layout Plain Layout
3590 Indices created with sub- and superscripts:
3595 <cell alignment="center" valignment="top" usebox="none">
3598 \begin_layout Plain Layout
3599 \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
3609 <cell alignment="center" valignment="top" usebox="none">
3612 \begin_layout Plain Layout
3618 <cell alignment="center" valignment="top" usebox="none">
3621 \begin_layout Plain Layout
3622 \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
3636 \begin_inset Note Note
3639 \begin_layout Plain Layout
3646 is only used as spacer.
3654 \begin_layout Standard
3655 The shorter index is by default placed below or above the first character
3656 of the longer index.
3657 To avoid this there is the command
3664 \begin_inset Index idx
3667 \begin_layout Plain Layout
3675 or the math toolbar button
3676 \begin_inset space \thinspace{}
3683 \begin_layout Plain Layout
3684 can be found in the submenu of the toolbar button
3685 \begin_inset Graphics
3686 filename ../images/math/space.png
3697 \begin_inset Graphics
3698 filename ../images/math/phantom.png
3703 that creates one or more phantom characters.
3710 a small blue box appears that is superposed with two red arrows.
3711 The arrows indicate that the complete width and height of the box content
3712 will be created as placeholder.
3713 Phantom characters are accordingly placeholders with the size of the characters.
3716 \begin_layout Standard
3718 \begin_inset Tabular
3719 <lyxtabular version="3" rows="4" columns="2">
3720 <features rotate="0" tabularvalignment="middle">
3721 <column alignment="center" valignment="top">
3722 <column alignment="center" valignment="top">
3724 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3727 \begin_layout Plain Layout
3733 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3736 \begin_layout Plain Layout
3738 \begin_inset Note Note
3741 \begin_layout Plain Layout
3748 is only used as spacer.
3760 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3763 \begin_layout Plain Layout
3768 \begin_layout Plain Layout
3783 \begin_layout Plain Layout
3793 \begin_inset Formula $\to$
3800 \begin_layout Plain Layout
3814 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3817 \begin_layout Plain Layout
3818 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
3828 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3831 \begin_layout Plain Layout
3836 \begin_layout Plain Layout
3851 \begin_layout Plain Layout
3861 \begin_inset Formula $\to$
3868 \begin_layout Plain Layout
3882 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3885 \begin_layout Plain Layout
3886 \begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
3896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
3899 \begin_layout Plain Layout
3906 \begin_layout Plain Layout
3921 \begin_layout Plain Layout
3931 \begin_inset Formula $\to$
3938 \begin_layout Plain Layout
3952 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
3955 \begin_layout Plain Layout
3956 \begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
3972 \begin_layout Standard
3973 Furthermore there are the commands
3980 \begin_inset Index idx
3983 \begin_layout Plain Layout
3992 \begin_inset space ~
3996 \begin_inset Graphics
3997 filename ../images/math/vphantom.png
4009 \begin_inset Index idx
4012 \begin_layout Plain Layout
4021 \begin_inset space ~
4025 \begin_inset Graphics
4026 filename ../images/math/hphantom.png
4038 creates only space for the maximal height of the characters in the box
4039 but not for its width.
4046 creates only space for the width of the box content.
4047 Therefore the boxes of both commands have only one red arrow.
4050 \begin_layout Standard
4051 For example the command
4061 \begin_layout Plain Layout
4076 creates space for the height of the integral sign,
4080 \begin_layout Plain Layout
4087 creates an integral sign, see
4088 \begin_inset CommandInset ref
4090 reference "sub:Big-Operators"
4099 because this is the larger character.
4100 An example application is in
4101 \begin_inset CommandInset ref
4103 reference "sub:Multiline-Brackets"
4110 \begin_layout Standard
4111 Placeholders can also be used for text when they are inserted via the menu
4114 Insert\SpecialChar \menuseparator
4115 Formatting\SpecialChar \menuseparator
4121 \begin_layout Standard
4123 \begin_inset Newline newline
4127 \begin_inset Phantom Phantom
4130 \begin_layout Plain Layout
4139 \begin_layout Subsection
4141 \begin_inset Index idx
4144 \begin_layout Plain Layout
4151 \begin_inset Index idx
4154 \begin_layout Plain Layout
4155 Formula ! underlined
4163 \begin_layout Standard
4165 \begin_inset Tabular
4166 <lyxtabular version="3" rows="4" columns="2">
4167 <features rotate="0" tabularvalignment="middle">
4168 <column alignment="center" valignment="top" width="0pt">
4169 <column alignment="center" valignment="top" width="0pt">
4171 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4174 \begin_layout Plain Layout
4180 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4183 \begin_layout Plain Layout
4185 \begin_inset Note Note
4188 \begin_layout Plain Layout
4195 is only used as spacer.
4207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4210 \begin_layout Plain Layout
4217 \begin_layout Plain Layout
4227 \begin_inset Index idx
4230 \begin_layout Plain Layout
4243 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4246 \begin_layout Plain Layout
4247 \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
4257 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
4260 \begin_layout Plain Layout
4267 \begin_layout Plain Layout
4277 \begin_inset Index idx
4280 \begin_layout Plain Layout
4293 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
4296 \begin_layout Plain Layout
4297 \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
4307 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4310 \begin_layout Plain Layout
4317 \begin_layout Plain Layout
4332 \begin_layout Plain Layout
4346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4349 \begin_layout Plain Layout
4350 \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
4366 \begin_layout Standard
4367 In the last example it doesn't matter if first
4382 \begin_layout Standard
4383 To double underline use
4392 \begin_layout Standard
4393 It is possible to place up to 6 lines above or below characters.
4396 \begin_layout Standard
4397 \begin_inset VSpace bigskip
4400 Custom lines can be created using the command
4407 \begin_inset Index idx
4410 \begin_layout Plain Layout
4418 which has the following scheme:
4421 \begin_layout Standard
4426 rule[vertical offset]{length}{thickness}
4429 \begin_layout Standard
4430 The optional vertical offset shifts the line upwards (or downwards, when
4431 the value is negative).
4433 \begin_inset CommandInset ref
4435 reference "tab:Available-units"
4439 can be used for the values.
4440 Here are two example lines created with the commands
4441 \begin_inset Newline newline
4448 rule[-2ex]{3cm}{2pt}
4459 \begin_layout Standard
4461 \begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$
4467 \begin_layout Standard
4474 can also be used for text when a line is inserted via the menu
4476 Insert\SpecialChar \menuseparator
4477 Formatting\SpecialChar \menuseparator
4479 \begin_inset space ~
4487 \begin_layout Standard
4489 \begin_inset CommandInset line
4500 \begin_layout Subsection
4502 \begin_inset CommandInset label
4509 \begin_inset Index idx
4512 \begin_layout Plain Layout
4521 \begin_layout Standard
4522 There are different types of ellipses available.
4526 \begin_layout Plain Layout
4527 In the math toolbar in the submenu of the button
4528 \begin_inset Graphics
4529 filename ../images/math/ldots.png
4539 For listings dots at the baseline are used (
4546 \begin_inset Index idx
4549 \begin_layout Plain Layout
4557 ), while for operations dots are needed that are on the same height as the
4565 \begin_inset Index idx
4568 \begin_layout Plain Layout
4577 When using the command
4584 \begin_inset Index idx
4587 \begin_layout Plain Layout
4595 , LaTeX decides on the basis of the next character what type is used.
4598 \begin_layout Standard
4600 \begin_inset Tabular
4601 <lyxtabular version="3" rows="9" columns="2">
4602 <features rotate="0" tabularvalignment="middle">
4603 <column alignment="center" valignment="top" width="0pt">
4604 <column alignment="center" valignment="top" width="0pt">
4606 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4609 \begin_layout Plain Layout
4615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4618 \begin_layout Plain Layout
4626 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4629 \begin_layout Plain Layout
4634 \begin_layout Plain Layout
4649 \begin_layout Plain Layout
4663 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4666 \begin_layout Plain Layout
4667 \begin_inset Formula $A_{1},\dots,A_{n}$
4677 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4680 \begin_layout Plain Layout
4685 \begin_layout Plain Layout
4700 \begin_layout Plain Layout
4714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4717 \begin_layout Plain Layout
4718 \begin_inset Formula $A_{1}+\dots+A_{n}$
4728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4731 \begin_layout Plain Layout
4736 \begin_layout Plain Layout
4751 \begin_layout Plain Layout
4765 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4768 \begin_layout Plain Layout
4769 \begin_inset Formula $A_{1},\ldots,A_{n}$
4779 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4782 \begin_layout Plain Layout
4787 \begin_layout Plain Layout
4802 \begin_layout Plain Layout
4816 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4819 \begin_layout Plain Layout
4820 \begin_inset Formula $A_{1}+\cdots+A_{n}$
4830 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4833 \begin_layout Plain Layout
4841 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4844 \begin_layout Plain Layout
4845 \begin_inset Formula $\vdots$
4855 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
4858 \begin_layout Plain Layout
4866 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
4869 \begin_layout Plain Layout
4870 \begin_inset Formula $\ddots$
4880 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4883 \begin_layout Plain Layout
4891 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4894 \begin_layout Plain Layout
4895 \begin_inset Formula $\iddots$
4905 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
4908 \begin_layout Plain Layout
4910 \begin_inset space \thinspace{}
4913 matrix with the different dots
4918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
4921 \begin_layout Plain Layout
4922 \begin_inset Formula $\begin{array}{ccc}
4923 A_{11} & \cdots & A_{1m}\\
4924 \vdots & \ddots & \vdots\\
4925 A_{n1} & \cdots & A_{nm}
4942 \begin_layout Standard
4943 The ellipses available in menu
4945 Insert\SpecialChar \menuseparator
4947 \begin_inset space ~
4961 \begin_layout Standard
4962 \begin_inset VSpace medskip
4971 , one of the options
4973 Use mathdots package (automatically)
4975 must be set in the document settings under
4978 \begin_inset space ~
4984 \begin_inset Newline newline
4989 Use mathdots package
4991 will improve the appearance of all dots in the documents if their font
4992 style or size is not the default.
4995 \begin_layout Standard
4996 \begin_inset VSpace medskip
4999 Specially for matrices there are ellipses that span over several columns.
5000 They are created with the command
5007 \begin_inset Index idx
5010 \begin_layout Plain Layout
5018 , that has the following scheme:
5021 \begin_layout Standard
5026 hdotsfor[distance]{number of columns}
5029 \begin_layout Standard
5030 The number of columns specifies how many columns should be spanned.
5031 Distance is a factor for the distance between the dots.
5034 \begin_layout Standard
5035 In the following matrix the command
5041 was inserted in the first box of the second line, to get an ellipsis with
5042 a dot distance twice as long as with the command
5049 \begin_inset Formula
5051 \left(\begin{array}{cccc}
5060 Note that the matrix fields that should be spanned must be empty, otherwise
5061 you get LaTeX-errors.
5064 \begin_layout Standard
5065 \begin_inset VSpace bigskip
5068 Furthermore you can fill with the command
5075 \begin_inset Index idx
5078 \begin_layout Plain Layout
5086 the rest of a line with dots.
5087 The effect of these commands is the same as with
5094 \begin_inset CommandInset ref
5096 reference "sub:Variable-Space"
5103 \begin_layout Standard
5104 For example the command
5112 \begin_layout Plain Layout
5126 \begin_layout Standard
5127 \begin_inset Formula $A\dotfill B$
5133 \begin_layout Standard
5140 there is for a line the command
5147 \begin_inset Index idx
5150 \begin_layout Plain Layout
5161 \begin_layout Standard
5162 \begin_inset Formula $A\hrulefill B$
5168 \begin_layout Standard
5169 To use the commands for text, they have to be inserted in TeX-mode.
5172 \begin_layout Section
5174 \begin_inset CommandInset label
5181 \begin_inset Index idx
5184 \begin_layout Plain Layout
5193 \begin_layout Standard
5194 Matrices can be inserted via the math toolbar button
5195 \begin_inset Graphics
5196 filename ../images/dialog-show_mathmatrix.png
5203 Insert\SpecialChar \menuseparator
5204 Math\SpecialChar \menuseparator
5208 In the matrix dialog you can specify the number of columns and rows, the
5209 alignment and the decoration.
5210 The vertical alignment is only of importance for matrices in inline formulas:
5213 \begin_layout Standard
5214 The first matrix is top
5215 \begin_inset Formula $\begin{array}[t]{cccc}
5223 \begin_inset Formula $\begin{array}{cccc}
5230 and the third bottom
5231 \begin_inset Formula $\begin{array}[b]{cccc}
5241 \begin_layout Standard
5242 The horizontal alignment specifies how the column entries should be aligned.
5243 It is set by entering a letter for every column.
5248 denotes left aligned,
5257 To create for example a 4
5262 \begin_inset space ~
5265 matrix where the first column is left aligned, the second and third are
5266 centered and the last one is right aligned, one enters for the horizontal
5272 Normally in a matrix all columns are centered, therefore the default for
5280 \begin_layout Standard
5281 Horizontal alignment:
5284 \begin_layout Standard
5290 \begin_inset Formula $\begin{array}{lll}
5302 \begin_inset Formula $\begin{array}{ccc}
5314 \begin_inset Formula $\begin{array}{rrr}
5324 \begin_layout Standard
5325 To add or delete rows and columns subsequently, the math toolbar buttons
5327 \begin_inset Graphics
5328 filename ../images/tabular-feature_append-row.png
5334 \begin_inset Graphics
5335 filename ../images/tabular-feature_delete-row.png
5341 \begin_inset space \thinspace{}
5346 Edit\SpecialChar \menuseparator
5350 New rows can also be created with
5353 arg "newline-insert newline"
5359 \begin_layout Standard
5360 \begin_inset VSpace bigskip
5367 adds parentheses in the selected style around the matrix.
5368 Alternatively, parentheses can can either be created with the commands
5376 \begin_inset Index idx
5379 \begin_layout Plain Layout
5394 \begin_inset Index idx
5397 \begin_layout Plain Layout
5408 \begin_inset space ~
5414 \begin_inset CommandInset ref
5416 reference "sub:Automatic-Bracket-Size"
5420 , or by using the following commands:
5421 \begin_inset VSpace medskip
5427 \begin_layout Standard
5428 \begin_inset space \hfill{}
5432 \begin_inset Tabular
5433 <lyxtabular version="3" rows="4" columns="2">
5434 <features rotate="0" tabularvalignment="middle">
5435 <column alignment="center" valignment="top">
5436 <column alignment="center" valignment="top">
5438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5441 \begin_layout Plain Layout
5447 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5450 \begin_layout Plain Layout
5452 \begin_inset Note Note
5455 \begin_layout Plain Layout
5462 is only used as spacer.
5474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5477 \begin_layout Plain Layout
5484 \begin_layout Plain Layout
5498 \begin_inset space \thinspace{}
5506 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5509 \begin_layout Plain Layout
5510 \begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
5511 0 & \textrm{-}\mathrm{i}\\
5513 \end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
5523 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
5526 \begin_layout Plain Layout
5533 \begin_layout Plain Layout
5547 \begin_inset space \thinspace{}
5555 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5558 \begin_layout Plain Layout
5559 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
5560 0 & \textrm{-}\mathrm{i}\\
5562 \end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
5572 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5575 \begin_layout Plain Layout
5582 \begin_layout Plain Layout
5596 \begin_inset space \thinspace{}
5604 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5607 \begin_layout Plain Layout
5608 \begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
5609 0 & \textrm{-}\mathrm{i}\\
5611 \end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
5625 \begin_inset space \hfill{}
5629 \begin_inset Tabular
5630 <lyxtabular version="3" rows="4" columns="2">
5631 <features rotate="0" tabularvalignment="middle">
5632 <column alignment="center" valignment="top">
5633 <column alignment="center" valignment="top">
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
5665 \begin_layout Plain Layout
5679 \begin_inset space \thinspace{}
5687 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
5690 \begin_layout Plain Layout
5691 \begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
5692 0 & \textrm{-}\mathrm{i}\\
5694 \end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
5704 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5707 \begin_layout Plain Layout
5714 \begin_layout Plain Layout
5728 \begin_inset space \thinspace{}
5736 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5739 \begin_layout Plain Layout
5740 \begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
5741 0 & \textrm{-}\mathrm{i}\\
5743 \end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
5753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
5756 \begin_layout Plain Layout
5763 \begin_layout Plain Layout
5777 \begin_inset space \thinspace{}
5785 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
5788 \begin_layout Plain Layout
5789 \begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
5790 0 & \textrm{-}\mathrm{i}\\
5792 \end{array}\end{matrix}\raisebox{-5.3mm}{}$
5806 \begin_inset space \hfill{}
5812 \begin_layout Standard
5813 \begin_inset VSpace medskip
5817 \begin_inset space \thinspace{}
5821 \begin_inset space \space{}
5830 is inserted, a blue box appears between two vertical lines where the matrix
5832 \begin_inset Newline newline
5835 Note that decorated matrices ignore the vertical alignment.
5838 \begin_layout Standard
5839 \begin_inset VSpace bigskip
5842 As all multiline formulas are matrices, the length
5849 \begin_inset Index idx
5852 \begin_layout Plain Layout
5860 that is described in
5861 \begin_inset CommandInset ref
5863 reference "sub:Column-Separation"
5867 can also be used to change the column separation of matrices.
5870 \begin_layout Standard
5871 To change the row separation, the command
5878 \begin_inset Index idx
5881 \begin_layout Plain Layout
5890 It is used as follows:
5893 \begin_layout Standard
5900 arraystretch}{stretch factor}
5901 \begin_inset Index idx
5904 \begin_layout Plain Layout
5915 \begin_layout Standard
5922 assigns the stretch factor to the predefined command
5930 \begin_inset space \thinspace{}
5934 \begin_inset space \space{}
5937 the row separation, use the factor 2.
5938 This is then used for all following matrices.
5939 To go back to the original separation, assign the factor 1 to
5948 \begin_layout Standard
5949 To set matrices into a text line, the command
5956 \begin_inset Index idx
5959 \begin_layout Plain Layout
5968 When it is inserted a blue box with two dashed lines appears.
5969 In this box the matrix is inserted.
5972 \begin_layout Standard
5974 \begin_inset Formula $\left(\begin{smallmatrix}A & B\\
5976 \end{smallmatrix}\right)$
5982 \begin_layout Section
5983 Brackets and Delimiters
5984 \begin_inset Index idx
5987 \begin_layout Plain Layout
5994 \begin_inset Index idx
5997 \begin_layout Plain Layout
6006 \begin_layout Subsection
6007 Vertical Brackets and Delimiters
6008 \begin_inset Index idx
6011 \begin_layout Plain Layout
6020 \begin_layout Standard
6021 \begin_inset space \hfill{}
6025 \begin_inset Tabular
6026 <lyxtabular version="3" rows="9" columns="2">
6027 <features rotate="0" tabularvalignment="middle">
6028 <column alignment="center" valignment="top" width="0pt">
6029 <column alignment="center" valignment="top" width="0pt">
6031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6034 \begin_layout Plain Layout
6040 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6043 \begin_layout Plain Layout
6051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6054 \begin_layout Plain Layout
6060 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6063 \begin_layout Plain Layout
6064 \begin_inset Formula $($
6074 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6077 \begin_layout Plain Layout
6083 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6086 \begin_layout Plain Layout
6087 \begin_inset Formula $\{$
6097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6100 \begin_layout Plain Layout
6106 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6109 \begin_layout Plain Layout
6110 \begin_inset Formula $[$
6120 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6123 \begin_layout Plain Layout
6131 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6134 \begin_layout Plain Layout
6135 \begin_inset Formula $\langle$
6145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6148 \begin_layout Plain Layout
6156 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6159 \begin_layout Plain Layout
6160 \begin_inset Formula $\lceil$
6170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6173 \begin_layout Plain Layout
6181 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6184 \begin_layout Plain Layout
6185 \begin_inset Formula $\lfloor$
6195 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6198 \begin_layout Plain Layout
6204 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6207 \begin_layout Plain Layout
6208 \begin_inset Formula $/$
6218 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6221 \begin_layout Plain Layout
6227 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6230 \begin_layout Plain Layout
6231 \begin_inset Formula $|$
6245 \begin_inset space \hfill{}
6249 \begin_inset Tabular
6250 <lyxtabular version="3" rows="9" columns="2">
6251 <features rotate="0" tabularvalignment="middle">
6252 <column alignment="center" valignment="top" width="0pt">
6253 <column alignment="center" valignment="top" width="0pt">
6255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6258 \begin_layout Plain Layout
6264 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6267 \begin_layout Plain Layout
6275 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6278 \begin_layout Plain Layout
6284 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6287 \begin_layout Plain Layout
6288 \begin_inset Formula $)$
6298 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6301 \begin_layout Plain Layout
6307 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6310 \begin_layout Plain Layout
6311 \begin_inset Formula $\}$
6321 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6324 \begin_layout Plain Layout
6330 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6333 \begin_layout Plain Layout
6334 \begin_inset Formula $]$
6344 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6347 \begin_layout Plain Layout
6355 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6358 \begin_layout Plain Layout
6359 \begin_inset Formula $\rangle$
6369 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6372 \begin_layout Plain Layout
6380 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6383 \begin_layout Plain Layout
6384 \begin_inset Formula $\rceil$
6394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6397 \begin_layout Plain Layout
6405 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6408 \begin_layout Plain Layout
6409 \begin_inset Formula $\rfloor$
6419 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6422 \begin_layout Plain Layout
6432 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6435 \begin_layout Plain Layout
6436 \begin_inset Formula $\backslash$
6446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6449 \begin_layout Plain Layout
6457 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6460 \begin_layout Plain Layout
6461 \begin_inset Formula $\|$
6475 \begin_inset space \hfill{}
6481 \begin_layout Standard
6484 \begin_inset Note Greyedout
6487 \begin_layout Plain Layout
6492 In TeX-mode the command
6499 \begin_inset Index idx
6502 \begin_layout Plain Layout
6510 must be used for the backslash, because the command
6518 produces a line break there.
6526 \begin_layout Standard
6527 For all characters listed above the size can be adjusted with the commands
6528 described in the following two subsections.
6529 When using these commands, the characters < and > can directly be used
6530 instead of the commands
6545 \begin_layout Subsubsection
6547 \begin_inset CommandInset label
6549 name "sub:Manual-Bracket-Size"
6554 \begin_inset Index idx
6557 \begin_layout Plain Layout
6558 Bracket size ! manual
6566 \begin_layout Standard
6567 The bracket size can be specified manually by the LaTeX-commands
6574 \begin_inset Index idx
6577 \begin_layout Plain Layout
6610 denotes the smallest and
6616 the largest bracket size.
6619 \begin_layout Standard
6620 These commands are used to emphasize levels of brackets:
6623 \begin_layout Standard
6625 \begin_inset Tabular
6626 <lyxtabular version="3" rows="2" columns="2">
6627 <features rotate="0" tabularvalignment="middle">
6628 <column alignment="center" valignment="top" width="0pt">
6629 <column alignment="center" valignment="top" width="0pt">
6631 <cell alignment="center" valignment="top" usebox="none">
6634 \begin_layout Plain Layout
6635 all brackets in the same size:
6640 <cell alignment="center" valignment="top" usebox="none">
6643 \begin_layout Plain Layout
6644 \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
6654 <cell alignment="center" valignment="top" usebox="none">
6657 \begin_layout Plain Layout
6663 <cell alignment="center" valignment="top" usebox="none">
6666 \begin_layout Plain Layout
6667 \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
6681 \begin_inset Note Note
6684 \begin_layout Plain Layout
6691 is only used as spacer.
6699 \begin_layout Standard
6700 For the second formula the command
6710 \begin_layout Plain Layout
6724 \begin_layout Standard
6725 Here is an overview about all bracket sizes:
6728 \begin_layout Standard
6748 \begin_layout Plain Layout
6765 \begin_layout Plain Layout
6778 \begin_layout Plain Layout
6794 \begin_layout Standard
6796 \begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
6802 \begin_layout Standard
6809 -commands there is the variant
6816 \begin_inset Index idx
6819 \begin_layout Plain Layout
6827 that adds a bit more space between the bracket and its content, and the
6841 \begin_inset Index idx
6844 \begin_layout Plain Layout
6854 , that don't add additional space.
6859 at the end of the command
6865 is for a left bracket; for a right bracket this will be replaced by an
6871 A left or right bracket can each be an opening or closing bracket.
6874 \begin_layout Standard
6875 In the following table is a comparison of the variants:
6878 \begin_layout Standard
6880 \begin_inset Tabular
6881 <lyxtabular version="3" rows="5" columns="2">
6882 <features rotate="0" tabularvalignment="middle">
6883 <column alignment="center" valignment="middle">
6884 <column alignment="center" valignment="middle">
6886 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
6889 \begin_layout Plain Layout
6895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
6898 \begin_layout Plain Layout
6900 \begin_inset Note Note
6903 \begin_layout Plain Layout
6910 is only used as spacer.
6922 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6925 \begin_layout Plain Layout
6940 \begin_layout Plain Layout
6958 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
6961 \begin_layout Plain Layout
6962 \begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
6972 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
6975 \begin_layout Plain Layout
6990 \begin_layout Plain Layout
7008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7011 \begin_layout Plain Layout
7012 \begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
7022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7025 \begin_layout Plain Layout
7040 \begin_layout Plain Layout
7058 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7061 \begin_layout Plain Layout
7062 \begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
7072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7075 \begin_layout Plain Layout
7087 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7090 \begin_layout Plain Layout
7091 \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
7107 \begin_layout Subsubsection
7108 Automatic Bracket Size
7109 \begin_inset CommandInset label
7111 name "sub:Automatic-Bracket-Size"
7116 \begin_inset Index idx
7119 \begin_layout Plain Layout
7120 Bracket size ! automatic
7128 \begin_layout Standard
7129 Brackets with variable size can be inserted with the commands
7136 \begin_inset Index idx
7139 \begin_layout Plain Layout
7154 \begin_inset Index idx
7157 \begin_layout Plain Layout
7165 or via the math toolbar button
7166 \begin_inset Graphics
7167 filename ../images/dialog-show_mathdelimiter.png
7185 the wanted bracket must be inserted.
7186 The bracket size will then automatically be calculated for the output.
7189 \begin_layout Standard
7191 normal bracket: The command
7201 \begin_layout Plain Layout
7211 \begin_inset Formula $\downarrow$
7218 \begin_layout Plain Layout
7230 \begin_inset Formula
7240 \begin_layout Standard
7242 multiline bracket: The command
7254 \begin_layout Plain Layout
7264 \begin_inset Formula $\downarrow$
7271 \begin_layout Plain Layout
7285 \begin_inset Formula
7287 \ln\left(\frac{A}{C}\right)
7295 \begin_layout Standard
7311 \begin_inset space ~
7317 This has the advantage that you can see in LyX immediately the real bracket
7318 size and that the matching right bracket will be created too.
7319 \begin_inset Newline newline
7322 The command for the last example would then be:
7336 \begin_layout Plain Layout
7346 \begin_inset Formula $\downarrow$
7352 \begin_layout Standard
7353 To omit a left or right bracket, a dot is inserted for the omitted bracket.
7354 For example the command
7364 \begin_layout Plain Layout
7374 \begin_inset Formula $\downarrow$
7381 \begin_layout Plain Layout
7397 \begin_inset Formula
7399 \left.\frac{A}{B}\right\}
7418 will be converted by LyX to brackets in the right size when the document
7419 is reloaded and an omitted bracket will appear as dashed line.
7422 \begin_layout Standard
7423 \begin_inset VSpace bigskip
7426 Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
7434 \begin_inset Index idx
7437 \begin_layout Plain Layout
7445 is additionally available for all brackets and limits.
7446 With this command the height of the following character is adapted to the
7447 one of the surrounding brackets, what is e.
7448 \begin_inset space \thinspace{}
7452 \begin_inset space \space{}
7455 needed for physical vectors:
7456 \begin_inset Formula
7458 \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
7463 For physical vectors there is a special LaTeX-package, described in
7464 \begin_inset CommandInset ref
7466 reference "sub:Physical-Vectors"
7473 \begin_layout Subsection
7475 \begin_inset Index idx
7478 \begin_layout Plain Layout
7479 Brackets ! horizontal
7487 \begin_layout Standard
7489 \begin_inset Tabular
7490 <lyxtabular version="3" rows="4" columns="2">
7491 <features rotate="0" tabularvalignment="middle">
7492 <column alignment="center" valignment="top" width="0pt">
7493 <column alignment="center" valignment="top" width="0pt">
7495 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7498 \begin_layout Plain Layout
7500 \begin_inset Note Note
7503 \begin_layout Plain Layout
7510 is only used as spacer.
7520 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7523 \begin_layout Plain Layout
7531 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
7534 \begin_layout Plain Layout
7538 \begin_layout Plain Layout
7553 \begin_layout Plain Layout
7566 \begin_layout Plain Layout
7579 \begin_layout Plain Layout
7592 \begin_layout Plain Layout
7600 \begin_inset Index idx
7603 \begin_layout Plain Layout
7616 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
7619 \begin_layout Plain Layout
7620 \begin_inset Formula $\overbrace{A+B}^{3}$
7630 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7633 \begin_layout Plain Layout
7637 \begin_layout Plain Layout
7652 \begin_layout Plain Layout
7665 \begin_layout Plain Layout
7678 \begin_layout Plain Layout
7686 \begin_inset Index idx
7689 \begin_layout Plain Layout
7702 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7705 \begin_layout Plain Layout
7706 \begin_inset Formula $\underbrace{A+B}_{5}$
7716 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
7719 \begin_layout Plain Layout
7726 \begin_layout Plain Layout
7741 \begin_layout Plain Layout
7754 \begin_layout Plain Layout
7767 \begin_layout Plain Layout
7780 \begin_layout Plain Layout
7793 \begin_layout Plain Layout
7806 \begin_layout Plain Layout
7820 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
7823 \begin_layout Plain Layout
7824 \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
7840 \begin_layout Standard
7841 In the last example it doesn't matter if
7853 is inserted at first.
7856 \begin_layout Standard
7857 \begin_inset VSpace bigskip
7860 When brackets are needed that overlap each other, multiline formulas, as
7862 \begin_inset CommandInset ref
7864 reference "sec:Multiline-Formulas"
7869 \begin_inset Formula
7871 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
7872 & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
7877 In the first row the formula is inserted together with the first brace.
7878 It is hereby important that the space command
7882 \begin_layout Plain Layout
7883 Space commands are explained in
7884 \begin_inset CommandInset ref
7886 reference "sub:Predefined-Space"
7901 is inserted before the first
7902 \begin_inset Formula $d$
7905 , because the brace that ends behind the
7906 \begin_inset Formula $q$
7909 prevents that the following
7910 \begin_inset Quotes eld
7914 \begin_inset Quotes erd
7917 is surrounded by space.
7921 \begin_layout Plain Layout
7922 because a bracket is not handled as a character, see
7923 \begin_inset CommandInset ref
7925 reference "sub:Binary-Operators"
7934 In the second row the second brace is inserted.
7935 As it should begin before the
7936 \begin_inset Formula $b$
7951 \begin_layout Plain Layout
7959 \begin_inset CommandInset ref
7961 reference "sub:Placeholders"
7970 This space is needed because the
7971 \begin_inset Quotes eld
7975 \begin_inset Quotes erd
7978 is also surrounded by space in the formula.
7979 The brace is placed under the command
7988 \begin_layout Standard
7989 It gets more complicated when brackets overlap each other, like in the following
7994 \begin_layout Plain Layout
8006 \begin_inset Formula
8008 & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
8009 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
8018 \begin_layout Plain Layout
8029 The first formula row is the same as the second row of the previous example,
8030 with the difference that the brace is above.
8031 The second row contains the formula together with the second brace.
8032 To avoid that there is space between the upper brace in the first row and
8033 the formula, the row spacing needs to be reduced.
8034 This is not easily possible due to a bug in LyX
8038 \begin_layout Plain Layout
8039 \begin_inset CommandInset href
8041 name "LyX-bug #1505"
8042 target "http://www.lyx.org/trac/ticket/1505"
8052 As a solution for the problem, the global formula row separation
8059 \begin_inset Index idx
8062 \begin_layout Plain Layout
8070 must be changed to -6
8071 \begin_inset space \thinspace{}
8074 pt before the formula with the command
8089 is set back after the formula to the standard value of 3
8090 \begin_inset space \thinspace{}
8093 pt using the same command.
8094 More about the row separation in formulas is explained in
8095 \begin_inset CommandInset ref
8097 reference "sub:Line-Separation"
8104 \begin_layout Section
8106 \begin_inset Index idx
8109 \begin_layout Plain Layout
8118 \begin_layout Standard
8119 Arrows can be inserted via the math toolbar button
8120 \begin_inset Graphics
8121 filename ../images/math/leftarrow.png
8126 or the commands listed in the following subsections.
8129 \begin_layout Subsection
8131 \begin_inset Index idx
8134 \begin_layout Plain Layout
8143 \begin_layout Standard
8144 \begin_inset space \hfill{}
8148 \begin_inset Tabular
8149 <lyxtabular version="3" rows="8" columns="2">
8150 <features rotate="0" tabularvalignment="middle">
8151 <column alignment="center" valignment="top" width="0pt">
8152 <column alignment="center" valignment="top" width="0pt">
8154 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8157 \begin_layout Plain Layout
8163 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8166 \begin_layout Plain Layout
8174 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8177 \begin_layout Plain Layout
8185 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8188 \begin_layout Plain Layout
8189 \begin_inset Formula $\gets$
8199 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8202 \begin_layout Plain Layout
8210 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8213 \begin_layout Plain Layout
8214 \begin_inset Formula $\Leftarrow$
8224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8227 \begin_layout Plain Layout
8235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8238 \begin_layout Plain Layout
8239 \begin_inset Formula $\longleftarrow$
8249 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8252 \begin_layout Plain Layout
8260 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8263 \begin_layout Plain Layout
8264 \begin_inset Formula $\Longleftarrow$
8274 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8277 \begin_layout Plain Layout
8285 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8288 \begin_layout Plain Layout
8289 \begin_inset Formula $\leftharpoonup$
8299 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8302 \begin_layout Plain Layout
8310 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8313 \begin_layout Plain Layout
8314 \begin_inset Formula $\leftharpoondown$
8324 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8327 \begin_layout Plain Layout
8335 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8338 \begin_layout Plain Layout
8339 \begin_inset Formula $\hookleftarrow$
8353 \begin_inset space \hfill{}
8357 \begin_inset Tabular
8358 <lyxtabular version="3" rows="8" columns="2">
8359 <features rotate="0" tabularvalignment="middle">
8360 <column alignment="center" valignment="top" width="0pt">
8361 <column alignment="center" valignment="top" width="0pt">
8363 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8366 \begin_layout Plain Layout
8372 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8375 \begin_layout Plain Layout
8383 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8386 \begin_layout Plain Layout
8394 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8397 \begin_layout Plain Layout
8398 \begin_inset Formula $\to$
8408 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8411 \begin_layout Plain Layout
8419 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8422 \begin_layout Plain Layout
8423 \begin_inset Formula $\Rightarrow$
8433 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8436 \begin_layout Plain Layout
8444 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8447 \begin_layout Plain Layout
8448 \begin_inset Formula $\longrightarrow$
8458 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8461 \begin_layout Plain Layout
8469 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8472 \begin_layout Plain Layout
8473 \begin_inset Formula $\Longrightarrow$
8483 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8486 \begin_layout Plain Layout
8494 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8497 \begin_layout Plain Layout
8498 \begin_inset Formula $\rightharpoonup$
8508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8511 \begin_layout Plain Layout
8519 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8522 \begin_layout Plain Layout
8523 \begin_inset Formula $\rightharpoondown$
8533 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
8536 \begin_layout Plain Layout
8544 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
8547 \begin_layout Plain Layout
8548 \begin_inset Formula $\hookrightarrow$
8562 \begin_inset space \hfill{}
8568 \begin_layout Standard
8569 \begin_inset space \hfill{}
8573 \begin_inset Tabular
8574 <lyxtabular version="3" rows="6" columns="2">
8575 <features rotate="0" tabularvalignment="middle">
8576 <column alignment="center" valignment="top" width="0pt">
8577 <column alignment="center" valignment="top" width="0pt">
8579 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8582 \begin_layout Plain Layout
8588 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8591 \begin_layout Plain Layout
8599 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8602 \begin_layout Plain Layout
8610 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8613 \begin_layout Plain Layout
8614 \begin_inset Formula $\leftrightarrow$
8624 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8627 \begin_layout Plain Layout
8635 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8638 \begin_layout Plain Layout
8639 \begin_inset Formula $\Leftrightarrow$
8649 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8652 \begin_layout Plain Layout
8660 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8663 \begin_layout Plain Layout
8664 \begin_inset Formula $\longleftrightarrow$
8674 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8677 \begin_layout Plain Layout
8685 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8688 \begin_layout Plain Layout
8689 \begin_inset Formula $\Longleftrightarrow$
8699 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8702 \begin_layout Plain Layout
8710 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8713 \begin_layout Plain Layout
8714 \begin_inset Formula $\rightleftharpoons$
8728 \begin_inset space \hspace{}
8733 \begin_inset space \hfill{}
8737 \begin_inset Tabular
8738 <lyxtabular version="3" rows="5" columns="2">
8739 <features rotate="0" tabularvalignment="middle">
8740 <column alignment="center" valignment="top" width="0pt">
8741 <column alignment="center" valignment="top" width="0pt">
8743 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8746 \begin_layout Plain Layout
8752 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8755 \begin_layout Plain Layout
8763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8766 \begin_layout Plain Layout
8774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8777 \begin_layout Plain Layout
8778 \begin_inset Formula $\mapsto$
8788 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8791 \begin_layout Plain Layout
8799 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8802 \begin_layout Plain Layout
8803 \begin_inset Formula $\longmapsto$
8813 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
8816 \begin_layout Plain Layout
8824 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
8827 \begin_layout Plain Layout
8828 \begin_inset Formula $\leadsto$
8838 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8841 \begin_layout Plain Layout
8849 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8852 \begin_layout Plain Layout
8853 \begin_inset Formula $\dasharrow$
8867 \begin_inset space \hfill{}
8873 \begin_layout Standard
8874 \begin_inset VSpace medskip
8877 Arrows used as accents like e.
8878 \begin_inset space \thinspace{}
8882 \begin_inset space \space{}
8885 vector arrows are listed in
8886 \begin_inset CommandInset ref
8888 reference "sec:Accents"
8895 \begin_layout Standard
8896 \begin_inset VSpace bigskip
8899 Furthermore there are the labeled arrows
8900 \begin_inset Index idx
8903 \begin_layout Plain Layout
8916 \begin_inset Index idx
8919 \begin_layout Plain Layout
8934 \begin_inset Index idx
8937 \begin_layout Plain Layout
8944 \begin_layout Plain Layout
8959 When inserting one of these commands in a formula, an arrow with two blue
8960 boxes appear where the label can be inserted.
8961 The length of the arrow adapts to the label width.
8964 \begin_layout Standard
8966 \begin_inset Tabular
8967 <lyxtabular version="3" rows="3" columns="2">
8968 <features rotate="0" tabularvalignment="middle">
8969 <column alignment="center" valignment="top" width="0pt">
8970 <column alignment="center" valignment="top" width="0pt">
8972 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
8975 \begin_layout Plain Layout
8981 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
8984 \begin_layout Plain Layout
8986 \begin_inset Note Note
8989 \begin_layout Plain Layout
8996 is only used as spacer.
9008 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9011 \begin_layout Plain Layout
9018 \begin_layout Plain Layout
9028 \begin_inset Formula $\downarrow$
9032 \begin_inset Formula $\to$
9040 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9043 \begin_layout Plain Layout
9044 \begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
9054 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9057 \begin_layout Plain Layout
9064 \begin_layout Plain Layout
9074 \begin_inset Formula $\downarrow$
9078 \begin_inset Formula $\to$
9086 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9089 \begin_layout Plain Layout
9090 \begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
9106 \begin_layout Subsection
9107 Vertical and diagonal Arrows
9108 \begin_inset Index idx
9111 \begin_layout Plain Layout
9118 \begin_inset Index idx
9121 \begin_layout Plain Layout
9130 \begin_layout Standard
9131 \begin_inset space \hfill{}
9135 \begin_inset Tabular
9136 <lyxtabular version="3" rows="7" columns="2">
9137 <features rotate="0" tabularvalignment="middle">
9138 <column alignment="center" valignment="top" width="0pt">
9139 <column alignment="center" valignment="top" width="0pt">
9141 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9144 \begin_layout Plain Layout
9150 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9153 \begin_layout Plain Layout
9161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9164 \begin_layout Plain Layout
9172 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9175 \begin_layout Plain Layout
9176 \begin_inset Formula $\uparrow$
9186 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9189 \begin_layout Plain Layout
9197 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9200 \begin_layout Plain Layout
9201 \begin_inset Formula $\Uparrow$
9211 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9214 \begin_layout Plain Layout
9222 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9225 \begin_layout Plain Layout
9226 \begin_inset Formula $\updownarrow$
9236 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9239 \begin_layout Plain Layout
9247 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9250 \begin_layout Plain Layout
9251 \begin_inset Formula $\Updownarrow$
9261 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9264 \begin_layout Plain Layout
9272 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9275 \begin_layout Plain Layout
9276 \begin_inset Formula $\Downarrow$
9286 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9289 \begin_layout Plain Layout
9297 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9300 \begin_layout Plain Layout
9301 \begin_inset Formula $\downarrow$
9315 \begin_inset space \hfill{}
9319 \begin_inset Tabular
9320 <lyxtabular version="3" rows="5" columns="2">
9321 <features rotate="0" tabularvalignment="middle">
9322 <column alignment="center" valignment="top" width="0pt">
9323 <column alignment="center" valignment="top" width="0pt">
9325 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9328 \begin_layout Plain Layout
9334 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9337 \begin_layout Plain Layout
9345 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9348 \begin_layout Plain Layout
9356 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9359 \begin_layout Plain Layout
9360 \begin_inset Formula $\nearrow$
9370 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
9373 \begin_layout Plain Layout
9381 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
9384 \begin_layout Plain Layout
9385 \begin_inset Formula $\searrow$
9395 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9398 \begin_layout Plain Layout
9406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9409 \begin_layout Plain Layout
9410 \begin_inset Formula $\swarrow$
9420 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9423 \begin_layout Plain Layout
9431 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9434 \begin_layout Plain Layout
9435 \begin_inset Formula $\nwarrow$
9449 \begin_inset space \hfill{}
9455 \begin_layout Standard
9456 \begin_inset VSpace medskip
9459 Vertical arrows can be used also as delimiters together with the commands
9461 \begin_inset CommandInset ref
9463 reference "sub:Manual-Bracket-Size"
9468 \begin_inset CommandInset ref
9470 reference "sub:Automatic-Bracket-Size"
9477 \begin_layout Section
9479 \begin_inset CommandInset label
9486 \begin_inset Index idx
9489 \begin_layout Plain Layout
9498 \begin_layout Standard
9499 Accents can be inserted via the math toolbar button
9500 \begin_inset Graphics
9501 filename ../images/math/hat.png
9506 or the commands listed in the following subsections.
9509 \begin_layout Subsection
9510 Accents for one Character
9514 \begin_layout Plain Layout
9527 \begin_layout Plain Layout
9529 \begin_inset CommandInset ref
9531 reference "sub:Accents-in-Text"
9544 \begin_layout Plain Layout
9552 \begin_inset Note Note
9555 \begin_layout Plain Layout
9562 is used to avoid that the footnote appears in the PDF-bookmark.
9565 \begin_layout Plain Layout
9573 \begin_inset CommandInset ref
9575 reference "sub:Formulas-in-Section"
9585 \begin_inset CommandInset label
9587 name "sub:Accents-for-one"
9592 \begin_inset Index idx
9595 \begin_layout Plain Layout
9596 Accents ! for one character
9604 \begin_layout Standard
9605 \begin_inset space \hfill{}
9609 \begin_inset Tabular
9610 <lyxtabular version="3" rows="8" columns="2">
9611 <features rotate="0" tabularvalignment="middle">
9612 <column alignment="center" valignment="top" width="0pt">
9613 <column alignment="center" valignment="top" width="0pt">
9615 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9618 \begin_layout Plain Layout
9624 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9627 \begin_layout Plain Layout
9629 \begin_inset Note Note
9632 \begin_layout Plain Layout
9639 is only used as spacer.
9651 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9654 \begin_layout Plain Layout
9661 \begin_layout Plain Layout
9675 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9678 \begin_layout Plain Layout
9679 \begin_inset Formula $\raisebox{5mm}{}\dot{A}$
9689 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9692 \begin_layout Plain Layout
9699 \begin_layout Plain Layout
9713 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9716 \begin_layout Plain Layout
9717 \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
9727 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9730 \begin_layout Plain Layout
9737 \begin_layout Plain Layout
9751 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9754 \begin_layout Plain Layout
9755 \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
9765 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9768 \begin_layout Plain Layout
9775 \begin_layout Plain Layout
9789 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9792 \begin_layout Plain Layout
9793 \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
9803 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9806 \begin_layout Plain Layout
9813 \begin_layout Plain Layout
9823 \begin_inset Index idx
9826 \begin_layout Plain Layout
9837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9840 \begin_layout Plain Layout
9841 \begin_inset Formula $\raisebox{5mm}{}\vec{A}$
9851 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9854 \begin_layout Plain Layout
9861 \begin_layout Plain Layout
9875 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9878 \begin_layout Plain Layout
9879 \begin_inset Formula $\raisebox{5mm}{}\bar{A}$
9889 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
9892 \begin_layout Plain Layout
9899 \begin_layout Plain Layout
9913 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
9916 \begin_layout Plain Layout
9917 \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
9931 \begin_inset space \hfill{}
9935 \begin_inset Tabular
9936 <lyxtabular version="3" rows="7" columns="2">
9937 <features rotate="0" tabularvalignment="middle">
9938 <column alignment="center" valignment="top" width="0pt">
9939 <column alignment="center" valignment="top" width="0pt">
9941 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9944 \begin_layout Plain Layout
9950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9953 \begin_layout Plain Layout
9961 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
9964 \begin_layout Plain Layout
9971 \begin_layout Plain Layout
9985 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
9988 \begin_layout Plain Layout
9989 \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
9999 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10002 \begin_layout Plain Layout
10009 \begin_layout Plain Layout
10023 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10026 \begin_layout Plain Layout
10027 \begin_inset Formula $\raisebox{5mm}{}\hat{A}$
10037 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10040 \begin_layout Plain Layout
10047 \begin_layout Plain Layout
10061 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10064 \begin_layout Plain Layout
10065 \begin_inset Formula $\raisebox{5mm}{}\check{A}$
10075 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10078 \begin_layout Plain Layout
10085 \begin_layout Plain Layout
10099 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10102 \begin_layout Plain Layout
10103 \begin_inset Formula $\raisebox{5mm}{}\acute{A}$
10113 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10116 \begin_layout Plain Layout
10123 \begin_layout Plain Layout
10137 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10140 \begin_layout Plain Layout
10141 \begin_inset Formula $\raisebox{5mm}{}\grave{A}$
10151 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10154 \begin_layout Plain Layout
10161 \begin_layout Plain Layout
10175 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10178 \begin_layout Plain Layout
10179 \begin_inset Formula $\raisebox{5mm}{}\breve{A}$
10193 \begin_inset space \hfill{}
10199 \begin_layout Standard
10200 \begin_inset VSpace bigskip
10206 \begin_layout Standard
10207 You can directly insert accents like é to formulas.
10208 LyX will transform them to the corresponding accent command.
10210 \begin_inset Index idx
10213 \begin_layout Plain Layout
10219 it is better to insert a quotation mark before the vowel.
10220 These two characters are then treated by LaTeX as
10224 character when the formula part with the umlaut is marked as German.
10232 \begin_inset Quotes eld
10236 \begin_inset Quotes erd
10239 umlauts are created as demonstrated in the following example:
10242 \begin_layout Standard
10243 \begin_inset VSpace -2mm
10249 \begin_layout Standard
10251 \begin_inset Tabular
10252 <lyxtabular version="3" rows="3" columns="2">
10253 <features rotate="0" tabularvalignment="middle">
10254 <column alignment="center" valignment="top">
10255 <column alignment="center" valignment="top">
10257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10260 \begin_layout Plain Layout
10266 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10269 \begin_layout Plain Layout
10271 \begin_inset Note Note
10274 \begin_layout Plain Layout
10282 \begin_inset space \thinspace{}
10285 pt space are only used as spacer.
10297 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
10300 \begin_layout Plain Layout
10303 \begin_inset Quotes grd
10311 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
10314 \begin_layout Plain Layout
10315 \begin_inset space \hspace{}
10322 \begin_inset Formula $"i$
10332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10335 \begin_layout Plain Layout
10342 \begin_layout Plain Layout
10356 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10359 \begin_layout Plain Layout
10360 \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
10376 \begin_layout Standard
10377 Another advantage to
10383 is that umlauts can directly be converted to mathematical text because
10384 the accent commands above are
10390 in mathematical text
10393 To convert an accented character to mathematical text, only the character
10394 under the accent may be converted.
10395 This applies also for all other conversions, e.
10396 \begin_inset space \thinspace{}
10400 \begin_inset space \space{}
10406 \begin_layout Standard
10407 In mathematical text, umlauts and other accented characters can directly
10411 \begin_layout Subsection
10412 Accents for several Characters
10413 \begin_inset Index idx
10416 \begin_layout Plain Layout
10417 Accents ! for several characters
10425 \begin_layout Standard
10426 \begin_inset space \hfill{}
10430 \begin_inset Tabular
10431 <lyxtabular version="3" rows="5" columns="2">
10432 <features rotate="0" tabularvalignment="middle">
10433 <column alignment="center" valignment="top" width="0pt">
10434 <column alignment="center" valignment="top" width="0pt">
10436 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10439 \begin_layout Plain Layout
10445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10448 \begin_layout Plain Layout
10450 \begin_inset Note Note
10453 \begin_layout Plain Layout
10460 is only used as spacer.
10472 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10475 \begin_layout Plain Layout
10482 \begin_layout Plain Layout
10496 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10499 \begin_layout Plain Layout
10500 \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
10510 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10513 \begin_layout Plain Layout
10520 \begin_layout Plain Layout
10534 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10537 \begin_layout Plain Layout
10538 \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
10548 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10551 \begin_layout Plain Layout
10558 \begin_layout Plain Layout
10572 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10575 \begin_layout Plain Layout
10576 \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
10586 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10589 \begin_layout Plain Layout
10592 underleftrightarrow
10596 \begin_layout Plain Layout
10610 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10613 \begin_layout Plain Layout
10614 \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
10628 \begin_inset space \hfill{}
10632 \begin_inset Tabular
10633 <lyxtabular version="3" rows="5" columns="2">
10634 <features rotate="0" tabularvalignment="middle">
10635 <column alignment="center" valignment="top" width="0pt">
10636 <column alignment="center" valignment="top" width="0pt">
10638 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10641 \begin_layout Plain Layout
10647 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10650 \begin_layout Plain Layout
10658 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
10661 \begin_layout Plain Layout
10668 \begin_layout Plain Layout
10682 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
10685 \begin_layout Plain Layout
10686 \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
10696 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10699 \begin_layout Plain Layout
10706 \begin_layout Plain Layout
10720 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10723 \begin_layout Plain Layout
10724 \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
10734 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10737 \begin_layout Plain Layout
10744 \begin_layout Plain Layout
10758 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10761 \begin_layout Plain Layout
10762 \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
10772 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
10775 \begin_layout Plain Layout
10782 \begin_layout Plain Layout
10796 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
10799 \begin_layout Plain Layout
10800 \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
10814 \begin_inset space \hfill{}
10820 \begin_layout Standard
10821 \begin_inset VSpace medskip
10824 With these commands as many characters as you like can be accented.
10837 will only be set in the output with a length of three characters, as shown
10838 in the following example:
10839 \begin_inset Formula
10841 \widetilde{A+B=C-D}
10849 \begin_layout Standard
10857 \begin_inset Index idx
10860 \begin_layout Plain Layout
10875 \begin_inset Index idx
10878 \begin_layout Plain Layout
10886 described in the previous subsection it is also possible to accent several
10896 \begin_layout Plain Layout
10906 \begin_inset Formula $\downarrow$
10912 \begin_inset Formula
10914 \underset{***}{A=B}
10922 \begin_layout Standard
10923 \begin_inset Newpage newpage
10929 \begin_layout Section
10931 \begin_inset CommandInset label
10938 \begin_inset Index idx
10941 \begin_layout Plain Layout
10950 \begin_layout Subsection
10952 \begin_inset CommandInset label
10954 name "sub:Predefined-Space"
10959 \begin_inset Index idx
10962 \begin_layout Plain Layout
10963 Space ! horizontal ! predefined
10971 \begin_layout Standard
10972 Sometimes it is necessary to insert horizontal space into a formula.
10973 This is done by inserting a protected space (shortcut
10976 arg "command-alternatives space-insert protected ; math-space"
10981 \begin_inset Quotes eld
10990 \begin_layout Plain Layout
11002 \begin_inset Quotes erd
11005 appears and by pressing
11009 several times one can select one of eight different space sizes.
11010 The spaces can also be inserted using the math toolbar button
11011 \begin_inset Graphics
11012 filename ../images/math/space.png
11017 or special commands.
11018 Independent from the inserted command, one can select the size again by
11026 \begin_layout Standard
11029 \begin_inset VSpace -5mm
11033 \begin_inset Tabular
11034 <lyxtabular version="3" rows="3" columns="7">
11035 <features rotate="0" tabularvalignment="middle">
11036 <column alignment="center" valignment="middle" width="6.8cm">
11037 <column alignment="center" valignment="top">
11038 <column alignment="center" valignment="top">
11039 <column alignment="center" valignment="top">
11040 <column alignment="center" valignment="top">
11041 <column alignment="center" valignment="top">
11042 <column alignment="center" valignment="top">
11044 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11047 \begin_layout Plain Layout
11053 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11056 \begin_layout Plain Layout
11064 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11067 \begin_layout Plain Layout
11075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11078 \begin_layout Plain Layout
11086 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11089 \begin_layout Plain Layout
11097 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11100 \begin_layout Plain Layout
11108 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11111 \begin_layout Plain Layout
11121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11124 \begin_layout Plain Layout
11129 keystrokes after inserting the protected space
11134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11137 \begin_layout Plain Layout
11143 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11146 \begin_layout Plain Layout
11152 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11155 \begin_layout Plain Layout
11161 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11164 \begin_layout Plain Layout
11170 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11173 \begin_layout Plain Layout
11179 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11182 \begin_layout Plain Layout
11190 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11193 \begin_layout Plain Layout
11199 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11202 \begin_layout Plain Layout
11203 \begin_inset Formula $A\, B$
11211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11214 \begin_layout Plain Layout
11215 \begin_inset Formula $A\: B$
11223 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11226 \begin_layout Plain Layout
11227 \begin_inset Formula $A\; B$
11235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11238 \begin_layout Plain Layout
11239 \begin_inset Formula $A\quad B$
11247 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11250 \begin_layout Plain Layout
11251 \begin_inset Formula $A\qquad B$
11259 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11262 \begin_layout Plain Layout
11263 \begin_inset Formula $A\! B$
11279 \begin_layout Standard
11280 The last size seem to produce no space.
11281 It is displayed red in LyX contrary to the other sizes, because it is a
11283 There are two more negative spaces:
11286 \begin_layout Standard
11288 \begin_inset Tabular
11289 <lyxtabular version="3" rows="3" columns="3">
11290 <features rotate="0" tabularvalignment="middle">
11291 <column alignment="center" valignment="middle" width="6.8cm">
11292 <column alignment="center" valignment="top" width="0pt">
11293 <column alignment="center" valignment="top" width="0pt">
11295 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11298 \begin_layout Plain Layout
11304 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11307 \begin_layout Plain Layout
11315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11318 \begin_layout Plain Layout
11328 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11331 \begin_layout Plain Layout
11336 keystrokes after inserting the protected space
11341 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11344 \begin_layout Plain Layout
11350 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11353 \begin_layout Plain Layout
11361 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11364 \begin_layout Plain Layout
11370 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
11373 \begin_layout Plain Layout
11374 \begin_inset Formula $A\negmedspace B$
11382 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
11385 \begin_layout Plain Layout
11386 \begin_inset Formula $A\negthickspace B$
11402 \begin_layout Standard
11403 Negative spaces can lead to characters overlapping each other.
11404 Thus they can be used to enforce ligatures, which are e.
11405 \begin_inset space \thinspace{}
11409 \begin_inset space \space{}
11412 useful for summation operators:
11415 \begin_layout Standard
11417 \begin_inset Tabular
11418 <lyxtabular version="3" rows="3" columns="2">
11419 <features rotate="0" tabularvalignment="middle">
11420 <column alignment="center" valignment="top">
11421 <column alignment="center" valignment="top">
11423 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11426 \begin_layout Plain Layout
11432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11435 \begin_layout Plain Layout
11437 \begin_inset Note Note
11440 \begin_layout Plain Layout
11447 is only used as spacer.
11459 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11462 \begin_layout Plain Layout
11471 \begin_layout Plain Layout
11485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11488 \begin_layout Plain Layout
11489 \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
11499 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11502 \begin_layout Plain Layout
11513 \begin_layout Plain Layout
11527 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11530 \begin_layout Plain Layout
11531 \begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
11547 \begin_layout Standard
11548 Relations like for example equal signs, are always surrounded by space.
11549 To suppress this, the equal sign is placed into a TeX-brace.
11550 The following example demonstrates this:
11553 \begin_layout Standard
11555 \begin_inset Tabular
11556 <lyxtabular version="3" rows="2" columns="2">
11557 <features rotate="0" tabularvalignment="middle">
11558 <column alignment="center" valignment="top" width="0pt">
11559 <column alignment="center" valignment="top" width="0pt">
11561 <cell alignment="center" valignment="top" usebox="none">
11564 \begin_layout Plain Layout
11570 <cell alignment="center" valignment="top" usebox="none">
11573 \begin_layout Plain Layout
11574 \begin_inset Formula $A=B$
11584 <cell alignment="center" valignment="top" usebox="none">
11587 \begin_layout Plain Layout
11588 \begin_inset Note Note
11591 \begin_layout Plain Layout
11598 is only used as spacer.
11604 \begin_inset Formula $\raisebox{5mm}{}$
11607 equation without space
11612 <cell multicolumn="1" alignment="center" valignment="top" usebox="none">
11615 \begin_layout Plain Layout
11616 \begin_inset Formula $A{=}B$
11632 \begin_layout Standard
11634 The command for the last formula is:
11639 \begin_inset Formula $\to$
11645 \begin_layout Standard
11646 \begin_inset VSpace bigskip
11649 Spaces are needed for physical units, because the space between the value
11650 and the unit is the smallest one and not a normal space.
11651 For units in text, the smallest space is inserted via the menu
11653 Insert\SpecialChar \menuseparator
11654 Formatting\SpecialChar \menuseparator
11656 \begin_inset space ~
11664 arg "space-insert thin"
11670 \begin_layout Standard
11671 An example to visualize the difference:
11674 \begin_layout Standard
11675 \begin_inset Tabular
11676 <lyxtabular version="3" rows="2" columns="2">
11677 <features rotate="0" tabularvalignment="middle">
11678 <column alignment="left" valignment="top">
11679 <column alignment="left" valignment="top">
11681 <cell alignment="center" valignment="top" usebox="none">
11684 \begin_layout Plain Layout
11686 \begin_inset Formula $\cdot$
11694 <cell alignment="center" valignment="top" usebox="none">
11697 \begin_layout Plain Layout
11698 space between value and unit
11705 <cell alignment="center" valignment="top" usebox="none">
11708 \begin_layout Plain Layout
11710 \begin_inset space \thinspace{}
11714 \begin_inset Formula $\cdot$
11722 <cell alignment="center" valignment="top" usebox="none">
11725 \begin_layout Plain Layout
11726 smallest space between value and unit
11739 \begin_layout Subsection
11744 \begin_layout Plain Layout
11757 \begin_layout Plain Layout
11758 for vertical space in formulas see
11759 \begin_inset CommandInset ref
11761 reference "sub:Line-Separation"
11774 \begin_layout Plain Layout
11782 \begin_inset Note Note
11785 \begin_layout Plain Layout
11788 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
11791 \begin_layout Plain Layout
11794 texorpdfstring is in section
11795 \begin_inset CommandInset ref
11797 reference "sub:Formulas-in-Section"
11807 \begin_inset CommandInset label
11809 name "sub:Variable-Space"
11814 \begin_inset Index idx
11817 \begin_layout Plain Layout
11818 Space ! horizontal ! variable
11826 \begin_layout Standard
11827 Space with a defined length can be inserted with the command
11834 \begin_inset Index idx
11837 \begin_layout Plain Layout
11847 \begin_inset Quotes eld
11856 \begin_layout Plain Layout
11868 \begin_inset Quotes erd
11872 The length can be specified by left-clicking on the
11873 \begin_inset Quotes eld
11882 \begin_layout Plain Layout
11894 \begin_inset Quotes erd
11898 The length may also be negative.
11899 To insert as much space as is available, the command
11906 \begin_inset Index idx
11909 \begin_layout Plain Layout
11920 \begin_layout Standard
11921 \begin_inset VSpace -1mm
11927 \begin_layout Standard
11929 \begin_inset Tabular
11930 <lyxtabular version="3" rows="4" columns="2">
11931 <features rotate="0" tabularvalignment="middle">
11932 <column alignment="center" valignment="top">
11933 <column alignment="center" valignment="top">
11935 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
11938 \begin_layout Plain Layout
11946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
11949 \begin_layout Plain Layout
11957 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
11960 \begin_layout Plain Layout
11967 \begin_layout Plain Layout
11977 \begin_inset Formula $\to$
11983 \begin_inset space \thinspace{}
11991 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
11994 \begin_layout Plain Layout
11995 \begin_inset Formula $A=B\hspace{3cm}A\not=C$
12005 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12008 \begin_layout Plain Layout
12015 \begin_layout Plain Layout
12025 \begin_inset Formula $\to$
12031 \begin_inset space \thinspace{}
12039 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12042 \begin_layout Plain Layout
12043 \begin_inset Formula $A\hspace{-1mm}A\not=A$
12053 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12056 \begin_layout Plain Layout
12063 \begin_layout Plain Layout
12077 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12080 \begin_layout Plain Layout
12081 \begin_inset Formula $A=A\hfill B=B$
12097 \begin_layout Standard
12098 In the last example the available space is given by the longest column entry
12100 In an inline formula the space depends on the length of the line in which
12108 Thus, when the line uses the full width, no space will be created.
12115 only has an effect on displayed formulas when the formula style
12120 (Formula styles are explained in
12121 \begin_inset CommandInset ref
12123 reference "sec:Formula-Styles"
12130 \begin_layout Standard
12137 , there are the commands
12149 that fill the space with a pattern, see
12150 \begin_inset CommandInset ref
12152 reference "sub:Ellipses"
12159 \begin_layout Standard
12160 For text, variable space can be inserted via the menu
12162 Insert\SpecialChar \menuseparator
12163 Formatting\SpecialChar \menuseparator
12165 \begin_inset space ~
12173 \begin_layout Standard
12174 This is a line with
12175 \begin_inset space \hspace{}
12180 \begin_inset space \thinspace{}
12186 \begin_layout Standard
12187 This is a line with
12188 \begin_inset space \hfill{}
12194 \begin_layout Subsection
12195 Space besides inline Formulas
12196 \begin_inset Index idx
12199 \begin_layout Plain Layout
12200 Space ! besides inline formulas
12208 \begin_layout Standard
12209 The space that surrounds inline formulas can be adjusted with the length
12217 \begin_inset Index idx
12220 \begin_layout Plain Layout
12229 The value of a length is set with the command
12236 \begin_inset Index idx
12239 \begin_layout Plain Layout
12247 which has the following scheme:
12250 \begin_layout Standard
12255 setlength{length name}{value}
12258 \begin_layout Standard
12266 \begin_inset space \thinspace{}
12272 \begin_layout Standard
12282 \begin_layout Standard
12283 is inserted in TeX-mode.
12285 \begin_inset space \thinspace{}
12288 mm space will now be set around all inline formulas:
12292 \begin_layout Plain Layout
12306 \begin_layout Standard
12307 This is a line with an inline formula
12308 \begin_inset Formula $A=B$
12312 \begin_inset space \thinspace{}
12315 mm surrounding space.
12319 \begin_layout Plain Layout
12333 \begin_layout Standard
12334 To return to the predefined value,
12340 is set to the value 0
12341 \begin_inset space \thinspace{}
12347 \begin_layout Section
12349 \begin_inset Index idx
12352 \begin_layout Plain Layout
12359 \begin_inset Index idx
12362 \begin_layout Plain Layout
12367 \begin_layout Plain Layout
12378 \begin_layout Plain Layout
12393 \begin_layout Standard
12394 Boxes for text are described in chapter
12401 \begin_inset space ~
12409 \begin_layout Subsection
12411 \begin_inset CommandInset label
12413 name "sub:Boxes-with-Frame"
12418 \begin_inset Index idx
12421 \begin_layout Plain Layout
12430 \begin_layout Standard
12431 It is possible to frame a formula or part of one with the commands
12438 \begin_inset Index idx
12441 \begin_layout Plain Layout
12456 \begin_inset Index idx
12459 \begin_layout Plain Layout
12470 \begin_layout Standard
12471 When one of these commands is inserted in a formula, a blue box appears
12472 within a frame to enter formula parts.
12479 an additional formula has to be created by
12483 within this box, because the box content will otherwise be treated as mathemati
12491 is used, a new formula is automatically created inside the frame.
12494 \begin_layout Standard
12501 is not suitable to frame displayed formulas because the formula will always
12502 be set in the size of the text.
12509 is in contrary not suitable to frame inline formulas, because the formula
12510 will always be set in the size of a displayed formula.
12513 \begin_layout Standard
12527 \begin_inset Index idx
12530 \begin_layout Plain Layout
12538 where additionally the frame width and the alignment can be specified.
12545 is used in the following scheme:
12548 \begin_layout Standard
12553 framebox[frame width][position]{box content}
12556 \begin_layout Standard
12557 The position can either be
12574 right aligns the formula in the box.
12575 When no position is given, the formula will be centered.
12576 \begin_inset Newline newline
12579 If no width is given, also no position can be given.
12580 In this case the frame width is adjusted to the box content like for
12589 \begin_layout Standard
12596 is inserted, a box appears containing three blue boxes.
12597 The first two boxes are surrounded by brackets and denote the two optional
12599 The third box is for formula parts like for
12608 \begin_layout Standard
12609 \begin_inset Newpage newpage
12615 \begin_layout Standard
12617 \begin_inset Tabular
12618 <lyxtabular version="3" rows="5" columns="2">
12619 <features rotate="0" tabularvalignment="middle">
12620 <column alignment="center" valignment="top">
12621 <column alignment="center" valignment="top">
12623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12626 \begin_layout Plain Layout
12632 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12635 \begin_layout Plain Layout
12637 \begin_inset Note Note
12640 \begin_layout Plain Layout
12647 is only used as spacer.
12659 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12662 \begin_layout Plain Layout
12669 \begin_layout Plain Layout
12688 \begin_layout Plain Layout
12702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12705 \begin_layout Plain Layout
12706 \begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$
12716 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12719 \begin_layout Plain Layout
12726 \begin_layout Plain Layout
12741 \begin_layout Plain Layout
12755 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12758 \begin_layout Plain Layout
12759 \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
12769 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
12772 \begin_layout Plain Layout
12779 \begin_layout Plain Layout
12793 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
12796 \begin_layout Plain Layout
12797 \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
12807 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
12810 \begin_layout Plain Layout
12817 \begin_layout Plain Layout
12827 \begin_inset Formula $\to$
12831 \begin_inset Formula $\to$
12844 \begin_layout Plain Layout
12854 \begin_inset Formula $\downarrow$
12862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
12865 \begin_layout Plain Layout
12866 \begin_inset Formula $\raisebox{6mm}{}$
12870 \begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$
12874 \begin_inset Formula $\raisebox{-4mm}{}$
12890 \begin_layout Standard
12891 The frame thickness can also be adjusted.
12892 To do this the following commands have to be inserted in TeX-mode before
12896 \begin_layout Standard
12906 \begin_inset Quotes eld
12910 \begin_inset Quotes erd
12924 \begin_inset Quotes eld
12928 \begin_inset Quotes erd
12934 \begin_layout Standard
12935 \begin_inset Quotes eld
12939 \begin_inset Quotes erd
12942 specifies the minimal distance between the frame and the first character
12944 An example for this is the following framed formula:
12948 \begin_layout Plain Layout
12960 \begin_inset Formula
12967 Before this formula the commands
12970 \begin_layout Standard
12992 \begin_layout Standard
12993 were inserted in TeX-mode.
12994 The given values are used for all following boxes.
12997 \begin_layout Standard
12998 To return to the standard frame size, the command
13001 \begin_layout Standard
13026 \begin_layout Plain Layout
13040 \begin_layout Standard
13041 is inserted in TeX-mode before the next formula.
13044 \begin_layout Subsection
13045 Boxes without Frame
13046 \begin_inset CommandInset label
13048 name "sub:Boxes-without-Frame"
13053 \begin_inset Index idx
13056 \begin_layout Plain Layout
13057 Boxes ! without frame
13065 \begin_layout Standard
13066 For boxes without a frame there are the following box commands:
13073 \begin_inset Index idx
13076 \begin_layout Plain Layout
13091 \begin_inset Index idx
13094 \begin_layout Plain Layout
13109 \begin_inset Index idx
13112 \begin_layout Plain Layout
13123 \begin_layout Standard
13130 a box can be super- or subscripted.
13131 But in contrary to normal super- and subscripting, the characters in the
13132 box keep their font size.
13139 is used in the following scheme:
13142 \begin_layout Standard
13147 raisebox{height}{box content}
13150 \begin_layout Standard
13151 When the box should contain a formula, an extra formula is needed like for
13162 \begin_inset Note Greyedout
13165 \begin_layout Plain Layout
13176 this extra formula is created by pressing
13180 twice instead of once because LyX doesn't yet support
13194 \begin_layout Standard
13196 \begin_inset Tabular
13197 <lyxtabular version="3" rows="4" columns="2">
13198 <features rotate="0" tabularvalignment="middle">
13199 <column alignment="center" valignment="top">
13200 <column alignment="center" valignment="top">
13202 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13205 \begin_layout Plain Layout
13211 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13214 \begin_layout Plain Layout
13222 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13225 \begin_layout Plain Layout
13229 \begin_inset Formula $\to$
13235 \begin_inset Formula $\to$
13243 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13246 \begin_layout Plain Layout
13247 \begin_inset Formula $H\raisebox{2mm}{al}lo$
13257 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13260 \begin_layout Plain Layout
13264 \begin_inset Formula $\to$
13270 \begin_inset Formula $\to$
13278 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13281 \begin_layout Plain Layout
13282 \begin_inset Formula $H\raisebox{-2mm}{al}lo$
13292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13295 \begin_layout Plain Layout
13299 \begin_inset Formula $\to$
13318 \begin_layout Plain Layout
13332 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13335 \begin_layout Plain Layout
13336 \begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$
13352 \begin_layout Standard
13377 , with the difference that there is no frame.
13380 \begin_layout Subsection
13382 \begin_inset CommandInset label
13384 name "sub:Colored-Boxes"
13389 \begin_inset Index idx
13392 \begin_layout Plain Layout
13401 \begin_layout Standard
13402 To be able to use all commands explained in this section, the LaTeX-package
13411 \begin_layout Plain Layout
13416 is part of every LaTeX standard installation.
13422 \begin_inset Index idx
13425 \begin_layout Plain Layout
13431 has to be loaded in the LaTeX-preamble with the line
13435 \begin_layout Plain Layout
13436 When text is colored somewhere in the document with a predefined color,
13437 LyX loads the LaTeX-package
13442 Thus it is possible that the package is loaded twice, but this does not
13449 \begin_inset Note Note
13452 \begin_layout Plain Layout
13453 To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
13462 \begin_layout Standard
13470 \begin_layout Standard
13471 \begin_inset VSpace medskip
13474 To color boxes, the command
13481 \begin_inset Index idx
13484 \begin_layout Plain Layout
13492 is used in the following scheme:
13495 \begin_layout Standard
13500 colorbox{color}{box content}
13503 \begin_layout Standard
13504 The box content can also be a box and a
13510 can also be part of another box (see the 2nd and 3rd example).
13511 When the box should contain a formula, an extra formula has to be created,
13512 the same way as for
13522 \begin_layout Plain Layout
13523 This also applies for the command
13537 \begin_layout Standard
13538 One of the following predefined colors can be chosen:
13541 \begin_layout Standard
13575 \begin_layout Standard
13577 \begin_inset Tabular
13578 <lyxtabular version="3" rows="4" columns="2">
13579 <features rotate="0" tabularvalignment="middle">
13580 <column alignment="center" valignment="top">
13581 <column alignment="center" valignment="top">
13583 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13586 \begin_layout Plain Layout
13592 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13595 \begin_layout Plain Layout
13597 \begin_inset Note Note
13600 \begin_layout Plain Layout
13607 is only used as spacer.
13619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13622 \begin_layout Plain Layout
13626 \begin_inset Formula $\to$
13636 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13639 \begin_layout Plain Layout
13640 \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
13650 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
13653 \begin_layout Plain Layout
13657 \begin_inset Formula $\to$
13668 \begin_layout Plain Layout
13682 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
13685 \begin_layout Plain Layout
13686 \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
13696 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
13699 \begin_layout Plain Layout
13706 \begin_layout Plain Layout
13718 \begin_inset Formula $\to$
13737 \begin_layout Plain Layout
13751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
13754 \begin_layout Plain Layout
13755 \begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$
13771 \begin_layout Standard
13778 only colors the box but not the characters in the box.
13779 To color all characters, the whole formula is highlighted and the desired
13780 color is chosen in the
13783 \begin_inset space ~
13789 The dialog can be called with the toolbar button
13790 \begin_inset Graphics
13791 filename ../images/dialog-show_character.png
13798 Edit\SpecialChar \menuseparator
13800 \begin_inset space ~
13803 Style\SpecialChar \menuseparator
13807 The formula number then has the same color as the formula.
13808 When the formula number should get another color than the formula characters,
13809 the color must be changed within the formula.
13812 \begin_layout Standard
13816 \begin_layout Standard
13819 \begin_inset Formula
13821 \int A=B\label{eq:red}
13829 \begin_inset Formula
13831 \textcolor{red}{\int A=B}\label{eq:redgreen}
13839 \begin_layout Standard
13841 \begin_inset CommandInset ref
13847 is completely colored red.
13848 \begin_inset Newline newline
13852 \begin_inset CommandInset ref
13854 reference "eq:redgreen"
13858 was first completely colored green to set the color for the formula number.
13859 Subsequently the formula characters were colored red.
13862 \begin_layout Standard
13863 \begin_inset VSpace bigskip
13866 To color the frame different than the rest of the box, the command
13873 \begin_inset Index idx
13876 \begin_layout Plain Layout
13884 is used in the following scheme:
13887 \begin_layout Standard
13892 fcolorbox{frame color}{color}{box content}
13895 \begin_layout Standard
13902 is an extension of the command
13909 The frame width is set, like for
13932 \begin_layout Plain Layout
13944 \begin_inset Formula
13946 \fcolorbox{cyan}{magenta}{A=B}
13955 \begin_layout Plain Layout
13969 \begin_layout Standard
13970 This formula was created with the command
13971 \begin_inset Newline newline
13979 \begin_inset Formula $\to$
13985 \begin_inset Formula $\to$
13995 \begin_layout Standard
13996 \begin_inset VSpace bigskip
13999 To use other colors than the predefined ones, they have to be defined first.
14002 \begin_layout Standard
14003 One can for example define the color
14004 \begin_inset Quotes eld
14012 \begin_inset Quotes erd
14015 with the LaTeX-preamble line:
14018 \begin_layout Standard
14023 definecolor{darkgreen}{cmyk}{0.5,
14038 \begin_inset Index idx
14041 \begin_layout Plain Layout
14052 \begin_layout Standard
14057 is the color space that denotes the colors
14074 The four comma separated numbers are the portion factor for the corresponding
14075 colors of the color space.
14076 The factors can be in the range of 0
14077 \begin_inset space \thinspace{}
14081 \begin_inset space \thinspace{}
14089 also the color space
14093 can be used for definitions.
14110 , so that there are in this case three portion factors for the corresponding
14112 Furthermore there is the color space
14116 with one portion factor for the gray value.
14119 \begin_layout Standard
14120 As example a framed box with the new defined color
14124 where the characters have been colored
14129 \begin_inset Formula
14131 \colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
14139 \begin_layout Standard
14140 Self-defined colors can also be used for text with the help of the command
14148 \begin_inset Index idx
14151 \begin_layout Plain Layout
14160 \begin_layout Standard
14164 \begin_layout Plain Layout
14168 textcolor{darkgreen}{
14174 \begin_inset Quotes eld
14178 \begin_inset Quotes erd
14185 \begin_layout Plain Layout
14195 \begin_layout Standard
14203 \begin_inset Index idx
14206 \begin_layout Plain Layout
14214 is used in the scheme
14218 textcolor{color}{characters to color}
14223 \begin_layout Subsection
14225 \begin_inset CommandInset label
14227 name "sub:Paragraph-Boxes"
14232 \begin_inset Index idx
14235 \begin_layout Plain Layout
14236 Boxes ! as paragraph
14244 \begin_layout Standard
14245 A box that can contain several lines and paragraphs, a so-called paragraph
14246 box (parbox), can be created with the menu
14248 Insert\SpecialChar \menuseparator
14251 or the toolbar button
14252 \begin_inset Graphics
14253 filename ../images/box-insert.png
14261 \begin_layout Standard
14262 The following example shows a framed parbox in a line:
14265 \begin_layout Standard
14266 \begin_inset VSpace medskip
14270 \begin_inset Box Boxed
14280 height_special "totalheight"
14283 \begin_layout Plain Layout
14284 This is a paragraph box.
14286 \begin_inset space \thinspace{}
14289 cm long and can also contain formulas:
14290 \begin_inset Formula $\int A\,\mathrm{d}s=C$
14301 \begin_layout Standard
14302 \begin_inset VSpace medskip
14308 \begin_layout Standard
14309 Such a box is created by right-clicking on the gray box inset.
14310 A dialog pops up showing the box properties.
14324 \begin_inset space \thinspace{}
14329 Vertical Box Alignment
14334 \begin_layout Standard
14335 \begin_inset VSpace medskip
14338 In LaTeX a parbox is created with the command
14345 \begin_inset Index idx
14348 \begin_layout Plain Layout
14356 which has the following scheme:
14359 \begin_layout Standard
14364 parbox[position]{width}{box content}
14367 \begin_layout Standard
14382 \begin_inset Quotes eld
14386 \begin_inset Quotes erd
14389 means that the box is aligned within the surrounding text with its last
14396 \begin_inset Quotes eld
14400 \begin_inset Quotes erd
14403 this is done with the first line.
14404 When no position is given, the box will be vertically centered, see section
14412 \begin_inset space ~
14417 manual for examples.
14420 \begin_layout Standard
14421 \begin_inset VSpace bigskip
14424 To frame formulas completely, including the formula number, the formula
14425 must be set into a parbox.
14426 To do this, the command
14440 is inserted in TeX-mode before the formula.
14448 \begin_inset Index idx
14451 \begin_layout Plain Layout
14459 is hereby the line width set for the document.
14460 Because the frame is outside the parbox, 2
14461 \begin_inset space \thinspace{}
14464 times the frame separation and the frame thickness must be subtracted from
14466 As this is not automatically done by LyX due to a bug
14470 \begin_layout Plain Layout
14471 \begin_inset CommandInset href
14473 name "LyX-bug #4483"
14474 target "http://www.lyx.org/trac/ticket/4483"
14483 , TeX-mode has to be used.
14484 To be able to multiply and subtract in arguments, the LaTeX-package
14492 \begin_layout Plain Layout
14497 is part of every LaTeX standard installation.
14503 \begin_inset Index idx
14506 \begin_layout Plain Layout
14512 must be loaded in the LaTeX-preamble with the line
14515 \begin_layout Standard
14523 \begin_layout Standard
14524 Behind the formula both boxes are closed by entering
14529 Here is an example:
14533 \begin_layout Plain Layout
14547 \begin_layout Standard
14551 \begin_layout Plain Layout
14569 \begin_inset Formula
14571 \int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
14580 \begin_layout Plain Layout
14591 \begin_layout Plain Layout
14605 \begin_layout Standard
14606 \begin_inset VSpace medskip
14609 As a parbox is used as the argument of
14615 , there is in this case no difference between
14630 \begin_layout Standard
14631 \begin_inset VSpace bigskip
14634 Paragraph boxes are very useful to comment formulas directly.
14641 is used in combination with the command
14655 \begin_inset CommandInset ref
14657 reference "sub:User-defined-Numbering"
14664 \begin_layout Standard
14665 An example of a formula commented with
14674 \begin_layout Standard
14678 \begin_layout Plain Layout
14691 This is a description.
14692 It is distinctly separated from the formula and multiline.
14696 \begin_layout Plain Layout
14708 \begin_layout Standard
14709 Such a formula must be inserted completely in TeX-mode because LyX does
14710 not yet support the command
14717 The formula is created with the following command sequence:
14720 \begin_layout Standard
14733 is inserted in TeX-mode.
14737 \begin_layout Plain Layout
14738 When the formula style
14750 can also be replaced by
14757 (formula styles see
14758 \begin_inset CommandInset ref
14760 reference "sec:Formula-Styles"
14769 Then the description follows as normal text and finally
14775 is inserted in TeX-mode.
14788 hereby create a displayed formula.
14791 \begin_layout Standard
14798 can be seen in this example that was
14799 \begin_inset Quotes eld
14803 \begin_inset Quotes erd
14806 using the mathematical textmode:
14807 \begin_inset Formula
14809 5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
14817 \begin_layout Section
14819 \begin_inset Index idx
14822 \begin_layout Plain Layout
14831 \begin_layout Subsection
14833 \begin_inset CommandInset label
14835 name "sub:Big-Operators"
14840 \begin_inset Index idx
14843 \begin_layout Plain Layout
14850 \begin_inset Index idx
14853 \begin_layout Plain Layout
14860 \begin_inset Index idx
14863 \begin_layout Plain Layout
14872 \begin_layout Standard
14873 To be able to use all integral operators listed here, the option
14875 Use esint package automatically
14877 must be set in the document settings under
14880 \begin_inset space ~
14888 \begin_layout Standard
14889 \begin_inset space \hfill{}
14893 \begin_inset Tabular
14894 <lyxtabular version="3" rows="11" columns="2">
14895 <features rotate="0" tabularvalignment="middle">
14896 <column alignment="center" valignment="top" width="0pt">
14897 <column alignment="center" valignment="top" width="0pt">
14899 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
14902 \begin_layout Plain Layout
14908 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
14911 \begin_layout Plain Layout
14919 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14922 \begin_layout Plain Layout
14926 \begin_inset Index idx
14929 \begin_layout Plain Layout
14942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14945 \begin_layout Plain Layout
14946 \begin_inset Formula $\int$
14956 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14959 \begin_layout Plain Layout
14967 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14970 \begin_layout Plain Layout
14971 \begin_inset Formula $\oint$
14981 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
14984 \begin_layout Plain Layout
14992 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
14995 \begin_layout Plain Layout
14996 \begin_inset Formula $\ointctrclockwise$
15006 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15009 \begin_layout Plain Layout
15017 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15020 \begin_layout Plain Layout
15021 \begin_inset Formula $\ointclockwise$
15031 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15034 \begin_layout Plain Layout
15042 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15045 \begin_layout Plain Layout
15046 \begin_inset Formula $\sqint$
15056 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15059 \begin_layout Plain Layout
15067 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15070 \begin_layout Plain Layout
15072 \begin_inset Formula $\fint$
15082 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15085 \begin_layout Plain Layout
15093 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15096 \begin_layout Plain Layout
15098 \begin_inset Formula $\landupint$
15108 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15111 \begin_layout Plain Layout
15119 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15122 \begin_layout Plain Layout
15124 \begin_inset Formula $\landdownint$
15134 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15137 \begin_layout Plain Layout
15145 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15148 \begin_layout Plain Layout
15149 \begin_inset Formula $\bigcap$
15159 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15162 \begin_layout Plain Layout
15170 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15173 \begin_layout Plain Layout
15174 \begin_inset Formula $\bigcup$
15188 \begin_inset space \hfill{}
15192 \begin_inset Tabular
15193 <lyxtabular version="3" rows="11" columns="2">
15194 <features rotate="0" tabularvalignment="middle">
15195 <column alignment="center" valignment="top" width="0pt">
15196 <column alignment="center" valignment="top" width="0pt">
15198 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15201 \begin_layout Plain Layout
15207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15210 \begin_layout Plain Layout
15218 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15221 \begin_layout Plain Layout
15225 \begin_inset Index idx
15228 \begin_layout Plain Layout
15241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15244 \begin_layout Plain Layout
15245 \begin_inset Formula $\sum$
15255 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15258 \begin_layout Plain Layout
15262 \begin_inset Index idx
15265 \begin_layout Plain Layout
15272 \begin_layout Plain Layout
15291 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15294 \begin_layout Plain Layout
15295 \begin_inset Formula $\prod$
15305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15308 \begin_layout Plain Layout
15316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15319 \begin_layout Plain Layout
15320 \begin_inset Formula $\coprod$
15330 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15333 \begin_layout Plain Layout
15341 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15344 \begin_layout Plain Layout
15345 \begin_inset Formula $\bigodot$
15355 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15358 \begin_layout Plain Layout
15366 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15369 \begin_layout Plain Layout
15370 \begin_inset Formula $\bigotimes$
15380 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15383 \begin_layout Plain Layout
15391 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15394 \begin_layout Plain Layout
15395 \begin_inset Formula $\bigoplus$
15405 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15408 \begin_layout Plain Layout
15416 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15419 \begin_layout Plain Layout
15420 \begin_inset Formula $\bigwedge$
15430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15433 \begin_layout Plain Layout
15441 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15444 \begin_layout Plain Layout
15445 \begin_inset Formula $\bigvee$
15455 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15458 \begin_layout Plain Layout
15466 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15469 \begin_layout Plain Layout
15470 \begin_inset Formula $\bigsqcup$
15480 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15483 \begin_layout Plain Layout
15491 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15494 \begin_layout Plain Layout
15495 \begin_inset Formula $\biguplus$
15509 \begin_inset space \hfill{}
15515 \begin_layout Standard
15516 All big operators can also be inserted via the math toolbar button
15517 \begin_inset Graphics
15518 filename ../images/math/intop.png
15526 \begin_layout Standard
15527 The operators are called big because they are bigger than the sometimes
15528 equal looking binary operators.
15529 All big operators can have limits as described in the next subsection.
15532 \begin_layout Standard
15533 For all integral operators there is a second version available, ending in
15551 These operators are different from
15558 \begin_inset space \space{}
15561 in the style the operator limits are displayed, see
15562 \begin_inset CommandInset ref
15564 reference "sub:Operator-Limits"
15572 \begin_layout Subsubsection*
15573 Advice for Integrals
15576 \begin_layout Standard
15581 in an integral is an operator, that therefore has to be set upright.
15582 This is done by highlighting the
15586 and using the keyboard shortcut
15596 \begin_layout Plain Layout
15602 \begin_inset CommandInset ref
15604 reference "sub:Font-Styles"
15614 Finally the smallest space is inserted before the
15618 , as this is usual for operators.
15622 \begin_layout Standard
15624 \begin_inset Formula $\int A(x)dx$
15628 \begin_inset Newline newline
15632 \begin_inset Phantom HPhantom
15635 \begin_layout Plain Layout
15642 \begin_inset Formula $\int A(x)\,\mathrm{d}x$
15648 \begin_layout Standard
15649 For multiple integrals there are the following commands:
15650 \begin_inset VSpace medskip
15656 \begin_layout Standard
15657 \begin_inset space \hfill{}
15661 \begin_inset Tabular
15662 <lyxtabular version="3" rows="4" columns="2">
15663 <features rotate="0" tabularvalignment="middle">
15664 <column alignment="center" valignment="top">
15665 <column alignment="center" valignment="top">
15667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15670 \begin_layout Plain Layout
15676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15679 \begin_layout Plain Layout
15681 \begin_inset Note Note
15684 \begin_layout Plain Layout
15691 is only used as spacer.
15703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15706 \begin_layout Plain Layout
15714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15717 \begin_layout Plain Layout
15718 \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
15728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15731 \begin_layout Plain Layout
15739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15742 \begin_layout Plain Layout
15743 \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
15753 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15756 \begin_layout Plain Layout
15764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15767 \begin_layout Plain Layout
15768 \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
15782 \begin_inset space \hfill{}
15786 \begin_inset Tabular
15787 <lyxtabular version="3" rows="4" columns="2">
15788 <features rotate="0" tabularvalignment="middle">
15789 <column alignment="center" valignment="top">
15790 <column alignment="center" valignment="top">
15792 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15795 \begin_layout Plain Layout
15801 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15804 \begin_layout Plain Layout
15812 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15815 \begin_layout Plain Layout
15823 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15826 \begin_layout Plain Layout
15827 \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
15837 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
15840 \begin_layout Plain Layout
15848 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
15851 \begin_layout Plain Layout
15852 \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
15862 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15865 \begin_layout Plain Layout
15873 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15876 \begin_layout Plain Layout
15877 \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
15891 \begin_inset space \hfill{}
15897 \begin_layout Standard
15898 \begin_inset Newpage newpage
15904 \begin_layout Subsection
15906 \begin_inset CommandInset label
15908 name "sub:Operator-Limits"
15913 \begin_inset Index idx
15916 \begin_layout Plain Layout
15925 \begin_layout Standard
15926 Limits are created by super- and subscripts:
15929 \begin_layout Standard
15931 \begin_inset Tabular
15932 <lyxtabular version="3" rows="2" columns="2">
15933 <features rotate="0" tabularvalignment="middle">
15934 <column alignment="center" valignment="top" width="0pt">
15935 <column alignment="center" valignment="top" width="0pt">
15937 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15940 \begin_layout Plain Layout
15946 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
15949 \begin_layout Plain Layout
15951 \begin_inset Note Note
15954 \begin_layout Plain Layout
15961 is only used as spacer.
15973 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
15976 \begin_layout Plain Layout
15985 \begin_layout Plain Layout
15995 \begin_inset Formula $\to$
15999 \begin_inset Formula $\to$
16007 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16010 \begin_layout Plain Layout
16011 \begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
16027 \begin_layout Standard
16028 Limits of inline formulas are set right beside the operator.
16029 Limits in displayed formulas are set above or below the operator, except
16030 for integral limits.
16033 \begin_layout Standard
16034 To force that the limits are set beside the operator, the cursor is set
16035 directly behind the operator and the limits type is changed with the menu
16038 Edit\SpecialChar \menuseparator
16039 Math\SpecialChar \menuseparator
16058 \begin_layout Standard
16059 The default limits type is this:
16060 \begin_inset Formula
16062 \sum_{x=0}^{\infty}\frac{1}{x^{2}}
16067 This is how it looks when the limits type was changed to
16074 \begin_inset Formula
16076 \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
16081 For integrals, except those ending with
16097 etc., the limits are by default set beside the operator.
16098 But for multiple integrals the limits are often set below the operator.
16099 In the following example the limits type was therefore set to
16103 and so set below the integrals:
16104 \begin_inset Formula
16106 \iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
16114 \begin_layout Standard
16115 \begin_inset VSpace medskip
16118 To specify conditions for limits, the commands
16125 \begin_inset Index idx
16128 \begin_layout Plain Layout
16143 \begin_inset Index idx
16146 \begin_layout Plain Layout
16155 To create for example this expression
16156 \begin_inset Formula
16158 \sum_{\begin{subarray}{c}
16162 \end{subarray}}^{n}k^{-2}\label{eq:substack}
16170 \begin_layout Standard
16171 the following has to be done:
16172 \begin_inset Newline newline
16187 \begin_layout Plain Layout
16199 One is now in a blue box under the summation operator and insert there
16208 \begin_layout Plain Layout
16220 The blue box is now within a purple box and now several lines can be written
16222 A new line is created by inserting a line break (
16225 arg "newline-insert newline"
16230 \begin_inset Newline newline
16235 0<k<1000 Ctrl+Return
16236 \begin_inset Newline newline
16241 is typed in, a new box appears below for the new line.
16244 \begin_layout Standard
16245 The alignment of the lines can be changed to left aligned with the
16255 Edit\SpecialChar \menuseparator
16259 To get right alignment,
16267 \begin_layout Plain Layout
16278 is inserted at the beginning of the line.
16281 \begin_layout Standard
16294 with the difference that the lines are always centered.
16297 \begin_layout Standard
16298 \begin_inset VSpace bigskip
16302 \begin_inset CommandInset ref
16304 reference "eq:substack"
16308 there can be too much space beside an operator, because the characters
16309 following the operator are set beside the limits.
16312 \begin_layout Standard
16313 To avoid this, the following macro can be used in the LaTeX-preamble:
16316 \begin_layout Standard
16330 \begin_inset Newline newline
16342 \begin_inset Newline newline
16349 mathclapinternal #1#2{
16353 mathsurround =0pt #1{#2}$}}
16356 \begin_layout Standard
16357 This defines the command
16364 \begin_inset Index idx
16367 \begin_layout Plain Layout
16375 that sets the width of the limit to 0
16376 \begin_inset space \thinspace{}
16380 The command scheme is
16383 \begin_layout Standard
16391 \begin_layout Standard
16392 where the limit can consist of several conditions.
16395 \begin_layout Standard
16397 \begin_inset CommandInset ref
16399 reference "eq:substack"
16403 , one uses the command
16406 \begin_layout Standard
16419 \begin_layout Plain Layout
16428 0<k<1000 Ctrl+Return
16431 \begin_layout Standard
16432 to create the lower limit.
16433 The summand is now directly behind the summation operator:
16434 \begin_inset Formula
16436 \sum_{\mathclap{\substack{0<k<1000\\
16448 \begin_layout Standard
16449 \begin_inset VSpace bigskip
16452 How to use one limit for several operators is described in
16453 \begin_inset CommandInset ref
16455 reference "sub:Self-defined-Operators"
16462 \begin_layout Subsection
16463 Decoration for Operators
16464 \begin_inset Index idx
16467 \begin_layout Plain Layout
16468 Operators ! Decoration
16476 \begin_layout Standard
16484 \begin_inset Index idx
16487 \begin_layout Plain Layout
16502 \begin_inset Index idx
16505 \begin_layout Plain Layout
16513 characters can be placed above or below an operator, respectively.
16521 \begin_inset Index idx
16524 \begin_layout Plain Layout
16532 characters can be set before and behind a big operator.
16533 The command scheme is:
16536 \begin_layout Standard
16552 \begin_layout Standard
16559 must always be before the operator.
16560 You can decorate with several characters and even with other operators
16562 To place for example only characters behind a big operator, write nothing
16563 between the first braces but don't omit the braces.
16566 \begin_layout Standard
16567 For example the command
16572 \begin_inset Formula $\to$
16582 \begin_inset Formula $\to$
16591 \begin_layout Plain Layout
16607 \begin_inset Formula
16609 \sideset{}{'}\sum_{k=1}^{n}
16617 \begin_layout Standard
16618 \begin_inset Note Greyedout
16621 \begin_layout Plain Layout
16628 can only be used to decorate big operators, binary operators are not allowed.
16636 \begin_layout Standard
16649 can also be used to decorate symbols and characters.
16650 For example, the command
16658 \begin_layout Plain Layout
16673 \begin_layout Plain Layout
16685 \begin_inset Formula $\uparrow$
16693 \begin_inset Formula
16695 \overset{a}{\maltese}
16703 \begin_layout Subsection
16705 \begin_inset CommandInset label
16707 name "sub:Binary-Operators"
16712 \begin_inset Index idx
16715 \begin_layout Plain Layout
16724 \begin_layout Standard
16725 Binary operators are surrounded by space when there is a character before
16727 \begin_inset VSpace medskip
16733 \begin_layout Standard
16734 \begin_inset space \hfill{}
16738 \begin_inset Tabular
16739 <lyxtabular version="3" rows="13" columns="2">
16740 <features rotate="0" tabularvalignment="middle">
16741 <column alignment="center" valignment="top" width="0pt">
16742 <column alignment="center" valignment="top" width="0pt">
16744 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
16747 \begin_layout Plain Layout
16749 \begin_inset Note Note
16752 \begin_layout Plain Layout
16759 is only used as spacer.
16769 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
16772 \begin_layout Plain Layout
16780 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16783 \begin_layout Plain Layout
16789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16792 \begin_layout Plain Layout
16793 \begin_inset Formula $+$
16803 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16806 \begin_layout Plain Layout
16812 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16815 \begin_layout Plain Layout
16816 \begin_inset Formula $-$
16826 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16829 \begin_layout Plain Layout
16837 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16840 \begin_layout Plain Layout
16841 \begin_inset Formula $\pm$
16851 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16854 \begin_layout Plain Layout
16862 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16865 \begin_layout Plain Layout
16866 \begin_inset Formula $\mp$
16876 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16879 \begin_layout Plain Layout
16887 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16890 \begin_layout Plain Layout
16891 \begin_inset Formula $\cdot$
16901 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16904 \begin_layout Plain Layout
16912 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16915 \begin_layout Plain Layout
16916 \begin_inset Formula $\times$
16926 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16929 \begin_layout Plain Layout
16937 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16940 \begin_layout Plain Layout
16941 \begin_inset Formula $\div$
16951 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
16954 \begin_layout Plain Layout
16958 \begin_layout Plain Layout
16971 \begin_layout Plain Layout
16983 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
16986 \begin_layout Plain Layout
16987 \begin_inset Formula $*$
16997 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17000 \begin_layout Plain Layout
17008 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17011 \begin_layout Plain Layout
17012 \begin_inset Formula $\star$
17022 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17025 \begin_layout Plain Layout
17033 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17036 \begin_layout Plain Layout
17037 \begin_inset Formula $\circ$
17047 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17050 \begin_layout Plain Layout
17058 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17061 \begin_layout Plain Layout
17062 \begin_inset Formula $\diamond$
17072 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17075 \begin_layout Plain Layout
17083 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17086 \begin_layout Plain Layout
17087 \begin_inset Formula $\bullet$
17101 \begin_inset space \hfill{}
17105 \begin_inset Tabular
17106 <lyxtabular version="3" rows="13" columns="2">
17107 <features rotate="0" tabularvalignment="middle">
17108 <column alignment="center" valignment="top" width="0pt">
17109 <column alignment="center" valignment="top" width="0pt">
17111 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17114 \begin_layout Plain Layout
17120 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17123 \begin_layout Plain Layout
17131 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17134 \begin_layout Plain Layout
17142 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17145 \begin_layout Plain Layout
17146 \begin_inset Formula $\nabla$
17156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17159 \begin_layout Plain Layout
17167 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17170 \begin_layout Plain Layout
17171 \begin_inset Formula $\bigtriangledown$
17181 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17184 \begin_layout Plain Layout
17192 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17195 \begin_layout Plain Layout
17196 \begin_inset Formula $\bigtriangleup$
17206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17209 \begin_layout Plain Layout
17217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17220 \begin_layout Plain Layout
17221 \begin_inset Formula $\Box$
17231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17234 \begin_layout Plain Layout
17242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17245 \begin_layout Plain Layout
17246 \begin_inset Formula $\cap$
17256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17259 \begin_layout Plain Layout
17267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17270 \begin_layout Plain Layout
17271 \begin_inset Formula $\cup$
17281 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17284 \begin_layout Plain Layout
17292 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17295 \begin_layout Plain Layout
17296 \begin_inset Formula $\dagger$
17306 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17309 \begin_layout Plain Layout
17317 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17320 \begin_layout Plain Layout
17321 \begin_inset Formula $\ddagger$
17331 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17334 \begin_layout Plain Layout
17342 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17345 \begin_layout Plain Layout
17346 \begin_inset Formula $\wr$
17356 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17359 \begin_layout Plain Layout
17367 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17370 \begin_layout Plain Layout
17371 \begin_inset Formula $\bigcirc$
17381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17384 \begin_layout Plain Layout
17392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17395 \begin_layout Plain Layout
17396 \begin_inset Formula $\wedge$
17406 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17409 \begin_layout Plain Layout
17417 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17420 \begin_layout Plain Layout
17421 \begin_inset Formula $\vee$
17435 \begin_inset space \hfill{}
17439 \begin_inset Tabular
17440 <lyxtabular version="3" rows="13" columns="2">
17441 <features rotate="0" tabularvalignment="middle">
17442 <column alignment="center" valignment="top" width="0pt">
17443 <column alignment="center" valignment="top" width="0pt">
17445 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17448 \begin_layout Plain Layout
17454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17457 \begin_layout Plain Layout
17465 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17468 \begin_layout Plain Layout
17476 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17479 \begin_layout Plain Layout
17480 \begin_inset Formula $\oplus$
17490 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17493 \begin_layout Plain Layout
17501 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17504 \begin_layout Plain Layout
17505 \begin_inset Formula $\ominus$
17515 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17518 \begin_layout Plain Layout
17526 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17529 \begin_layout Plain Layout
17530 \begin_inset Formula $\otimes$
17540 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17543 \begin_layout Plain Layout
17551 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17554 \begin_layout Plain Layout
17555 \begin_inset Formula $\oslash$
17565 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17568 \begin_layout Plain Layout
17576 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17579 \begin_layout Plain Layout
17580 \begin_inset Formula $\odot$
17590 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17593 \begin_layout Plain Layout
17601 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17604 \begin_layout Plain Layout
17605 \begin_inset Formula $\amalg$
17615 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17618 \begin_layout Plain Layout
17626 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17629 \begin_layout Plain Layout
17630 \begin_inset Formula $\uplus$
17640 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17643 \begin_layout Plain Layout
17651 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17654 \begin_layout Plain Layout
17655 \begin_inset Formula $\setminus$
17665 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17668 \begin_layout Plain Layout
17676 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17679 \begin_layout Plain Layout
17680 \begin_inset Formula $\sqcap$
17690 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17693 \begin_layout Plain Layout
17701 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17704 \begin_layout Plain Layout
17705 \begin_inset Formula $\sqcup$
17715 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
17718 \begin_layout Plain Layout
17726 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
17729 \begin_layout Plain Layout
17730 \begin_inset Formula $\triangleleft$
17740 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
17743 \begin_layout Plain Layout
17751 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
17754 \begin_layout Plain Layout
17755 \begin_inset Formula $\triangleright$
17769 \begin_inset space \hfill{}
17775 \begin_layout Standard
17776 All binary operators can also be inserted via the math toolbar button
17777 \begin_inset Graphics
17778 filename ../images/math/pm.png
17786 \begin_layout Standard
17787 To typeset the Laplace operator also
17804 \begin_inset Formula $\nabla^{2}$
17807 ) can be used instead of
17816 \begin_layout Standard
17823 Insert\SpecialChar \menuseparator
17835 \begin_layout Subsection
17836 Self-defined Operators
17837 \begin_inset CommandInset label
17839 name "sub:Self-defined-Operators"
17844 \begin_inset Index idx
17847 \begin_layout Plain Layout
17848 Operators ! self-defined
17856 \begin_layout Standard
17857 With the help of the command
17861 DeclareMathOperator
17864 \begin_inset Index idx
17867 \begin_layout Plain Layout
17872 DeclareMathOperator
17877 custom operators can be defined in the LaTeX-preamble.
17878 Its command scheme is:
17881 \begin_layout Standard
17886 DeclareMathOperator{new command}{display}
17889 \begin_layout Standard
17890 Display can be characters or symbols that define how the operator looks
17892 To define a big operator a * is set behind the command.
17893 All self-defined big operators can have limits as described in
17894 \begin_inset CommandInset ref
17896 reference "sub:Operator-Limits"
17903 \begin_layout Standard
17904 For example the LaTeX-preamble line
17907 \begin_layout Standard
17912 DeclareMathOperator*{
17919 \begin_layout Standard
17920 defines the command
17926 , that inserts a big operator consisting of the lozenge symbol from
17927 \begin_inset CommandInset ref
17929 reference "sub:Miscellaneous-Symbols"
17934 \begin_inset Formula
17936 \Lozenge_{n=1}^{\infty}
17941 The command for this formula is:
17952 \begin_inset Formula $\to$
17958 \begin_layout Standard
17959 \begin_inset VSpace bigskip
17962 When self-defined operators are not used several times in the document,
17963 they can also be defined with the commands
17970 \begin_inset Index idx
17973 \begin_layout Plain Layout
17988 \begin_inset Index idx
17991 \begin_layout Plain Layout
17999 , which have the following scheme:
18002 \begin_layout Standard
18016 \begin_layout Standard
18023 defines big operators,
18032 \begin_layout Standard
18040 \begin_inset space \thinspace{}
18044 \begin_inset space \space{}
18047 be used to use one limit for several operators:
18050 \begin_layout Standard
18051 \begin_inset Formula
18053 \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
18061 \begin_layout Standard
18062 The command for the formula above is:
18063 \begin_inset Newline newline
18082 \begin_layout Plain Layout
18094 \begin_inset Formula $\to$
18103 \begin_layout Plain Layout
18117 \begin_layout Section
18119 \begin_inset Index idx
18122 \begin_layout Plain Layout
18131 \begin_layout Subsection
18133 \begin_inset CommandInset label
18135 name "sub:Font-Styles"
18140 \begin_inset Index idx
18143 \begin_layout Plain Layout
18152 \begin_layout Standard
18153 Latin letters in formulas can be set in one of the following font styles:
18154 \begin_inset VSpace -2mm
18160 \begin_layout Standard
18162 \begin_inset Tabular
18163 <lyxtabular version="3" rows="7" columns="3">
18164 <features rotate="0" tabularvalignment="middle">
18165 <column alignment="center" valignment="top">
18166 <column alignment="center" valignment="top">
18167 <column alignment="center" valignment="top">
18169 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18172 \begin_layout Plain Layout
18178 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18181 \begin_layout Plain Layout
18187 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18190 \begin_layout Plain Layout
18198 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18201 \begin_layout Plain Layout
18210 \begin_layout Plain Layout
18226 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18229 \begin_layout Plain Layout
18230 \begin_inset Formula $\mathbb{ABC}$
18238 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18241 \begin_layout Plain Layout
18254 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18257 \begin_layout Plain Layout
18266 \begin_layout Plain Layout
18282 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18285 \begin_layout Plain Layout
18286 \begin_inset Formula $\mathbf{AbC}$
18294 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18297 \begin_layout Plain Layout
18310 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18313 \begin_layout Plain Layout
18322 \begin_layout Plain Layout
18338 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18341 \begin_layout Plain Layout
18342 \begin_inset Formula $\boldsymbol{AbC}$
18350 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18353 \begin_layout Plain Layout
18356 arg "font-boldsymbol"
18366 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18369 \begin_layout Plain Layout
18378 \begin_layout Plain Layout
18394 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18397 \begin_layout Plain Layout
18398 \begin_inset Formula $\mathcal{ABC}$
18406 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18409 \begin_layout Plain Layout
18422 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18425 \begin_layout Plain Layout
18434 \begin_layout Plain Layout
18450 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18453 \begin_layout Plain Layout
18454 \begin_inset Formula $\mathfrak{AbC}$
18462 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18465 \begin_layout Plain Layout
18473 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18476 \begin_layout Plain Layout
18485 \begin_layout Plain Layout
18501 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18504 \begin_layout Plain Layout
18505 \begin_inset Formula $\mathscr{AbC}$
18513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18516 \begin_layout Plain Layout
18530 \begin_layout Standard
18532 \begin_inset Tabular
18533 <lyxtabular version="3" rows="5" columns="3">
18534 <features rotate="0" tabularvalignment="middle">
18535 <column alignment="center" valignment="top">
18536 <column alignment="center" valignment="top">
18537 <column alignment="center" valignment="top">
18539 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18542 \begin_layout Plain Layout
18548 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18551 \begin_layout Plain Layout
18557 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18560 \begin_layout Plain Layout
18568 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18571 \begin_layout Plain Layout
18580 \begin_layout Plain Layout
18596 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18599 \begin_layout Plain Layout
18600 \begin_inset Formula $\mathit{AbC}$
18608 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18611 \begin_layout Plain Layout
18619 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18622 \begin_layout Plain Layout
18631 \begin_layout Plain Layout
18647 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18650 \begin_layout Plain Layout
18651 \begin_inset Formula $\mathrm{AbC}$
18659 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18662 \begin_layout Plain Layout
18675 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18678 \begin_layout Plain Layout
18687 \begin_layout Plain Layout
18703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
18706 \begin_layout Plain Layout
18707 \begin_inset Formula $\mathsf{AbC}$
18715 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
18718 \begin_layout Plain Layout
18731 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18734 \begin_layout Plain Layout
18743 \begin_layout Plain Layout
18759 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
18762 \begin_layout Plain Layout
18763 \begin_inset Formula $\mathtt{AbC}$
18771 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
18774 \begin_layout Plain Layout
18777 arg "font-typewriter"
18793 \begin_layout Standard
18794 \begin_inset Note Greyedout
18797 \begin_layout Plain Layout
18814 can only be used for big letters.
18822 \begin_layout Standard
18823 Predefined is the style
18832 \begin_layout Standard
18833 The style commands work also for letters in mathematical constructs:
18834 \begin_inset Formula
18836 \mathfrak{A=\frac{b}{C}}
18844 \begin_layout Standard
18845 Characters in mathematical text don't appear in a math font style but in
18846 the text font style
18853 That their style can't be set correctly via the text style dialog is a
18858 \begin_layout Plain Layout
18859 \begin_inset CommandInset href
18861 name "LyX-bug #4629"
18862 target "http://www.lyx.org/trac/ticket/4629"
18874 \begin_layout Standard
18875 Instead of the style commands the dialog
18877 Edit\SpecialChar \menuseparator
18878 Math\SpecialChar \menuseparator
18881 or the toolbar button
18882 \begin_inset Graphics
18883 filename ../images/math/font.png
18891 \begin_layout Subsection
18893 \begin_inset CommandInset label
18895 name "sub:Bold-Formulas"
18900 \begin_inset Index idx
18903 \begin_layout Plain Layout
18912 \begin_layout Standard
18913 To make a complete formula bold, the command
18919 from the previous subsection cannot be used, because it doesn't work for
18920 small Greek letters.
18921 Furthermore it prints Latin letters always upright, like in the following
18925 \begin_layout Standard
18926 \begin_inset Formula
18928 \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
18936 \begin_layout Standard
18937 To display the formula correctly, the command
18944 \begin_inset Formula
18946 \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
18951 It is also possible to set the formula in a
18953 boldmath environment
18956 This environment is created by inserting the command
18963 \begin_inset Index idx
18966 \begin_layout Plain Layout
18975 To end the environment, the command
18982 \begin_inset Index idx
18985 \begin_layout Plain Layout
18993 is inserted in TeX-mode.
18997 \begin_layout Plain Layout
19007 \begin_inset Formula
19009 \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
19018 \begin_layout Plain Layout
19030 \begin_layout Subsection
19032 \begin_inset Index idx
19035 \begin_layout Plain Layout
19044 \begin_layout Standard
19045 Formulas can be colored like normal text: Highlight a formula or a formula
19051 Here is a formula in magenta:
19052 \begin_inset Formula
19054 {\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
19062 \begin_layout Standard
19063 You can also define your own colors as described in
19064 \begin_inset CommandInset ref
19066 reference "sub:Colored-Boxes"
19071 They can be used with the TeX code command
19078 \begin_inset Index idx
19081 \begin_layout Plain Layout
19092 \begin_layout Standard
19097 textcolor{color}{characters or formula}
19100 \begin_layout Standard
19101 The following example was colored completely dark green and partly red:
19104 \begin_layout Standard
19108 \begin_layout Plain Layout
19112 textcolor{darkgreen}{
19118 \begin_inset Formula
19120 \int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
19129 \begin_layout Plain Layout
19139 \begin_layout Standard
19140 Due to a bug in LyX only complete formulas can be colored with self-defined
19145 \begin_layout Plain Layout
19146 \begin_inset CommandInset href
19148 name "LyX-bug #5269"
19149 target "http://www.lyx.org/trac/ticket/5269"
19161 \begin_layout Subsection
19163 \begin_inset CommandInset label
19165 name "sub:Font-Sizes"
19170 \begin_inset Index idx
19173 \begin_layout Plain Layout
19182 \begin_layout Standard
19183 For characters in formulas there are, analog to characters in text, the
19184 following size commands:
19187 \begin_layout Standard
19231 \begin_inset Newline newline
19253 \begin_layout Standard
19254 The size produced by the commands depends on the document font size, which
19255 corresponds to the command
19262 The other commands produce smaller or larger sizes than
19269 The font size can however not exceed a certain value.
19270 Is for example the document font size 12
19271 \begin_inset space \thinspace{}
19280 switches to the same size as
19290 \begin_layout Standard
19291 A size command is inserted in TeX-mode before the formula and sets the size
19292 for all following formula and text characters.
19293 To switch back to the initial size, the command
19299 is inserted behind the formula in TeX-mode.
19302 \begin_layout Standard
19303 Within a formula the size can be changed using the following size commands:
19306 \begin_layout Standard
19309 \begin_inset Tabular
19310 <lyxtabular version="3" rows="5" columns="2">
19311 <features rotate="0" tabularvalignment="middle">
19312 <column alignment="center" valignment="top">
19313 <column alignment="center" valignment="top">
19315 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19318 \begin_layout Plain Layout
19324 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19327 \begin_layout Plain Layout
19329 \begin_inset Note Note
19332 \begin_layout Plain Layout
19339 is only used as spacer.
19351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19354 \begin_layout Plain Layout
19358 \begin_inset Index idx
19361 \begin_layout Plain Layout
19374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19377 \begin_layout Plain Layout
19378 \begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$
19388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19391 \begin_layout Plain Layout
19399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19402 \begin_layout Plain Layout
19403 \begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$
19413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19416 \begin_layout Plain Layout
19424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19427 \begin_layout Plain Layout
19428 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19438 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19441 \begin_layout Plain Layout
19449 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19452 \begin_layout Plain Layout
19453 \begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$
19469 \begin_layout Standard
19470 After entering these commands, a blue box appears in which the formula parts
19474 \begin_layout Standard
19475 There is a further method to change the font size, that though only works
19476 for symbols or letters in mathematical text.
19477 To use it, one of the above text size commands is inserted in mathematical
19479 All following characters until the end of the mathematical text or until
19480 another size command will have the selected size.
19482 \begin_inset VSpace -2mm
19488 \begin_layout Standard
19492 \begin_layout Plain Layout
19502 \begin_inset Formula
19504 A=\frac{B}{c}\cdot\maltese
19510 \begin_inset Formula
19512 \maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
19521 \begin_layout Plain Layout
19533 \begin_layout Standard
19534 \begin_inset VSpace medskip
19537 Before both formulas the command
19544 The command for the second formula is:
19545 \begin_inset Newline newline
19556 \begin_layout Plain Layout
19571 \begin_layout Plain Layout
19586 \begin_layout Plain Layout
19601 \begin_layout Plain Layout
19611 \begin_inset Formula $\to$
19615 \begin_inset Formula $\to$
19619 \begin_inset Newline newline
19623 \begin_inset space \hspace*{}
19637 \begin_layout Plain Layout
19652 \begin_layout Plain Layout
19667 \begin_layout Plain Layout
19679 \begin_layout Standard
19680 If a symbol cannot be displayed in different sizes, it will always be displayed
19681 in the default size.
19684 \begin_layout Section
19686 \begin_inset Index idx
19689 \begin_layout Plain Layout
19698 \begin_layout Standard
19699 Greek letters can also be inserted via the toolbar button
19700 \begin_inset Graphics
19701 filename ../images/math/alpha.png
19707 All international typesetting norms purport that Greek letters in math
19708 have to be typeset italic/slanted.
19709 In some languages, like French or Russian, they are nevertheless sometimes
19713 \begin_layout Subsection
19715 \begin_inset Index idx
19718 \begin_layout Plain Layout
19719 Greek letters ! small
19727 \begin_layout Standard
19728 \begin_inset space \hfill{}
19732 \begin_inset Tabular
19733 <lyxtabular version="3" rows="11" columns="2">
19734 <features rotate="0" tabularvalignment="middle">
19735 <column alignment="center" valignment="top" width="0pt">
19736 <column alignment="center" valignment="top" width="0pt">
19738 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19741 \begin_layout Plain Layout
19747 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19750 \begin_layout Plain Layout
19758 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19761 \begin_layout Plain Layout
19769 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19772 \begin_layout Plain Layout
19773 \begin_inset Formula $\alpha$
19783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19786 \begin_layout Plain Layout
19794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19797 \begin_layout Plain Layout
19798 \begin_inset Formula $\beta$
19808 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19811 \begin_layout Plain Layout
19819 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19822 \begin_layout Plain Layout
19823 \begin_inset Formula $\gamma$
19833 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19836 \begin_layout Plain Layout
19844 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19847 \begin_layout Plain Layout
19848 \begin_inset Formula $\delta$
19858 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19861 \begin_layout Plain Layout
19869 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19872 \begin_layout Plain Layout
19873 \begin_inset Formula $\epsilon$
19883 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19886 \begin_layout Plain Layout
19894 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19897 \begin_layout Plain Layout
19898 \begin_inset Formula $\varepsilon$
19908 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19911 \begin_layout Plain Layout
19919 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19922 \begin_layout Plain Layout
19923 \begin_inset Formula $\zeta$
19933 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19936 \begin_layout Plain Layout
19944 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19947 \begin_layout Plain Layout
19948 \begin_inset Formula $\eta$
19958 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
19961 \begin_layout Plain Layout
19969 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
19972 \begin_layout Plain Layout
19973 \begin_inset Formula $\theta$
19983 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
19986 \begin_layout Plain Layout
19994 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
19997 \begin_layout Plain Layout
19998 \begin_inset Formula $\vartheta$
20012 \begin_inset space \hfill{}
20016 \begin_inset Tabular
20017 <lyxtabular version="3" rows="12" columns="2">
20018 <features rotate="0" tabularvalignment="middle">
20019 <column alignment="center" valignment="top" width="0pt">
20020 <column alignment="center" valignment="top" width="0pt">
20022 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20025 \begin_layout Plain Layout
20031 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20034 \begin_layout Plain Layout
20042 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20045 \begin_layout Plain Layout
20053 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20056 \begin_layout Plain Layout
20057 \begin_inset Formula $\iota$
20067 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20070 \begin_layout Plain Layout
20078 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20081 \begin_layout Plain Layout
20082 \begin_inset Formula $\kappa$
20092 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20095 \begin_layout Plain Layout
20103 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20106 \begin_layout Plain Layout
20107 \begin_inset Formula $\varkappa$
20117 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20120 \begin_layout Plain Layout
20128 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20131 \begin_layout Plain Layout
20132 \begin_inset Formula $\lambda$
20142 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20145 \begin_layout Plain Layout
20153 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20156 \begin_layout Plain Layout
20157 \begin_inset Formula $\mu$
20167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20170 \begin_layout Plain Layout
20178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20181 \begin_layout Plain Layout
20182 \begin_inset Formula $\nu$
20192 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20195 \begin_layout Plain Layout
20203 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20206 \begin_layout Plain Layout
20207 \begin_inset Formula $\xi$
20217 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20220 \begin_layout Plain Layout
20226 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20229 \begin_layout Plain Layout
20230 \begin_inset Formula $o$
20240 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20243 \begin_layout Plain Layout
20251 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20254 \begin_layout Plain Layout
20255 \begin_inset Formula $\pi$
20265 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20268 \begin_layout Plain Layout
20276 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20279 \begin_layout Plain Layout
20280 \begin_inset Formula $\varpi$
20290 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20293 \begin_layout Plain Layout
20301 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20304 \begin_layout Plain Layout
20305 \begin_inset Formula $\rho$
20319 \begin_inset space \hfill{}
20323 \begin_inset Tabular
20324 <lyxtabular version="3" rows="11" columns="2">
20325 <features rotate="0" tabularvalignment="middle">
20326 <column alignment="center" valignment="top" width="0pt">
20327 <column alignment="center" valignment="top" width="0pt">
20329 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20332 \begin_layout Plain Layout
20338 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20341 \begin_layout Plain Layout
20349 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20352 \begin_layout Plain Layout
20360 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20363 \begin_layout Plain Layout
20364 \begin_inset Formula $\varrho$
20374 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20377 \begin_layout Plain Layout
20385 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20388 \begin_layout Plain Layout
20389 \begin_inset Formula $\sigma$
20399 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20402 \begin_layout Plain Layout
20410 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20413 \begin_layout Plain Layout
20414 \begin_inset Formula $\varsigma$
20424 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20427 \begin_layout Plain Layout
20435 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20438 \begin_layout Plain Layout
20439 \begin_inset Formula $\tau$
20449 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20452 \begin_layout Plain Layout
20460 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20463 \begin_layout Plain Layout
20464 \begin_inset Formula $\upsilon$
20474 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20477 \begin_layout Plain Layout
20485 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20488 \begin_layout Plain Layout
20489 \begin_inset Formula $\phi$
20499 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20502 \begin_layout Plain Layout
20510 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20513 \begin_layout Plain Layout
20514 \begin_inset Formula $\varphi$
20524 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20527 \begin_layout Plain Layout
20535 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20538 \begin_layout Plain Layout
20539 \begin_inset Formula $\chi$
20549 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20552 \begin_layout Plain Layout
20560 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20563 \begin_layout Plain Layout
20564 \begin_inset Formula $\psi$
20574 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20577 \begin_layout Plain Layout
20585 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20588 \begin_layout Plain Layout
20589 \begin_inset Formula $\omega$
20603 \begin_inset space \hfill{}
20609 \begin_layout Standard
20610 \begin_inset VSpace medskip
20616 \begin_layout Standard
20617 How to create special upright Greek letters is explained in
20618 \begin_inset CommandInset ref
20620 reference "sub:Upright-small-Greek"
20627 \begin_layout Subsection
20629 \begin_inset Index idx
20632 \begin_layout Plain Layout
20633 Greek letters ! big
20641 \begin_layout Standard
20642 \begin_inset space \hfill{}
20646 \begin_inset Tabular
20647 <lyxtabular version="3" rows="7" columns="2">
20648 <features rotate="0" tabularvalignment="middle">
20649 <column alignment="center" valignment="top" width="0pt">
20650 <column alignment="center" valignment="top" width="0pt">
20652 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20655 \begin_layout Plain Layout
20661 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20664 \begin_layout Plain Layout
20672 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20675 \begin_layout Plain Layout
20683 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20686 \begin_layout Plain Layout
20687 \begin_inset Formula $\Gamma$
20697 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20700 \begin_layout Plain Layout
20708 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20711 \begin_layout Plain Layout
20712 \begin_inset Formula $\Delta$
20722 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20725 \begin_layout Plain Layout
20733 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20736 \begin_layout Plain Layout
20737 \begin_inset Formula $\Theta$
20747 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20750 \begin_layout Plain Layout
20758 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20761 \begin_layout Plain Layout
20762 \begin_inset Formula $\Lambda$
20772 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20775 \begin_layout Plain Layout
20783 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20786 \begin_layout Plain Layout
20787 \begin_inset Formula $\Xi$
20797 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20800 \begin_layout Plain Layout
20808 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20811 \begin_layout Plain Layout
20812 \begin_inset Formula $\Pi$
20826 \begin_inset space \hfill{}
20830 \begin_inset Tabular
20831 <lyxtabular version="3" rows="6" columns="2">
20832 <features rotate="0" tabularvalignment="middle">
20833 <column alignment="center" valignment="top" width="0pt">
20834 <column alignment="center" valignment="top" width="0pt">
20836 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20839 \begin_layout Plain Layout
20845 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20848 \begin_layout Plain Layout
20856 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20859 \begin_layout Plain Layout
20867 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20870 \begin_layout Plain Layout
20871 \begin_inset Formula $\Sigma$
20881 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20884 \begin_layout Plain Layout
20892 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20895 \begin_layout Plain Layout
20896 \begin_inset Formula $\Upsilon$
20906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20909 \begin_layout Plain Layout
20917 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20920 \begin_layout Plain Layout
20921 \begin_inset Formula $\Phi$
20931 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
20934 \begin_layout Plain Layout
20942 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
20945 \begin_layout Plain Layout
20946 \begin_inset Formula $\Psi$
20956 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
20959 \begin_layout Plain Layout
20967 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
20970 \begin_layout Plain Layout
20971 \begin_inset Formula $\Omega$
20985 \begin_inset space \hfill{}
20991 \begin_layout Standard
20992 \begin_inset VSpace medskip
20995 That the big Greek letters appear upright is caused by a design bug when
20997 To get correct italic big letters, begin every command with
21002 For example the command
21009 \begin_inset Formula $\varGamma$
21013 Another way is to load the package
21021 \begin_layout Plain Layout
21026 is part of the LaTeX-package
21031 \begin_inset Index idx
21034 \begin_layout Plain Layout
21039 \begin_layout Plain Layout
21059 \begin_inset Index idx
21062 \begin_layout Plain Layout
21068 with the LaTeX-preamble line
21071 \begin_layout Standard
21076 usepackage{fixmath}
21079 \begin_layout Standard
21080 Then all big Greek letters in a document will automatically be typeset italic.
21083 \begin_layout Subsection
21085 \begin_inset Index idx
21088 \begin_layout Plain Layout
21089 Greek letters ! bold
21097 \begin_layout Standard
21098 Greek letters cannot be set with different font styles like Latin letters.
21099 They can only be made bold with the command
21106 \begin_inset Index idx
21109 \begin_layout Plain Layout
21120 \begin_layout Standard
21122 \begin_inset Tabular
21123 <lyxtabular version="3" rows="3" columns="2">
21124 <features rotate="0" tabularvalignment="middle">
21125 <column alignment="center" valignment="top">
21126 <column alignment="center" valignment="top">
21128 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21131 \begin_layout Plain Layout
21137 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21140 \begin_layout Plain Layout
21148 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21151 \begin_layout Plain Layout
21163 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21166 \begin_layout Plain Layout
21167 \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
21177 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21180 \begin_layout Plain Layout
21192 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21195 \begin_layout Plain Layout
21196 \begin_inset Formula $\theta\boldsymbol{\theta}$
21212 \begin_layout Section
21217 \begin_layout Plain Layout
21230 \begin_layout Plain Layout
21231 A list with all symbols of most of the LaTeX-packages can be found in
21232 \begin_inset CommandInset citation
21247 \begin_layout Plain Layout
21255 \begin_inset Note Note
21258 \begin_layout Plain Layout
21261 texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
21264 \begin_layout Plain Layout
21267 texorpdfstring is in section
21268 \begin_inset CommandInset ref
21270 reference "sub:Formulas-in-Section"
21280 \begin_inset Index idx
21283 \begin_layout Plain Layout
21292 \begin_layout Standard
21293 Many of the symbols listed in this section can also be inserted via the
21295 \begin_inset Graphics
21296 filename ../images/math/nabla.png
21302 \begin_inset Graphics
21303 filename ../images/math/digamma.png
21311 \begin_layout Subsection
21312 Mathematical Symbols
21313 \begin_inset CommandInset label
21315 name "sub:Mathematical-Symbols"
21320 \begin_inset Index idx
21323 \begin_layout Plain Layout
21324 Symbols ! mathematical
21332 \begin_layout Standard
21333 \begin_inset space \hfill{}
21337 \begin_inset Tabular
21338 <lyxtabular version="3" rows="10" columns="2">
21339 <features rotate="0" tabularvalignment="middle">
21340 <column alignment="center" valignment="top" width="0pt">
21341 <column alignment="center" valignment="top" width="0pt">
21343 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21346 \begin_layout Plain Layout
21352 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21355 \begin_layout Plain Layout
21363 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21366 \begin_layout Plain Layout
21374 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21377 \begin_layout Plain Layout
21378 \begin_inset Formula $\neg$
21388 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21391 \begin_layout Plain Layout
21399 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21402 \begin_layout Plain Layout
21403 \begin_inset Formula $\Im$
21413 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21416 \begin_layout Plain Layout
21424 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21427 \begin_layout Plain Layout
21428 \begin_inset Formula $\Re$
21438 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21441 \begin_layout Plain Layout
21449 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21452 \begin_layout Plain Layout
21453 \begin_inset Formula $\aleph$
21463 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21466 \begin_layout Plain Layout
21474 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21477 \begin_layout Plain Layout
21478 \begin_inset Formula $\partial$
21488 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21491 \begin_layout Plain Layout
21499 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21502 \begin_layout Plain Layout
21503 \begin_inset Formula $\infty$
21513 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21516 \begin_layout Plain Layout
21524 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21527 \begin_layout Plain Layout
21528 \begin_inset Formula $\wp$
21538 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21541 \begin_layout Plain Layout
21549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21552 \begin_layout Plain Layout
21553 \begin_inset Formula $\imath$
21563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21566 \begin_layout Plain Layout
21574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21577 \begin_layout Plain Layout
21578 \begin_inset Formula $\jmath$
21592 \begin_inset space \hfill{}
21596 \begin_inset Tabular
21597 <lyxtabular version="3" rows="10" columns="2">
21598 <features rotate="0" tabularvalignment="middle">
21599 <column alignment="center" valignment="top" width="0pt">
21600 <column alignment="center" valignment="top" width="0pt">
21602 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21605 \begin_layout Plain Layout
21611 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21614 \begin_layout Plain Layout
21616 \begin_inset Note Note
21619 \begin_layout Plain Layout
21626 is only used as spacer.
21638 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21641 \begin_layout Plain Layout
21649 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21652 \begin_layout Plain Layout
21653 \begin_inset Formula $\forall$
21663 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21666 \begin_layout Plain Layout
21674 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21677 \begin_layout Plain Layout
21678 \begin_inset Formula $\exists$
21688 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21691 \begin_layout Plain Layout
21699 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21702 \begin_layout Plain Layout
21703 \begin_inset Formula $\nexists$
21713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21716 \begin_layout Plain Layout
21724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21727 \begin_layout Plain Layout
21728 \begin_inset Formula $\emptyset$
21738 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21741 \begin_layout Plain Layout
21749 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21752 \begin_layout Plain Layout
21753 \begin_inset Formula $\varnothing$
21763 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21766 \begin_layout Plain Layout
21774 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21777 \begin_layout Plain Layout
21778 \begin_inset Formula $\dag$
21788 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21791 \begin_layout Plain Layout
21799 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21802 \begin_layout Plain Layout
21803 \begin_inset Formula $\ddag$
21813 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
21816 \begin_layout Plain Layout
21824 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
21827 \begin_layout Plain Layout
21831 \begin_layout Plain Layout
21841 \begin_inset Formula $\complement$
21848 \begin_layout Plain Layout
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 $\Bbbk$
21891 \begin_inset space \hfill{}
21895 \begin_inset Tabular
21896 <lyxtabular version="3" rows="10" columns="2">
21897 <features rotate="0" tabularvalignment="middle">
21898 <column alignment="center" valignment="top" width="0pt">
21899 <column alignment="center" valignment="top" width="0pt">
21901 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
21904 \begin_layout Plain Layout
21910 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
21913 \begin_layout Plain Layout
21921 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21924 \begin_layout Plain Layout
21932 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21935 \begin_layout Plain Layout
21936 \begin_inset Formula $\prime$
21946 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21949 \begin_layout Plain Layout
21957 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21960 \begin_layout Plain Layout
21961 \begin_inset Formula $\backprime$
21971 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21974 \begin_layout Plain Layout
21982 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
21985 \begin_layout Plain Layout
21986 \begin_inset Formula $\mho$
21996 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
21999 \begin_layout Plain Layout
22007 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22010 \begin_layout Plain Layout
22011 \begin_inset Formula $\triangle$
22021 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22024 \begin_layout Plain Layout
22032 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22035 \begin_layout Plain Layout
22036 \begin_inset Formula $\angle$
22046 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22049 \begin_layout Plain Layout
22057 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22060 \begin_layout Plain Layout
22061 \begin_inset Formula $\measuredangle$
22071 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22074 \begin_layout Plain Layout
22082 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22085 \begin_layout Plain Layout
22086 \begin_inset Formula $\sphericalangle$
22096 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22099 \begin_layout Plain Layout
22107 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22110 \begin_layout Plain Layout
22111 \begin_inset Formula $\top$
22121 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22124 \begin_layout Plain Layout
22132 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22135 \begin_layout Plain Layout
22136 \begin_inset Formula $\bot$
22150 \begin_inset space \hfill{}
22156 \begin_layout Subsection
22157 Miscellaneous Symbols
22158 \begin_inset CommandInset label
22160 name "sub:Miscellaneous-Symbols"
22165 \begin_inset Index idx
22168 \begin_layout Plain Layout
22169 Symbols ! miscellaneous
22177 \begin_layout Standard
22180 \begin_inset Tabular
22181 <lyxtabular version="3" rows="10" columns="2">
22182 <features rotate="0" tabularvalignment="middle">
22183 <column alignment="center" valignment="top" width="0pt">
22184 <column alignment="center" valignment="top" width="0pt">
22186 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22189 \begin_layout Plain Layout
22195 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22198 \begin_layout Plain Layout
22206 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22209 \begin_layout Plain Layout
22217 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22220 \begin_layout Plain Layout
22221 \begin_inset Formula $\flat$
22231 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22234 \begin_layout Plain Layout
22242 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22245 \begin_layout Plain Layout
22246 \begin_inset Formula $\natural$
22256 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22259 \begin_layout Plain Layout
22267 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22270 \begin_layout Plain Layout
22271 \begin_inset Formula $\sharp$
22281 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22284 \begin_layout Plain Layout
22292 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22295 \begin_layout Plain Layout
22296 \begin_inset Formula $\surd$
22306 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22309 \begin_layout Plain Layout
22317 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22320 \begin_layout Plain Layout
22321 \begin_inset Formula $\checkmark$
22331 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22334 \begin_layout Plain Layout
22342 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22345 \begin_layout Plain Layout
22346 \begin_inset Formula $\yen$
22356 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22359 \begin_layout Plain Layout
22367 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22370 \begin_layout Plain Layout
22371 \begin_inset Formula $\pounds$
22381 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22384 \begin_layout Plain Layout
22390 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22393 \begin_layout Plain Layout
22394 \begin_inset Formula $\$$
22404 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22407 \begin_layout Plain Layout
22413 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22416 \begin_layout Plain Layout
22417 \begin_inset Formula $§$
22431 \begin_inset Tabular
22432 <lyxtabular version="3" rows="10" columns="2">
22433 <features rotate="0" tabularvalignment="middle">
22434 <column alignment="center" valignment="top">
22435 <column alignment="center" valignment="top">
22437 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22440 \begin_layout Plain Layout
22446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22449 \begin_layout Plain Layout
22457 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22460 \begin_layout Plain Layout
22468 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22471 \begin_layout Plain Layout
22472 \begin_inset Formula $\hbar$
22482 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22485 \begin_layout Plain Layout
22493 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22496 \begin_layout Plain Layout
22497 \begin_inset Formula $\hslash$
22507 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22510 \begin_layout Plain Layout
22518 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22521 \begin_layout Plain Layout
22522 \begin_inset Formula $\clubsuit$
22532 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22535 \begin_layout Plain Layout
22543 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22546 \begin_layout Plain Layout
22547 \begin_inset Formula $\spadesuit$
22557 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22560 \begin_layout Plain Layout
22568 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22571 \begin_layout Plain Layout
22572 \begin_inset Formula $\bigstar$
22582 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22585 \begin_layout Plain Layout
22593 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22596 \begin_layout Plain Layout
22597 \begin_inset Formula $\blacklozenge$
22607 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22610 \begin_layout Plain Layout
22618 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22621 \begin_layout Plain Layout
22622 \begin_inset Formula $\blacktriangle$
22632 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22635 \begin_layout Plain Layout
22643 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22646 \begin_layout Plain Layout
22647 \begin_inset Formula $\blacktriangledown$
22657 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22660 \begin_layout Plain Layout
22668 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22671 \begin_layout Plain Layout
22672 \begin_inset Formula $\bullet$
22686 \begin_inset Tabular
22687 <lyxtabular version="3" rows="10" columns="2">
22688 <features rotate="0" tabularvalignment="middle">
22689 <column alignment="center" valignment="top" width="0pt">
22690 <column alignment="center" valignment="top" width="0pt">
22692 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22695 \begin_layout Plain Layout
22701 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22704 \begin_layout Plain Layout
22712 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22715 \begin_layout Plain Layout
22723 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22726 \begin_layout Plain Layout
22727 \begin_inset Formula $\diamondsuit$
22737 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22740 \begin_layout Plain Layout
22748 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22751 \begin_layout Plain Layout
22752 \begin_inset Formula $\Diamond$
22762 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
22765 \begin_layout Plain Layout
22773 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
22776 \begin_layout Plain Layout
22777 \begin_inset Formula $\heartsuit$
22787 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
22790 \begin_layout Plain Layout
22798 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
22801 \begin_layout Plain Layout
22802 \begin_inset Formula $\P$
22812 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22815 \begin_layout Plain Layout
22823 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22826 \begin_layout Plain Layout
22827 \begin_inset Formula $\copyright$
22837 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22840 \begin_layout Plain Layout
22848 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22851 \begin_layout Plain Layout
22852 \begin_inset Formula $\circledR$
22862 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22865 \begin_layout Plain Layout
22873 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22876 \begin_layout Plain Layout
22877 \begin_inset Formula $\maltese$
22887 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22890 \begin_layout Plain Layout
22898 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22901 \begin_layout Plain Layout
22902 \begin_inset Formula $\diagup$
22912 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
22915 \begin_layout Plain Layout
22923 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
22926 \begin_layout Plain Layout
22927 \begin_inset Formula $\diagdown$
22943 \begin_layout Standard
22944 \begin_inset VSpace medskip
22947 More symbols are listed in
22948 \begin_inset CommandInset ref
22950 reference "sub:Miscellaneous-special-Characters"
22957 \begin_layout Standard
22958 Some symbols can be displayed in different sizes, see
22959 \begin_inset CommandInset ref
22961 reference "sub:Font-Sizes"
22968 \begin_layout Subsection
22970 \begin_inset Index idx
22973 \begin_layout Plain Layout
22974 Symbols ! Euro-symbol
22980 \begin_inset Index idx
22983 \begin_layout Plain Layout
22990 \begin_layout Plain Layout
23007 \begin_layout Standard
23008 To use the Euro symbol in formulas, the LaTeX-package
23013 \begin_inset Index idx
23016 \begin_layout Plain Layout
23022 must be installed and loaded with the LaTeX-preamble line
23025 \begin_layout Standard
23030 usepackage[gennarrow]{eurosym}
23033 \begin_layout Standard
23034 The Euro symbol can now be inserted with the command
23041 \begin_inset Index idx
23044 \begin_layout Plain Layout
23055 \begin_layout Standard
23056 The Euro symbol can directly be inserted with the € key in mathematical
23057 text, without having
23072 can also be inserted in TeX-mode.
23073 The official currency symbol can then be inserted with the command
23080 \begin_inset Index idx
23083 \begin_layout Plain Layout
23091 , that is only available in TeX-mode.
23094 \begin_layout Standard
23098 \begin_layout Plain Layout
23108 \begin_inset Note Note
23111 \begin_layout Plain Layout
23112 The following table will only be displayed when the LaTeX-package
23124 \begin_layout Standard
23125 An overview about the different Euro symbols:
23128 \begin_layout Standard
23130 \begin_inset Tabular
23131 <lyxtabular version="3" rows="4" columns="3">
23132 <features rotate="0" tabularvalignment="middle">
23133 <column alignment="center" valignment="top" width="0pt">
23134 <column alignment="center" valignment="top" width="0pt">
23135 <column alignment="center" valignment="top" width="0pt">
23137 <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
23140 \begin_layout Plain Layout
23146 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23149 \begin_layout Plain Layout
23155 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23158 \begin_layout Plain Layout
23166 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23169 \begin_layout Plain Layout
23175 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23178 \begin_layout Plain Layout
23186 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23189 \begin_layout Plain Layout
23190 \begin_inset Formula $\euro$
23200 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23203 \begin_layout Plain Layout
23209 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23212 \begin_layout Plain Layout
23218 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23221 \begin_layout Plain Layout
23222 \begin_inset Formula $\mbox{€}$
23232 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23235 \begin_layout Plain Layout
23241 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23244 \begin_layout Plain Layout
23252 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23255 \begin_layout Plain Layout
23259 \begin_layout Plain Layout
23281 \begin_layout Standard
23285 \begin_layout Plain Layout
23295 \begin_inset Note Note
23298 \begin_layout Plain Layout
23299 The following will be displayed when the LaTeX-package
23311 \begin_layout Standard
23312 You need to install the LaTeX-package
23316 to see the rest of this subsection in the output.
23319 \begin_layout Standard
23323 \begin_layout Plain Layout
23335 \begin_layout Section
23337 \begin_inset CommandInset label
23339 name "sec:Relations"
23344 \begin_inset Index idx
23347 \begin_layout Plain Layout
23354 \begin_inset Index idx
23357 \begin_layout Plain Layout
23362 \begin_layout Plain Layout
23373 \begin_layout Plain Layout
23388 \begin_layout Standard
23389 All relations can also be inserted via the toolbar button
23390 \begin_inset Graphics
23391 filename ../images/math/leq.png
23399 \begin_layout Standard
23400 \begin_inset space \hfill{}
23404 \begin_inset Tabular
23405 <lyxtabular version="3" rows="17" columns="2">
23406 <features rotate="0" tabularvalignment="middle">
23407 <column alignment="center" valignment="top" width="0pt">
23408 <column alignment="center" valignment="top" width="0pt">
23410 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23413 \begin_layout Plain Layout
23419 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23422 \begin_layout Plain Layout
23430 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23433 \begin_layout Plain Layout
23439 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23442 \begin_layout Plain Layout
23443 \begin_inset Formula $<$
23453 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23456 \begin_layout Plain Layout
23464 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23467 \begin_layout Plain Layout
23468 \begin_inset Formula $\le$
23478 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23481 \begin_layout Plain Layout
23489 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23492 \begin_layout Plain Layout
23493 \begin_inset Formula $\ll$
23503 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23506 \begin_layout Plain Layout
23514 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23517 \begin_layout Plain Layout
23518 \begin_inset Formula $\prec$
23528 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23531 \begin_layout Plain Layout
23539 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23542 \begin_layout Plain Layout
23543 \begin_inset Formula $\preceq$
23553 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23556 \begin_layout Plain Layout
23564 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23567 \begin_layout Plain Layout
23568 \begin_inset Formula $\subset$
23578 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23581 \begin_layout Plain Layout
23589 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23592 \begin_layout Plain Layout
23593 \begin_inset Formula $\subseteq$
23603 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23606 \begin_layout Plain Layout
23614 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23617 \begin_layout Plain Layout
23618 \begin_inset Formula $\sqsubseteq$
23628 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23631 \begin_layout Plain Layout
23639 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23642 \begin_layout Plain Layout
23643 \begin_inset Formula $\in$
23653 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23656 \begin_layout Plain Layout
23664 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23667 \begin_layout Plain Layout
23668 \begin_inset Formula $\vdash$
23678 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23681 \begin_layout Plain Layout
23689 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23692 \begin_layout Plain Layout
23693 \begin_inset Formula $\smile$
23703 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23706 \begin_layout Plain Layout
23714 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23717 \begin_layout Plain Layout
23718 \begin_inset Formula $\lhd$
23728 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23731 \begin_layout Plain Layout
23739 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23742 \begin_layout Plain Layout
23743 \begin_inset Formula $\unlhd$
23753 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23756 \begin_layout Plain Layout
23764 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23767 \begin_layout Plain Layout
23768 \begin_inset Formula $\gtrless$
23778 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23781 \begin_layout Plain Layout
23789 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23792 \begin_layout Plain Layout
23793 \begin_inset Formula $\mid$
23803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23806 \begin_layout Plain Layout
23814 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23817 \begin_layout Plain Layout
23818 \begin_inset Formula $\nmid$
23832 \begin_inset space \hfill{}
23836 \begin_inset Tabular
23837 <lyxtabular version="3" rows="17" columns="2">
23838 <features rotate="0" tabularvalignment="middle">
23839 <column alignment="center" valignment="top" width="0pt">
23840 <column alignment="center" valignment="top" width="0pt">
23842 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
23845 \begin_layout Plain Layout
23851 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
23854 \begin_layout Plain Layout
23862 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23865 \begin_layout Plain Layout
23871 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23874 \begin_layout Plain Layout
23875 \begin_inset Formula $=$
23885 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23888 \begin_layout Plain Layout
23896 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23899 \begin_layout Plain Layout
23900 \begin_inset Formula $\not=$
23910 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23913 \begin_layout Plain Layout
23921 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23924 \begin_layout Plain Layout
23925 \begin_inset Formula $\equiv$
23935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23938 \begin_layout Plain Layout
23946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23949 \begin_layout Plain Layout
23950 \begin_inset Formula $\sim$
23960 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23963 \begin_layout Plain Layout
23971 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23974 \begin_layout Plain Layout
23975 \begin_inset Formula $\simeq$
23985 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
23988 \begin_layout Plain Layout
23996 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
23999 \begin_layout Plain Layout
24000 \begin_inset Formula $\approx$
24010 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24013 \begin_layout Plain Layout
24021 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24024 \begin_layout Plain Layout
24025 \begin_inset Formula $\cong$
24035 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24038 \begin_layout Plain Layout
24046 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24049 \begin_layout Plain Layout
24050 \begin_inset Formula $\bowtie$
24060 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24063 \begin_layout Plain Layout
24071 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24074 \begin_layout Plain Layout
24075 \begin_inset Formula $\notin$
24085 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24088 \begin_layout Plain Layout
24096 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24099 \begin_layout Plain Layout
24100 \begin_inset Formula $\perp$
24110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24113 \begin_layout Plain Layout
24121 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24124 \begin_layout Plain Layout
24125 \begin_inset Formula $\propto$
24135 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24138 \begin_layout Plain Layout
24146 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24149 \begin_layout Plain Layout
24150 \begin_inset Formula $\asymp$
24160 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24163 \begin_layout Plain Layout
24171 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24174 \begin_layout Plain Layout
24175 \begin_inset Formula $\doteq$
24185 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24188 \begin_layout Plain Layout
24196 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24199 \begin_layout Plain Layout
24200 \begin_inset Formula $\circeq$
24210 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24213 \begin_layout Plain Layout
24221 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24224 \begin_layout Plain Layout
24225 \begin_inset Formula $\models$
24235 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24238 \begin_layout Plain Layout
24246 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24249 \begin_layout Plain Layout
24250 \begin_inset Formula $\widehat{=}$
24264 \begin_inset space \hfill{}
24268 \begin_inset Tabular
24269 <lyxtabular version="3" rows="17" columns="2">
24270 <features rotate="0" tabularvalignment="middle">
24271 <column alignment="center" valignment="top" width="0pt">
24272 <column alignment="center" valignment="top" width="0pt">
24274 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24277 \begin_layout Plain Layout
24283 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24286 \begin_layout Plain Layout
24294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24297 \begin_layout Plain Layout
24303 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24306 \begin_layout Plain Layout
24307 \begin_inset Formula $>$
24317 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24320 \begin_layout Plain Layout
24328 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24331 \begin_layout Plain Layout
24332 \begin_inset Formula $\ge$
24342 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24345 \begin_layout Plain Layout
24353 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24356 \begin_layout Plain Layout
24357 \begin_inset Formula $\gg$
24367 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24370 \begin_layout Plain Layout
24378 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24381 \begin_layout Plain Layout
24382 \begin_inset Formula $\succ$
24392 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24395 \begin_layout Plain Layout
24403 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24406 \begin_layout Plain Layout
24407 \begin_inset Formula $\succeq$
24417 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24420 \begin_layout Plain Layout
24428 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24431 \begin_layout Plain Layout
24432 \begin_inset Formula $\supset$
24442 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24445 \begin_layout Plain Layout
24453 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24456 \begin_layout Plain Layout
24457 \begin_inset Formula $\supseteq$
24467 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24470 \begin_layout Plain Layout
24478 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24481 \begin_layout Plain Layout
24482 \begin_inset Formula $\sqsupseteq$
24492 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24495 \begin_layout Plain Layout
24503 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24506 \begin_layout Plain Layout
24507 \begin_inset Formula $\ni$
24517 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24520 \begin_layout Plain Layout
24528 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24531 \begin_layout Plain Layout
24532 \begin_inset Formula $\dashv$
24542 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24545 \begin_layout Plain Layout
24553 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24556 \begin_layout Plain Layout
24557 \begin_inset Formula $\frown$
24567 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24570 \begin_layout Plain Layout
24578 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24581 \begin_layout Plain Layout
24582 \begin_inset Formula $\rhd$
24592 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24595 \begin_layout Plain Layout
24603 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24606 \begin_layout Plain Layout
24607 \begin_inset Formula $\unrhd$
24617 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24620 \begin_layout Plain Layout
24628 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24631 \begin_layout Plain Layout
24632 \begin_inset Formula $\lessgtr$
24642 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
24645 \begin_layout Plain Layout
24653 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
24656 \begin_layout Plain Layout
24657 \begin_inset Formula $\parallel$
24667 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24670 \begin_layout Plain Layout
24678 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24681 \begin_layout Plain Layout
24682 \begin_inset Formula $\nparallel$
24696 \begin_inset space \hfill{}
24702 \begin_layout Standard
24703 \begin_inset VSpace medskip
24718 are bigger than the equal looking operators
24733 \begin_layout Standard
24734 Relations are, in contrary to symbols, always surrounded by space.
24737 \begin_layout Standard
24738 Relations with labels can be created with the command
24745 \begin_inset Index idx
24748 \begin_layout Plain Layout
24759 \begin_layout Standard
24761 \begin_inset Tabular
24762 <lyxtabular version="3" rows="2" columns="2">
24763 <features rotate="0" tabularvalignment="middle">
24764 <column alignment="center" valignment="top">
24765 <column alignment="center" valignment="top">
24767 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24770 \begin_layout Plain Layout
24776 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24779 \begin_layout Plain Layout
24781 \begin_inset Note Note
24784 \begin_layout Plain Layout
24791 is only used as spacer.
24803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24806 \begin_layout Plain Layout
24813 \begin_layout Plain Layout
24830 \begin_layout Plain Layout
24840 \begin_inset Formula $\downarrow$
24849 \begin_layout Plain Layout
24862 \begin_layout Plain Layout
24876 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24879 \begin_layout Plain Layout
24880 \begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
24896 \begin_layout Section
24900 \begin_layout Subsection
24901 Predefined Functions
24902 \begin_inset CommandInset label
24904 name "sub:Predefined-Functions"
24909 \begin_inset Index idx
24912 \begin_layout Plain Layout
24913 Functions ! predefined
24921 \begin_layout Standard
24922 In general, variables are set
24926 in mathematical expressions, but not function names, because
24927 \begin_inset Formula $sin$
24930 could be misunderstood as
24931 \begin_inset Formula $s\cdot i\cdot n$
24935 Therefore there are predefined functionswhich are additionally a bit separated
24937 They are inserted as commands starting with a backslash before their name.
24940 \begin_layout Standard
24942 \begin_inset Tabular
24943 <lyxtabular version="3" rows="2" columns="4">
24944 <features rotate="0" tabularvalignment="middle">
24945 <column alignment="center" valignment="top" width="0pt">
24946 <column alignment="center" valignment="top" width="0pt">
24947 <column alignment="center" valignment="top" width="0pt">
24948 <column alignment="center" valignment="top" width="0pt">
24950 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24953 \begin_layout Plain Layout
24959 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24962 \begin_layout Plain Layout
24968 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24971 \begin_layout Plain Layout
24977 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
24980 \begin_layout Plain Layout
24988 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
24991 \begin_layout Plain Layout
24997 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25000 \begin_layout Plain Layout
25001 \begin_inset Formula $Asin(x)+B$
25009 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25012 \begin_layout Plain Layout
25020 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25023 \begin_layout Plain Layout
25024 \begin_inset Formula $A\sin(x)+B$
25040 \begin_layout Standard
25041 The following functions are predefined:
25044 \begin_layout Standard
25045 \begin_inset VSpace -2mm
25051 \begin_layout Standard
25053 \begin_inset Tabular
25054 <lyxtabular version="3" rows="9" columns="4">
25055 <features rotate="0" tabularvalignment="middle">
25056 <column alignment="center" valignment="top" width="0pt">
25057 <column alignment="center" valignment="top" width="0pt">
25058 <column alignment="center" valignment="top" width="0pt">
25059 <column alignment="center" valignment="top" width="0pt">
25061 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25064 \begin_layout Plain Layout
25070 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25073 \begin_layout Plain Layout
25079 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25082 \begin_layout Plain Layout
25088 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25091 \begin_layout Plain Layout
25099 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25102 \begin_layout Plain Layout
25110 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25113 \begin_layout Plain Layout
25121 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25124 \begin_layout Plain Layout
25132 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25135 \begin_layout Plain Layout
25145 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25148 \begin_layout Plain Layout
25156 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25159 \begin_layout Plain Layout
25167 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25170 \begin_layout Plain Layout
25178 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25181 \begin_layout Plain Layout
25191 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25194 \begin_layout Plain Layout
25202 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25205 \begin_layout Plain Layout
25213 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25216 \begin_layout Plain Layout
25224 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25227 \begin_layout Plain Layout
25237 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25240 \begin_layout Plain Layout
25248 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25251 \begin_layout Plain Layout
25259 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25262 \begin_layout Plain Layout
25270 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25273 \begin_layout Plain Layout
25283 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25286 \begin_layout Plain Layout
25294 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25297 \begin_layout Plain Layout
25305 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25308 \begin_layout Plain Layout
25316 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25319 \begin_layout Plain Layout
25329 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25332 \begin_layout Plain Layout
25340 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25343 \begin_layout Plain Layout
25351 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25354 \begin_layout Plain Layout
25362 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25365 \begin_layout Plain Layout
25375 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25378 \begin_layout Plain Layout
25386 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25389 \begin_layout Plain Layout
25397 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
25400 \begin_layout Plain Layout
25408 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
25411 \begin_layout Plain Layout
25421 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25424 \begin_layout Plain Layout
25432 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25435 \begin_layout Plain Layout
25443 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25446 \begin_layout Plain Layout
25454 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25457 \begin_layout Plain Layout
25473 \begin_layout Standard
25474 They can also be inserted with the math toolbar button
25475 \begin_inset Graphics
25476 filename ../images/math/functions.png
25484 \begin_layout Subsection
25485 Self-defined Functions
25486 \begin_inset Index idx
25489 \begin_layout Plain Layout
25490 Functions ! self-defined
25498 \begin_layout Standard
25499 To use a function that is not predefined, like for example the sign function
25500 sgn(x), there are two possibilities:
25503 \begin_layout Itemize
25504 Define the function by inserting the following line to the LaTeX-preamble
25508 \begin_layout Plain Layout
25513 DeclareMathOperator
25516 \begin_inset CommandInset ref
25518 reference "sub:Self-defined-Operators"
25528 \begin_inset Newline newline
25532 \begin_inset VSpace -3mm
25536 \begin_inset Newline newline
25543 DeclareMathOperator{
25548 \begin_inset Index idx
25551 \begin_layout Plain Layout
25556 DeclareMathOperator
25562 \begin_inset Newline newline
25566 \begin_inset VSpace -2mm
25570 \begin_inset Newline newline
25573 Now the new defined function can be called with the command
25582 \begin_layout Itemize
25583 Write the formula as usual, mark the formula name, in our example the letters
25588 , and change it to mathematical text.
25589 Finally, a space is inserted between prefactor and function.
25592 \begin_layout Standard
25593 The result is the same with both methods as with a predefined function
25597 \begin_layout Plain Layout
25598 In LyX self-defined functions are displayed red, predefined ones black.
25606 \begin_layout Standard
25608 \begin_inset Tabular
25609 <lyxtabular version="3" rows="3" columns="2">
25610 <features rotate="0" tabularvalignment="middle">
25611 <column alignment="center" valignment="top" width="0pt">
25612 <column alignment="center" valignment="top" width="0pt">
25614 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25617 \begin_layout Plain Layout
25623 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25626 \begin_layout Plain Layout
25634 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25637 \begin_layout Plain Layout
25645 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25648 \begin_layout Plain Layout
25649 \begin_inset Formula $A\sgn(x)+B$
25659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25662 \begin_layout Plain Layout
25666 \begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$
25674 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25677 \begin_layout Plain Layout
25678 \begin_inset Formula $A\,\textrm{sgn}(x)+B$
25694 \begin_layout Standard
25695 The first method is more suitable when the self-defined function should
25696 be used several times.
25699 \begin_layout Subsection
25701 \begin_inset Index idx
25704 \begin_layout Plain Layout
25713 \begin_layout Standard
25714 For limits, in addition to the commands
25721 \begin_inset Index idx
25724 \begin_layout Plain Layout
25744 the following functions are defined:
25747 \begin_layout Standard
25749 \begin_inset Tabular
25750 <lyxtabular version="3" rows="5" columns="2">
25751 <features rotate="0" tabularvalignment="middle">
25752 <column alignment="center" valignment="top">
25753 <column alignment="center" valignment="top">
25755 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
25758 \begin_layout Plain Layout
25764 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
25767 \begin_layout Plain Layout
25769 \begin_inset Note Note
25772 \begin_layout Plain Layout
25779 is only used as spacer.
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
25806 \begin_inset Formula $\varliminf$
25816 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25819 \begin_layout Plain Layout
25827 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25830 \begin_layout Plain Layout
25831 \begin_inset Formula $\varlimsup$
25841 <cell alignment="center" valignment="top" leftline="true" usebox="none">
25844 \begin_layout Plain Layout
25852 <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
25855 \begin_layout Plain Layout
25856 \begin_inset Formula $\varprojlim$
25866 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
25869 \begin_layout Plain Layout
25877 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
25880 \begin_layout Plain Layout
25881 \begin_inset Formula $\varinjlim$
25885 \begin_inset Formula $\raisebox{-2.5mm}{}$
25901 \begin_layout Standard
25902 \begin_inset VSpace medskip
25905 The limit is created by inserting a subscript.
25906 It is set right beside the function in an inline formula:
25909 \begin_layout Standard
25911 \begin_inset Tabular
25912 <lyxtabular version="3" rows="2" columns="2">
25913 <features rotate="0" tabularvalignment="middle">
25914 <column alignment="center" valignment="top" width="0pt">
25915 <column alignment="center" valignment="top" width="0pt">
25917 <cell alignment="center" valignment="top" usebox="none">
25920 \begin_layout Plain Layout
25926 <cell alignment="center" valignment="top" usebox="none">
25929 \begin_layout Plain Layout
25930 \begin_inset space \hspace{}
25935 \begin_inset Note Note
25938 \begin_layout Plain Layout
25945 are used here as spacer.
25957 <cell alignment="center" valignment="top" usebox="none">
25960 \begin_layout Plain Layout
25969 \begin_layout Plain Layout
25982 \begin_layout Plain Layout
25996 <cell alignment="center" valignment="top" usebox="none">
25999 \begin_layout Plain Layout
26000 \begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
26016 \begin_layout Standard
26017 In a displayed formula the limit is set below the formula, as usual:
26018 \begin_inset Formula
26028 \begin_layout Subsection
26030 \begin_inset Index idx
26033 \begin_layout Plain Layout
26034 Functions ! modulo-
26042 \begin_layout Standard
26043 The modulo-function is special, because it exists in four variants.
26044 The variants in a displayed formula are:
26045 \begin_inset Formula
26047 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26048 \mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
26049 \mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
26050 \mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
26051 \mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b
26059 \begin_layout Standard
26060 In an inline formula less space is set before the function names for all
26062 By default the modulo-functions take only the first following character
26064 To use more than one character, one has to put them into TeX-braces:
26065 \begin_inset Formula
26067 \underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
26068 \mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\
26069 \mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d
26077 \begin_layout Section
26079 \begin_inset Index idx
26082 \begin_layout Plain Layout
26091 \begin_layout Subsection
26092 Special Characters in Mathematical Text
26095 \begin_layout Standard
26096 The following commands can only be used in mathematical text or in TeX-mode:
26099 \begin_layout Standard
26100 \begin_inset space \hfill{}
26104 \begin_inset Tabular
26105 <lyxtabular version="3" rows="8" columns="2">
26106 <features rotate="0" tabularvalignment="middle">
26107 <column alignment="block" valignment="top">
26108 <column alignment="block" valignment="top">
26110 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26113 \begin_layout Plain Layout
26119 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26122 \begin_layout Plain Layout
26130 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26133 \begin_layout Plain Layout
26141 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26144 \begin_layout Plain Layout
26145 \begin_inset Formula $\textrm{œ}$
26155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26158 \begin_layout Plain Layout
26166 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26169 \begin_layout Plain Layout
26170 \begin_inset Formula $\textrm{Œ}$
26180 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26183 \begin_layout Plain Layout
26191 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26194 \begin_layout Plain Layout
26195 \begin_inset Formula $\textrm{æ}$
26205 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26208 \begin_layout Plain Layout
26216 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26219 \begin_layout Plain Layout
26220 \begin_inset Formula $\textrm{Æ}$
26230 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26233 \begin_layout Plain Layout
26241 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26244 \begin_layout Plain Layout
26245 \begin_inset Formula $\textrm{\aa}$
26255 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26258 \begin_layout Plain Layout
26262 \begin_inset Index idx
26265 \begin_layout Plain Layout
26272 \begin_layout Plain Layout
26293 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26296 \begin_layout Plain Layout
26297 \begin_inset Formula $\textrm{Å}$
26307 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26310 \begin_layout Plain Layout
26318 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26321 \begin_layout Plain Layout
26322 \begin_inset Formula $\textrm{ı}$
26336 \begin_inset space \hfill{}
26340 \begin_inset Tabular
26341 <lyxtabular version="3" rows="8" columns="2">
26342 <features rotate="0" tabularvalignment="middle">
26343 <column alignment="block" valignment="top">
26344 <column alignment="center" valignment="top">
26346 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26349 \begin_layout Plain Layout
26351 \begin_inset Note Note
26354 \begin_layout Plain Layout
26356 \begin_inset space \thinspace{}
26359 mm is used for separation, because otherwise the output will be ¡ and ¿
26370 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26373 \begin_layout Plain Layout
26381 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26384 \begin_layout Plain Layout
26392 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26395 \begin_layout Plain Layout
26396 \begin_inset Formula $\textrm{ø}$
26406 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26409 \begin_layout Plain Layout
26417 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26420 \begin_layout Plain Layout
26421 \begin_inset Formula $\textrm{Ø}$
26431 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26434 \begin_layout Plain Layout
26442 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26445 \begin_layout Plain Layout
26446 \begin_inset Formula $\textrm{ł}$
26456 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26459 \begin_layout Plain Layout
26467 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26470 \begin_layout Plain Layout
26471 \begin_inset Formula $\textrm{Ł}$
26481 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26484 \begin_layout Plain Layout
26486 \begin_inset space \hspace{}
26494 \begin_layout Plain Layout
26508 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26511 \begin_layout Plain Layout
26512 \begin_inset Formula $\textrm{!`}$
26522 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26525 \begin_layout Plain Layout
26527 \begin_inset space \hspace{}
26535 \begin_layout Plain Layout
26549 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26552 \begin_layout Plain Layout
26553 \begin_inset Formula $\textrm{?`}$
26563 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26566 \begin_layout Plain Layout
26574 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26577 \begin_layout Plain Layout
26578 \begin_inset Formula $\textrm{ȷ}$
26592 \begin_inset space \hfill{}
26598 \begin_layout Standard
26600 \begin_inset Formula $\textrm{\textrm{Å}}$
26604 \begin_inset Formula $\textrm{\textrm{Ø}}$
26607 can also be inserted via the math toolbar button
26608 \begin_inset Graphics
26609 filename ../images/math/digamma.png
26617 \begin_layout Standard
26618 An exception are the commands
26621 \begin_inset space \hspace{}
26630 \begin_inset space \hspace{}
26636 , because they can be inserted in LyX directly to text.
26639 \begin_layout Subsection
26641 \begin_inset CommandInset label
26643 name "sub:Accents-in-Text"
26648 \begin_inset Index idx
26651 \begin_layout Plain Layout
26660 \begin_layout Standard
26661 With the following commands all letters can be accented.
26662 The commands must be inserted in TeX-mode.
26665 \begin_layout Standard
26666 \begin_inset space \hfill{}
26670 \begin_inset Tabular
26671 <lyxtabular version="3" rows="8" columns="2">
26672 <features rotate="0" tabularvalignment="middle">
26673 <column alignment="block" valignment="top">
26674 <column alignment="block" valignment="top">
26676 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26679 \begin_layout Plain Layout
26685 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26688 \begin_layout Plain Layout
26696 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26699 \begin_layout Plain Layout
26703 \begin_inset Quotes grd
26711 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26714 \begin_layout Plain Layout
26718 \begin_layout Plain Layout
26734 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26737 \begin_layout Plain Layout
26745 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26748 \begin_layout Plain Layout
26752 \begin_layout Plain Layout
26768 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26771 \begin_layout Plain Layout
26778 \begin_layout Plain Layout
26792 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26795 \begin_layout Plain Layout
26799 \begin_layout Plain Layout
26815 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26818 \begin_layout Plain Layout
26826 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26829 \begin_layout Plain Layout
26833 \begin_layout Plain Layout
26849 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
26852 \begin_layout Plain Layout
26859 \begin_layout Plain Layout
26873 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
26876 \begin_layout Plain Layout
26880 \begin_layout Plain Layout
26896 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
26899 \begin_layout Plain Layout
26906 \begin_layout Plain Layout
26920 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
26923 \begin_layout Plain Layout
26927 \begin_layout Plain Layout
26943 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
26946 \begin_layout Plain Layout
26953 \begin_layout Plain Layout
26967 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
26970 \begin_layout Plain Layout
26974 \begin_layout Plain Layout
26994 \begin_inset space \hfill{}
26998 \begin_inset Tabular
26999 <lyxtabular version="3" rows="8" columns="2">
27000 <features rotate="0" tabularvalignment="middle">
27001 <column alignment="block" valignment="top">
27002 <column alignment="center" valignment="top">
27004 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27007 \begin_layout Plain Layout
27013 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27016 \begin_layout Plain Layout
27024 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27027 \begin_layout Plain Layout
27034 \begin_layout Plain Layout
27048 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27051 \begin_layout Plain Layout
27055 \begin_layout Plain Layout
27071 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27074 \begin_layout Plain Layout
27082 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27085 \begin_layout Plain Layout
27089 \begin_layout Plain Layout
27105 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27108 \begin_layout Plain Layout
27112 \begin_inset Index idx
27115 \begin_layout Plain Layout
27126 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27129 \begin_layout Plain Layout
27133 \begin_layout Plain Layout
27149 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27152 \begin_layout Plain Layout
27160 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27163 \begin_layout Plain Layout
27167 \begin_layout Plain Layout
27183 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27186 \begin_layout Plain Layout
27193 \begin_layout Plain Layout
27207 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27210 \begin_layout Plain Layout
27214 \begin_layout Plain Layout
27230 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27233 \begin_layout Plain Layout
27240 \begin_layout Plain Layout
27254 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27257 \begin_layout Plain Layout
27261 \begin_layout Plain Layout
27277 <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
27280 \begin_layout Plain Layout
27287 \begin_layout Plain Layout
27301 <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
27304 \begin_layout Plain Layout
27308 \begin_layout Plain Layout
27328 \begin_inset space \hfill{}
27334 \begin_layout Standard
27335 \begin_inset VSpace medskip
27344 also two different characters can be accented.
27353 \begin_layout Plain Layout
27368 \begin_layout Plain Layout
27380 \begin_layout Standard
27393 can in combination with vowels directly be inserted with the keyboard without
27395 The same applies for the tilde
27399 \begin_layout Plain Layout
27400 This only applies for keyboards where the tilde is defined as accent.
27409 in combination with
27424 \begin_layout Standard
27467 and accents that are inserted directly with the keyboard are also available
27468 in mathematical text.
27469 For the other accents there are special math commands to be used in formulas,
27471 \begin_inset CommandInset ref
27473 reference "sub:Accents-for-one"
27480 \begin_layout Standard
27481 \begin_inset VSpace bigskip
27484 Furthermore, with the command
27491 \begin_inset Index idx
27494 \begin_layout Plain Layout
27502 all numbers and letters can be set into a circle, quasi accented with a
27503 circle, similar to the copyright symbol.
27506 \begin_layout Standard
27508 \begin_inset Tabular
27509 <lyxtabular version="3" rows="3" columns="2">
27510 <features rotate="0" tabularvalignment="middle">
27511 <column alignment="center" valignment="top">
27512 <column alignment="center" valignment="top">
27514 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27517 \begin_layout Plain Layout
27523 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27526 \begin_layout Plain Layout
27528 \begin_inset Note Note
27531 \begin_layout Plain Layout
27538 is only used as spacer.
27550 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27553 \begin_layout Plain Layout
27561 <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27564 \begin_layout Plain Layout
27568 \begin_layout Plain Layout
27584 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27587 \begin_layout Plain Layout
27598 raisebox{-1.5pt}{W}}
27603 <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27606 \begin_layout Plain Layout
27607 \begin_inset Formula $\raisebox{4.5mm}{}$
27614 \begin_layout Plain Layout
27632 \begin_inset Formula $\raisebox{-2mm}{}$
27648 \begin_layout Standard
27649 One has to take care that the character fits in the circle.
27660 \begin_layout Plain Layout
27662 \begin_inset CommandInset ref
27664 reference "sub:Font-Sizes"
27673 specifies thereby the size of the circle.
27684 \begin_layout Plain Layout
27686 \begin_inset CommandInset ref
27688 reference "sub:Boxes-without-Frame"
27697 the character can be centered.
27700 \begin_layout Subsection
27702 \begin_inset Index idx
27705 \begin_layout Plain Layout
27714 \begin_layout Standard
27715 Old-style figures (also known as old-style numerals) are created with the
27723 \begin_inset Index idx
27726 \begin_layout Plain Layout
27735 The command can be used in formulas and in TeX-mode.
27736 The command scheme is:
27739 \begin_layout Standard
27744 oldstylenums{number}
27747 \begin_layout Standard
27752 oldstylenums{0123456789
27755 \begin_inset Formula $\oldstylenums{0123456789}$
27761 \begin_layout Subsection
27762 Miscellaneous special Characters
27763 \begin_inset CommandInset label
27765 name "sub:Miscellaneous-special-Characters"
27770 \begin_inset Index idx
27773 \begin_layout Plain Layout
27774 Special characters ! miscellaneous
27782 \begin_layout Standard
27783 The following characters can only be inserted to formulas by using commands:
27786 \begin_layout Standard
27788 \begin_inset Tabular
27789 <lyxtabular version="3" rows="4" columns="2">
27790 <features rotate="0" tabularvalignment="middle">
27791 <column alignment="center" valignment="top">
27792 <column alignment="center" valignment="top">
27794 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27797 \begin_layout Plain Layout
27803 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27806 \begin_layout Plain Layout
27814 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27817 \begin_layout Plain Layout
27824 \begin_layout Plain Layout
27838 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27841 \begin_layout Plain Layout
27842 \begin_inset Formula $\mathcircumflex$
27852 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
27855 \begin_layout Plain Layout
27863 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
27866 \begin_layout Plain Layout
27867 \begin_inset Formula $\_$
27877 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
27880 \begin_layout Plain Layout
27885 \begin_layout Plain Layout
27897 \begin_inset Index idx
27900 \begin_layout Plain Layout
27913 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
27916 \begin_layout Plain Layout
27917 \begin_inset Formula $^{\circ}$
27933 \begin_layout Standard
27934 The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
27935 contains the following line
27939 \begin_layout Plain Layout
27940 More about this is described in
27941 \begin_inset CommandInset ref
27943 reference "sub:Text-Characters-in"
27955 \begin_layout Standard
27960 DeclareInputtext{176}{
27973 \begin_layout Section
27975 \begin_inset CommandInset label
27977 name "sec:Formula-Styles"
27982 \begin_inset Index idx
27985 \begin_layout Plain Layout
27994 \begin_layout Itemize
27995 There are two different alignment styles:
27999 \begin_layout Description
28000 Centered is the predefined standard
28003 \begin_layout Description
28004 Indented for this the option
28008 must be inserted in the menu
28010 Document\SpecialChar \menuseparator
28016 \begin_inset space ~
28022 \begin_layout Standard
28027 is used, the indentation can be adjusted with the length
28034 \begin_inset Index idx
28037 \begin_layout Plain Layout
28046 Should the distance be 15
28047 \begin_inset space \thinspace{}
28050 mm, the following command line is inserted in the LaTeX-preamble
28053 \begin_layout Standard
28063 \begin_layout Standard
28064 When no length is specified, the predefined value of 30
28065 \begin_inset space \thinspace{}
28072 \begin_layout Itemize
28073 And two different numbering styles:
28077 \begin_layout Description
28078 Right is the predefined standard
28081 \begin_layout Description
28082 Left for this the option
28086 must be inserted in the menu
28088 Document\SpecialChar \menuseparator
28094 \begin_inset space ~
28101 \begin_layout Standard
28110 can also be used together.
28111 In this case both options are inserted, separated by a comma.
28114 \begin_layout Standard
28115 The chosen styles are used for all displayed formulas of the document.
28116 When both, centered and indented formulas should be created in a document,
28122 The indented formulas are then set in a flalign environment, see
28123 \begin_inset CommandInset ref
28125 reference "sub:Flalign-Environment"
28132 \begin_layout Section
28134 \begin_inset CommandInset label
28136 name "sec:Multiline-Formulas"
28141 \begin_inset Index idx
28144 \begin_layout Plain Layout
28145 Formula ! multiline
28153 \begin_layout Subsection
28157 \begin_layout Standard
28158 In LyX multiline formulas are created by pressing
28163 arg "newline-insert newline"
28169 This creates either an
28171 eqnarray environment
28173 that is described in
28174 \begin_inset CommandInset ref
28176 reference "sub:Eqnarray-Environment"
28180 or, when the option
28182 Use AMS math package
28184 in the document settings is selected, an
28188 that is described in
28189 \begin_inset CommandInset ref
28191 reference "sub:Standard-align-Environment"
28196 The align environment is recommended because it provides in any case a
28197 typographically correct output.
28200 \begin_layout Standard
28201 There are other multiline formula environments that can be created via the
28204 Insert\SpecialChar \menuseparator
28208 These environments are described in the following sections.
28211 \begin_layout Standard
28212 In all multiline formula environments a new line is created by pressing
28216 arg "newline-insert newline"
28220 To add or delete lines, the math toolbar buttons
28221 \begin_inset Graphics
28222 filename ../images/tabular-feature_append-row.png
28228 \begin_inset Graphics
28229 filename ../images/tabular-feature_delete-row.png
28234 , respectively, or the menu
28236 Edit\SpecialChar \menuseparator
28242 \begin_layout Subsubsection
28244 \begin_inset CommandInset label
28246 name "sub:Line-Separation"
28251 \begin_inset Index idx
28254 \begin_layout Plain Layout
28255 Formula ! multiline ! Line separation
28263 \begin_layout Standard
28264 There is sometimes not enough space in multiline formulas between the lines:
28265 \begin_inset Formula
28267 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}\\
28268 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
28276 \begin_layout Standard
28277 In LaTeX additional line space is specified as optional argument of the
28279 This is not yet possible in LyX
28283 \begin_layout Plain Layout
28285 \begin_inset CommandInset href
28287 name "LyX-bug #1505"
28288 target "http://www.lyx.org/trac/ticket/1505"
28297 , therefore the whole formula must be inserted in TeX-mode.
28298 To add in our example space, the command
28306 is inserted at the end of the first line.
28311 \begin_layout Plain Layout
28318 \begin_layout Plain Layout
28320 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
28323 textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
28330 \begin_layout Plain Layout
28334 left(B^{2}+x_{0}^{2}
28342 left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
28347 \begin_layout Plain Layout
28359 \begin_layout Standard
28360 \begin_inset VSpace bigskip
28363 To set the line separation for all lines in a formula, the length
28370 \begin_inset Index idx
28373 \begin_layout Plain Layout
28383 \begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
28394 \begin_inset space \thinspace{}
28399 \begin_inset space \thinspace{}
28402 mm additional line separation as in the previous example, the command
28405 \begin_layout Standard
28415 \begin_layout Standard
28416 is inserted in TeX-mode before the formula.
28417 This requires that the LaTeX-package
28425 \begin_layout Plain Layout
28430 is part of every LaTeX standard installation.
28436 \begin_inset Index idx
28439 \begin_layout Plain Layout
28445 was loaded in LaTeX-preamble with the line
28448 \begin_layout Standard
28456 \begin_layout Standard
28461 \begin_layout Plain Layout
28473 \begin_inset Formula
28475 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}\\
28476 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
28484 \begin_layout Standard
28488 \begin_layout Plain Layout
28499 To get back to the predefined distance,
28505 is set to the value 3
28506 \begin_inset space \thinspace{}
28512 \begin_layout Subsubsection
28514 \begin_inset CommandInset label
28516 name "sub:Column-Separation"
28521 \begin_inset Index idx
28524 \begin_layout Plain Layout
28525 Formula ! multiline ! Column separation
28533 \begin_layout Standard
28534 Multiline formulas form a matrix.
28535 A formula in the eqnarray environment is for example a matrix with three
28537 By changing the column separation in this environment, the space beside
28538 the relation sign can be changed.
28541 \begin_layout Standard
28542 The column separation is specified with the length
28549 \begin_inset Index idx
28552 \begin_layout Plain Layout
28561 \begin_inset Newline newline
28564 column separation = 2
28565 \begin_inset space \thinspace{}
28575 \begin_inset Newline newline
28581 \begin_layout Standard
28591 \begin_layout Standard
28592 inserted in TeX-mode, sets for all following formulas a column separation
28594 \begin_inset space \thinspace{}
28598 To get back to the predefined distance,
28605 \begin_inset space \thinspace{}
28611 \begin_layout Standard
28613 \begin_inset space \thinspace{}
28616 cm column separation:
28620 \begin_layout Plain Layout
28632 \begin_inset Formula
28640 A formula with the predefined column separation for matrices of 10
28641 \begin_inset space \thinspace{}
28648 \begin_layout Plain Layout
28660 \begin_inset Formula
28671 \begin_layout Subsubsection
28673 \begin_inset Index idx
28676 \begin_layout Plain Layout
28685 \begin_layout Standard
28686 Long formulas can be typeset using these methods:
28689 \begin_layout Itemize
28690 When one side of the equation is much shorter than the line width, this
28691 one is chosen for the left side and the right side is typeset over two
28693 \begin_inset Formula
28695 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 \\
28696 & & -\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:shortlong}
28701 The minus sign at the beginning of the second line does normally not appear
28702 as an operator because it is the first character of the line.
28703 Thus it would not be surrounded by space and could not be distinguished
28704 from the fraction bar.
28706 \begin_inset space \thinspace{}
28709 pt space was inserted behind the minus sign with the command
28719 \begin_layout Plain Layout
28727 \begin_inset CommandInset ref
28729 reference "sub:Variable-Space"
28739 \begin_inset Index idx
28742 \begin_layout Plain Layout
28753 \begin_layout Itemize
28754 When both sides of the equation are too long, the command
28761 \begin_inset Index idx
28764 \begin_layout Plain Layout
28773 It is inserted in the first column of the first line and causes all further
28774 insertions to overwrite the following columns:
28775 \begin_inset Formula
28777 \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 \\
28778 & & -\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 \\
28779 & & =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}
28784 After the insertion of
28790 , the cursor is in a purple box that is a bit shifted to the left from the
28792 In this the formula is inserted.
28793 \begin_inset Newline newline
28796 The content of the further lines is inserted to the second or another formula
28798 The greater the column number where it was inserted, the larger the indentation.
28799 \begin_inset VSpace medskip
28803 \begin_inset Newline newline
28807 \begin_inset Note Greyedout
28810 \begin_layout Plain Layout
28811 Note the following when using
28820 \begin_layout Itemize
28821 The formula doesn't use the full page width.
28823 \begin_inset space \thinspace{}
28827 \begin_inset space \space{}
28831 \begin_inset Formula $-B^{2}$
28834 is added to the first line in the above example, it would have been outside
28836 To better use the width, negative space can be inserted at the beginning
28840 \begin_layout Itemize
28841 Due to a bug in LyX the cursor cannot be set with the mouse into the first
28846 \begin_layout Plain Layout
28847 \begin_inset CommandInset href
28849 name "LyX-bug #1429"
28850 target "http://www.lyx.org/trac/ticket/1429"
28859 One can only set the cursor at the beginning of the line and move it with
28868 \begin_layout Itemize
28869 Other methods to set long formulas are offered by the environments described
28871 \begin_inset CommandInset ref
28873 reference "sub:Multline-Environment"
28878 \begin_inset CommandInset ref
28880 reference "sub:Multiline-Formula-Parts"
28887 \begin_layout Subsubsection
28889 \begin_inset CommandInset label
28891 name "sub:Multiline-Brackets"
28896 \begin_inset Index idx
28899 \begin_layout Plain Layout
28900 Brackets ! for multiline expressions
28908 \begin_layout Standard
28909 For brackets spanning multiple lines the following problem occurs:
28910 \begin_inset Formula
28912 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
28913 & & \left.\cdots+B-D\right]
28921 \begin_layout Standard
28922 The closing bracket is smaller than the opening bracket because brackets
28923 with variable size may not span multiple lines.
28926 \begin_layout Standard
28927 To set the bracket size for the second line correctly, the first line is
28935 \begin_inset Index idx
28938 \begin_layout Plain Layout
28946 and the second line with
28954 \begin_layout Plain Layout
28968 \begin_inset CommandInset ref
28970 reference "sub:Automatic-Bracket-Size"
28982 \begin_inset Index idx
28985 \begin_layout Plain Layout
29011 \begin_layout Plain Layout
29030 \begin_layout Plain Layout
29049 \begin_layout Plain Layout
29061 \begin_inset Formula $\downarrow$
29067 \begin_inset Index idx
29070 \begin_layout Plain Layout
29078 is inserted, because the multiplication operator with its limits is the
29079 largest symbol in the first line and this should be the size for the bracket
29080 in the second line.
29083 \begin_layout Standard
29084 The result is this:
29085 \begin_inset Formula
29087 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
29088 & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
29096 \begin_layout Subsection
29100 \begin_layout Standard
29101 Align environments can be used for every kind of multiline formulas.
29102 They are especially useful to set several formulas side by side.
29105 \begin_layout Standard
29106 Align environments consist of columns.
29107 The odd columns are right aligned, the even ones left aligned.
29108 Every line in an Align environment can be numbered.
29111 \begin_layout Standard
29112 Align environments are created via the menu
29114 Insert\SpecialChar \menuseparator
29120 Edit\SpecialChar \menuseparator
29121 Math\SpecialChar \menuseparator
29122 Change Formula Type
29124 already existing formulas can be converted to Align environments.
29127 \begin_layout Standard
29128 To add or delete columns, the math toolbar buttons
29129 \begin_inset Graphics
29130 filename ../images/tabular-feature_append-column.png
29136 \begin_inset Graphics
29137 filename ../images/tabular-feature_delete-column.png
29142 , respectively, or the menu
29144 Edit\SpecialChar \menuseparator
29150 \begin_layout Subsubsection
29151 Standard align Environment
29152 \begin_inset CommandInset label
29154 name "sub:Standard-align-Environment"
29159 \begin_inset Index idx
29162 \begin_layout Plain Layout
29163 Formula ! multiline ! align environment
29171 \begin_layout Standard
29172 This Align environment is created by pressing
29175 arg "newline-insert newline"
29178 in a formula or by the menu
29180 Insert\SpecialChar \menuseparator
29181 Math\SpecialChar \menuseparator
29182 AMS align Environment
29187 \begin_layout Standard
29188 An example for two formulas set side by side, that are created with a four
29189 column align environment:
29190 \begin_inset Formula
29192 A & =\sin(B) & C & =D\\
29193 C & \ne A & B & \ne D
29198 As it can be seen, the formulas in this environment are placed so as if
29207 \begin_layout Plain Layout
29215 \begin_inset CommandInset ref
29217 reference "sub:Variable-Space"
29228 before the first and after every even column.
29229 When the formula style
29235 \begin_layout Plain Layout
29237 \begin_inset CommandInset ref
29239 reference "sec:Formula-Styles"
29250 is used, the formula is set without the
29256 before the first column.
29259 \begin_layout Subsubsection
29260 Alignat Environment
29261 \begin_inset Index idx
29264 \begin_layout Plain Layout
29265 Formula ! multiline ! alignat environment
29273 \begin_layout Standard
29274 The alignat environment has no predefined column separation.
29275 It can be inserted manually with the spaces that are described
29276 \begin_inset CommandInset ref
29278 reference "sub:Space"
29285 \begin_layout Standard
29286 The above example in the alignat environment where 1
29287 \begin_inset space \thinspace{}
29290 cm space was inserted at the beginning of the second formula:
29291 \begin_inset Formula
29292 \begin{alignat*}{2}
29293 A & =\sin(B) & \hspace{1cm}C & =D\\
29294 C & \ne A & B & \ne D
29299 Because the column separation can be set separately for every column, this
29300 environment is especially suitable to set three and more formulas side
29304 \begin_layout Subsubsection
29305 Flalign Environment
29306 \begin_inset CommandInset label
29308 name "sub:Flalign-Environment"
29313 \begin_inset Index idx
29316 \begin_layout Plain Layout
29317 Formula ! multiline ! flalign environment
29325 \begin_layout Standard
29326 In this environment the first two columns are always set as much as possible
29327 to the left and the last two ones to the right.
29329 \begin_inset Formula
29331 A & =1 & B & =2 & C & =3\\
29332 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
29340 \begin_layout Standard
29341 By creating a flalign environment with an odd number of columns where an
29342 empty TeX-brace is inserted to the last column, several formulas in a document
29343 can be set to the left, although the formula style
29348 As example the indented formula
29349 \begin_inset CommandInset ref
29351 reference "eq:VolInt"
29356 \begin_inset Formula
29358 \hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
29363 The first two columns contain the formula.
29364 To indent it as with the formula style
29369 \begin_inset space \thinspace{}
29372 pt space was inserted at the beginning of the first column.
29375 \begin_layout Subsection
29376 Eqnarray Environment
29377 \begin_inset CommandInset label
29379 name "sub:Eqnarray-Environment"
29384 \begin_inset Index idx
29387 \begin_layout Plain Layout
29388 Formula ! multiline ! eqnarray environment
29396 \begin_layout Standard
29397 When this environment has been created, three blue boxes appear.
29398 The content of the first box is right aligned, the content of the last
29400 The content of the middle box appears centered and a bit smaller, because
29401 it is designed to insert there only relation characters.
29402 \begin_inset Formula
29404 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
29414 \begin_layout Subsection
29416 \begin_inset Index idx
29419 \begin_layout Plain Layout
29420 Formula ! multiline ! gather environment
29428 \begin_layout Standard
29429 This environment consists of only one centered column.
29430 Every line can be numbered.
29431 \begin_inset Formula
29442 \begin_layout Subsection
29443 Multline Environment
29444 \begin_inset CommandInset label
29446 name "sub:Multline-Environment"
29451 \begin_inset Index idx
29454 \begin_layout Plain Layout
29455 Formula ! multiline ! multline environment
29463 \begin_layout Standard
29464 The multline environment consists, like the gather environment, of only
29466 But the first line is left aligned, the last one right aligned.
29467 All other lines are centered.
29468 Therefore this environment is suitable for long formulas.
29470 \begin_inset CommandInset ref
29472 reference "eq:lefteqn"
29476 in the multline environment:
29477 \begin_inset Formula
29479 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}\\
29480 -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}\\
29481 =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}}
29489 \begin_layout Standard
29490 In the output only the last (first) line of a multline environment appears
29491 numbered when the document numbering is right (left).
29495 \begin_layout Plain Layout
29496 numbering styles see
29497 \begin_inset CommandInset ref
29499 reference "sec:Formula-Styles"
29511 \begin_layout Standard
29519 \begin_inset Index idx
29522 \begin_layout Plain Layout
29537 \begin_inset Index idx
29540 \begin_layout Plain Layout
29548 a centered line can be right or left aligned, respectively.
29549 The commands are used as follows:
29552 \begin_layout Standard
29557 shoveright{line content}
29563 shoveleft{line content}
29566 \begin_layout Standard
29567 \begin_inset VSpace medskip
29577 \begin_inset Index idx
29580 \begin_layout Plain Layout
29588 specifies the distance of the first line from the left page margin.
29589 Predefined is the length 0
29590 \begin_inset space \thinspace{}
29596 \begin_layout Standard
29597 As example the above formula where the command
29600 \begin_layout Standard
29610 \begin_layout Standard
29611 was inserted in TeX-mode before:
29615 \begin_layout Plain Layout
29627 \begin_inset Formula
29629 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}\\
29630 \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}}\\
29631 =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}}
29640 \begin_layout Plain Layout
29651 The second line was left aligned using
29660 \begin_layout Subsection
29661 Multiline Formula Parts
29662 \begin_inset CommandInset label
29664 name "sub:Multiline-Formula-Parts"
29669 \begin_inset Index idx
29672 \begin_layout Plain Layout
29673 Formula ! multiline ! formula parts
29681 \begin_layout Standard
29682 To display only parts of a formula with multiple lines, one of the following
29683 environments is used:
29700 They can be inserted via the menu
29702 Insert\SpecialChar \menuseparator
29705 or by using the commands described in this section.
29708 \begin_layout Standard
29709 The first three have the same properties as the corresponding multiline
29710 formula environments, but it is possible to set further formula parts beside
29713 \begin_inset Formula
29715 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
29716 \Delta E\Delta t & \ge\frac{\hbar}{2}
29718 \right\} \textrm{Uncertainty relations}
29726 \begin_layout Standard
29727 To get this formula, a displayed formula is created where the command
29734 \begin_inset Index idx
29737 \begin_layout Plain Layout
29746 A purple box appears around the blue formula box where now columns and
29747 lines can be added.
29748 Outside the multiline environment other formula parts can be set, like
29752 \begin_layout Standard
29753 The aligned environment is also suitable for long formulas whose lines are
29754 horizontally aligned.
29755 Using aligned in a displayed formula has the advantage that the formula
29756 number is vertically centered behind the lines.
29758 \begin_inset CommandInset ref
29760 reference "eq:shortlong"
29764 in the aligned environment:
29765 \begin_inset Formula
29767 \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}|}\\
29768 & -\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}|}
29777 \begin_layout Standard
29778 To use the environments
29797 \begin_inset Index idx
29800 \begin_layout Plain Layout
29815 \begin_inset Index idx
29818 \begin_layout Plain Layout
29833 \begin_inset Index idx
29836 \begin_layout Plain Layout
29844 are inserted, respectively.
29845 The split environment has the same properties as the aligned environment
29846 but it can only have two columns.
29849 \begin_layout Subsection
29850 Text in multiline Formulas
29851 \begin_inset CommandInset label
29853 name "sub:Text-in-multiline"
29858 \begin_inset Index idx
29861 \begin_layout Plain Layout
29868 \begin_inset Index idx
29871 \begin_layout Plain Layout
29872 Formula ! multiline ! text
29880 \begin_layout Standard
29881 In the Align environments, and the multline and gather environment, text
29882 can be inserted that will appear in a separate line and doesn't affect
29883 the column alignment.
29884 To do this, the command
29891 \begin_inset Index idx
29894 \begin_layout Plain Layout
29902 is used in the following scheme:
29905 \begin_layout Standard
29913 \begin_layout Standard
29914 The text should not be longer than a line because it cannot be hyphenated.
29915 As LyX doesn't yet support
29921 directly, the text is written as mathematical text.
29928 must hereby be at the beginning of a line and appears in the output above
29930 An example where the text was inserted at the beginning of the second line:
29931 \begin_inset Formula
29933 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
29934 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
29942 \begin_layout Section
29944 \begin_inset Index idx
29947 \begin_layout Plain Layout
29954 \begin_inset Index idx
29957 \begin_layout Plain Layout
29958 Formula ! numbering|see
29962 \begin_layout Plain Layout
29973 \begin_layout Plain Layout
29988 \begin_layout Subsection
29992 \begin_layout Standard
29993 Numbered formulas can be created with the menu
29995 Insert\SpecialChar \menuseparator
29996 Math\SpecialChar \menuseparator
29998 \begin_inset space ~
30006 \begin_inset space ~
30012 Existing formulas can be numbered with the menu
30014 Edit\SpecialChar \menuseparator
30015 Math\SpecialChar \menuseparator
30017 \begin_inset space ~
30025 arg "math-number-toggle"
30029 The formula number is displayed in LyX behind the formula as a number sign
30031 The number sign is replaced in the output by the formula number.
30034 \begin_layout Standard
30035 When numbering is turned on in multiline formulas, all lines will be numbered.
30036 But the numbering can be controlled with the menu
30038 Edit\SpecialChar \menuseparator
30039 Math\SpecialChar \menuseparator
30041 \begin_inset space ~
30045 \begin_inset space ~
30049 \begin_inset space ~
30057 arg "math-number-line-toggle"
30063 \begin_layout Standard
30064 Except for inline formulas, all formulas can be numbered with two different
30066 \begin_inset CommandInset ref
30068 reference "sec:Formula-Styles"
30075 \begin_layout Subsection
30077 \begin_inset Index idx
30080 \begin_layout Plain Layout
30081 Cross-references ! to formulas
30089 \begin_layout Standard
30090 All labeled formulas can be cross-referenced.
30091 A label is added by the menu
30093 Insert\SpecialChar \menuseparator
30096 or the toolbar button
30097 \begin_inset Graphics
30098 filename ../images/label-insert.png
30104 The cursor must hereby be inside a displayed formula.
30105 Alternatively you can right-click on the formula and choose
30110 A dialog pops up displaying the prefix
30115 The label is inserted there behind the prefix.
30116 The predefined prefix means
30117 \begin_inset Quotes eld
30121 \begin_inset Quotes erd
30124 and makes it easier to find labels in large documents because it marks
30125 it as formula label to divide it from e.
30126 \begin_inset space \thinspace{}
30130 \begin_inset space \space{}
30134 To change a label, the menu
30136 Insert\SpecialChar \menuseparator
30139 is used again or you right-click on a formula and then on
30146 \begin_layout Standard
30147 The name of the label is displayed in LyX within two parentheses behind
30149 A formula with a label is always numbered.
30152 \begin_layout Standard
30153 Cross-references are inserted via the menu
30155 Insert\SpecialChar \menuseparator
30158 or with the toolbar button
30159 \begin_inset Graphics
30160 filename ../images/dialog-show-new-inset_ref.png
30166 A formula cross-reference appears in the output as formula number.
30167 When in the cross-reference dialog window the format
30171 is chosen, the cross-reference appears in the output as formula number
30173 \begin_inset Newline newline
30176 By right-clicking on a cross-reference in LyX, one jumps to the formula
30177 that is referenced.
30180 \begin_layout Standard
30181 Here are as examples cross-references to formulas of the following subsections:
30182 \begin_inset Note Note
30185 \begin_layout Plain Layout
30186 Note the different cross-reference types.
30194 \begin_layout Standard
30196 \begin_inset CommandInset ref
30203 \begin_inset CommandInset ref
30211 \begin_inset CommandInset ref
30217 ) big Latin letters are used for the numbering in contrary to (
30218 \begin_inset CommandInset ref
30227 \begin_layout Standard
30228 \begin_inset VSpace medskip
30231 When the argument of
30239 \begin_layout Plain Layout
30247 \begin_inset CommandInset ref
30249 reference "sub:User-defined-Numbering"
30260 contains a box like in
30261 \begin_inset CommandInset ref
30263 reference "sub:Paragraph-Boxes"
30267 , the formula cannot be referenced.
30270 \begin_layout Subsection
30272 \begin_inset Index idx
30275 \begin_layout Plain Layout
30276 Formula numbering ! subnumbering
30284 \begin_layout Standard
30285 With the help of the commands
30289 begin{subequations}
30297 formulas can be subnumbered.
30298 Both commands are inserted in TeX-mode.
30301 \begin_layout Standard
30303 \begin_inset Formula
30314 \begin_layout Plain Layout
30318 addtocounter{equation}{-1}
30327 \begin_layout Plain Layout
30331 begin{subequations}
30337 \begin_inset VSpace -5mm
30341 \begin_inset Formula
30349 \begin_inset Formula
30359 \begin_layout Standard
30363 \begin_layout Plain Layout
30375 \begin_layout Standard
30376 To create the example, the following is done:
30379 \begin_layout Enumerate
30380 first formula is inserted
30383 \begin_layout Enumerate
30388 addtocounter{equation}{-1}
30390 begin{subequations}
30391 \begin_inset Index idx
30394 \begin_layout Plain Layout
30403 \begin_inset Newline newline
30408 is inserted after the first formula
30411 \begin_layout Enumerate
30412 second formula is inserted
30415 \begin_layout Enumerate
30416 third formula is inserted
30419 \begin_layout Enumerate
30426 is inserted after the third formula
30429 \begin_layout Standard
30430 Every formula between the commands
30442 is subnumbered as a, b,
30443 \begin_inset Newline linebreak
30446 c, \SpecialChar \ldots{}
30447 For multiline formulas every line will be subnumbered.
30448 All subnumbered formulas are treated as
30453 But as every numbered formula increases the counter
30457 by one, the command
30463 is needed to decrease it.
30464 Otherwise the formulas
30465 \begin_inset CommandInset ref
30472 \begin_inset CommandInset ref
30479 \begin_inset CommandInset ref
30485 would be numbered as
30486 \begin_inset CommandInset ref
30493 \begin_inset CommandInset ref
30500 \begin_inset CommandInset ref
30509 \begin_layout Standard
30510 By inserting the commands in TeX-mode, a space is created between the first
30513 \begin_inset space \thinspace{}
30516 mm vertical space is inserted after the command
30520 begin{subequations}
30523 When the formula style
30529 \begin_layout Plain Layout
30531 \begin_inset CommandInset ref
30533 reference "sec:Formula-Styles"
30545 \begin_inset space \thinspace{}
30548 mm space is inserted instead.
30551 \begin_layout Standard
30552 Here is an example for a multiline formula where the numbering was turned
30553 off for the second line:
30557 \begin_layout Plain Layout
30561 begin{subequations}
30567 \begin_inset Formula
30569 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
30570 & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
30571 & = & B^{2}-2BZ+Z^{2}\label{eq:f}
30580 \begin_layout Plain Layout
30592 \begin_layout Subsection
30593 User-defined Numbering
30594 \begin_inset CommandInset label
30596 name "sub:User-defined-Numbering"
30601 \begin_inset Index idx
30604 \begin_layout Plain Layout
30605 Formula numbering ! user-defined
30613 \begin_layout Standard
30614 \begin_inset Index idx
30617 \begin_layout Plain Layout
30618 Formula numbering ! self-defined delimiters
30623 With the standard numbering parentheses are set around the formula number.
30624 To replace the parentheses for example by vertical bars, the following
30625 line is added to the LaTeX-preamble:
30628 \begin_layout Standard
30640 \begin_inset Note Note
30643 \begin_layout Plain Layout
30644 This macro is already declared in the LaTeX-preamble for testing.
30645 To activate it, remove the percent sign at the beginning.
30653 \begin_layout Standard
30654 To use other characters, the vertical bars besides the
30658 are replaced by one ore more characters.
30659 To get only the formula number the vertical bars are omitted.
30662 \begin_layout Standard
30663 \begin_inset VSpace bigskip
30666 When there should be an expression of your choice instead of the consecutive
30667 formula number in parentheses behind the formula, the command
30674 \begin_inset Index idx
30677 \begin_layout Plain Layout
30686 \begin_inset Formula
30688 A+B=C\tag{something}\label{eq:tag}
30693 In this example the command
30701 \begin_layout Plain Layout
30712 was inserted in the formula.
30715 \begin_layout Standard
30724 \begin_layout Plain Layout
30735 is inserted instead, the star prevents the parentheses around the expression:
30736 \begin_inset Formula
30738 A+B=C\tag*{something}
30746 \begin_layout Standard
30747 \begin_inset VSpace bigskip
30750 To restart the formula numbering with new document parts or sections, the
30751 following command is used:
30754 \begin_layout Standard
30759 @addtoreset{equation}{part}
30762 \begin_inset Index idx
30765 \begin_layout Plain Layout
30770 \begin_layout Plain Layout
30781 \begin_layout Plain Layout
30794 \begin_layout Plain Layout
30805 \begin_layout Plain Layout
30818 \begin_inset Newline newline
30822 \begin_inset Newline newline
30829 @addtoreset{equation}{section}
30832 \begin_layout Standard
30833 To be able to use these commands in TeX-mode, the
30834 \begin_inset Quotes eld
30838 \begin_inset Quotes erd
30841 character has to be made
30842 \begin_inset Quotes eld
30846 \begin_inset Quotes erd
30849 for LaTeX using the command
30863 So the command sequence in TeX-mode is:
30866 \begin_layout Standard
30872 \begin_inset Newline newline
30877 @addtoreset{equation}{section}
30878 \begin_inset Newline newline
30886 \begin_layout Standard
30887 In the LaTeX-preamble
30899 can be omitted as they are automatically internally inserted by LyX.
30902 \begin_layout Standard
30917 \begin_layout Plain Layout
30922 is part of the LaTeX-package
30927 \begin_inset Index idx
30930 \begin_layout Plain Layout
30931 Packages ! carlisle
30936 that is part of every LaTeX standard installation.
30942 \begin_inset Index idx
30945 \begin_layout Plain Layout
30946 Packages ! remreset
30951 has to be loaded in the LaTeX-preamble with the line
30954 \begin_layout Standard
30959 usepackage{remreset}
30962 \begin_layout Standard
30970 \begin_inset Index idx
30973 \begin_layout Plain Layout
30978 \begin_layout Plain Layout
30989 \begin_layout Plain Layout
31002 \begin_layout Plain Layout
31013 \begin_layout Plain Layout
31025 can be used with the same scheme as
31034 \begin_layout Standard
31035 \begin_inset VSpace bigskip
31038 Sometimes formulas should be numbered in the following form:
31041 \begin_layout Standard
31044 (section number.formula number)
31047 \begin_layout Standard
31048 The formula number should start with every section with
31049 \begin_inset Quotes eld
31053 \begin_inset Quotes erd
31059 \begin_layout Standard
31060 For this case there is the command
31067 \begin_inset Index idx
31070 \begin_layout Plain Layout
31078 , which is used with the following scheme:
31081 \begin_layout Standard
31086 numberwithin{counter}{sectioning}
31089 \begin_layout Standard
31090 Counter denotes what kind of numbering is affected, sectioning denotes what
31091 number is before the dot.
31094 \begin_layout Standard
31095 Thus in our case the following LaTeX-preamble or TeX code line is used:
31098 \begin_layout Standard
31103 numberwithin{equation}{section}
31106 \begin_layout Standard
31107 This is the result:
31111 \begin_layout Plain Layout
31115 numberwithin{equation}{section}
31121 \begin_inset Formula
31131 \begin_layout Standard
31133 \begin_inset space \thinspace{}
31137 \begin_inset space \space{}
31140 tables so that the number of the part is the sectioning,
31141 \begin_inset Newline newline
31148 numberwithin{table}{part}
31153 \begin_layout Standard
31154 To go back to the standard numbering or to prevent this kind of numbering
31155 when it is defined by the document class, the following command is inserted
31156 as TeX code or to the LaTeX-preamble:
31159 \begin_layout Standard
31169 \begin_inset Index idx
31172 \begin_layout Plain Layout
31186 \begin_layout Plain Layout
31202 \begin_inset Newline newline
31210 \begin_inset Newline newline
31222 \begin_layout Standard
31229 uses internally the command
31235 , described above, that also needs to be reverted.
31239 \begin_layout Plain Layout
31246 \begin_layout Plain Layout
31250 @removefromreset{equation}{section}
31253 \begin_layout Plain Layout
31265 \begin_layout Subsection
31266 Numbering with Roman Numbers and Letters
31267 \begin_inset Index idx
31270 \begin_layout Plain Layout
31271 Formula numbering ! with letters
31277 \begin_inset Index idx
31280 \begin_layout Plain Layout
31281 Formula numbering ! with Roman numbers
31289 \begin_layout Standard
31290 Formulas can also be numbered with Roman numbers and Latin letters.
31291 To number for example with small Roman numbers, the command
31294 \begin_layout Standard
31306 \begin_layout Standard
31307 is inserted before the formula in TeX-mode.
31315 \begin_inset Index idx
31318 \begin_layout Plain Layout
31326 redefines the predefined command
31342 \begin_layout Plain Layout
31349 has the same scheme like the command
31355 that is described in
31356 \begin_inset CommandInset ref
31358 reference "sub:The-Command-newcommand"
31371 is the formula counter.
31378 is used as prefix for a counter, the value of the counter is output as
31380 When a formula is numbered, LaTeX sets internally the command
31386 behind the formula.
31392 \begin_inset Index idx
31395 \begin_layout Plain Layout
31405 outputs the counter as small Roman number.
31408 \begin_layout Standard
31409 All formulas behind the command
31419 are now numbered Roman.
31420 To switch to numbering with big Roman numbers, the command is inserted
31434 \begin_inset Index idx
31437 \begin_layout Plain Layout
31449 \begin_inset Quotes eld
31453 \begin_inset Quotes erd
31456 with small Latin letters there is the command
31463 \begin_inset Index idx
31466 \begin_layout Plain Layout
31474 , for big ones there is the command
31481 \begin_inset Index idx
31484 \begin_layout Plain Layout
31497 \begin_layout Standard
31498 \begin_inset Note Greyedout
31501 \begin_layout Plain Layout
31508 \begin_inset space ~
31511 formulas can be numbered with Latin letters in one document.
31519 \begin_layout Standard
31523 \begin_layout Plain Layout
31539 \begin_layout Standard
31540 \begin_inset Formula
31542 A=\textrm{small roman}
31551 \begin_layout Plain Layout
31565 \begin_inset Formula
31567 B=\textrm{big Roman}\label{eq:Rom}
31576 \begin_layout Plain Layout
31590 \begin_inset Formula
31592 C=\textrm{small Latin}
31601 \begin_layout Plain Layout
31615 \begin_inset Formula
31617 D=\textrm{big Latin}\label{eq:Lat}
31625 \begin_layout Standard
31626 To switch back to the default numbering, insert the command:
31629 \begin_layout Standard
31639 \begin_inset Index idx
31642 \begin_layout Plain Layout
31653 \begin_layout Standard
31657 \begin_layout Plain Layout
31671 \begin_inset Formula
31681 \begin_layout Standard
31682 \begin_inset VSpace medskip
31685 As you see, formulas are numbered serially independent from the numbering
31687 When then numbering should start with
31688 \begin_inset Quotes eld
31692 \begin_inset Quotes erd
31695 when the style is changed, new equation counters have to be defined.
31696 A description about this can be found in the file
31697 \begin_inset CommandInset href
31699 name "Formula-numbering.lyx"
31700 target "run:Formula-numbering.lyx"
31707 \begin_layout Standard
31708 \begin_inset Newpage newpage
31714 \begin_layout Section
31715 Chemical Symbols and Equations
31716 \begin_inset CommandInset label
31718 name "sub:Chemical-Symbols-and"
31723 \begin_inset Index idx
31726 \begin_layout Plain Layout
31727 Chemical characters ! Symbols
31733 \begin_inset Index idx
31736 \begin_layout Plain Layout
31743 \begin_inset Index idx
31746 \begin_layout Plain Layout
31755 \begin_layout Standard
31756 An example text from chemistry:
31759 \begin_layout Quote
31761 \begin_inset Formula $\mathrm{SO_{4}^{2-}}$
31764 -ion reacts with two
31765 \begin_inset Formula $\mathrm{Na^{+}}$
31768 -ions to sodium sulfate
31769 \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
31773 The chemical equation for this is:
31774 \begin_inset Formula
31776 \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
31784 \begin_layout Standard
31785 This chemical equation can directly be created as formula.
31786 To avoid that the symbols appear italic, everything is highlighted and
31787 changed by the shortcut
31793 to the upright font style.
31797 \begin_layout Plain Layout
31803 \begin_inset CommandInset ref
31805 reference "sub:Font-Styles"
31817 \begin_layout Standard
31818 A more convenient way to typeset chemical formulas is to use the command
31826 \begin_inset Index idx
31829 \begin_layout Plain Layout
31837 that is available when the LaTeX-package
31842 \begin_inset Index idx
31845 \begin_layout Plain Layout
31858 to a formula a new blue box appears where chemical formulas can be inserted
31859 in an intuitive way.
31862 \begin_layout Standard
31864 \begin_inset Tabular
31865 <lyxtabular version="3" rows="9" columns="2">
31866 <features rotate="0" tabularvalignment="middle">
31867 <column alignment="center" valignment="top">
31868 <column alignment="center" valignment="top">
31870 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
31873 \begin_layout Plain Layout
31879 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
31882 \begin_layout Plain Layout
31884 \begin_inset Note Note
31887 \begin_layout Plain Layout
31894 is only used as spacer.
31906 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31909 \begin_layout Plain Layout
31916 \begin_layout Plain Layout
31930 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31933 \begin_layout Plain Layout
31934 \begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$
31944 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31947 \begin_layout Plain Layout
31954 \begin_layout Plain Layout
31968 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
31971 \begin_layout Plain Layout
31972 \begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$
31982 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
31985 \begin_layout Plain Layout
31992 \begin_layout Plain Layout
32006 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32009 \begin_layout Plain Layout
32010 \begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$
32020 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32023 \begin_layout Plain Layout
32030 \begin_layout Plain Layout
32044 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32047 \begin_layout Plain Layout
32048 \begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$
32058 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32061 \begin_layout Plain Layout
32068 \begin_layout Plain Layout
32083 \begin_layout Plain Layout
32098 \begin_layout Plain Layout
32112 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32115 \begin_layout Plain Layout
32116 \begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$
32126 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32129 \begin_layout Plain Layout
32136 \begin_layout Plain Layout
32146 \begin_inset Formula $\downarrow$
32150 \begin_inset Formula $\to$
32158 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32161 \begin_layout Plain Layout
32162 \begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$
32172 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
32175 \begin_layout Plain Layout
32182 \begin_layout Plain Layout
32195 \begin_layout Plain Layout
32208 \begin_layout Plain Layout
32221 \begin_layout Plain Layout
32234 \begin_layout Plain Layout
32248 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
32251 \begin_layout Plain Layout
32252 \begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$
32262 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
32265 \begin_layout Plain Layout
32272 \begin_layout Plain Layout
32285 \begin_layout Plain Layout
32298 \begin_layout Plain Layout
32311 \begin_layout Plain Layout
32328 \begin_layout Plain Layout
32342 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
32345 \begin_layout Plain Layout
32346 \begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$
32362 \begin_layout Standard
32363 \begin_inset Note Greyedout
32366 \begin_layout Plain Layout
32372 Inserting a formula to a
32378 box will lead to LaTeX errors due to a LyX bug.
32384 \begin_layout Plain Layout
32385 \begin_inset CommandInset href
32387 name "LyX-bug #8566"
32388 target "http://www.lyx.org/trac/ticket/8566"
32399 In this case TeX code has to be used like for
32413 \begin_layout Plain Layout
32434 \begin_layout Standard
32435 \begin_inset Note Greyedout
32438 \begin_layout Plain Layout
32444 It is not possible in LyX to use the character ^ to get an up-arrow as
32450 One instead uses a negative thin space followed by the command
32457 \begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$
32468 \begin_layout Standard
32475 the command for equation
32476 \begin_inset space ~
32480 \begin_inset CommandInset ref
32482 reference "eq:chem-reaction"
32487 \begin_inset Newline newline
32498 \begin_layout Plain Layout
32511 \begin_layout Plain Layout
32524 \begin_layout Plain Layout
32537 \begin_layout Plain Layout
32550 \begin_layout Plain Layout
32563 \begin_layout Plain Layout
32575 \begin_layout Standard
32576 To create multiline chemical equations first a multiline formula is created
32578 \begin_inset CommandInset ref
32580 reference "sec:Multiline-Formulas"
32585 Afterwards the command
32591 is used in every small blue box of the formula.
32593 \begin_inset CommandInset ref
32595 reference "eq:TEOS-reaction-1"
32600 \begin_inset CommandInset ref
32602 reference "eq:TEOS-reaction-2"
32606 are an example of a multi-stage chemical reaction where every equation
32607 has its own number.
32608 \begin_inset Formula
32610 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
32611 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
32619 \begin_layout Standard
32630 package provides the command
32637 \begin_inset Index idx
32640 \begin_layout Plain Layout
32648 that has to be used for special cases.
32649 For more information about
32655 and more examples have a look at the documentation of
32660 \begin_inset CommandInset citation
32669 \begin_layout Section
32673 \begin_layout Standard
32674 LyX supports two types of commutative diagrams:
32682 that are explained in the following.
32685 \begin_layout Subsection
32687 \begin_inset Index idx
32690 \begin_layout Plain Layout
32699 \begin_layout Standard
32700 Diagrams of this type visualize relations by vertical and horizontal lines
32702 \begin_inset Formula
32704 \begin{CD}A@>>>B@>>>C\\
32715 \begin_layout Standard
32716 To get them, the command
32721 \begin_inset Index idx
32724 \begin_layout Plain Layout
32734 is inserted to a formula.
32735 A blue box appears with two dashed lines where further commands can be
32740 arg "newline-insert newline"
32743 a new line is created.
32744 Horizontal relations are inserted in odd, vertical in even formula lines.
32747 \begin_layout Standard
32748 To create the relations there are the following commands:
32751 \begin_layout Itemize
32756 creates a left arrow,
32767 \begin_layout Itemize
32772 creates an up arrow,
32780 a vertical equal sign
32783 \begin_layout Itemize
32789 is a placeholder for non-existent relations
32792 \begin_layout Standard
32793 All arrows can be labeled as follows:
32796 \begin_layout Itemize
32797 If text inserted between the first and second < or >, resp., it is placed
32799 When it is inserted between the second and third one, it appears under
32803 \begin_layout Itemize
32804 When text for vertical arrows is inserted between the first and second A
32805 or V, resp., it is placed left beside the arrow.
32806 When it is inserted between the second and third one, it appears right
32808 If the text contains an A or V, these letters must be set into a TeX-brace.
32811 \begin_layout Standard
32812 As example a diagram with all possible relations:
32815 \begin_layout Standard
32816 \begin_inset Formula
32818 \begin{CD}A@>j>>B@>>k>C@=F\\
32829 \begin_layout Standard
32830 The command for this is:
32831 \begin_inset Newline newline
32842 \begin_layout Plain Layout
32851 A@>j>>B@>>k>C@=F Ctrl+Return
32852 \begin_inset Newline newline
32856 \begin_inset Phantom HPhantom
32859 \begin_layout Plain Layout
32868 \begin_layout Plain Layout
32887 \begin_inset Formula $\to$
32893 \begin_inset Newline newline
32897 \begin_inset Phantom HPhantom
32900 \begin_layout Plain Layout
32909 \begin_layout Plain Layout
32926 \begin_layout Subsection
32928 \begin_inset Index idx
32931 \begin_layout Plain Layout
32932 Diagrams ! xymatrix
32940 \begin_layout Standard
32941 To be able to use xymatrices, the LaTeX-package
32946 A xymatrix is created by inserting the command
32953 Then you are able to add new matrix columns and rows like for normal matrices,
32955 \begin_inset CommandInset ref
32957 reference "sec:Matrices"
32964 \begin_layout Standard
32965 In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows,
32967 All possibilities to create commutative diagrams and decorations are explained
32972 that you find in the menu
32974 Help\SpecialChar \menuseparator
32976 \begin_inset space ~
32984 \begin_layout Subsection
32990 \begin_inset Index idx
32993 \begin_layout Plain Layout
33002 \begin_layout Standard
33007 -diagrams, the LaTeX-package
33016 -diagram is created by inserting the command
33023 Then you are able to add new matrix columns and rows like for normal matrices,
33025 \begin_inset CommandInset ref
33027 reference "sec:Matrices"
33034 \begin_layout Standard
33035 Examples how to create
33039 diagrams in LyX is given in the
33041 Feynman-diagram manual
33043 that you find in the menu
33045 Help\SpecialChar \menuseparator
33047 \begin_inset space ~
33055 \begin_layout Standard
33056 \begin_inset Newpage newpage
33062 \begin_layout Section
33063 User-defined Commands
33064 \begin_inset Index idx
33067 \begin_layout Plain Layout
33068 User-defined commands
33076 \begin_layout Standard
33077 \begin_inset Note Greyedout
33080 \begin_layout Plain Layout
33085 The names of user-defined commands and macros may only consist of Latin
33094 \begin_layout Subsection
33098 \begin_inset CommandInset label
33100 name "sub:The-Command-newcommand"
33105 \begin_inset Index idx
33108 \begin_layout Plain Layout
33109 User-defined commands !
33117 \begin_inset Index idx
33120 \begin_layout Plain Layout
33131 \begin_layout Standard
33132 Many LaTeX-commands are too long to be used frequently.
33133 But it is possible to define with the command
33139 new shorter commands.
33142 \begin_layout Standard
33143 The command scheme of
33152 \begin_layout Standard
33157 newcommand{new command name}[number of arguments][optional
33162 \begin_inset Newline newline
33166 \begin_inset Phantom HPhantom
33169 \begin_layout Plain Layout
33179 {command definition}
33182 \begin_layout Standard
33183 \begin_inset Note Greyedout
33186 \begin_layout Plain Layout
33191 Assure that the name of the new command is not already used in your document
33192 or by LaTeX-packages that you use.
33193 When you for example define the command
33205 , you get an error message because
33211 is already defined as command for
33212 \begin_inset Quotes eld
33216 \begin_inset Formula $\le$
33220 \begin_inset Quotes erd
33231 \begin_layout Standard
33232 The number of arguments is an integer in the range 0
33233 \begin_inset space \thinspace{}
33237 \begin_inset space \thinspace{}
33240 9 and specifies how many arguments the new command should have.
33241 With the optional value a value for an optional argument can be predefined.
33242 When this is done, the
33250 rgument of the new command is automatically an optional one.
33253 \begin_layout Standard
33254 Here are some examples:
33257 \begin_layout Itemize
33258 To define the command
33270 , the LaTeX-preamble line is:
33271 \begin_inset VSpace medskip
33275 \begin_inset Newline newline
33289 \begin_layout Itemize
33290 To define the command
33302 , the argument (that should be underlined) must be taken into account.
33303 For this the preamble line is:
33304 \begin_inset VSpace medskip
33308 \begin_inset Newline newline
33322 \begin_inset VSpace medskip
33326 \begin_inset Newline newline
33333 acts as argument placeholder, the
33337 behind it denotes that it is the placeholder for the first argument.
33340 \begin_layout Itemize
33348 \begin_inset space \thinspace{}
33352 \begin_inset space \space{}
33362 \begin_inset VSpace medskip
33366 \begin_inset Newline newline
33377 framebox#1#2{$#3$}}
33380 \begin_inset VSpace medskip
33384 \begin_inset Newline newline
33387 The two Dollar signs creates the extra formula needed for
33394 \begin_inset CommandInset ref
33396 reference "sub:Boxes-with-Frame"
33403 \begin_layout Itemize
33404 To create a new command for
33410 where the color for the box need not be specified, the argument for the
33411 color is defined optional:
33412 \begin_inset VSpace medskip
33416 \begin_inset Newline newline
33427 fcolorbox{#2}{#1}{$#3$}}
33430 \begin_inset VSpace medskip
33434 \begin_inset Newline newline
33437 When the color is not specified when using
33443 , the predefined color
33450 \begin_layout Standard
33451 A test of the new defined commands:
33454 \begin_layout Standard
33456 \begin_inset Tabular
33457 <lyxtabular version="3" rows="6" columns="2">
33458 <features rotate="0" tabularvalignment="middle">
33459 <column alignment="center" valignment="top">
33460 <column alignment="center" valignment="top">
33462 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33465 \begin_layout Plain Layout
33471 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33474 \begin_layout Plain Layout
33476 \begin_inset Note Note
33479 \begin_layout Plain Layout
33486 is only used as spacer.
33498 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33501 \begin_layout Plain Layout
33508 \begin_layout Plain Layout
33522 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33525 \begin_layout Plain Layout
33526 \begin_inset Formula $A\gr B$
33536 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33539 \begin_layout Plain Layout
33547 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33550 \begin_layout Plain Layout
33551 \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
33561 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33564 \begin_layout Plain Layout
33568 \begin_inset Formula $\to$
33574 \begin_inset Formula $\to$
33585 \begin_layout Plain Layout
33599 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33602 \begin_layout Plain Layout
33603 \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
33613 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
33616 \begin_layout Plain Layout
33620 \begin_inset Formula $\to$
33631 \begin_layout Plain Layout
33645 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
33648 \begin_layout Plain Layout
33649 \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
33659 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
33662 \begin_layout Plain Layout
33668 \begin_inset Formula $\to$
33679 \begin_layout Plain Layout
33693 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
33696 \begin_layout Plain Layout
33697 \begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
33713 \begin_layout Subsection
33715 \begin_inset Index idx
33718 \begin_layout Plain Layout
33719 User-defined commands! Math macros
33725 \begin_inset Index idx
33728 \begin_layout Plain Layout
33737 \begin_layout Standard
33738 User-defined commands are especially convenient for complex expressions.
33739 When you are for example dealing with a document that has quadratic equations,
33740 the same solution type occurs several times.
33741 The general form of a quadratic equation is
33742 \begin_inset Formula
33744 0=\lambda^{2}+p\lambda+q
33749 The general form of the solution is
33750 \begin_inset Formula
33752 \lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
33760 \begin_layout Standard
33761 To define a command for the solution formula where only the three parameters
33763 \begin_inset Formula $\lambda$
33767 \begin_inset Formula $p$
33771 \begin_inset Formula $q$
33774 need to be specified and the index of
33775 \begin_inset Formula $\lambda$
33778 can be given optionally, the LaTeX-preamble line is
33779 \begin_inset Newline newline
33795 \begin_inset Newline newline
33799 \begin_inset Phantom HPhantom
33802 \begin_layout Plain Layout
33816 frac{#3^{2}}{4}-#4}}
33819 \begin_layout Standard
33820 To create with this the solution formula, the command
33821 \begin_inset Newline newline
33831 \begin_inset Formula $\to$
33837 \begin_inset Formula $\to$
33844 is inserted to a formula
33849 \begin_layout Standard
33850 The definition of the new command is unintuitive because one has to know
33851 the schemes of all used LaTeX commands, e.
33852 \begin_inset space \thinspace{}
33856 \begin_inset space \space{}
33859 that a fraction is inserted in LaTeX as
33863 frac{numerator}{denominator}
33866 Furthermore one can easily forget a brace in the definition and cannot
33867 see in LyX what the new command is doing.
33868 To avoid these problems LyX offers the possibility to use math macros instead
33878 \begin_layout Standard
33879 A math macro is created by using the menu
33881 Insert\SpecialChar \menuseparator
33882 Math\SpecialChar \menuseparator
33885 or the toolbar button
33886 \begin_inset Graphics
33887 filename ../images/math-macro_newmacroname_newcommand.png
33893 The math macro toolbar appears together with the following box where the
33895 \begin_inset Newline newline
33899 \begin_inset space \hspace*{\fill}
33903 \begin_inset Graphics
33904 filename clipart/macrobox.png
33909 \begin_inset space \hspace*{\fill}
33913 \begin_inset Newline newline
33917 \begin_inset FormulaMacro
33918 \newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
33923 newmacroname is the default name of the macro that should be changed to
33924 something sensible.
33925 The wanted formula is inserted in the first blue box.
33926 An argument placeholder is inserted with the command
33933 \begin_inset space \thinspace{}
33937 \begin_inset space \space{}
33946 or by using the macro toolbar button
33947 \begin_inset Graphics
33948 filename ../images/math-macro-add-param.png
33954 Argument placeholders are displayed red.
33956 \begin_inset space ~
33959 arguments are possible.
33960 Optional arguments are created with the toolbar button
33961 \begin_inset Graphics
33962 filename ../images/math-macro-add-optional-param.png
33968 The first non-optional argument can be transformed to an optional one with
33970 \begin_inset Graphics
33971 filename ../images/math-macro-make-optional.png
33977 In the second blue box the appearance of the macro in LyX can be defined.
33978 Normally you want to see it as it is defined, so the box is kept empty.
33979 But when you have created a macro that needs lot of space on the screen,
33980 you can insert in the box for example
33981 \begin_inset Newline newline
34011 \begin_inset Newline newline
34016 For the macro only the arguments with the macro name in front of them will
34017 then be displayed in LyX, leading to a better overview.
34018 The formula appears in the output as defined in the first box.
34019 \begin_inset Newline newline
34022 The appearance of macros in formulas can furthermore be changed for single
34023 macros by setting the cursor in the macro and using the menu
34025 View\SpecialChar \menuseparator
34027 \begin_inset space ~
34031 \begin_inset space ~
34039 \begin_layout Standard
34040 To use a macro, the macro name is inserted as command to a formula, in our
34048 Our macro looks in LyX like this:
34049 \begin_inset Newline newline
34053 \begin_inset space \hspace*{\fill}
34057 \begin_inset Graphics
34058 filename clipart/macrouse.png
34063 \begin_inset space \hspace*{\fill}
34067 \begin_inset Newline newline
34070 Here is our macro example with the arguments
34071 \begin_inset Formula $x$
34075 \begin_inset Formula $\ln(x)$
34079 \begin_inset Formula $B$
34085 \begin_layout Standard
34086 \begin_inset Formula
34096 \begin_layout Standard
34097 LyX offers in the menu
34099 Tools\SpecialChar \menuseparator
34100 Preferences\SpecialChar \menuseparator
34101 Editing\SpecialChar \menuseparator
34104 different styles to edit macros.
34105 To find the style that suits you the most, choose a style and set the cursor
34106 in a macro formula to see the difference.
34109 \begin_layout Standard
34110 A math macro is transformed internally to a
34116 command when exporting the document.
34123 command is not placed in the LaTeX-preamble, therefore macros can only
34124 be used in formulas that are in the document below the macro definition
34128 \begin_layout Standard
34129 Math macros can also be directly created from a
34136 When writing for example the command
34139 \begin_inset Newline newline
34148 xleftarrow[#2]{#1}}
34149 \begin_inset Newline newline
34154 in LyX as normal text, highlighting it completely and using then the shortcut
34159 , the command will be transformed to a math macro.
34160 Using this method you need to be careful that the
34166 command is typed correctly, otherwise you get a faulty macro leading to
34170 \begin_layout Standard
34171 Math macros currently have the problem that further formulas in macro definition
34172 s are handled wrongly.
34173 Therefore the example
34180 \begin_inset CommandInset ref
34182 reference "sub:The-Command-newcommand"
34186 cannot be created as macro.
34189 \begin_layout Standard
34190 When the cursor is in a macro definition box, you will see the macro toolbar
34194 \begin_layout Standard
34195 \begin_inset VSpace defskip
34201 \begin_layout Standard
34202 \begin_inset Graphics
34203 filename clipart/MacroToolbar.png
34208 \begin_inset Index idx
34211 \begin_layout Plain Layout
34220 \begin_layout Standard
34221 \begin_inset VSpace defskip
34227 \begin_layout Standard
34228 The macro toolbar contains from left to right the following buttons:
34231 \begin_layout Standard
34232 \begin_inset VSpace defskip
34238 \begin_layout Standard
34239 \begin_inset Tabular
34240 <lyxtabular version="3" rows="9" columns="2">
34241 <features rotate="0" islongtable="true" longtabularalignment="center">
34242 <column alignment="left" valignment="top">
34243 <column alignment="left" valignment="top" width="85col%">
34244 <row interlinespace="2.5mm">
34245 <cell alignment="center" valignment="top" usebox="none">
34248 \begin_layout Plain Layout
34249 \begin_inset Graphics
34250 filename ../images/math-macro-remove-param.png
34251 rotateOrigin center
34260 <cell alignment="center" valignment="top" usebox="none">
34263 \begin_layout Plain Layout
34266 Edit\SpecialChar \menuseparator
34267 Math\SpecialChar \menuseparator
34269 \begin_inset space ~
34272 Definition\SpecialChar \menuseparator
34273 Remove Last Argument
34279 <row interlinespace="2.5mm">
34280 <cell alignment="center" valignment="top" usebox="none">
34283 \begin_layout Plain Layout
34284 \begin_inset Graphics
34285 filename ../images/math-macro-add-param.png
34286 rotateOrigin center
34295 <cell alignment="center" valignment="top" usebox="none">
34298 \begin_layout Plain Layout
34301 Edit\SpecialChar \menuseparator
34302 Math\SpecialChar \menuseparator
34304 \begin_inset space ~
34307 Definition\SpecialChar \menuseparator
34314 <row interlinespace="2.5mm">
34315 <cell alignment="center" valignment="top" usebox="none">
34318 \begin_layout Plain Layout
34319 \begin_inset Graphics
34320 filename ../images/math-macro-make-optional.png
34321 rotateOrigin center
34330 <cell alignment="center" valignment="top" usebox="none">
34333 \begin_layout Plain Layout
34336 Edit\SpecialChar \menuseparator
34337 Math\SpecialChar \menuseparator
34339 \begin_inset space ~
34342 Definition\SpecialChar \menuseparator
34343 Make First Non-Optional into
34344 \begin_inset Newline newline
34348 \begin_inset Phantom HPhantom
34351 \begin_layout Plain Layout
34354 Edit\SpecialChar \menuseparator
34355 Math\SpecialChar \menuseparator
34357 \begin_inset space ~
34360 Definition\SpecialChar \menuseparator
34372 <row interlinespace="2.5mm">
34373 <cell alignment="center" valignment="top" usebox="none">
34376 \begin_layout Plain Layout
34377 \begin_inset Graphics
34378 filename ../images/math-macro-make-nonoptional.png
34379 rotateOrigin center
34388 <cell alignment="center" valignment="top" usebox="none">
34391 \begin_layout Plain Layout
34394 Edit\SpecialChar \menuseparator
34395 Math\SpecialChar \menuseparator
34397 \begin_inset space ~
34400 Definition\SpecialChar \menuseparator
34401 Make Last Optional into
34402 \begin_inset Newline newline
34406 \begin_inset Phantom HPhantom
34409 \begin_layout Plain Layout
34412 Edit\SpecialChar \menuseparator
34413 Math\SpecialChar \menuseparator
34415 \begin_inset space ~
34418 Definition\SpecialChar \menuseparator
34424 Non-Optional Argument
34430 <row interlinespace="2.5mm">
34431 <cell alignment="center" valignment="top" usebox="none">
34434 \begin_layout Plain Layout
34435 \begin_inset Graphics
34436 filename ../images/math-macro-remove-optional-param.png
34437 rotateOrigin center
34446 <cell alignment="center" valignment="top" usebox="none">
34449 \begin_layout Plain Layout
34452 Edit\SpecialChar \menuseparator
34453 Math\SpecialChar \menuseparator
34455 \begin_inset space ~
34458 Definition\SpecialChar \menuseparator
34459 Remove Optional Argument
34465 <row interlinespace="2.5mm">
34466 <cell alignment="center" valignment="top" usebox="none">
34469 \begin_layout Plain Layout
34470 \begin_inset Graphics
34471 filename ../images/math-macro-add-optional-param.png
34472 rotateOrigin center
34481 <cell alignment="center" valignment="top" usebox="none">
34484 \begin_layout Plain Layout
34487 Edit\SpecialChar \menuseparator
34488 Math\SpecialChar \menuseparator
34490 \begin_inset space ~
34493 Definition\SpecialChar \menuseparator
34494 Insert Optional Argument
34500 <row interlinespace="2.5mm">
34501 <cell alignment="center" valignment="top" usebox="none">
34504 \begin_layout Plain Layout
34505 \begin_inset Graphics
34506 filename ../images/math-macro-remove-greedy-param.png
34507 rotateOrigin center
34516 <cell alignment="center" valignment="top" usebox="none">
34519 \begin_layout Plain Layout
34522 Edit\SpecialChar \menuseparator
34523 Math\SpecialChar \menuseparator
34525 \begin_inset space ~
34528 Definition\SpecialChar \menuseparator
34529 Remove Last Argument
34530 \begin_inset Newline newline
34534 \begin_inset Phantom HPhantom
34537 \begin_layout Plain Layout
34540 Edit\SpecialChar \menuseparator
34541 Math\SpecialChar \menuseparator
34543 \begin_inset space ~
34546 Definition\SpecialChar \menuseparator
34552 Spitting Out To The Right
34558 <row interlinespace="2.5mm">
34559 <cell alignment="center" valignment="top" usebox="none">
34562 \begin_layout Plain Layout
34563 \begin_inset Graphics
34564 filename ../images/math-macro-append-greedy-param.png
34565 rotateOrigin center
34574 <cell alignment="center" valignment="top" usebox="none">
34577 \begin_layout Plain Layout
34580 Edit\SpecialChar \menuseparator
34581 Math\SpecialChar \menuseparator
34583 \begin_inset space ~
34586 Definition\SpecialChar \menuseparator
34588 \begin_inset Newline newline
34592 \begin_inset Phantom HPhantom
34595 \begin_layout Plain Layout
34598 Edit\SpecialChar \menuseparator
34599 Math\SpecialChar \menuseparator
34601 \begin_inset space ~
34604 Definition\SpecialChar \menuseparator
34610 Eating From The Right
34616 <row interlinespace="2.5mm">
34617 <cell alignment="center" valignment="top" usebox="none">
34620 \begin_layout Plain Layout
34621 \begin_inset Graphics
34622 filename ../images/math-macro-add-greedy-optional-param.png
34623 rotateOrigin center
34632 <cell alignment="center" valignment="top" usebox="none">
34635 \begin_layout Plain Layout
34638 Edit\SpecialChar \menuseparator
34639 Math\SpecialChar \menuseparator
34641 \begin_inset space ~
34644 Definition\SpecialChar \menuseparator
34645 Append Optional Argument
34646 \begin_inset Newline newline
34650 \begin_inset Phantom HPhantom
34653 \begin_layout Plain Layout
34656 Edit\SpecialChar \menuseparator
34657 Math\SpecialChar \menuseparator
34659 \begin_inset space ~
34662 Definition\SpecialChar \menuseparator
34668 Eating From The Right
34681 \begin_layout Section
34682 Computer Algebra Systems
34685 \begin_layout Standard
34686 LyX offers the exchange between mathematical expressions written in LyX's
34687 math editor and external applications or user defined scripts.
34688 Currently supported applications are
34705 Note that the set of supported mathematical constructs is limited only
34706 to very simple cases.
34709 \begin_layout Subsection
34713 \begin_layout Standard
34714 Write some expression in a formula, go to the
34716 Edit\SpecialChar \menuseparator
34717 Math\SpecialChar \menuseparator
34718 Use Computer Algebra System
34720 menu and choose the application you have installed on the computer.
34721 After that the result of computation should show on the right side of the
34722 expression together with the
34723 \begin_inset Quotes eld
34727 \begin_inset Quotes erd
34733 \begin_layout Standard
34734 Here are few simple examples (with results from
34738 ) to show what kind of computations can be performed:
34741 \begin_layout Itemize
34742 \begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
34748 \begin_layout Itemize
34749 \begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
34755 \begin_layout Itemize
34756 \begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
34762 \begin_layout Itemize
34763 \begin_inset Formula $\det\left[\begin{array}{ccc}
34767 \end{array}\right]=-56$
34773 \begin_layout Itemize
34774 \begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
34780 \begin_layout Subsection
34784 \begin_layout Standard
34785 Currently there is no keyboard shortcut for calling the algebra applications.
34786 One can easily bind a shortcut to the
34790 LyX function (see the
34798 \begin_inset space \thinspace{}
34802 \begin_inset space \space{}
34809 key inside the math editor.
34814 one would use this shortcut definition command:
34817 \begin_layout Standard
34820 command-alternatives break-paragraph;math-extern maxima
34823 \begin_layout Section
34825 \begin_inset Index idx
34828 \begin_layout Plain Layout
34837 \begin_layout Subsection
34839 \begin_inset Index idx
34842 \begin_layout Plain Layout
34851 \begin_layout Standard
34852 Negative numbers often look ugly in formulas because the minus sign before
34853 the number is set with the same length as the minus operator sign.
34854 When writing the negative number in normal text, the minus sign appears
34858 \begin_layout Standard
34859 Thus, the problem disappears when converting the minus sign to mathematical
34863 \begin_layout Standard
34864 An example to visualize the problem:
34867 \begin_layout Standard
34869 \begin_inset Tabular
34870 <lyxtabular version="3" rows="3" columns="2">
34871 <features rotate="0" tabularvalignment="middle">
34872 <column alignment="right" valignment="top">
34873 <column alignment="left" valignment="top">
34875 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
34878 \begin_layout Plain Layout
34884 <cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
34887 \begin_layout Plain Layout
34895 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34898 \begin_layout Plain Layout
34904 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34907 \begin_layout Plain Layout
34908 \begin_inset Formula $x=-2$
34918 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
34921 \begin_layout Plain Layout
34927 <cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
34930 \begin_layout Plain Layout
34931 \begin_inset Formula $x=\textrm{-}2$
34947 \begin_layout Subsection
34948 Comma as decimal Separator
34949 \begin_inset Index idx
34952 \begin_layout Plain Layout
34961 \begin_layout Standard
34962 In LaTeX a comma inside a formula is used, according to the English convention,
34963 as number group separator.
34964 So there will be space added behind all commas in formulas.
34967 \begin_layout Standard
34968 To avoid this, the comma is highlighted and changed to mathematical text
34978 \begin_layout Standard
34979 To use all formula commas in the document as decimal separator, the file
34988 \begin_layout Plain Layout
34993 is part of the LaTeX-package
34998 \begin_inset Index idx
35001 \begin_layout Plain Layout
35006 \begin_layout Plain Layout
35026 \begin_inset Index idx
35029 \begin_layout Plain Layout
35035 is loaded with the LaTeX-preamble line
35038 \begin_layout Standard
35046 \begin_layout Subsection
35048 \begin_inset CommandInset label
35050 name "sub:Physical-Vectors"
35055 \begin_inset Index idx
35058 \begin_layout Plain Layout
35067 \begin_layout Standard
35068 Predefined vectors are offered by the LaTeX-package
35073 \begin_inset Index idx
35076 \begin_layout Plain Layout
35082 that is loaded with the LaTeX-preamble line
35085 \begin_layout Standard
35093 \begin_layout Standard
35097 \begin_layout Plain Layout
35107 \begin_inset Note Note
35110 \begin_layout Plain Layout
35111 The following table will only be displayed when the LaTeX-package
35123 \begin_layout Standard
35124 The following commands are defined:
35127 \begin_layout Standard
35129 \begin_inset Tabular
35130 <lyxtabular version="3" rows="4" columns="2">
35131 <features rotate="0" tabularvalignment="middle">
35132 <column alignment="center" valignment="top">
35133 <column alignment="center" valignment="top">
35135 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35138 \begin_layout Plain Layout
35144 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35147 \begin_layout Plain Layout
35155 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35158 \begin_layout Plain Layout
35168 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35171 \begin_layout Plain Layout
35172 \begin_inset Formula $\Bra{\psi}$
35182 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35185 \begin_layout Plain Layout
35195 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35198 \begin_layout Plain Layout
35199 \begin_inset Formula $\Ket{\psi}$
35209 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35212 \begin_layout Plain Layout
35224 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35227 \begin_layout Plain Layout
35228 \begin_inset Formula $\Braket{\psi|\phi}$
35244 \begin_layout Standard
35251 assures that all vertical bars are set in the size of the surrounding brackets:
35252 \begin_inset Formula
35254 \Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
35263 \begin_layout Plain Layout
35273 \begin_inset Note Note
35276 \begin_layout Plain Layout
35277 The following will be displayed when the LaTeX-package
35289 \begin_layout Standard
35290 You need to install the LaTeX-package
35294 to see the rest of this subsection in the output.
35297 \begin_layout Standard
35301 \begin_layout Plain Layout
35313 \begin_layout Standard
35320 can also be achieved using the command
35326 , that is described in
35327 \begin_inset CommandInset ref
35329 reference "sub:Automatic-Bracket-Size"
35336 \begin_layout Subsection
35337 Self-defined Fractions
35338 \begin_inset CommandInset label
35340 name "sub:Self-defined-Fractions"
35345 \begin_inset Index idx
35348 \begin_layout Plain Layout
35349 Fractions ! self-defined
35357 \begin_layout Standard
35358 To define custom commands for fractions, the command
35365 \begin_inset Index idx
35368 \begin_layout Plain Layout
35375 \begin_layout Plain Layout
35389 is used in the following scheme:
35392 \begin_layout Standard
35405 bracket}{fraction bar thickness}{style}
35406 \begin_inset Newline newline
35410 \begin_inset Phantom HPhantom
35413 \begin_layout Plain Layout
35423 {numerator}{denominator}
35426 \begin_layout Standard
35427 The style is a number in the range of 0
35428 \begin_inset space \thinspace{}
35432 \begin_inset space \thinspace{}
35438 \begin_layout Standard
35440 \begin_inset Tabular
35441 <lyxtabular version="3" rows="5" columns="2">
35442 <features rotate="0" tabularvalignment="middle">
35443 <column alignment="center" valignment="top">
35444 <column alignment="center" valignment="top">
35446 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35449 \begin_layout Plain Layout
35455 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35458 \begin_layout Plain Layout
35466 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35469 \begin_layout Plain Layout
35475 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35478 \begin_layout Plain Layout
35479 display style formula
35486 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35489 \begin_layout Plain Layout
35495 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35498 \begin_layout Plain Layout
35506 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35509 \begin_layout Plain Layout
35515 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35518 \begin_layout Plain Layout
35526 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35529 \begin_layout Plain Layout
35535 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35538 \begin_layout Plain Layout
35552 \begin_layout Standard
35553 When no style is given, the size is adjusted to the surrounding environment
35554 like for the command
35563 \begin_layout Standard
35564 When no fraction bar thickness is given, the predefined value of 0.4
35565 \begin_inset space \thinspace{}
35571 \begin_layout Standard
35572 \begin_inset VSpace medskip
35575 For example, the commands
35588 \begin_inset CommandInset ref
35590 reference "sub:Fractions"
35594 are defined with the commands
35597 \begin_layout Standard
35606 genfrac{}{}{}{0}{#1}{#2}}
35609 \begin_layout Standard
35613 \begin_layout Standard
35622 genfrac{(}{)}{0pt}{1}{#1}{#2}}
35625 \begin_layout Standard
35626 \begin_inset VSpace medskip
35629 To define a fraction where the fraction bar thickness can be given as optional
35630 argument, the following line is inserted to the LaTeX-preamble:
35633 \begin_layout Standard
35642 genfrac{}{}{#1}{}{#2}{#3}}
35645 \begin_layout Standard
35647 \begin_inset Formula
35649 \text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
35650 \text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}
35655 As one can see, the distance of the numerator and the denominator to the
35656 fraction bar is round about three times the bar thickness.
35659 \begin_layout Subsection
35661 \begin_inset Index idx
35664 \begin_layout Plain Layout
35673 \begin_layout Standard
35674 To cancel formulas or formula parts, the LaTeX-package
35679 \begin_inset Index idx
35682 \begin_layout Plain Layout
35688 has to be loaded with the LaTeX-preamble line
35691 \begin_layout Standard
35699 \begin_layout Standard
35703 \begin_layout Plain Layout
35713 \begin_inset Note Note
35716 \begin_layout Plain Layout
35717 The following table will only be displayed when the LaTeX-package
35729 \begin_layout Standard
35730 There are four ways to cancel formulas:
35733 \begin_layout Standard
35735 \begin_inset Tabular
35736 <lyxtabular version="3" rows="5" columns="2">
35737 <features rotate="0" tabularvalignment="middle">
35738 <column alignment="center" valignment="top">
35739 <column alignment="center" valignment="top">
35741 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35744 \begin_layout Plain Layout
35750 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35753 \begin_layout Plain Layout
35755 \begin_inset Note Note
35758 \begin_layout Plain Layout
35765 are used here as spacer.
35777 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35780 \begin_layout Plain Layout
35789 \begin_layout Plain Layout
35803 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35806 \begin_layout Plain Layout
35807 \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
35817 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
35820 \begin_layout Plain Layout
35829 \begin_layout Plain Layout
35843 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
35846 \begin_layout Plain Layout
35847 \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
35857 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35860 \begin_layout Plain Layout
35869 \begin_layout Plain Layout
35883 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35886 \begin_layout Plain Layout
35887 \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
35897 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
35900 \begin_layout Plain Layout
35904 \begin_inset Formula $\to$
35915 \begin_layout Plain Layout
35929 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
35932 \begin_layout Plain Layout
35933 \begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
35949 \begin_layout Standard
35956 is especially suitable to visualize the reduction of fractions within formulas:
35957 \begin_inset Formula
35959 \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}}}
35967 \begin_layout Standard
35968 To change the size of
35975 \begin_inset Quotes eld
35979 \begin_inset Quotes erd
35982 value one can load the package
35986 with either the option
35990 which leads to the same size as for the canceled value or with the option
35995 which makes is it a bit smaller than the size one gets without using a
36001 was loaded with this line:
36004 \begin_layout Standard
36009 usepackage[samesize]{cancel}
36012 \begin_layout Standard
36013 To color the cancellation bar one adds this command as TeX code:
36016 \begin_layout Standard
36028 \begin_layout Standard
36033 can be replaced by a color of your choice.
36036 \begin_layout Standard
36040 \begin_layout Plain Layout
36056 \begin_layout Standard
36057 \begin_inset Formula
36059 \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}}}
36067 \begin_layout Standard
36071 \begin_layout Plain Layout
36085 \begin_inset Note Note
36088 \begin_layout Plain Layout
36097 \begin_layout Standard
36098 For further customizations, see the documentation of the package
36103 \begin_inset CommandInset citation
36112 \begin_layout Standard
36116 \begin_layout Plain Layout
36126 \begin_inset Note Note
36129 \begin_layout Plain Layout
36130 The following will be displayed when the LaTeX-package
36142 \begin_layout Standard
36143 You need to install the LaTeX-package
36147 to see the rest of this subsection in the output.
36150 \begin_layout Standard
36154 \begin_layout Plain Layout
36166 \begin_layout Standard
36167 \begin_inset Newpage newpage
36173 \begin_layout Subsection
36174 Formulas in Section Headings
36175 \begin_inset CommandInset label
36177 name "sub:Formulas-in-Section"
36182 \begin_inset Index idx
36185 \begin_layout Plain Layout
36186 Formula ! in section headings
36194 \begin_layout Standard
36195 When formulas are used in section headings, the following has to be taken
36199 \begin_layout Standard
36200 \begin_inset Note Greyedout
36203 \begin_layout Plain Layout
36209 \begin_inset Index idx
36212 \begin_layout Plain Layout
36213 Packages ! hyperref
36218 support is enabled in the document settings dialog under
36221 \begin_inset space ~
36226 , PDF-bookmarks are created for every section heading in the table of contents.
36227 If a section heading contains formulas, they are incorrectly displayed
36228 in the bookmark text, because formulas in bookmarks infringe the PDF convention
36237 \begin_layout Standard
36238 Both problems can be solved by inserting at the end of the section heading
36239 a short title with the menu
36241 Insert\SpecialChar \menuseparator
36243 \begin_inset space ~
36249 Short titles are used as alternative for multiline section headings to
36250 keep the table of contents clearly arranged.
36251 Only the short title appears in the table of contents and therefore also
36252 in the PDF-bookmark.
36255 \begin_layout Standard
36256 When formulas should be used in the table of contents but
36260 is used, one can use the following command in TeX-mode:
36263 \begin_layout Standard
36268 texorpdfstring{part}{alternative}
36269 \begin_inset Index idx
36272 \begin_layout Plain Layout
36283 \begin_layout Standard
36284 Part is the part of the heading that shouldn't appear in the PDF-bookmark.
36285 This can be characters, formulas, footnotes, but also cross-references.
36286 The alternative is used instead of the part for the bookmark.
36289 \begin_layout Standard
36290 Here are two example headings:
36291 \begin_inset VSpace -3mm
36298 \begin_layout Plain Layout
36310 \begin_layout Subsubsection
36311 Heading without formula in table of contents
36312 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36316 \begin_inset Argument 1
36319 \begin_layout Plain Layout
36320 Heading without formula in table of contents
36328 \begin_layout Subsubsection
36329 Heading with formula in table of contents
36333 \begin_layout Plain Layout
36343 \begin_inset Formula $\sqrt{-1}=\mathrm{i}$
36350 \begin_layout Plain Layout
36360 \begin_layout Standard
36364 \begin_layout Plain Layout
36373 In the first heading a short title was used, in the second one
36382 \begin_layout Standard
36383 To get the same formatting as for the other headings, the complete heading
36392 \begin_layout Plain Layout
36394 \begin_inset CommandInset ref
36396 reference "sub:Bold-Formulas"
36408 \begin_layout Subsection
36409 Formulas in multi-column Text
36410 \begin_inset Index idx
36413 \begin_layout Plain Layout
36414 Formula ! in multi-column text
36422 \begin_layout Standard
36423 Formulas in multi-column text are often too wide to fit into a column and
36424 thus need to be set over the whole page width.
36425 This is done by using the LaTeX-package
36433 \begin_layout Plain Layout
36438 is part of every LaTeX standard installation.
36444 \begin_inset Index idx
36447 \begin_layout Plain Layout
36448 Packages ! multicol
36453 , that is loaded with the LaTeX-preamble line
36456 \begin_layout Standard
36461 usepackage{multicol}
36464 \begin_layout Standard
36465 \begin_inset Note Greyedout
36468 \begin_layout Plain Layout
36469 Note that in this case the setting
36472 \begin_inset space ~
36479 Document\SpecialChar \menuseparator
36485 \begin_inset space ~
36505 \begin_layout Standard
36506 Before the multi-column text the command
36509 \begin_layout Standard
36514 begin{multicols}{column number}
36517 \begin_layout Standard
36518 is written in TeX-mode.
36519 The column number is a number in the range of 2
36520 \begin_inset space \thinspace{}
36524 \begin_inset space \thinspace{}
36528 Before the formula the multi-column text is ended by inserting the command
36531 \begin_layout Standard
36539 \begin_layout Standard
36543 \begin_layout Standard
36544 Due to the command some space is automatically added before the formula.
36546 \begin_inset space \thinspace{}
36549 mm vertical space is inserted before the formula.
36550 When the formula style
36556 \begin_layout Plain Layout
36558 \begin_inset CommandInset ref
36560 reference "sec:Formula-Styles"
36572 \begin_inset space \thinspace{}
36575 mm space is inserted instead.
36578 \begin_layout Standard
36579 As example a multi-column text with a displayed formula:
36582 \begin_layout Standard
36588 \begin_layout Plain Layout
36592 begin{multicols}{2}
36597 Das Spektrum wird fouriertransformiert.
36598 Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
36599 , Lösungsmittel) zu trennen.
36600 Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
36601 nun das Aussehen des Ausgangssignals.
36602 Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
36603 über alle Phasen integrieren muss.
36605 \begin_inset Formula $S$
36608 unser normiertes Ausgangssignal und
36609 \begin_inset Formula $P$
36612 die Phasenverteilungsfunktion, so ergibt sich die Beziehung
36616 \begin_layout Plain Layout
36626 \begin_inset VSpace -6mm
36630 \begin_inset Formula
36632 S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
36641 \begin_layout Plain Layout
36645 begin{multicols}{2}
36651 \begin_inset Formula $S_{0}$
36654 das Signal ohne Gradient ist und die Normierungsbedingung
36655 \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
36659 Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
36661 \begin_inset Formula $\nicefrac{\pi}{2}$
36665 \begin_inset space \thinspace{}
36668 -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
36669 das Signal zusätzlich abschwächt.
36670 Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
36672 \begin_inset Formula $T_{2}$
36678 \begin_layout Standard
36684 \begin_layout Plain Layout
36696 \begin_layout Subsection
36697 Formulas with Description of Variables
36698 \begin_inset Index idx
36701 \begin_layout Plain Layout
36702 Formula ! with description of variables
36710 \begin_layout Standard
36711 To describe variables within a formula, like in formula
36712 \begin_inset CommandInset ref
36714 reference "eq:within"
36723 \begin_inset Formula $n$
36727 \begin_inset space ~
36730 matrix is used with left aligned columns for the
36731 \begin_inset Formula $n$
36738 \begin_layout Plain Layout
36740 \begin_inset CommandInset ref
36742 reference "sec:Matrices"
36751 To set the description in a smaller size, before the matrix e.
36752 \begin_inset space \thinspace{}
36756 \begin_inset space \space{}
36769 \begin_layout Plain Layout
36771 \begin_inset CommandInset ref
36773 reference "sub:Font-Sizes"
36785 \begin_layout Standard
36786 When the formula style
36792 \begin_layout Plain Layout
36794 \begin_inset CommandInset ref
36796 reference "sec:Formula-Styles"
36817 \begin_layout Plain Layout
36824 only works in formulas with the style
36829 \begin_inset CommandInset ref
36831 reference "sub:Variable-Space"
36840 is inserted before and after the matrix to have the same separation of
36841 the matrix from the equation and the side margin.
36844 \begin_layout Standard
36845 When the formula style
36849 is used, the method described in
36850 \begin_inset CommandInset ref
36852 reference "sub:Flalign-Environment"
36856 is used to indent formulas.
36858 \begin_inset CommandInset ref
36860 reference "eq:within"
36864 consists of five columns where in the first two columns contain the equation,
36865 the third the matrix and the last one an empty TeX-brace.
36866 \begin_inset Formula
36868 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
36869 \rho & \textrm{density}\\
36870 V & \textrm{volume}\\
36871 g & \textrm{gravitational acceleration}
36872 \end{array} & & {}\label{eq:within}
36880 \begin_layout Subsection
36881 Upright small Greek Letters
36882 \begin_inset CommandInset label
36884 name "sub:Upright-small-Greek"
36889 \begin_inset Index idx
36892 \begin_layout Plain Layout
36893 Greek letters ! upright
36901 \begin_layout Standard
36902 Most of the math fonts only provide italic small Greek letters.
36903 But for symbols of elementary particles like pions and neutrinos, upright
36904 Greek letters are needed.
36913 \begin_layout Plain Layout
36918 is part of the LaTeX-package
36923 \begin_inset Index idx
36926 \begin_layout Plain Layout
36931 \begin_layout Plain Layout
36951 \begin_inset Index idx
36954 \begin_layout Plain Layout
36960 that is loaded with the LaTeX-preamble line
36963 \begin_layout Standard
36968 usepackage{upgreek}
36971 \begin_layout Standard
36977 \begin_layout Plain Layout
36987 \begin_inset Note Note
36990 \begin_layout Plain Layout
36991 The following table will only be displayed when the LaTeX-package
37000 They are created when the command for a small Greek letter is started with
37006 For example the command
37013 \begin_inset Formula $\uptau$
37019 \begin_layout Standard
37020 With these commands reactions of elementary particles can be typeset:
37021 \begin_inset Formula
37023 \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
37031 \begin_layout Standard
37032 The upright letters are more bold and wider than the italic ones.
37033 They should therefore not be used for units like
37034 \begin_inset Quotes eld
37038 \begin_inset Quotes erd
37044 \begin_layout Standard
37048 \begin_layout Plain Layout
37058 \begin_inset Note Note
37061 \begin_layout Plain Layout
37062 The following will be displayed when the LaTeX-package
37074 \begin_layout Standard
37075 You need to install the LaTeX-package
37079 to see the rest of this subsection in the output.
37082 \begin_layout Standard
37086 \begin_layout Plain Layout
37098 \begin_layout Subsection
37099 Text Characters in Formulas
37100 \begin_inset CommandInset label
37102 name "sub:Text-Characters-in"
37107 \begin_inset Index idx
37110 \begin_layout Plain Layout
37119 \begin_layout Standard
37120 In some cases you might want to insert text characters directly into formulas.
37121 When for example the centered dot · is often used in formulas like
37122 \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
37125 , one would have to insert the command
37135 \begin_layout Plain Layout
37137 \begin_inset CommandInset ref
37139 reference "sub:Binary-Operators"
37148 all the time, because this character is defined in all encodings as text
37150 But the encoding can be changed by this LaTeX-preamble line:
37153 \begin_layout Standard
37158 Declare Inputtext{183}{
37168 f\SpecialChar \textcompwordmark{}
37172 \begin_layout Standard
37173 The character encoding (menu
37175 Document\SpecialChar \menuseparator
37176 Settings\SpecialChar \menuseparator
37179 ) specifies what character appears when a keyboard key is pressed.
37180 When the key for the character '·' is pressed, internally the command
37187 But this command is not available in a formula so that you would get LaTeX-erro
37189 With the changed encoding the right command is chosen automatically, depending
37190 on if the character was inserted into a formula or not.
37193 \begin_layout Standard
37194 The encoding of several characters is saved in definition files.
37195 For example the encoding
37199 is defined in the file
37203 which is in the installation folder of LaTeX.
37204 Encodings should only be changed via the LaTeX-preamble and not in the
37206 Otherwise documents could not be edited by other LyX users working on other
37210 \begin_layout Standard
37211 \begin_inset VSpace medskip
37214 Besides the centered dot, in this document the degree sign ° is defined
37215 with the following LaTeX-preamble line so that it can be directly inserted
37219 \begin_layout Standard
37224 DeclareInputtext{176}{
37234 f\SpecialChar \textcompwordmark{}
37238 \begin_layout Standard
37239 \begin_inset Newpage newpage
37245 \begin_layout Section
37248 \begin_inset Index idx
37251 \begin_layout Plain Layout
37260 \begin_layout Standard
37261 This section is a summary of the most important typographic rules, listed
37266 \begin_layout Plain Layout
37267 This collection was partly taken from the German semi-official dictionary
37269 \begin_inset Quotes eld
37273 \begin_inset Quotes erd
37277 \begin_inset CommandInset citation
37283 that lists some of the ISO rules.
37284 More rules are listed in
37285 \begin_inset CommandInset citation
37299 \begin_layout Itemize
37308 \begin_layout Plain Layout
37309 done with font styles, see
37310 \begin_inset CommandInset ref
37312 reference "sub:Font-Styles"
37321 , no matter if they appear in italic text: 30
37322 \begin_inset space \thinspace{}
37326 \begin_inset Newline newline
37329 Between the value and the unit is the smallest space, see
37330 \begin_inset CommandInset ref
37332 reference "sub:Predefined-Space"
37337 \begin_inset Newline newline
37340 This convention is automatically fulfilled when the command
37347 When it is entered to a formula, two boxes appear.
37348 In the first one the value is inserted, in the second one the unit, and
37350 \begin_inset Formula $\unit[30]{km/h}$
37354 \begin_inset space \thinspace{}
37364 is not a real LaTeX command but the command
37370 , therefore you cannot use it in TeX code.
37373 \begin_layout Itemize
37374 Percent and perthousand signs are set like physical units:
37375 \begin_inset Newline newline
37379 \begin_inset space \thinspace{}
37385 \begin_layout Itemize
37386 The degree sign follows directly on the value: 15°, but not when it is used
37388 \begin_inset space \thinspace{}
37394 \begin_layout Itemize
37395 In numbers with more than four digits the smallest space is inserted before
37396 every third digit to group them:
37406 \begin_inset space \thinspace{}
37410 \begin_inset space \thinspace{}
37416 \begin_layout Itemize
37417 For dimensions like 120×90×40
37418 \begin_inset space \thinspace{}
37421 cm the multiplication sign
37422 \begin_inset Quotes eld
37426 \begin_inset Quotes erd
37430 It is available either via the command
37438 Insert\SpecialChar \menuseparator
37439 Special Character\SpecialChar \menuseparator
37445 \begin_layout Itemize
37446 Functions with names consisting of several letters are set upright to avoid
37448 \begin_inset CommandInset ref
37450 reference "sub:Predefined-Functions"
37457 \begin_layout Itemize
37458 Indices consisting of several letters, are set upright:
37459 \begin_inset Formula $E_{\mathrm{kin}}$
37463 \begin_inset Newline newline
37466 Components of matrices are set italic:
37467 \begin_inset Formula $\hat{H}_{kl}$
37473 \begin_layout Itemize
37474 The differentiation/integration operator 'd', the Euler's number 'e' and
37475 the imaginary unit 'i' should be set upright, to avoid mixing them up with
37479 \begin_layout Itemize
37480 The character that denotes a
37484 transformation is inserted either by the command
37492 \begin_layout Plain Layout
37505 Insert\SpecialChar \menuseparator
37506 Special Character\SpecialChar \menuseparator
37507 Symbols\SpecialChar \menuseparator
37509 \begin_inset space ~
37515 \begin_inset Formula $\mathscr{F}$
37521 \begin_layout Standard
37522 \begin_inset Newpage newpage
37528 \begin_layout Section
37530 \begin_inset Index idx
37533 \begin_layout Plain Layout
37542 \begin_layout Standard
37543 Some characters and symbols can be created with several commands.
37544 Here is a list of the synonym commands:
37547 \begin_layout Standard
37548 \begin_inset VSpace bigskip
37552 \begin_inset space \hfill{}
37556 \begin_inset Tabular
37557 <lyxtabular version="3" rows="12" columns="2">
37558 <features rotate="0" tabularvalignment="middle">
37559 <column alignment="center" valignment="top" width="0pt">
37560 <column alignment="center" valignment="top" width="0pt">
37562 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37565 \begin_layout Plain Layout
37571 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37574 \begin_layout Plain Layout
37576 \begin_inset Note Note
37579 \begin_layout Plain Layout
37586 is only used as spacer.
37598 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37601 \begin_layout Plain Layout
37609 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37612 \begin_layout Plain Layout
37616 \begin_layout Plain Layout
37629 \begin_layout Plain Layout
37643 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37646 \begin_layout Plain Layout
37654 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37657 \begin_layout Plain Layout
37667 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37670 \begin_layout Plain Layout
37678 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37681 \begin_layout Plain Layout
37691 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37694 \begin_layout Plain Layout
37702 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37705 \begin_layout Plain Layout
37713 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37716 \begin_layout Plain Layout
37724 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37727 \begin_layout Plain Layout
37735 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37738 \begin_layout Plain Layout
37746 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37749 \begin_layout Plain Layout
37759 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37762 \begin_layout Plain Layout
37770 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37773 \begin_layout Plain Layout
37783 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37786 \begin_layout Plain Layout
37794 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37797 \begin_layout Plain Layout
37807 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37810 \begin_layout Plain Layout
37818 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37821 \begin_layout Plain Layout
37831 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37834 \begin_layout Plain Layout
37842 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37845 \begin_layout Plain Layout
37853 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37856 \begin_layout Plain Layout
37864 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37867 \begin_layout Plain Layout
37879 \begin_inset space \hfill{}
37883 \begin_inset Tabular
37884 <lyxtabular version="3" rows="12" columns="2">
37885 <features rotate="0" tabularvalignment="middle">
37886 <column alignment="center" valignment="top" width="0pt">
37887 <column alignment="center" valignment="top" width="0pt">
37889 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
37892 \begin_layout Plain Layout
37898 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
37901 \begin_layout Plain Layout
37909 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37912 \begin_layout Plain Layout
37920 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37923 \begin_layout Plain Layout
37935 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37938 \begin_layout Plain Layout
37946 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37949 \begin_layout Plain Layout
37959 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37962 \begin_layout Plain Layout
37970 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37973 \begin_layout Plain Layout
37983 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
37986 \begin_layout Plain Layout
37994 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
37997 \begin_layout Plain Layout
38005 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38008 \begin_layout Plain Layout
38016 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38019 \begin_layout Plain Layout
38027 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38030 \begin_layout Plain Layout
38038 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38041 \begin_layout Plain Layout
38051 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38054 \begin_layout Plain Layout
38062 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38065 \begin_layout Plain Layout
38075 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
38078 \begin_layout Plain Layout
38086 <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
38089 \begin_layout Plain Layout
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38181 \begin_layout Standard
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38202 The LaTeX Companion
38205 Addison Wesley, 2004
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38210 LatexCommand bibitem
38216 \begin_inset CommandInset href
38219 target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf"
38223 of LaTeX's math abilities
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38265 \begin_inset CommandInset href
38268 target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf"
38272 of all symbols available with LaTeX-packages
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38286 target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf"
38290 of the LaTeX-package
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38315 \begin_inset CommandInset href
38317 name "Documentation"
38318 target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf"
38322 of the LaTeX-package
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38331 Packages ! hyperref
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38347 \begin_inset CommandInset href
38349 name "Documentation"
38350 target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf"
38354 of the LaTeX-package
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38379 \begin_inset CommandInset href
38382 target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
38393 \begin_inset CommandInset ref
38395 reference "sub:Operator-Limits"
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38427 Auflage, Duden 2001
38430 \begin_layout Bibliography
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38432 LatexCommand bibitem
38438 \begin_inset CommandInset href
38441 target "http://physics.nist.gov/Document/checklist.pdf"
38445 for reviewing manuscripts
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38450 LatexCommand printindex